Czochralski Growth of Silicon Crystals

Czochralski Growth of Silicon Crystals

Chapter 2 Czochralski Growth of Silicon Crystals Olli Anttila Silicom Ltd., Helsinki, Finland Czochralski (CZ) growth of silicon has been named afte...

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Chapter 2

Czochralski Growth of Silicon Crystals Olli Anttila Silicom Ltd., Helsinki, Finland

Czochralski (CZ) growth of silicon has been named after the Polish scientist Jan Czochralski, who in 1918 published his report on the growth of single-crystal metal filaments from melt [1]. The present method is largely attributable to Teal and Little and dates back to the early 1950s when it was not yet clear whether single-crystal semiconductor material would have any significant advantage over polycrystalline materials and the material of choice was germanium more often than silicon [24]. The differences in the method developed by Teal and Little were so large compared with the original method by Czochralski that it would probably be more just to call it the TealLittle method [4]. The existence of another method, zone refining, that was originally used to purify germanium polycrystalline material for semiconductor applications and from which the float-zone (FZ) method was developed, may have had an influence on the choice of the name of the method: The abbreviations now form a nice match. In this chapter, only CZ crystal growth is discussed. This is because CZ material dominates the industry by a large margin, crystal availability is good, modern techniques also allow growth of high-resistivity silicon, and all commercial crystal sizes can be made with CZ technique. Only if very high-resistivity silicon (.510 kΩ-cm) or silicon without dissolved oxygen is needed, should FZ material be used. Today the availability of FZ crystals is still limited to 200 mm in diameter. Those interested in learning more about the FZ technique should consult, for example, reviews of Dietze [5], Zulehner [6], or Mu¨hlbauer [7]. In the late 1950s, Dash significantly improved the method of growing silicon crystals by adding a necking step to avoid dislocations [8]. This improvement is routinely used for both CZ and FZ crystals. The role of this step is explained later in more detail. The CZ growth method has remained fundamentally unchanged since, and it is the workhorse that produces the vast majority of single-crystal silicon used even today, more than 50 years after its introduction. Major evolutionary steps have been 18

made; for example, maximum crystal weights are several hundreds of kilograms, magnetic fields are applied for better control of the melt behavior, all imaginable quality requirements have been reviewed several times, and the productivity has experienced enormous improvements.

2.1 THE CZ CRYSTAL-GROWING FURNACE The CZ furnace is a vacuum furnace that consists of the following subassemblies: crucible lifting and rotating system, growth chamber that houses the hot zone (HZ), vacuum interlocks, receiving chamber for the grown crystal, and crystal rotating and lifting system. For more details, see Ref. [9], Figure 81(a) and (b). Modern CZ systems are able to grow crystals larger than 450 mm in diameter, and charge sizes may exceed 500 kg. In MEMS applications, however, the maximum size of the crystal is 200 mm in diameter, and charge size remains below 200 kg. In Figure 2.1, a CZ grower is shown, with a resistive so-called cusp magnet [10].

2.1.1 Crucible An essential part of CZ growth is that the semiconductor single crystal is pulled out of melt that is contained in a refractory crucible. No solvent is used; that is, the melt consists of the same elements as the growing crystal. In the case of silicon, the melt is almost pure elemental silicon, at about 1420 C. The crucible and the crystal are both rotated, and the crystal is slowly pulled upwards in such a manner that a cylindrical body of desired diameter is achieved. When making use of transverse magnetic field, the crucible rotation is, however, usually very close to zero (see Section 2.7.2). Molten silicon reacts with all known materials to the extent that there are very few potential materials for a crucible [9]. The only available crucible material for high-quality crystals is silicon dioxide in its amorphous

Handbook of Silicon Based MEMS Materials and Technologies. DOI: http://dx.doi.org/10.1016/B978-0-323-29965-7.00002-6 © 2015 Elsevier Inc. All rights reserved.

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FIGURE 2.2 Used medium sized crucible, after fewer than 50 hot hours. The dissolution pattern is typical, with small brownish rings, indicating the presence of silicon monoxide, growing larger with time. The size of the rings is bigger near the bottom outer corner, where the temperature is the highest, and the melt contact has been maintained for a long time. FIGURE 2.1 Silicon CZ grower, equipped with a resistive cusp magnet. The bulge on the right front side of the otherwise cylindrical magnet houses electrical and cooling water connections into the copper coils. A superconducting magnet would look fairly similar but there are usually more than one but smaller protuberances that accommodate the cooling units, and they usually extend some distance above the magnet.

state, silica. A glimpse at the periodic table of the elements and the knowledge of the deleterious impact that most elements have on silicon material quality, even in very minute quantities, lead to only few candidates. Almost all metals are excluded because the allowed concentrations are only in parts-per-trillion-atomic (ppta) range or less. Group III and group V elements are electrically active dopants that often may be tolerated at much higher levels, typically to parts-per-billion-atomic (ppba) range, but this concentration is also far too low to allow crucibles to be made with compounds of these elements. Ceramic materials are excluded as well, either because they contain one of the aforementioned elements or because they contain other elements whose concentrations likewise must be held very low. Nitrogen (e.g., from silicon nitride crucible) is poorly soluble to the crystals, and the growing crystal tends to strongly reject it. The same applies to carbon. Concentrations of these elements in the melt are then highest very near the freezing interface, and as solubility is approached in the melt, there will be small particles nucleated that destroy the single-crystalline structure of the growing crystal. Furthermore, neither nitrogen nor even less so carbon is allowed in the crystal in levels even close to their solubilities, though nitrogen is sometimes intentionally introduced into the material, especially for FZ crystals. However, this topic will not be pursued any further here.

The situation with oxygen is, fortunately, different. Oxygen is tolerated in the crystal in a fairly large concentration, typically in 10 parts-per-million-atomic (ppma) range; and in most applications for silicon wafers, oxygen is a desired element, in controlled quantities, with clear beneficial effects. Furthermore, oxygen does not tend to be rejected by the crystal; that is, its segregation coefficient (see Section 2.9 for better definition) is close to unity [11], and there is no risk of oxide particles being created near the freezing interface. In addition to this, silicon has a volatile oxide, contrary to its carbides and nitrides: At high temperatures, in an oxygen-lean environment, silicon tends to form silicon monoxide rather than silicon dioxide. This monoxide is easily volatilizable, with vapor pressure of about 12 mbar at silicon melting temperature [6,9]. In practice, the vast majority (9899%) of oxygen that is being dissolved from the silica crucible wall by the highly reactive silicon melt will be evaporated into the grower atmosphere and purged away by the inert gas flow that is mandatory for successful growth. Typically, only 12% of the dissolved oxygen ends up in the growing crystal itself, but process conditions like the use of magnetic field and the size of the crystal relative to the crucible may change this ratio somewhat. Figure 2.2 depicts a medium-sized crucible after the process. The introduction of the reactive silicon monoxide to the otherwise inert gas flow is a major factor that causes unwanted reactions on the hot surfaces around the crucible and melt. The gas flow patterns inside the grower must be designed to take the potentially harmful effects of monoxide into account, especially as the quantity of oxygen released into the gas flow over one growth may be in the range of hundreds of grams in today’s large furnaces.

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PART | I Silicon as MEMS Material

2.1.2 HZ Materials The basic building material for a HZ for silicon CZ crystal growth is high-purity graphite. The term “hot zone” is used in this book to define the structural and insulating parts inside of the vacuum compatible chamber of a crystal grower, which are essential in creating a proper temperature distribution around the semiconductor melt and the growing crystal. Furthermore, the HZ design largely defines purge gas flow patterns inside the grower. Graphite is the material of choice because of its good availability in large blocks, its machinability, as well as its high temperature characteristics. Carbon in the form of diamond or graphite has the highest melting point of any element or almost any chemical compound. The material is reasonably strong, especially at high temperatures. It is also a fairly good conductor of electricity and heat. Its electrical conductivity makes it suitable as heater material, and its thermal conductivity is often desirable, as heat needs to be distributed uniformly from the heater(s) to the crucible and elsewhere inside the HZ. However, radiation is typically the dominant mode of heat transfer at these high temperatures, especially over long distances. The most commonly used insulator material is graphite felt, in different forms. The felt is made out of thin fibers, which act as insulation as they block thermal radiation many times over a short distance. Soft felt is woven into a relatively thin sheet of material, which may then be cut into desired shapes and bent over reasonably tight radii. Rigid felt is made of originally similar fiber material, but a carbon-containing binder is used to tie the separate fibers to a more solid, self-supporting body. Instead of a binder, chemical vapor deposition (CVD) of carbon may also be used to enhance the mechanical performance of the material. Oftentimes, the outer surfaces of rigid felt insulation are coated with a more continuous layer of graphite paint or foil, to reduce erosion and wear as well as particulate contamination. Other types of carbon-based insulation also exist, such as carbon foam. Generally, graphitized materials are clearly preferred, as graphitization reduces drastically the surface area of the fibers. Therefore, it is much less time-consuming to pump a grower into a proper vacuum, as outgassing from these high-surface-area materials is significantly reduced. The graphite parts are manufactured initially from fine carbonaceous particles that are mixed with a carbonaceous binder to form a mass that can be molded either by extrusion or in an isostatic press. Higher-quality parts are customarily isostatically pressed. The molded blocks are first carbonized and finally graphitized at very high temperature, close to 3000 C. The parts that are machined out of these blocks are typically purified in a halogencontaining atmosphere at an elevated temperature, to remove metallic contamination in order to comply with

requirements by the semiconductor industry. However, even after proper purification, the metal contamination levels are several orders of magnitude higher than what is allowed for silicon single-crystal material. Care must therefore be taken in the HZ design to prevent contamination from these parts from accessing the melt or the crystal surface. The graphite material is also slightly porous, which makes it possible for the remaining metals deep inside to reach the surfaces fairly easily. Furthermore, silicon monoxide that is present in the purge gas around the graphite surfaces is able to penetrate deep into the bulk of material and react there. Many other materials are used to create HZs. Carbonfiber-reinforced graphite (CFC) is mechanically much stronger; but it is also more expensive and poses other limitations to the design. Silicon carbide (SiC) is in many respects a better-performing material than graphite, but it has significantly higher cost, and availability of largesized components is poor. However, SiC is often used as a CVD coating to enhance the lifetime of graphite parts that are exposed to corrosive silicon monoxide, or to reduce contamination from graphite. The dense CVD coating effectively blocks contaminants inside of the slightly porous graphite material from getting to the surface. Another possibility is CVD carbon, which also forms a very dense layer on top of a graphite part. Other high-temperature refractory materials, such as molybdenum or ceramic materials that are compatible with the environment, may be used in locations where there is no risk of contamination to the melt. However, oxide ceramics usually have limited applicability in direct contact with graphite containing materials, at high temperature. If electrical insulation is required there, few alternatives remain. One is hexagonal boron nitride (sometimes called white graphite due to similar properties), but it is mechanically quite feeble. Molybdenum is often used at reasonably high temperatures because of its only moderately high cost, as well as its low diffusivity into silicon crystal and its very low segregation coefficient of about 5 3 1028 [12], which allows substantial molybdenum contamination in the melt before a damaging concentration may enter into the crystal.

2.1.3 HZ Structure A traditional HZ, as shown in Figure 2.3, contains a graphite susceptor around the silica crucible (which is often called quartz crucible), a cylindrical heater, and a heat shield around and below the heater. The susceptor is required because the high temperature causes the crucible to soften, and a proper mechanical support is therefore needed. The susceptor also helps distribute heat around the silica crucible a little bit more uniformly.

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Neck Graphite heater Crystal Low pressure argon gas

Silica crucible Meniscus Melt Graphite susceptor Heat shield

Silica crucible

Si crystal

SiO

Spill tray Si melt

FIGURE 2.3 Basic HZ structure. The melt is contained in a silica crucible, out of which the crystal is slowly pulled. Around the heater there are thermally insulating elements to reduce heat losses, and a spill tray is located below the melt to collect the liquid in case the crucible were to break. Modern HZs may be considerably more complex.

The heater is usually connected to two or four electrodes at its lower edge, typically by some kind of supporting elements also made of graphite. The electrodes deliver the required power, which is at least tens of kilowatts, but often well exceeds 100 kW. The heater is normally of picket type, which means that it has vertical slits cut into it in a manner that forces the electric current flow up and down, in opposite directions in neighboring pickets (see Figure 2.8). The voltage is quite low and amperage is high, mainly because of the high electrical conductance of the heater, but also because of the poor electrical insulation properties of the inert gas at the low pressure and high temperature normally used in silicon CZ growth. A heater would radiate approximately 400 kW per square meter, at silicon melting point with no insulation around the HZ. The heat shield drastically reduces the power consumption, and it also helps create a more controlled temperature distribution around the susceptor. The insulation itself is usually supported and shielded by structural graphite parts, but these graphite parts have much less impact on the temperature distribution. Typically, only a small fraction of the total power fed to the heater is lost through the insulation. Careful design is needed to control heat losses via such structural parts that extend through the insulation, such as the heater supports, as well as at all openings that are needed, including the additional open spaces around the heater supports and any openings for gas flows. There is also a small hole for an optical pyrometer, sometimes two, whose task is to measure the heater temperature. Structural parts stretching through the insulation may easily lead to several, or even more than ten kilowatts, of additional power losses per such part, and more poorly controlled temperature distribution usually will result.

O from crucible

Graphite heater

Graphite support

FIGURE 2.4 Schematic picture of inert purge gas flow. Oxygen is dissolved from the crucible, and the purge gas removes volatile silicon monoxide from the vicinity of the melt and the crystal. Only a small fraction of total dissolved oxygen ends up in the growing crystal.

Under the heater there is a so-called spill tray whose function is damage containment in the unfortunate event that the crucible should break while there is melt inside. This is a rare but risky situation, as the molten silicon is capable of making its way through the walls of the water-cooled vacuum chamber. Should this happen, there is a significant risk of a dangerous steam explosion. The role of the spill tray is to collect all molten silicon and stop it before it makes contact with the stainless surfaces of the chamber or damages the expensive mechanisms lower in the grower that are responsible for crucible rotation and lift.

2.1.4 Gas Flow Silicon CZ growth takes place under a continuous flow of inert gas. A schematic picture of the gas flow pattern is shown in Figure 2.4. Considering the high temperature and the reactivity of silicon melt, noble gases are the only ones allowed. Argon is the gas of choice because of its much lower cost than that of other noble gases. Argon has also the advantage of poor thermal conductivity compared with, for example, helium, and this feature facilitates the effort to insulate hot areas around the melt from the water-cooled vacuum-chamber walls. However, helium remains an option in situations where more efficient

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cooling is desirable, for example, to enhance cooling of the grower after the power has been shut off. Typical gas pressure is in the 1550 mbar range, and gas flow is in the tens to more than one hundred standardliters-per-minute (slpm) range. Lowered pressure is used to reduce gas consumption relative to atmospheric growth. As an example, if the process is running at 60 slpm/ 25 mbar and the receiving chamber of the grower has an inner diameter of 12 in., the resulting gas velocity in that part of the grower would be 0.50.6 m/s, which is enough to ensure clean laminar flow. Larger pressure would require also a higher mass flow of purge gas, to maintain a flow pattern that would not be overly influenced by temperature differences in the gas and to avoid undesired thermal convection. Furthermore, the oxygen containing gas that evaporates from the melt must be transported away in a controlled manner, which requires sufficient volume flow and gas velocity. The reduced pressure also helps with the insulation to a certain degree. The practical lower limit is close to 12 mbar, which is the vapor pressure of silicon monoxide in equilibrium with silicon melt, at melting point [9]. The monoxide concentration of the melt is close to saturation near the silica crucible wall, where the temperature is also typically a few tens of degrees higher than the melting point. If the pressure is lowered too much, the melt starts to “boil,” as the gas pressure is no longer sufficient to prevent monoxide from escaping in a manner not unlike boiling water. In a traditional HZ, there is a large open space above the melt (Figure 2.5), which is limited from above by the water-cooled chamber walls. This large continuous space allows uncontrolled convection to take place as the gas experiences heating from below, and the hotter and lighter gas wants to travel upwards, against the incoming gas flow. Silicon monoxide from the melt, traveling with this convection and meeting with the chamber wall, condenses on the cool surface. There are also other surfaces above the melt that are not quite that cold, but cool enough for monoxide to deposit. These layers threaten to cause macroscopic particles to fall back into the melt, with a high risk of destroying the single crystalline structure of the growing ingot. Such poorly controlled gas flows also tend to bring in other contamination, such as carbon, from the exposed surfaces of the HZ. There is also a more subtle mechanism through which the evaporating silicon monoxide risks killing the crystal. The saturation vapor pressure of the monoxide is strongly dependent on the gas temperature. As the monoxide containing gas travels upwards, it cools down, and tiny monoxide particles are formed. (It is not clear whether these particles are really made of silicon monoxide or whether the composition is rather a very-fine-grained mixture of silicon dioxide and elemental silicon.) The poor control of gas flow allows a part of this cloud of tiny particles to go

FIGURE 2.5 Neck, crown, and beginning of the body of a crystal. Around the crystal a bright ring, or meniscus, is visible. It is used to control the diameter of the crystal. This picture represents what is known as the open HZ, old design with some serious shortcomings.

back down towards the melt, and some of them may survive the hotter conditions until they make contact with the melt surface very close to the freezing interface. Marangoni convection (see Section 2.6.4) then takes the particles directly to the crystal, again with a chance of loss of structure (L/S).

2.2 STAGES OF GROWTH PROCESS The first step of a growth run is to charge the silicon into the crucible. Silicon is normally stored in clean double bags, typically 5 kg in a bag, though larger containers may also be used. Double bags also make it possible to remove the outer bag separately before bringing the silicon into the charging area, to reduce any contamination that could be transported into the crucible. The crucible may be charged as it already sits inside the grower. In order to save time at the grower and also to avoid contamination, the charge may be prepared in a separate area, after which the full crucible, with or without the susceptor, is transported to the grower and lifted into place. Handling of a full crucible is challenging, as its weight varies from tens to hundreds of kilograms, depending on the HZ size; the material is hard and brittle, allowing no shocks or scratching; and contamination is an eternal foe. Figure 2.6 shows a charged crucible in its susceptor. Note, however, that the kind of charging with small sized chips on top, as shown in the picture, can only be utilized if the HZ design is such that the upward heat losses are very small during the melting step. The way in which different sizes of silicon pieces are stacked into the crucible is an art of its own kind. The charging is usually started with relatively small sized chunks of silicon, to create a protective layer on the bottom of the container. Only then will larger pieces be added, as the smaller sized material reduces the risk that

Czochralski Growth of Silicon Crystals Chapter | 2

FIGURE 2.6 Charged crucible ready for the grower to close and the process to start. Small sized chip is used on top, which helps melting to proceed more from the bottom, as the silicon layer acts as a kind of thermal insulator. However, this kind of charging can only be used if the upper parts of the HZ remain quite hot throughout the melt-down, otherwise, bridging, splashing and sagging may occur.

one of those bigger chunks might cause damage to the brittle silica crucible. However, granular poly or very small silicon chips are not recommended at the bottom of the bowl (see Section 2.2.1). During the time that the temperature is raised, the charge experiences significant thermal expansion. However, dimensions of the silica crucible remain almost unchanged. There is a clear risk that the expanding charge will chip or even crack the crucible if large chunks are stacked without sufficient caution. Furthermore, the charge takes a considerably larger space before than after it has molten. Normally, the charge extends well above the rim of the crucible, but after melting the crucible is only about two-thirds full. There may be some “hangers” on the walls: chunks that remain attached to the walls; and some of them may interfere with the growth or may chip the crucible before falling down. These hangers remain cooler than the crucible, as they are free to radiate heat to the empty space above. Very high power, which could cause the crucible wall to soften and sag, would be required to make them lose contact. Careful stacking of the charge reduces the risk of problematic hanger formation. The batch melts starting from the edges, and a high column of silicon chunks, which are fused together, often forms. This column may create a considerable splash as it falls down. Furthermore, problems in stacking and how the melting is performed may result in a bridge in which the batch is molten from below in such a way that a layer of fused chunks remains connected to the walls, high above the melt level. As this bridge plunges, a severe splash may result. There is also a significant risk of crucible sag (Figure 2.7), should heavy chunks, fused together, remain unsupported from below. A crack in the crucible is always a serious situation, and its consequences must be taken into account in the design of the HZ as well as in the process considerations.

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FIGURE 2.7 Moderately sagged, medium sized crucible after grow. The white spots and layers near and on top of the crucible and high on the outer edge witness of high temperature, as well as of moderately large metallic contamination. On the inside, one can see horizontal lines caused by meltbacks, and wear patterns tell of long hot hours.

Silicon melt is very fluid and wets various surfaces, and that is why it is capable of penetrating through narrow holes and gaps. Therefore, even though a hole or a crack in the crucible is a rare or very rare occasion, most HZs are designed to take the full silicon or almost full silicon charge into the spill tray. The HZ and silicon melt are both sensitive to any oxidizing components in the surrounding gas, and that is why the growth takes place in inert gas ambient, and at reduced pressure. The growth chamber must therefore be highly vacuum proof, and it must be properly evacuated and purged before the temperature may be raised. Oftentimes a leak test is performed at this stage: The purge gas flow is shut down, the chamber is evacuated further, vacuum valves are closed, and the pressure in the chamber is monitored. The process is allowed to continue only if the leak rate is under a predetermined level. This is done to ensure that there are no leaks in the system that could introduce air, and thus contamination, into the melt and the surroundings during the long process hours. Another policy is to perform a leak test after the growth. The test may then use tighter acceptance values, as there are no fresh materials that could outgas in the chamber. Therefore, this kind of leak test better ensures the overall vacuum compatibility of the system; and furthermore, the overall cycle time may be somewhat shortened. As there is seldom the need to open more than a couple of vacuum seals to remove the grown crystal, clean the furnace, and charge it again, this approach is quite valid, as those seals are carefully cleaned before the furnace is closed for a new run.

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PART | I Silicon as MEMS Material

2.2.1 Melting

2.2.2 Neck

The next step, melting, takes a few hours, during which the temperature inside of the HZ is first brought to close to 1500 C, and then maintained there to bring enough heat to fully melt the batch. The temperature margin is not very wide, as the silica crucible is already quite soft at those temperatures, and excessive heat is avoided in order to prevent the crucible walls from sagging (see Figure 2.7). Furthermore, the hottest area of the crucible, typically the low corner area, will start to wear as soon as it is in contact with the melt. Excessive heat would enhance the wear and shorten the useful time available before the material is so worn that difficulties are created in maintaining the dislocation-free (DF) structure of the crystal, later in the process. After the whole batch is molten the crucible is lifted to the desired starting position, which is typically higher up than during the meltdown. The temperature is then stabilized close to the preferred starting value, based on experience about previous growths, and the seed crystal is ready to be dipped. The stabilization of the temperature is customarily controlled by a twocolor pyrometer that senses the surface temperature close to where the seed will be dipped. However, if the HZ itself and the instrumentation that measures the temperature inside the grower are stable, the heater pyrometer may also be used to indicate right conditions for the dip. There may be an additional delay before the next stage, during the stabilization of the melt temperature, to continue dissolving any potential small particles that may have stayed in the melt this far, as well as to reduce the number of tiny gas bubbles that may have adhered to the crucible wall or bottom. If, during the building of the charge, very small sized silicon was placed at the bottom, there was very likely a larger number of these gas bubbles trapped there, which bubbles are then gradually released into the melt. In addition to the proper charging practices, the way the melting is executed also influences how these bubbles may impact the growth process, later on. It is quite common to find small round cavities inside otherwise DF crystals, though sometimes also quite large cavities may be observed, extending through several wafers that are cut out of an ingot. The risk that an individual bubble may “kill” the crystal can be quite low, estimated at well less than 10%, for such growth processes that create relatively low level thermal stresses. In thin polished wafers, like those used for typical MEMS applications, it is very rare to see these cavities, as they are almost always larger than the thickness of such a wafer, and therefore, they get caught in one of the visual or other inspections before the final steps of wafer making.

At the right temperature for the dip, the end of the seed will melt away and a meniscus (see Section 2.3.1) will form. As the seed is slowly pulled upwards, new material will be crystallized in the end of the seed, obeying the original crystal structure. The seed is usually not DF at this point, as the temperature shock caused by the contact to the melt tends to create dislocations even if the original seed was free of them. That is why a necking step normally follows (see Figures 2.3 and 2.5), and the same seed may be used over and over again without excessive concerns about whether the DF structure is maintained or not, through the thermal shock by the dip. The basic idea in the necking step, originally introduced by Dash in the late 1950s [8], is that dislocations have limited mobility in silicon, and if the crystal is grown rapidly and thin enough, the dislocations will grow out from the sides of the neck and eventually be frozen and excluded from the material. There are a few requirements for this to happen. The dislocations in silicon have a preferred axis in a ,110 . direction. Should one try to grow a neck of uniform thickness to this crystal orientation, some of the dislocations would have no difficulty in staying within the neck; they would simply grow in length together with the neck. The more the growth axis deviates from the nearest ,110 . direction, the easier it will be to get rid of dislocations. That is why other common crystal orientations, (100) and (111), are relatively easy to grow DF, but growth of DF (110) material is much more challenging. The other requirements are that thermal stresses are low, pull speed is high, and to sum up, that the rate of climb of dislocations in the direction of the neck axis remains smaller than the pull rate. A thin neck combined with low thermal gradient reduces stress. The climb, which is essentially silicon interstitials (or vacancies) attaching to the edge of the additional atomic plane, which edge forms the dislocation line proper, is a much slower process than slip. Slip often occurs when silicon wafers are processed, or in the crystal if the DF structure is lost, and also in the end of the tailing step (see Section 2.2.5) as the crystal is detached from the melt. High pull speed also favors silicon vacancies, which slows down the climb towards the melt interface. Pull speed of the order of 3 mm/min is usually adequate, the thickness seldom much exceeds 45 mm, and a few centimeters in the proper speed/diameter range suffices. The idea of climb being the limiting factor for dislocation movement applies to edge dislocations as well as to those of so-called 60 type. The thermal stresses try to drive these line defects down towards the freezing interface. Pure screw dislocations do not need the climb process to move downwards in the neck, as they can slip in any plane where the dislocation is located. However, a

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screw dislocation does not experience similar driving force towards the melt surface, created by the thermal stresses, as a dislocation with an edge component does. The crystals used for today’s bulk MEMS applications are still lightweight enough that a regular Dash neck is applicable to orientations other than (110). However, crystals used for IC applications may be so heavy that a standard neck would no longer be able to carry the weight of the crystal safely. Several approaches have been used to address this issue, such as enabling the use of a thicker neck, constructing an additional mechanical means to support the weight, or developing ways to grow DF crystals without any necking procedure at all. This topic will be expanded in Section 2.10.1. Some of the measures that help grow very heavy crystals are also relevant for the growth of (110) material. However, the production of DF material to that orientation will not be covered in this chapter. There exists some confusion about the density of dislocations in CZ silicon crystals. Because of historical reasons, specifications often allow nonzero dislocation density, for example, less than 100 count/cm2; however, today it is much easier to grow large crystals that contain zero dislocations than it is to grow crystals that contain a small but nonzero number of them. The neck is an effective means of eliminating all linear dislocations from the material, and it is more difficult to create the first dislocation into DF material than for an existing one to multiply to a large number. Oftentimes, the neck is grown longer than would actually be required for DF structure. This adds a certain safeguard to the quality of material in the end of the neck, but the primary reason for doing this is related to the often slow thermal response of the system: It is desirable that the melt temperature in the beginning of the next step, the crown, is correct to about 1 C. The thin neck acts as a very reproducible temperature sensor, better than the pyrometers used in the instrumentation. As soon as the neck diameter and average growth rate have reached the desired window for a sufficient time, the temperature is also correct.

2.2.3 Crown When the proper length of the neck as well as the right temperature have been reached, the crown is started. Pull speed and temperature are lowered, crystal and crucible rotation speeds may be changed, and melt level may also be adjusted gradually. The purpose is to create suitable conditions in which the crystal acquires diameter at a proper pace: Too slow results in an unnecessarily long process time, loss of valuable material that decreases the body length, as well as increased probability of structure loss, as the melt is also warmer and therefore less stable than is optimal. On the other hand, too large a

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growth rate increases the risk of L/S, as the excessively cool melt causes an untenable growth rate in some crystal orientations. The larger the diameter of the crown, the cooler must the melt also be, and that is why there is a continual decrease in the heater power/temperature. The typical heater temperature difference between the end of the necking step and the beginning of the full diameter body is several tens of degrees Centigrade, and most of that is needed during the crown. On the melt surface, diameter increase may be observed (see Figure 2.5), but there are also things taking place under the surface, which we cannot see. The freezing interface usually becomes increasingly convex towards the melt, and that shape has a significant impact on the chances of success of the crown and subsequent steps. A very slow pull speed in crown results in a flat crown shape that is economical when it comes to the usage of original silicon material in the charge. The freezing interface then tends to be highly convex. However, the interface is inclined to be fairly straight or even concave during the body, depending on thermal conditions, melt flows and the pull speed. Therefore, the shape of the growth boundary needs to experience a very significant change towards the end of the crown and the beginning of the body. The actual speeds of crystallization near the center axis of the crystal and near the edge will then be very different, and a L/S will be more probable than if those speeds are closer to each other. Especially in the case of material doped heavily with antimony or other volatile n-type dopants (which is, in general, more difficult to grow than lightly doped or heavily boron-doped material), this change of interface shape may easily be fatal for the crystal. Why this should be so, will be elaborated further in Section 2.9. On the other hand, if the diameter growth rate is kept small and the pull speed relatively high, the crown shape will be more conical and the freezing interface will experience a smaller change towards the body. This will make it easier to make the transition to the body, but at the cost of more time spent and poorer silicon material usage. That is why a suitable tradeoff is chosen, with a high probability of success for the crown and early phases of the body, but with as little time and material spent as is feasible.

2.2.4 Body The cylindrical part of the crystal, out of which the actual wafers will be fabricated, is called the body. Between this section and the crown there is a transitory period that we call here the shoulder. The shoulder is started a little before the desired diameter for the body is reached, and the pull speed is raised significantly. This cuts the growth

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PART | I Silicon as MEMS Material

in the diameter over a relatively short distance, and ideally the growth turns vertical at the same diameter as is chosen for the body, or slightly above. At that point, the pull speed is lowered again, to match that of the early body. If the pull speed during the shoulder is maintained high for too long, the diameter of the crystal will start to diminish again. After completion of the shoulder, the body is started. At this point, some further, significant temperature drop is usually needed, but after a while, the temperature changes will be slower. Diameter is controlled through instantaneous pull speed, most often by using a PID (proportional-integrating-derivative) control loop that needs to be tuned properly, and average pull speed is maintained by adjusting the heater power, or temperature. If there is a bottom heater or other additional heaters, their power may be changed in a predetermined manner; or there may be instrumentation to measure the temperature, and a predetermined profile may be followed. Gas flow, pressure, as well as crucible and crystal rotation rates are among the controllable parameters along the body length, and there may be more, such as strength and shape of a magnetic field, melt level, etc.

down slowly, according to a suitable profile followed in order to produce a desired thermal history of the crystal, especially to the last few tens of centimeters of the body. After the crystal has cooled down sufficiently, it is removed from the receiving chamber. This normally happens before the HZ is cold enough that it may be opened for cleaning and recharging, and for a new crystal to be grown. Cooling of the HZ may be enhanced to save process time, for example, by moving parts inside of the chamber to allow for a more effective escape of heat; by purging the system with a suitable high-volume gas flow; or by adding, for instance, helium into the chamber. The cleaning involves removal of the used crucible and the frozen residual melt (also called pot scrap), vacuuming any silicon-monoxide-containing dust from the surfaces, potential replacement of worn parts, and checking of overall condition of the HZ components.

2.2.5 Tail

2.3.1 Diameter Control

In the end of the body, a significant portion of the melt is still remaining, typically at least 10% of the original charge, though in some applications this portion may be smaller. For large diameter crystals, this portion may also be considerably more substantial see Section 2.10. A part of this remaining melt is used to form a so-called tail. This portion of the crystal is needed for two purposes: First, there will be a thermal shock that will almost inevitably introduce slip dislocations as the crystal is detached from the melt, at any non-trivial diameter. This slip will proceed a somewhat shorter distance upwards than if the growth were to have been disrupted at full diameter. In addition, a smaller volume of melt is consumed to produce a tail than to produce a corresponding length of full diameter. Altogether, a longer DF body can be produced from the same amount of melt. Secondly, there may be a desire to achieve a more uniform thermal history to the end of the body, more comparable to the other parts of the usable crystal. Should the ingot be detached at full diameter, the end portion would cool down much more rapidly than if a long tail is grown.

There is a clear-cut balance between the growth rate of the crystal and thermal gradients on both sides of the freezing interface. The growing crystal needs to be cooled, mainly through radiation, and to some extent also by the purge gas flow. Near the freezing interface, the heat flux density can be taken to be equal to the magnitude of thermal gradient multiplied with thermal conductivity, on both sides of the interface. However, the solidification process releases heat at a rate that is equal to the speed of crystallization times the latent heat. In a balanced situation, the external pull speed of the crystal is equal to the rate of solidification, and the thermal flux density on the crystal side is larger than that on the melt side by the amount released in the crystallization process. The crystal then tends to grow, maintaining its diameter, at least averaged over time. The time-dependent processes in the melt make temperature gradients at the liquid side vary over time, which creates striations to the crystal (see Figure 2.10), but as long as the balance is maintained averaged over time, no major difficulties should occur in the diameter control. The crystal diameter is almost always measured optically. The melting point of silicon is high enough to give ample intensity for optical measurements, and in practice, most of the available light and infrared radiation are filtered out. A traditional way was to observe the bright ring, known as the meniscus, around the crystal with a pyrometer that was focused on a small spot in such a manner that an

2.2.6 Shut-Off After the tail is complete, power to the heater(s) may be shut off and the crystal pulled into the receiving chamber to cool down. However, the lower end of the crystal may be left to stay for a while inside the HZ, while the power is ramped

2.3 SELECTED ISSUES OF CRYSTAL GROWTH In the following sections, diameter control, doping, and HZ lifetime are discussed.

Czochralski Growth of Silicon Crystals Chapter | 2

increase in diameter resulted in a larger signal, as the more radiant meniscus and the lower end of the crystal were taking a larger portion of the spot. More modern measurements rely on video feed that is processed to give either the chord length, obtained by measuring two points at the meniscus, or several point locations are identified and a best-fit calculation performed to get the diameter of the meniscus. The luminousness of the meniscus (Figure 2.5) is caused by the reflection of light from the melt surface at locations where the surface is curved upwards in such a way that the hotter crucible wall is reflected to the eye of an observer. The boundary between solid and molten material is very difficult to distinguish. The diameter is then measured at some suitable location in that meniscus, a few millimeters outside of the crystal edge. The physical properties of elemental silicon define what is known as the wetting angle, whose magnitude is 11 : This is the angle between the (vertical) edge of the growing silicon crystal and the melt, very close to the triple point (edge of the crystal at the solid-melt interface). As the crystal edge is vertical, the melt also turns almost vertically upwards to meet the solid, since the melt has quite a large affinity to the solid. The edge of the freezing interface is located as much as about 7 mm above the melt level, the latter measured a couple of centimeters outside the crystal. The balance between the surface tension of the melt and gravity dictates the shape of the melt-gas boundary near the crystal, that is, the shape of the meniscus. Should there be a need to adjust the diameter, the most commonly used approach is to change the external pull speed. For instance, if the diameter is too large, an increase in the pull speed will begin to change the diameter within a few tens of seconds to a few minutes. However, the increased pull speed does not immediately change the speed of crystallization, as it is dictated by thermal balance. In order for the crystal-melt system to adapt to the new situation, three alternatives are possible: (i) Heat transfer at the crystal side of the interface could be enhanced. However, if no changes take place there, this does not happen by itself. (ii) Heat transfer at the melt side could be lowered, but again, no intentional changes are made there. (iii) The production of latent heat may be brought back to the original value. As the heat produced at the interface equals the speed of solidification times latent heat times the surface area of the freezing interface, the increased pull speed results in decreased diameter. The rate at which the diameter starts to change, can also be quantified, if deemed necessary. If you pull faster than the speed of solidification, the triple point will start to move higher. As the shape of the meniscus curve is fixed, the melt-gas boundary will turn to be more vertical than the wetting angle of 11 . At that point, the growth angle at the crystal edge must also change, and it

27

will accommodate to the new situation; the diameter will taper in, the angle being dictated by the height of the meniscus, at a given moment in time. Should the average pull speed, after proper control of the diameter has been established, be off from the target, slower means of control are used. The target speed is typically in the 1 mm/min range, depending on the crystal diameter (larger crystals grow more slowly), HZ design (cooler environment experienced by the crystal allows larger growth rate), and quality issues. Some crystals are grown slowly to establish a suitable balance between growth rate and thermal gradients, this balance has an impact on very small vacancy-related defects, known as COPs, in dense IC circuits [13,38]. A crystal grows more rapidly from a cool melt, and this is again caused by the requirement of thermal balance: Colder melt delivers less heat to the freezing interface, and more heat may then be produced by the crystallization process. Change of the melt temperature has therefore an impact on the average growth rate, the average taken over several tens of minutes. There is a pyrometer watching the heater temperature(s), and a change in that temperature also changes the melt temperature after a significant time delay. Another possibility is to change the heater power. There are a couple of other options that have a speedier influence on the thermal balance, to control either diameter or the average pull speed, but these approaches are more seldom used. Thermal radiation at the crystal side may be changed by adding a heater, halogen, or IR lamps [14]; by other means of introducing energy to the crystal; or by changing its thermal environment in a more passive way. At the melt side, transport of heat from the crucible wall towards the freezing interface may be changed, for instance, through small changes in crucible rotation rate or magnetic field. These measures are faster than control through heater power or temperature, but also more complicated, as these other possible control parameters must also be kept close to their desired average values.

2.3.2 Doping Most material used for MEMS applications is lightly doped with boron or phosphorus, up to a few tens of ohm centimeters. This corresponds to 10151016 dopant atoms/ cm3, which translates to only milligrams of elemental dopant to a charge of tens of kilograms and more. A small quantity like this is very difficult to allot in a consistent manner, and therefore the dopant is usually introduced asdiluted to a larger amount of silicon. A suitable amount of dopant element may be melted together with silicon to make an alloy in which the dopant concentration is in the 0.010.1% range. If this alloy is prepared carefully so that the concentration is uniform, a very convenient

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PART | I Silicon as MEMS Material

amount of alloy may be mixed with the silicon charge to result in a reproducible concentration in the melt. There is a further advantage in using silicon alloy to introduce the dopant: Very little of the dopant will be able to vaporize during the melting of the charge. In mass production of silicon crystals, this alloy is usually prepared in a very simple manner: A very heavily doped single crystal is grown, its resistivity profile is measured, and wafers cut from this crystal are used to introduce dopant into hundreds of lightly doped crystals. Low resistivity crystals are usually doped using elemental dopants. Boron is essentially nonvolatile, and it may be introduced into the charge at the same time as the silicon chunks are laid into the crucible. However, the common n-type dopants antimony, arsenic, and phosphorus are highly volatile, and they are preferably put in only after the charge is molten. Antimony is relatively simple to pour into the melt, as it is readily available in granular form; that is, it flows easily from and through various cups and channels, and its density is high enough to take it into the bottom of the melt, with little evaporation or splashing. Arsenic and phosphorus, on the other hand, tend to volatilize at or above the melt, and a significant portion may be lost into the purge gas flow. This adds costs, as more high purity dopant material will be needed; there will be more dirt in the system, adding to chances of particles and yield losses; and the reproducibility of the amount of the dopant in the melt will be poorer. Furthermore, there will be added hazards to the cleaning of the equipment because of the additional burden posed by the superfluous dopant in the vacuum lines and on other cool surfaces. Various approaches have been developed to introduce these dopants into the melt in a more efficient and cleaner manner. The common n-type dopants normally reduce oxygen concentration in the grown crystals, as oxygen in the melt is depleted more efficiently near the gasmelt interface. Volatile oxides of the dopant are carried away by the purge gas just as oxygen is carried as silicon monoxide, adding to loss of oxygen. The faster evaporation rate of oxygen tends to increase the wear rate of the crucible, and extra care must be taken not to exceed its useful lifetime. On the other hand, heavy boron doping also increases the crucible dissolution rate, but as boron does not enhance volatilization, the oxygen contents of the growing crystal tends to go up. Furthermore, boron also influences the concentrations of intrinsic point defects, vacancies and interstitials, whose balance is also responsible for creation of COPs (see Section 2.3.1). In certain growth conditions, the boron-dependent vacancy concentration may create a situation, in which the wafer material exhibits anomalous, very swift oxygen precipitation behavior. It appears that n-type dopants display some effect to the intrinsic point defect concentrations, as well. This becomes evident for

the neck growth, for example, heavily arsenic doped crystals can be started more consistently, if the neck diameter is reduced compared to lightly doped material. As vacancies (and interstitials) play a role in the Dash neck, this suggests that vacancy concentrations would be impacted by the presence of arsenic dopant, too. n-type dopants have also some visible effect on surface tension and therefore to the melt flows near the surface (see Section 2.6.4). Heavily n-type doped material is often significantly more difficult to grow; this topic will be touched in Section 2.9.

2.3.3 HZ Lifetime HZ materials have only a limited lifetime, partly because of high temperatures and partly because of the corrosive action of silicon monoxide. The heater and the susceptor are those parts that typically suffer most rapidly. The heater is sensitized because it runs at a higher temperature than other parts of the HZ, and that is why the reactions with monoxide have the largest impact on it. Furthermore, its picket structure allows gas to attack it from several directions simultaneously, whereas, for example, the cylindrical heat shield made of graphite (sometimes called the heat-shield liner if the insulating part is called the heat shield) is attacked only from the inside. The resistivity distribution of the heater is also of major importance. The erosion is normally not uniform, and the power distribution of the heater then changes with its age (Figure 2.8), causing quality and yield problems. In a traditional HZ design, the purge gas, which contains also the corrosive silicon monoxide, is sucked down around the crucible and susceptor, and through and around the heater. Further downstream, the reactivity of the gas has already been reduced. The lifetime of a heater

FIGURE 2.8 Worn heater after tens or a few hundreds of crystal growth cycles. Silicon monoxide evaporating from the silicon melt reacts with carbon in the heater, attacking the hottest parts first. The heater comes from a HZ as shown schematically in Figure 2.3.

Czochralski Growth of Silicon Crystals Chapter | 2

may be as short as just twenty crystals, but with more sophisticated designs, it may be hundreds of runs or more. The susceptor is also enclosed in the hottest part of the furnace. Even though its temperature is not quite as hot as that of the heater, the susceptor is mechanically more strained. The main stress is experienced during cooling at the end of the cycle, as the susceptor material starts shrinking when the temperature goes down. The coefficient of the thermal expansion of the silica crucible is extremely small, only about one-tenth of that of the susceptor material. During the time the temperature was close to the silicon melting point, the crucible was soft enough to have accommodated the shape of the susceptor. During the early part of the cooling, the crucible hardened again, but the susceptor tended to shrink a further couple of millimeters. This cycle exposes the susceptor to tremendous stress. In order to alleviate the problem, the susceptor is normally cut to several (usually, three) sections. The cuts allow separate slices to move independently. However, in addition to reduced mechanical strength and stability, there is also a further price to pay for this. The intimate contact between the silica crucible and the graphite susceptor, together with the high temperature, makes graphite and silica react to form carbon and silicon monoxides, which are both volatile. This reaction wears the material in locations where there are easy escape paths for the gases and the temperature is the highest. Typically, the wear is the fastest in the vicinity of the cuts that allow susceptor sections to move relative to each other. Furthermore, the resultant production of carbon monoxide creates a significant risk of carbon contamination, as the source is close to the melt.

2.4 IMPROVED THERMAL AND GAS FLOW DESIGNS The CZ process has to be designed in such a way that energy consumption is minimized, HZ lifetime is maximized, and the crystal quality is good and repeatable. Computational modeling methods are indispensable in achieving these goals. Modern HZs utilize such structures above the melt that cut direct visibility between the hot crucible wall and the growing crystal (see Figure 2.9, compare also to Figure 2.5), except for the first few centimeters of the crystal above the melt [15]. This allows for better control of the temperature distribution in the crystal. Temperature gradients over the freezing interface experience smaller variations. Furthermore, growth rate in the body can be made essentially independent of the location in the crystal, contrary to traditional, or open HZs, in which the achievable growth rates decline towards the end of the body as the hot crucible rises gradually. All this gives a

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FIGURE 2.9 Crown and early body inside conical thermal shield. The shield above the melt helps modify thermal conditions that result into more homogeneous crystal material, radially and axially; as the process conditions change less through the length of the crystal, shorter process times also result. The gas flows are kept more laminar and brought closer to the melt, which helps avoid contamination and improves growth yields.

better and more reproducible quality. Furthermore, the freezing interface can be made straighter, and thermal stresses in the growing body are smaller, resulting in better growth yields. At the same time, there is a significant reduction in power consumption as the earlier intense heat loss from the surface of the melt and the upper parts of the HZ is reduced. The improved thermal insulation results in longer lifetimes of the HZ parts, as maximum temperatures inside the HZ are lowered and the wear of different parts becomes slower and more uniform. The stability of the whole process is further enhanced by the fact that improved insulation results in a situation, in which the temperature distribution becomes less dependent on where in the heater the heat is actually produced. In addition to thermal design, any structure above the melt must also be optimized for gas flows. The three main goals for better gas flow configuration, in addition to contributing to control of oxygen in the growing crystal, are to reduce the risk of particle formation in such locations, from where a particle may end up in the melt; to protect the melt from gaseous contamination; and to protect the most critical HZ parts from the corrosive action of the purge gas, after the gas has passed the melt surface. Aforementioned structures that help optimize the temperature distribution around the crystal may also serve to create more laminar gas flow patterns near the crystal and melt surfaces. However, as it is advantageous to go fairly close to the melt with such structures that help modify temperature distribution, a rule of thumb being that one should go to about one-quarter diameter of the growing

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PART | I Silicon as MEMS Material

crystal from the melt or even significantly closer, this may be somewhat too close to allow proper gas-flow control near the melt surface. Various schemes have been envisioned to give more independence between gas flows near the melt surface and thermal design in the same area. After the gas has passed by the melt surface and exited the crucible, it will unavoidably hit some hot surfaces and react there (unless some very expensive materials are being used). The resulting carbon monoxide will not get back into the melt if the gas flow is kept laminar after leaving the crucible. However, in order to extend the lifetimes of the heater, the susceptor, and other expensive HZ parts, it is preferable that the contact of the gas with these parts be kept to a minimum. Various approaches are available, which, however, all add to the complexity of the HZ design.

2.5 HEAT TRANSFER There are three significant modes of heat transfer that operate during silicon crystal growth: Conduction, convection, and radiation. Radiation is of major significance between surfaces that are separated from each other by a physical gap, but between which there is direct visibility. Most materials that are being utilized absorb heat so efficiently that heat transferred by reflected radiation is less significant; but, especially over the melt, it cannot be neglected. The importance of thermal radiation is enhanced by its strong dependence on temperature: The StefanBoltzmann law tells us that the radiant power density is proportional to the fourth power of the temperature. That is why, especially over longer distances, where the role of conduction is reduced, radiation plays an important and often dominant role. Conduction is the normal mode of heat transfer through a material, solid or fluid. Structural graphite materials are excellent conductors of heat at high temperatures, much better than, say, stainless steels. On the other hand, insulators are designed in such a manner that conduction is made difficult. For example, the graphite fibers conduct only along the fibers, and as there is limited contact between the filaments it is difficult for heat to be conducted through the thickness of an insulating layer. At the same time, the fibrous structure cuts the radiation repeatedly over a short distance, making radiation much less effective than transfer over free space. Furthermore, insulating material makes it difficult for the inert gas to flow through, cutting or seriously impeding convective heat transfer, too. A silica crucible has quite low thermal conductivity, but it also transfers heat through radiation. The crucible is manufactured in a process in which high-purity quartz sand is fused, using, say, an electric arc, into a dense,

solid material. However, the outer edge of the crucible contains a high density of small bubbles, which makes radiation less effective. The inside, on the other hand, is fused to be essentially bubble free (why this is will be explained in Section 2.8.3, see also Figure 2.15), and radiation may pass freely. Sometimes, the bubble structure of the crucible has a significant impact on its temperature distribution, as the wall may act almost as an optical guide for thermal radiation. In the melt, heat is transferred by conduction and convection. The melt is metallic in nature, its thermal conductivity is at par with graphite, and conduction must be considered as a substantial contributor to overall heat transfer. However, a simple analysis tends to show that convection should play the dominant role. This will be discussed a little later. The crystal also has these two components to the heat transfer, which must be included in analysis. This may sound slightly surprising, since the growth rate of the crystal is small, in 1 mm/min range only. The melt flows, driven by buoyant forces, have 23 orders of magnitude greater speeds than the typical pull rate. The purge gas flow has two components to the heat transfer, neither of which is usually very large; however, they cannot be ignored, especially where the impact is most significant. Even though the furnace pressure is usually low in the silicon CZ process and argon is a poor thermal conductor, the presence of the gas has nevertheless a significant negative impact on the insulating properties of the used fibrous materials. Another mode of heat loss by the gas flow is created by the need to heat up the incoming gas itself. Typically, the gas flow is in tens of slpms, and during the passage through the HZ, the temperature rises by well more than 1000 C. In most cases, a few, but no more than about five additional kilowatts escape from the HZ because of the conduction, convection, and heating up of the purge gas, which is relatively little compared with the power of 40 to well beyond 100 kW that the HZs consume. However, the action of the cool incoming purge gas may be quite local on the crystal as well as in the areas close to the melt surface, and then this effect may not be ignored, even if the magnitude of this additional, but local, heat loss is only in the 1 kW range: The total upward directed heat transfer rates in, say, 150200 mm crystals, seldom exceed 23 kW in today’s HZs, though this number may be increased to a very significantly larger value.

2.6 MELT CONVECTION The largest CZ crystals grown today weigh several hundreds of kilograms, and the size of the crucible corresponds to that of a small bathtub. The freezing interface is located at the top surface of the melt, and that is why

Czochralski Growth of Silicon Crystals Chapter | 2

the surface areas are colder than those deep in the melt. As the melt expands with the temperature, warmer melt close to the bottom is less dense, and it tends to rise up towards the surface. The viscosity of molten silicon is somewhat less than that of water; that is, there is very little that the viscosity does to slow down melt movements. That, combined with the large volume of the melt, makes it very difficult to control the melt behavior properly. The crystal sizes grown for MEMS applications are, fortunately, slightly smaller (the present charge sizes rarely exceed 150 kg). But even so, it is a major challenge to create such growth conditions that the instability of the melt does not cause serious impediments to the yield of the growth or to the quality of the growing crystal. The two major approaches to stabilizing the melt, in addition to creating a favorable temperature distribution, are crucible rotation and magnetic fields. The use of magnetic fields is very common for large melts and crystals, where crucible rotation tends to be insufficient to bring in adequate stabilization. For smaller melts, such as those used for MEMS crystals, magnetic fields are useful in extending crystal properties beyond what is straightforward to achieve without them, for example, in broadening the available range of oxygen concentration.

2.6.1 Free Convection CZ-grown silicon material shows oxygen and resistivity striations (Figures 2.10 and 2.16) because the melt is heated from below and from the sides, and this kind of temperature distribution is seldom stable. The hotter, less dense melt tends to move upwards, bringing heat with it; and at other locations in the melt the cooler and denser melt goes down. There are two dimensionless numbers that are commonly used to characterize the behavior of a volume of fluid as it comes to free, or natural, convection. The first one is the so-called Grashof number (Gr) that tells the ratio between buoyant forces and viscous forces. The buoyancy of the hotter melt closer to the bottom of the crucible is greater for deeper melt, larger temperature differences, and higher value for thermal expansion. Evidently, we do not consider the magnitude of gravity here (in microgravity, it would be much easier to achieve striation-free crystals). The viscous forces are directly related to the viscosity of the melt, which is, as mentioned earlier, quite low. As the Gr surpasses about 107, the flow ceases to be laminar and becomes turbulent. For large silicon melts, Gr is typically around 1010, that is, well above this turbulence limit [16]. However, the value is still so low that the turbulence is not very strong, and the turbulent vortices created by natural convection are relatively large, the smallest ones being in the 1 mm range. The second dimensionless number is known as the Rayleigh number (Ra), and it describes the ratio between

31

the convection of heat to the conduction of heat. This number may be easily calculated from Gr, as it is the Gr multiplied by the ratio of kinematic viscosity to thermal diffusivity. As the melt has low viscosity, but high thermal conductivity, this ratio is small, on the order of 0.01. However, as Gr is so large, Ra is also quite large, and based on its value, the convective transport of heat should clearly dominate over conduction. Free convection tends to form distinctly separate areas in the melt, both where hot melt goes up and in other areas where cooler melt goes down. The locations, sizes, and shapes of these areas change continuously; some of these vortices disappear and new ones are formed; and an accurate prediction of the melt flows is extremely difficult, as is often the case with turbulent flows. The growing crystal feels these volumes of different temperatures, and over cold spots the growth rate is greater than over hot spots, where the crystal may actually be even melting for a short period. The variations in growth rate have also an impact on the momentary dopant concentration that will be embedded into the growing crystal. These will then be visible as resistivity striations (Figure 2.10). As the crystal is rotated during growth, there is typically some component to the striations that is related to the rotation rate. In addition, there are longer-term variations that convey the time that it takes a new larger hot spot to arrive under the crystal, after the previous one has gone. The temperature disturbances may also result in the loss of the single crystalline structure; unstable melt behavior typically results in poorer yields. In addition to resistivity striations, oxygen striations may be found in a crystal after growth. They have some correlation to resistivity striations, as oxygen originates from the crucible wall and so does heat, however, oxygen has much lower diffusivity in the melt. Oxygen variations in the melt tend to be more sharply defined; and especially for fine vortices, the correlation between temperature and oxygen may be poor. That is why the time-dependent variations in oxygen concentration in the crystal do not follow too closely the resistivity striations. It was mentioned earlier that conduction significantly contributes to heat transfer in the melt, too, even though the Ra would suggest otherwise. The main reason for this discrepancy is forced convection by crucible and crystal rotations and the optional use of magnetic fields, or other potential means of stabilizing the melt against uncontrolled natural convection. If free convection is not the dominant convection mechanism, the inferences derived from these dimensionless numbers (Gr, Ra) may be grossly misleading.

2.6.2 Crucible Rotation In a typical CZ growth process, the melt as a whole rotates approximately with the crucible. Because of low viscosity,

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PART | I Silicon as MEMS Material

FIGURE 2.10 Lateral photovoltage scanning (LPS, [17]) map of a lightly doped 150 mm N100 crystal. The sample has been cut out of a 50 mm thick section of the crystal, as shown on right, and then etched. The freezing interface shape may be readily extracted from the map, and information about the amplitude spectrum of axial resistivity striations may also be obtained.

Growth axis

it may take a significant amount of time for the melt to adjust its rotation rate to that of the crucible, but this time is still very short compared with the total process time. Under the crystal, which is normally rotated in the opposite direction, the rotation rate of the melt is slower, just because the crystal opposes the rotation with the crucible. There are, however, exceptions to this general rule; for instance, magnetic forces may be used to make the melt rotate more slowly or faster than the crucible, or the crucible may be rotated in such a manner that its rotation rate changes quite quickly over time. The best known case in which the melt rotates at a rate that is clearly different from that of the crucible is if one uses a transverse magnetic field. A static transverse field exerts a strong decelerating force to a rotating body of electrically conducting fluid, and the melt will be almost non-rotational, independent of the crucible rotation rate. This case will be discussed in a little more detail in Section 2.7.2. Let us assume that the hottest spot in the melt is somewhere near the crucible radius, that is, far from the centerline. This is most often reality, too. The melt there would like to start going upwards, and it is pushing the melt on top sideways, towards the cooler crystal. The coldest spot is just under the crystal, where the temperature is very close to the melting point. That melt would like to go down, kind of completing the circle with the upward directed flow near the crucible edge. However, the situation is far more complex. First of all, the viscosity is too low to prevent the upward-going flow from turning down just a couple of centimeters inwards from the crucible wall. And correspondingly, the downward-going flow somewhere under the crystal would take up a much smaller area than that of the whole (large) crystal, and there would be upward-oriented channels of flow under and close to the crystal, too. This would be the effect of free convection and a large Gr. Secondly, the fairly large velocity component along the circumference of the crucible, the tangential, or

Sample cut

FIGURE 2.11 Low pressure system over the Norwegian Sea. Note the wind directions, the air flows rotate counterclockwise around the center, as the Earth’s rotation causes the incoming air to deviate from the straight path. Once rotational around the center of the low pressure, air has difficulty getting closer to the center, just like silicon melt spinning in a crucible.

azimuthal velocity, would pose a serious challenge for any fluid volume that would try to make its way too close to the crystal. The fluid would tend to keep its linear velocity when moving radially inwards. However, as the distance from the crucible centerline becomes smaller, the angular velocity would increase correspondingly. The same behavior may be seen in the case of tornadoes and hurricanes, where the wind approaching the eye of the storm rotates ever more rapidly. Figure 2.11 portrays wind directions around a low pressure system in the Norwegian Sea. Note that the winds mainly rotate around the center of the low pressure, rather than blow from areas of high pressure towards the center. This phenomenon, conservation of angular momentum and increased angular velocity with decreasing distance from the centerline, has a major impact on the centrifugal force that this fluid volume experiences. The higher the crucible rotation is, the shorter the distance will be that the fluid volume is able

Czochralski Growth of Silicon Crystals Chapter | 2

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FIGURE 2.12 Momentary but representative velocity profiles for various crucible rotation rates; left at 5 rpm and right at 15 rpm [19]. The results are calculated from two-dimensional simulations; full three-dimensional results would be more complicated. The velocity component perpendicular to the direction of rotation is shown, only. The velocity scale is in meters per second crucible size is 20 in.

0

0.01

0.02

to make towards the center, before the increase in rotation rate will stop it from going any further. An idea of the magnitude of the phenomenon may be gained if we consider a simple numerical example. Let us assume that the crucible rotates at 10 rpm, and we observe a volume of fluid that is at 200 mm radius. Should this fluid try to move inwards, say, to a radius of 180 mm, its rotation rate would tend to go up to 11 rpm. This volume of fluid that rotates at 11 rpm would experience about 100 N/m3 larger centrifugal force than fluid rotating at the original 10 rpm. This so-called body force may not sound very large (gravity makes melt experience a force of about 25 000 N/m3), but in practice this difference in centrifugal force is very significant. Gravity itself does not cause free convection, but differences in fluid density do, together with gravity. As a comparison, a vertical column of melt that is 5 K hotter than the surrounding melt, a significant temperature difference, would experience buoyant force that is 20 N/m3, that is, a considerably lesser force than that caused by relatively short radial travel. That is why, for reasonably high crucible rotation rates, the melt flow patterns tend to form vortices that are elongated in the vertical direction, and more so if the rotation rate is increased (Figure 2.12). On the other hand, narrow vortices may more easily exchange heat between the warm, upward-directed regions of flow and those colder regions that are going down. This exchange of heat reduces temperature differences between neighboring parts of vortices, and it also reduces the role of convection in the heat transfer. In principle, it would be possible to rotate the crucible so rapidly that the rotation alone would result in such small structures that the conductive heat transfer would effectively eliminate temperature differences between upward- and downward-directed portions of the vortices. At the same time, this balancing of temperatures would eliminate the driving force for free convection, and free convection would no longer play a role in heat transfer. However, several tens of revolutions per minute would be required, and in practice this would be very challenging to realize. Use of a suitable magnetic

0.03

0.04

0.05

field to support the stabilizing effect of melt rotation would seem to make this approach to stabilizing melt behavior somewhat more realizable [18].

2.6.3 Crystal Rotation The most evident reason for the rotation of the growing crystal is to keep its shape essentially round. The semiconductor industry is geared to using round wafers, and there is an abundance of good reasons for the practice of using that shape, which the wafer manufacturers must then also follow. However, the crystal rotation has also a significant impact on melt flows under the crystal. The classical approximation for the flow under the crystal is that of a rotating disc over stagnant fluid. This case has been widely studied, and it is one of the few situations where a three-dimensional fluid flow may be solved analytically [20]. The resulting flow pattern contains an upward-directed component that is independent of the distance from the centerline of the crystal. There is also a radially outward-directed component that is zero at the freezing interface and very far from it, and it has a maximum value quite close to the interface. In a thin layer, of the order of less than 1 mm thick, the flow is directed radially outwards in a spiral pattern. If the crystal rotation rate is increased, the thickness is reduced proportionally to the square root of the rotation rate, but at the same time, the velocity of the flow is increased linearly. This adds up to an increase in the mass flow that is directed outwards, which is consequently also proportional to the square root of the rotation rate. The driving force for this outward-bound flow is the rotational movement that the crystal causes. The melt under the crystal experiences centrifugal force that is strongest at the interface. However, the melt closest to the interface cannot effectively move outward, as the solid surface located just above slows down that portion of the melt. The same viscous forces that make the melt rotate in the first place prevent it from moving relative to the crystal. Far from the interface, the rotation rate is

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PART | I Silicon as MEMS Material

essentially zero and, therefore, so are the centrifugal force and radial velocity. The viscosity of the silicon melt is so low that only a thin layer under the crystal actually rotates with the crystal, and it is in this layer where the maximum radial velocity can be found. The outward-directed flow is quite important in distributing dopants and oxygen more uniformly into the crystal. Typically, the easiest solution for excessively high radial dopant or oxygen gradients is just to increase the crystal rotation rate. However, the solution may sometimes prove to be more complicated than that. The cool melt from under the crystal tends to reduce thermal gradients outside of the ingot radius, too. Any deviation out of the cylindrical shape has a better chance of surviving and growing into a significant disturbance if the temperature outside of the crystal increases only gradually. There are always such disturbances because of random fluctuations and because of the anisotropy of the growing single crystal. The most prominent anisotropic feature is the existence of four vertical growth nodes along the crystal, at 90 intervals, in case of (100) material. The nodes are caused by close packed {111} planes that try to grow a little further along the meniscus than other parts of the crystal. If the thermal gradients are made too small, uncontrolled growth over the meniscus and the loss of a single crystalline structure may result. Before that, if the crucible and crystal rotation rates are fairly large, threedimensional flow patterns will develop near the periphery of the crystal, again at fourfold symmetry, that cause the relatively narrow growth nodes to widen and flatten, and finally the crystal changes its shape to become somewhat star-shaped. Other deviations from nice round crystal shape may also ensue, due to high rotations and small thermal gradients on the melt surface. This simple and well-organized flow pattern by crystal rotation, as approximated by a rotating disc, is only a very partial truth. If we would only rotate the melt and the crystal would be still, the melt immediately under the crystal would rotate more slowly than the rest of the melt, and a simple flow configuration would again be born. In this case, the pattern would be identical to what was described previously, but the direction of the flow would be inversed [20]. This kind of configuration would create very large oxygen gradients over the radial dimension of the crystal, as well as a high dopant gradient in the case of a volatile dopant, such as antimony in low-resistivity material. As counter-rotation is the industry standard, where both the crucible and the crystal are being rotated, no easy analytical solution for the melt flow exists (even if we would not consider other components of flow, such as free convection). Normally, the crystal is rotated at a clearly faster pace than the crucible. However, because of the much larger surface area in contact with the crucible, most of the melt, also under the crystal, rotates in the

same direction as the crucible, though at a lower rate, under the crystal, than outside of the ingot radius. The melt immediately below the crystal rotates with it, but already, a few millimeters further, the direction of the rotation is normally the opposite. In between, there is a narrow layer where the actual rotation is close to zero. Above and below, the melt tends to flow outward, again because of centrifugal force, but in between there is a sheath of melt that flows inward. This flow is extremely important for the control and uniformity of oxygen in the growing crystal: The melt under this flow layer is quite oxygen rich, bringing oxygen from the bottom of the crucible; but this layer is more oxygen lean, as it flows in under the crystal after spending some time near the meltgas interface, where oxygen has been removed from the melt. However, three-dimensional turbulent effects complicate the flow patterns further.

2.6.4 Marangoni Convection and Gas Shear On the melt surface, there is a force that causes the melt flow towards the crystal in such a way that any small particle that would fall onto the surface of the melt would have high chances of hitting the crystal, thereby causing it to lose its DF structure. This force and flow is called Marangoni force and flow, and its origin is in the temperature dependence of surface tension at the meltgas interface. Surface tension is the phenomenon that causes small water droplets to try to take spherical shape: A volume of liquid wants to minimize its surface area. But it is the temperature dependence of surface tension that creates the Marangoni force, not surface tension itself. Farther away from the crystal, the surface temperature of the melt is higher, and that is why surface tension there is lower. Marangoni force, whose unit is force per area (N/m2), is therefore directed towards the cooler area, that is, towards the crystal, and its magnitude is larger for a larger temperature gradient. As the melt viscosity is low, this flow has limited impact on the melt behavior deeper down, but the flow velocity right at the surface cannot be ignored. There is another surface force that is opposing the Marangoni flow, in HZs where the purge gas flow or a significant part of it is directed close to the melt (see Section 2.4). At low pressure, hot purge gas may have a velocity in the 10 m/s range very near to the melt surface, and this creates a shear that is directed outwards. The magnitude of this shear is often in the same range as the Marangoni force. Especially if low oxygen material is desired, the efficient sweeping of oxygen containing gases is needed in the vicinity of the melt-gas interface, and this translates into high gas velocity. Oftentimes, if melt behavior during CZ growth is simulated computationally, oxygen is considered as not having an influence on melt flows. This makes the

Czochralski Growth of Silicon Crystals Chapter | 2

optimization of the growth process substantially easier, as the melt flows may be modeled on thermal considerations and forced convections, only. After having modeled the melt flow patterns, one may calculate oxygen distribution in the melt with varying purge gas flows. Proper simulation of the melt flow is a much more laborious exercise than that of gas flow or oxygen distribution. However, if the gas flow is high enough to cause significant shear to the melt interface, or if the cooling effect of the gas flow changes the temperature distribution in the crystal and around the crucible by a considerable amount, this approach is no longer valid. Then the melt flows should be recalculated, adding very significantly to the computational effort, for every major change in the gas flow.

2.7 MAGNETIC FIELDS There are two different kinds of static magnetic fields in widespread use to produce CZ silicon crystals, transverse and cusp fields [21]. Almost pure axial fields are poorly suited, as they tend to prevent transport of oxygen and dopant from under the crystal, therefore, the resulting oxygen concentration may be very high and variation of oxygen and dopant in the radial direction (radial gradient) is often large. Traditionally, wafer manufacturers based in Japan have favored transverse magnets, whereas western companies have relied mainly on cusp magnets. Magnets weigh usually several tons, and the power may be well beyond 100 kW; large CZ growers are able to accommodate magnets up to 20 tons. However, more power-hungry magnets have been increasingly replaced with superconducting (SC) magnets. Sometimes, especially older growers have been modified to take more lightweight resistive magnets, with less copper, despite the cost of higher electric current density and larger power loss, as the space around the vacuum chamber has been in short supply and the grower frame has not allowed for significant excess weight. Relatively lightweight SC cusp magnet designs are also available. Furthermore, if low field is considered sufficient, modern permanent magnet materials together with iron yokes have been considered. The movement of an electrically conducting fluid in a magnetic field causes an electromotive force that is perpendicular to both the field and the direction of movement. This electromotive force tends to create electric currents that, in interaction with the external magnetic field, oppose the fluid motion. The field strengths typical for magnetic CZ (MCZ) processes are sufficient to slow down various flow patterns very significantly. This has implications to a range of crystal properties such as oxygen and dopant distributions; but they also tend to reduce crucible wear, thus extending the lifetime of the crucible, and reduce thermal fluctuations in the melt, which,

35

together with reduced crucible wear, results in better DF growth yields. A cusp MCZ process may be very similar to a normal CZ process. As the melt is rotated, electromotive forces (electrical fields) are generated, but there are no return paths for the electric currents, and that is why, there is little force created that would try to stop the overall melt rotation, with the crucible. In this respect, the situation is very different for the transverse field that does not allow melt rotation. The electric currents fed into the HZ heaters also interact with external magnetic fields. In case of cusp field, these forces are usually too weak to cause concerns, however, they have to be considered for the more powerful transverse fields. Furthermore, the heater power supply may require additional consideration. The power supplies usually deliver DC current, on top of which there is a significant AC ripple. This AC component may cause disturbing vibrations in the grower, interacting with the DC magnetic field, and in a serious case, even a heater breakage may occur. The AC ripple in the heater current needs to be eliminated for both types of magnets.

2.7.1 Cusp Field Cusp magnetic field is essentially a field created by two round horizontal coils, with a distance between them, connected in such a way that their magnetic dipoles oppose each other. That is why there is a region of almost zero field that is usually close to the freezing interface [10]. The cylindrical symmetry is maintained. A typical shape of cusp field is shown in Figure 2.13. Far from the freezing interface, the magnetic field is strongest and its impact on reducing melt flows is also greatest. In a way, it may be considered that the cusp MCZ purports to grow the crystal from a melt that has been reduced in effective volume by creating circumstances in which the melt close to the freezing interface and below the crystal sees little effect of the field, and outside of the crystal radius the melt convection is largely suppressed. Oxygen concentration in an MCZ process is often considered to be substantially lower than in an otherwise similar process but with no magnetic field. This is not always true. It is proper to say that a magnetic field reduces the rate of dissolution of the crucible; that is, introduction of oxygen into the melt is diminished. However, it also has an impact on melt flows near the meltgas interface, reducing flows there. It is essentially the balance between the dissolution and evaporation of oxygen that dictates the oxygen concentration in the melt. As the magnetic field stabilizes the melt behavior, a more effective means, for instance higher gas flows, may be utilized to remove oxygen from the melt, and that is why the use of a magnetic field does allow to reach lower

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PART | I Silicon as MEMS Material

FIGURE 2.13 Shape of a typical cusp magnetic field within the melt volume and lower portion of the crystal. Maximum field strength (white color at scale value 1.0, in arbitrary units, typically about 0.1 T) is attained at the crucible corner. Near freezing interface, there is almost no field. Solid lines depict the magnetic lines of force.

0

0.2

0.4

oxygen levels. However, reduced oxygen concentration in the melt does not guarantee low oxygen in the crystal, in a straightforward manner. Growth processes are possible in which flow patterns under the crystal are such that if that region is oxygen rich, the crystal also becomes oxygen rich even if the melt outside of the crystal radius has relatively low oxygen contents. But such processes are normally not applied, as it would be quite difficult to control the radial uniformity of oxygen concentration.

2.7.2 Transverse Field A transverse magnetic field [22] is created from conventional copper or SC coils that are located in essentially vertical position; superconductive material is standard due to the desire to produce quite high fields, typically near or above 0.3 T. Heavy iron shields are used to shorten the magnetic path and to reduce the important stray fields. However, from the outside, it is not evident if a magnet is transverse or cusp, as both make use of cylindrical shields around the coils. Figure 2.14 depicts the flux density and directions in an iron shield of a magnet design, in which the coils are of the so-called saddle type. The coil shapes and the current loop directions are also shown. If one looks at Figure 2.1 that shows a CZ grower equipped with a cusp magnet, one can tell that it is a resistive magnet by the bulge on the right front side of the otherwise cylindrical magnet, in the picture. That protuberance houses the electrical and cooling water connections into the copper coils. However, a similar cusp magnet can also be built to be superconductive, at which point the bulge can be substantially smaller in size, but it usually also extends above the top surface of the iron shield, and there may be more than one of them. Just based on the external looks of the magnet, it may be very difficult to tell if it is of the SC transverse or cusp type, a transverse magnet could look exactly the same to the outside.

0.6

0.8

1

The powerful magnetic field in combination with large electric currents fed into the heater create quite significant side forces to the heater and the supports that carry it. These forces require additional design criteria set for the HZ, as compared to if no magnet, or cusp magnets are deployed; cusp magnets display weaker fields, furthermore, the forces are in directions that are easier to accommodate. The additional features may include larger air gaps and stiffer structures, or alternately, mechanical supports in the design, to make sure no electrical shorts are created. Mechanical support structures are challenging to fabricate due to the harsh combination of high temperature, chemically reducing environment made mainly out of carbon, relative movements of various HZ components because of thermal expansions, and the requirement that those supports be non-contaminating and electrically insulating. For example, common oxide ceramics do not survive the environment next to the heater. A transverse field has the unpleasant characteristic of breaking the otherwise almost perfect cylindrical symmetry of the growth geometry. However, as the field acts on the melt behavior only, and the melt flows in the case of large crystals and crucibles deviate from cylindrical symmetry in a significant manner anyway, this loss of symmetry is not as serious a breach as it may first seem. Furthermore, a transverse magnet usually displays a significantly larger stray field outside of the magnet than cusp. This can be fought by the use of a thicker and heavier shield, but typically, some amount of higher stray field is allowed, as a reasonable compromise. This has some impact on the instrumentation of the grower itself, and some devices may require additional shielding or relocation to a position with lower field. The presence of the potentially large magnetic field has to be considered in the design and materials of the tools and carts to be used in the vicinity of the growers, as well; there is also a risk of significant magnetic forces between the magnet

Czochralski Growth of Silicon Crystals Chapter | 2

37

FIGURE 2.14 Magnetic flux directions and density distribution in an SC transverse magnet, designed for silicon CZ growth. Only the cylindrical iron shield is shown (right) and the coil shapes (left). The coils are of so-called saddle type. Note the highest flux densities just behind the coils, in the iron shield, and the relatively low field areas inside the coils, as well as 90 apart, between them. Courtesy of Okmetic Oyj.

itself and the frame of the grower. Normally, there are no actual health concerns, though, as the field is strictly DC, and any persons with potential health concerns pertinent to magnetic fields will not be allowed to enter the grower hall, anyway. The crucible (and melt) rotation is normally relatively fast during growth, with no magnetic field to stabilize the fluid, but this is not the case for the transverse field. The lateral field, together with melt rotation, would create electric potential differences between the bottom and near-surface regions of the melt. These differences would be of varying magnitudes, depending on the angle between the direction of the field and the fluid velocity; and large electric currents opposing the rotation would flow. That is why, under any transverse magnetic field, the rotation rate of the bulk of the melt would be close to zero, essentially independent of the crucible rotation rate. The transverse magnetic field is very effective in calming down the visible melt behavior, though inside the melt, there are still flow patterns that bring heat from the crucible wall closer to the growing crystal [23]. The stabilizing effect can be seen, for example, in Figure 2.21 that portrays a 450 mm crown approaching its target diameter. The surface of the melt, as well as that of the crystal is significantly smoother than if grown in the absence of a magnetic field, or using a cusp magnet. The intensity of the field is high at the melt surface, which dampens effectively any waves, ripples, or flow vortices.

A further benefit of the high field at the melt-gas and crucible-melt interfaces is that both oxygen dissolution from the crucible and evaporation from the melt are greatly reduced. Consequently, a variety of potential crucible quality issues (see also Section 2.10) have less significance. Processes with long hot hours have clearly better chances of success, too, as the crucible wear and lifetime is one of the stumbling blocks.

2.7.3 Time-Dependent Fields Much more complex magnetic fields may be devised for improved control of melt behavior, and the fields may also be time dependent. However, these possibilities are discussed only shortly, in Section 2.10.8.

2.8 HOT RECHARGING AND CONTINUOUS FEED The CZ crystal growth process that has been described this far depicts a standard batch process, in which one crystal is pulled from the melt. Occasionally, for various reasons, two small crystals may be pulled from a single melt. However, this is a rarer occasion than so-called hot recharging, in which a relatively large residual melt is left in the crucible and new silicon material is added into the melt.

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PART | I Silicon as MEMS Material

2.8.1 Hot Recharging

2.8.3 Crucible Modifications

The easiest way of using the same crucible to grow several crystals is to use granular polysilicon, small spheres in the 14 mm diameter range that flow easily, even through small-diameter tubes or other structures, to make the feed. Granular polysilicon is made in fluidized bed reactors, which is more challenging a process than the present workhorse, the Siemens process [39], but also clearly more energy efficient. However, the availability has been very limited but that situation appears to be changing for the solar CZ industry (PV). There are some additional concerns, though, as it comes to the purity of available granular poly, for semiconductor use. Other types of materials are therefore also used: Smallsized chunks or chips may be fed in a manner similar to granular material, using larger-sized channels, though the feeder for that material is typically quite different. Or a vertical tube-like structure filled with smallish chunks, an internal hopper, may be lifted into the receiving chamber, after removal of the crystal, and a valve in the lower end of the tube opened to allow the charge to be replenished. Furthermore, large rods of material may be put hanging into the end of the seed cable/shaft and fed into the melt in a well-controlled manner, though this is rare. In all of these cases, the main goal is to reduce cost and save time compared with growing just one crystal from the melt. The price of the relatively expensive crucible, which will break during cooling down, will then be shared with a larger number of crystals. The residual melt will also be shared with several crystals, however, with the further expense of somewhat more contamination in the end of the last crystal than there would have been at the same position if only one crystal would have been pulled. However, today’s high purity processes typically allow for that. There will usually be some savings to the cycle time per produced kilograms of crystals, too, as there will be less time needed to heat up and cool down the HZ, again, per crystal pulled.

A major impediment to the use of hot recharging has been, in addition to the limited availability of granular poly material, the strain that the very long total hot time exposes the crucible to. There is a continual wear in the crucible wall. The possibility that the advancing wear will release small silica particles into the melt and thus cause a L/S increases as the erosion proceeds. The way the crucible wall has been fused makes the near inner surface usually of better quality than the deep bulk of the material. Over the years, various alternatives have been pursued to extend the lifetime, either through modifications to the way the crucible behaves when exposed to reactive silicon melt, or through changes made to the HZ design and the growth process, in order to reduce the wear at the crucible walls. Some approaches used within the industry today are modifications to the silica material itself, including the use of high-purity sand for an inside layer, sand that has been manufactured starting from high-purity gases, or fusing this inner layer to contain fewer bubbles (Figure 2.15) and other imperfections that would initiate non-uniform wear that may result in the release of small silica/quartz particles into the melt (see also Figure 2.2). Further possibilities are the application of small quantities of various elements whose role is to enhance the so-called devitrification of silica, in order to ensure that the wear takes place more homogeneously than in the absence of this uniform devitrified layer, and at the same time the crystal rejects those added elements so powerfully that the concentration in the crystal remains insignificant. Some further discussion about the crucible will follow in Section 2.10.

2.8.2 Charge Topping An even simpler approach to enhance the productivity, in a more moderate fashion, is what is called charge topping, and it is in wide-spread use. In this approach, the equipment is very similar to what is used for hot recharging, but just lesser in capacity, usually a simple internal hopper, filled with small sized polysilicon. During the melting of the charge, as the surface of the silicon has already dropped inside the crucible (see also Section 2.2), and there is only some fraction of the solid left unmelted, the hopper is lowered to the vicinity of the original charge. A valve in the bottom of the hopper is then opened and the additional silicon is dumped on top. The hopper gets removed and the rest of the process proceeds as in a regular batch process.

FIGURE 2.15 Cross sectional cut of a used crucible, after very long hot hours. The bubble free layer aims to cover nearly one half of the total wall thickness, but there are some large bubbles visible in this area, and smaller ones near the inner wall (bottom part of the picture). The outer wall (top part) contains a large density of small pores, which makes the material semi-opaque. Courtesy of Silfex, Inc., A Division of LAM Research.

Czochralski Growth of Silicon Crystals Chapter | 2

It is recommended to enhance the thermal design of the HZ in such a way as to reduce the crucible inner wall temperatures and thus to diminish wear through the lowered solubility of oxygen and reduced intensity of the melt flow patterns, as well as to use various magnetic fields to stabilize the melt. However, in applications that are notably cost sensitive like growth of solar silicon, the considerable expense of a magnet is often prohibitive. The price tag may exclude the very significant advantage to the crucible lifetime of, for example, transverse magnetic field, and the return on investment may simply not be there.

2.8.4 Continuous CZ Growth Continuous CZ (CCZ) is another means of growing more kilograms of good material out of a crucible, and more productively over unit time. The basic idea is that several long crystals will be produced while keeping the amount of melt in the crucible approximately constant, or letting it deplete only slowly. The concept of continuous feed to increase the productivity of solar grade silicon was introduced already in the mid-1970s, after the first oil crisis, to address the small silicon batch sizes of that time, which also lead to pioneering experimental work. The main emphasis was solar material then, as it is today. Both granular poly as well as so-called liquid feed was investigated [24,25]. The technological basis was established but the fairly moderate growth of the PV industry then and subsequent increases in the crucible and silicon charge sizes for semiconductor CZ resulted into putting CCZ on the back burner for a long time. Commercial production of solar CCZ silicon exists today, though the volume is still relatively small, compared with hot recharging. Continuous feed is technologically clearly more challenging, and it requires significant changes into the grower, the HZ and the crucible design. Furthermore, CCZ has suffered clearly from poor access to granular polysilicon, as well. The gradually emerging better availability of granular poly will undoubtedly increase the interest towards CCZ, in the future. The two main categories of CCZ are liquid feed, in which the silicon stock material is molten before channeling it into the crucible, and granular or small chip feed, in which silicon is added into the crucible still as solid. The latter is the favored approach in PV production today, and it requires clearly more moderate changes into the equipment and the process. However, even in this case, some significant modifications are required, to prevent the supplied silicon from reaching the growing crystal too quickly, with the resulting loss of single crystalline structure. There are several potential approaches, but the two most feasible ones are: (i) Some kind of double crucible, in which the melt surface area, where the silicon is fed to, is isolated from the growing crystal using another, smaller

39

sized crucible, or with a silica ring; the unmelted silicon will remain on the surface, at a definite distance. (ii) A large, shallow crucible, in which the melt flows are moderate, the distance to the crystal is large, the melt surface temperature can be maintained high, and additional process conditions like gas flows and crucible rotations can be used to keep the solid material away long enough, for it to melt properly. Liquid feed is technologically more demanding to make happen, and to the author’s knowledge, it is presently not utilized commercially. However, the author maintains that it is the more probable candidate, rather than solid feed, as it comes to increasing the crystal weights for very large diameter growth, in the future (see Section 2.10). In a way, this method of adding to the crystal weight, for very large diameter crystals, would not be strictly CCZ, as the feed rate would probably be clearly lower than the crystallization rate. The primary emphasis would not be to use the same crucible to grow several crystals, like in CCZ for PV, but rather, to use a moderately sized crucible to pull much heavier ingots. The main reasons for this assessment is that (i) for the larger, semiconductor quality crystals it is possible to add significantly more complexity and cost than for the PV applications, and (ii) the availability of high quality crucibles will very probably be one of the main challenges that preclude fairly straightforward steps to just simply switch to a larger crucible and batch sizes (see Section 2.10). That is why, a development that is easy on the crucible will likely be realized with less pain. For the liquid feed, there are also two potential approaches: (i) The feedstock can be melted in a separate crucible, outside the vacuum chamber and the HZ out of which the actual crystal is pulled. Or, (ii) silicon can be fed into the grower in granular form, or small chips, and melted there using a separate heater (and container), before being channeled into the crucible.

2.9 HEAVILY N-TYPE DOPED SILICON AND CONSTITUTIONAL SUPERCOOLING Different applications often require heavily doped p-type or n-type silicon. The dopant poses some additional challenges for the crystal growth, especially in case of n-type dopants, if the resistivity target is close to what is readily commercially available. Boron doped material does not usually require significant changes for the process, as long as the resistivity target is larger than about 1 mΩ-cm. For some additional details concerning heavy boron doping, refer also to Sections 2.3.2 and 2.10.1. However, n-type dopants are often more problematic, since the resistivity gets frequently pushed close to what is technologically practicable.

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The common n-type dopants are antimony, arsenic and phosphorus, in this order, as one considers the lowest feasible resistivity target for each dopant. Sb-doped material is usually grown to about 20 mΩ-cm range, As-doped down to 23 mΩ-cm. Below that value, phosphorus is the dominant dopant, down to less than 1 mΩ-cm specifications. Antimony is the most straightforward to handle of this group, both when considering crystal growth, wafer manufacture and subsequent wafer processing. Antimony as an element does not have the historical notoriety of arsenic and doping is fairly easy, see Section 2.3.2. Furthermore, its diffusivity in solid silicon is low, which, together with relatively small concentration, does not allow the dopant to move easily from the substrate to, for example, epitaxial layers. Use of arsenic in crystal growth is somewhat more challenging, due to more significant safety hazards and the more demanding doping procedures. Phosphorus adds to this, as it creates also significant fire risks at the time the grower gets opened after the process. Phosphorus is also the most mobile in solid silicon of this group of elements, and as its concentration is usually the highest, there is more challenge in preventing it from moving out of the substrate, during the device processing. The trend outside of the MEMS world is, however, to reach lower resistivities, especially for high current power devices. This drives development of processes of very heavily phosphorus doped crystals, and materials with other n-type dopants can also benefit of the acquired learning. All electrically active dopants in silicon favor melt over solid silicon, see, for example, Table 3.3. The equilibrium segregation coefficient, k0 tells how strong this trend may be. Boron has its coefficient quite close to unity, at 0.8; this means that the melt needs to have an additional 25% of boron over the concentration that one expects to have in the growing crystal. The solid rejects antimony quite effectively, the k0 is only 0.023, and the other common n-type dopants have their segregation coefficients near 0.3. The fact that the crystal rejects these dopants also makes it difficult to grow material with high dopant concentrations, and the limiting values are well lower than solid solubilities for the respective elements. Why this should be so will be covered next.

2.9.1 Constitutional Supercooling The risk for so called constitutional supercooling (CS) is very significant, when growing heavily doped n-type crystals, and to the author’s understanding, it is usually the dominant factor that limits the lowest available resistivities for these materials. In case of boron doping, the situation is much easier, in this respect. However, the CS is

FIGURE 2.16 Growth striations in 150 mm diameter As-doped silicon crystal. The undulating interface indicates CS. The growth rate was too high for the used dopant concentration and thermal and flow conditions in the melt. The crystal lost its DF structure soon thereafter. The cross sectional sample was polished and Wright-etched. The width of the visible area is about 1.2 mm. Courtesy of Jari Paloheimo at Okmetic Oyj.

not the only factor that poses additional challenges concerning growth of heavily doped n-type silicon. The influence to the neck diameter target was already mentioned in Section 2.3.2. Furthermore, small bubbles or cavities that are frequently seen in lightly doped material (see Section 2.2.1) are very rarely seen in very low resistivity n-type crystals. This suggests that material of this kind is significantly more sensitive to losing the DF structure, due to such small disturbances that are rarely lethal for lightly doped crystals, like small gas bubbles released from the crucible wall and bottom. But these observations are very qualitative, quite challenging to quantify. The situation is different regarding CS, for which the metallurgical background is quite well established. Figure 2.16 depicts growth striations in a 150 mm diameter As-doped silicon crystal that lost its DF structure soon thereafter. The picture of the cross sectional sample is taken near the centerline of the crystal, towards the end of the targeted body length, as the dopant concentration has increased to a relatively high value, due to segregation to the melt. The material resistivity here is about 1.9 mΩ-cm and the seed lift is quite high, too high at about 1.2 mm/min. Heavy doping with n-type element will have a relatively significant impact to the melting point of silicon, of the order of one degree Kelvin in magnitude. This change is not really visible in the grower but it may easily degrade the stability of the solidification process, near the freezing interface. The reason is that there will be a dopant profile immediately below the interface, which creates an associated gradient to the melting point.

Czochralski Growth of Silicon Crystals Chapter | 2

2.9.2 Melting Point Depression The dopant lowers the melting point in very similar fashion to adding common salt into clean water. As salt much rather stays in liquid water, adding that salt makes it more difficult for water to freeze, and as a result, the melting point goes down. The phenomenon is known as freezing or melting point depression [26]. Furthermore, a pure element like silicon has a single melting point, or chemical compound like water, but in the presence of dopant in high concentrations, we’ll have two separate temperatures for each dilution: liquidus and solidus. Liquidus is the higher one of these and also the one with the larger significance for us here, it is the temperature above which there is no solid left; in temperatures below solidus all the material has been crystallized. Note that a high concentration of dopant is still a relative notion in case of silicon, since we are still talking of quantities below 0.5%-atomic in the melt. For each dopant, there is a well-defined slope for how quickly the melting point drops for each fraction of a percentage point of dopant added. It can be quantified in terms of latent heat of fusion of silicon and the segregation coefficient of the dopant, only. Starting from thermodynamic considerations, it can be shown that the slope equals ΔTm;l 5 ðk0 2 1Þ  ðRTm2 Þ=Hm  Cd

(2.1)

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for small concentrations Cd of the dopant [27,28], where ΔTm,l is the change in the melting (liquidus) temperature, R gas constant, Tm melting point of silicon, and Hm is the latent heat of fusion. This dependence is known as van’t Hoff’s rule, in honor of the first Nobel Prize winner in chemistry. The behavior of the melting point with the dopant concentration is depicted in Figure 2.17. We take phosphorus here as an example. In Table 3.3 we see that its equilibrium segregation coefficient is ca. 0.35. In practice this means that we need nearly three times as much dopant in the melt as is our target for the growing crystal. This segregation coefficient corresponds to a melting point (liquidus) drop by about 0.3 K for each 0.1 percentage points (atomic) of phosphorus, in the melt. For other common dopants, this factor is about the same, for arsenic it is also about 0.3 K and antimony, about 0.5 K. However, if we look at the dopant concentration in the ingot, the differences between the various dopants are much larger, due to the fact that they get introduced into the growing crystal in largely different concentrations for the same melt concentration. Let us assume that we want to grow silicon crystals to 1 mΩ-cm resistivity targets, a nice, round number. Then, assuming we are successful, we can estimate the necessary changes in the melting point, which are shown in Table 2.1 for different dopants.

FIGURE 2.17 Melting point depression by phosphorus doping in silicon melt. The unique melting point at 1412 C (1685 K) splits into two curves, with increasing dopant concentration, solidus and liquidus. The drop in the melting point as well as the corresponding atomic concentrations are shown for a doping level that corresponds to 1 mΩ-cm (8 3 1019 atoms/cm3) silicon material.

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TABLE 2.1 Melting Point Depressions for Different Elements, as the Melt Is Doped to Concentrations That Correspond to 1 mΩ-cm Resistivity in the Growing Crystal B:

0.2 K

P:

1.3 K

As:

1.7 K

Sb:

(1.8 K)*

( )*: target is 10 mΩ-cm. Note that the target resistivity for antimony doping is 10-fold.

Note that it is not feasible to even try to grow Sb doped material to 1 mΩ-cm target, and that is why, a more reasonable goal of 10 mΩ-cm is displayed in the table, for that element.

2.9.3 Origin of Dopant Gradient in the Melt The growing crystal rejects most of the n-type dopant at the freezing interface. This surface becomes therefore effectively a source for that element. The profile is dictated by the concentration and diffusivity of the dopant, as well as by the melt flows. This includes the slow upward motion of the fluid, under the freezing interface, created by the growing crystal. The highest concentration can be found in the immediate vicinity of the solidification boundary. This dopant profile creates a corresponding gradient in the melting point, see Figure 2.18. The melting point increases as we go farther away from the crystal, and so does the actual melt temperature (Figure 2.19). If it would so happen that the melting point would increase more rapidly, going away from the phase change interface, than the actual melt temperature, we would have a potentially unstable situation. This condition, in which the thermal gradient in the liquid is smaller in magnitude than that of the melting point (Figure 2.19), is called constitutional supercooling (CS) [29]. The justification for the choice of words is that it is indeed the chemical constitution of the liquid that creates such conditions, in which the melt is actually supercooled at a finite distance away from the freezing boundary. If the supercooling is important enough, the growth rate will increase locally and the originally relatively flat and smooth crystallization interface develops serious oscillations (see Figure 2.16). Eventually, the DF single crystalline growth comes to an end, with significant material loss. The diffusion layer depth, through which the dopant concentration changes significantly, is typically less than 1 mm thick. The heat flux in the crystal, directed

upwards, typically originates from the latent heat of fusion, for the most part. As the thermal conductivity of the melt is high, the temperature gradient in this diffusion layer tends to be quite small, usually well less than a few degrees Kelvin per centimeter, that is, less than 1 K/mm. That is why, even the relatively small melting point difference over this diffusion layer, less than 1 K, changes the process considerations very significantly compared to the growth of lightly doped materials. In view of different dopant elements, this far we have only discussed the segregation coefficient. But other factors also play a role, like diffusivity in the melt and how readily the dopant evaporates during the growth. For example, the larger diffusion constant of phosphorus compared to arsenic [30,31] (note that literature shows large error margins here) results into a less steep dopant concentration profile below the interface, everything else being the same, therefore it is somewhat more straightforward to avoid conditions conducive to supercooling. This is one of the factors that contributes to the relative ease of growing very heavily phosphorus doped material compared with arsenic doping. The seed lift impacts the risk of supercooling through three different avenues that reinforce each other, for a given average dopant concentration in the melt: (i) Higher seed lift causes a decrease in the temperature gradient in the melt, as more heat is generated through solidification; (ii) It increases the effective segregation coefficient and thereby the dopant concentrations at the freezing boundary; (iii) It makes the dopant profile steeper as the melt moves faster towards the interface, and it is therefore harder for diffusion to remove excess dopant atoms farther away from the growing crystal. That is why it is imperative that slow growth rate is applied, in comparison to how effectively heat can be extracted from the crystal.

2.9.4 Path to Lower Resistivity After choosing the doping element, lowest resistivities, as limited by CS, are achieved if process conditions are tuned to result into (i) a large and uniform axial temperature gradient in the crystal, (ii) the seed lift is kept low and (iii) the diffusion layer is maintained relatively thick in the melt, under the crystal, during the early part of the body. Unfortunately, some of these requirements are often not very well compatible with certain other essential features of a well behaving, high yielding process. For example, the low seed lift requires hotter and therefore more unstable and reactive melt. Therefore, the risk of the loss of DF structure increases per unit time. Simultaneously, the process takes longer, due to slower growth. There are now two compounding factors that add to the risk of losing the growing crystal.

FIGURE 2.18 Dopant concentration (three curves, right scale) and melting point depression (thicker curve, left scale) near the growth interface. The temperature values are estimated for As-doped material and target resistivity at 1.9 mΩ-cm (4 3 1019 atoms/cm3). Note that the melting point gets lowered proportionally to the dopant concentration.

FIGURE 2.19 Dopant profile changes the melting point distribution just below the crystal. If the melting point increases significantly faster than actual melt temperature, CS and interface instability occur. Temperature profiles are plotted in the picture schematically, for three different gradient values. Typically, the laminar layer is thinner than 1 mm, underneath, the temperature gradients are flatter than sketched in the picture, where mixing of the melt occurs. Temperature values correspond to Figure 2.18.

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Concerning the width of the boundary layer under the crystal, it is often proposed that the sheet should be made thin, to reduce the accumulation of the dopant there, and the risk of CS. However, the resistivity target for the growing crystal is not arbitrary, and a thin diffusion layer would need to be compensated with more dopant in the bulk of the melt, in order to reach the given resistivity goal. That is why, there will be no advantage concerning the risk of CS, with a thinner diffusion layer. The dopant gradient right below the crystal is identical, in the first approximation, if the boundary layer is thin and more dopant is used, or if the layer is thicker, with less dopant in the bulk of the melt. As we can see in Figure 2.18, the dopant gradient at the interface does not really depend on the diffusion layer thickness at all, but just on the dopant concentration target in the crystal, and the growth rate. A thick dopant diffusion layer in the early part of the body allows us to use correspondingly a thinner layer in the crown, shoulder, and very early body, where the process is in transition and the DF structure is more challenging to maintain. The risk of CS should therefore be reduced during these interim stages of the process that produce no salable material. From then on, the conditions should be modified to create a thicker layer, to increase the dopant concentration in the ingot, to bring the resistivity down quickly to the target in the early body. The thick boundary layer early in the ingot will also result into less evaporation of the dopant, for the same resistivity target, as there will be less doping element needed in the melt. This results into the grower staying cleaner, reduced crucible wear, and lower cost of the dopant. As the growth proceeds further, the dopant segregates into the melt, depending mainly on the process parameters that define evaporation. That is why, the layer may need to be made gradually thinner, later in the body, to avoid CS to take place, however, still maintaining sufficient dopant concentration in the ingot. Figure 2.18 is, however, somewhat misleading, in the sense that it assumes non-rotational melt and no significant magnetic field in the vicinity of the growth interface. The reality is more complex. The effective segregation of the dopant to the crystal depends on both the growth rate and the melt flows under the freezing interface. The commonly used formula for the effective segregation coefficient (keff) that depends on the rates of crystal solidification and rotation, alone, known as the BPS model [32], is valid for non-rotational melt and very slow pull rate only, with flat interface. The basis for this model, the rotating disk approximation, gives further that keff is uniform over the whole interface. If we use realistically high seed rotation rates and lifts, the result for the keff changes just by a few percent, antimony showing a

somewhat larger error than phosphorus. That is why, in the absence of crucible rotation and magnetic fields at the interface, keff can be estimated quite accurately using the relatively simple BPS formula. However, the crucible rotation cannot usually be ignored, if there is no static magnetic field or with cusp field. Furthermore, transverse magnetic field changes the melt flows under the crystal substantially from the assumptions behind the rotating disk approximation. Additionally, the freezing interface deviates quite significantly from planar shape in the crown and very early body. Numerical simulation will be required to find reasonably accurate estimates for the dopant distributions and gradients in the vicinity of the growth interface. Use of magnetic field is beneficial for added melt stability, and to fight the faster crucible erosion rate, caused by the evaporation of oxygen with the dopant. Transverse magnetic field has an edge over cusp, as the crucible rotation rate will be very small (see Section 2.7.2), which allows low seed rotations if desired, without sacrificing radial resistivity and oxygen gradients. The lower rotations help maximize the thickness of the diffusion layer under the crystal, and therefore, they make it easier to reach low resistivity values in the early body. The high field at the freezing interface also tends to increase the thickness of the diffusion layer. (Note that the situation is opposite at the crucible inner surface, where the presence of cusp magnetic field favors high shear rate and thin interface, due to the fact that the wall is made out of electrically insulating material. Therefore, electric currents, born out of the interaction between the fluid movements and the field, cannot penetrate the wall, which effectively eliminates magnetic forces that try to reduce the shear.) Active cooling elements around the crystal are helpful in increasing the temperature gradient [15], to allow for a better trade-off between the seed lift and the thermal gradients in the melt. This is especially true after the crystal body is longer than about one full diameter. The inner surface of such a cooling element absorbs heat emitted by the crystal, and radiation originating from elsewhere in the grower is blocked from hitting the ingot surface, above a certain distance from the melt. The structure needs to take the heat farther away from the growing crystal, and various approaches can be utilized here. Solid conduction can be used over some limited distance, as long as the maximum temperature is maintained within proper bounds. The assembly may then be cooled internally with water based coolant, or with gas flow, the latter being quite a good option from the perspective of safety. A heat pipe approach is also a possibility. What is mandatory is to build a system in such a fashion that in case of failure and rupture, no hazardous amount of water or air can enter the vacuum chamber.

Czochralski Growth of Silicon Crystals Chapter | 2

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2.10 GROWTH OF LARGE DIAMETER CRYSTALS The driving force towards larger diameter silicon crystals and wafers have always been volumes, productivity and cost, especially for the semiconductor (IC) industry. A 50% increase in the wafer diameter multiplies the wafer area by a factor of 2.25. In case of large chips, their number goes up even faster with the diameter, as the lost area near the wafer edge is reduced, in relative terms, where the chips would be incomplete, and also the yield tends to be lower there. The wafer size for MEMS has always been smaller than for the ICs, but the trend is the same, for the same reasons. The previous major shift from 200 to 300 mm wafers in the IC industry was much more expensive and took years longer than originally planned and estimated. The development of high performance ICs, however, did not slow down. On the contrary, the linewidths and speeds experienced faster than expected evolution, to counter the delay in increase in the wafer size. The same amount of functionality was simply packaged in a smaller surface area, which also boosted speed of the high performance chips; wafer starts were also, of course, expanded as well, to meet the volume requirements [4]. However, the faster miniaturization could only carry the industry so far, and today, the vast majority of all semiconductors are made on 300 mm wafers. The volume of the semiconductor industry is increasing all the time, even though the rate is not always steady. To satisfy the future volumes, the next wafer size is fixed to 450 mm, but it is not clear, when it will be first introduced into volume production. The originally scheduled time is already gone, more than once, the three most important industrial players (Intel, Samsung, TSMC) are vague but indicate that the transition would happen some time late in this decade. And there are other heavyweights who suggest 450 mm would never happen. The 2013 Edition of the ITRS forecasts that volume production will start in 2018. The challenge is not so much technical but economical. The wafer manufacturers, process tool suppliers and the IC manufacturers themselves have to absorb billions and billions in R&D investments, and at the same time, the fabs grow more expensive and the risks larger. There will be very few companies that will be able to build 450 mm wafer fabs independently, at cost in the US $10B range and beyond, each, and this surely is one major factor causing delays in the transition. As it comes to wafer sizes, MEMS is typically one to two steps behind the IC industry, which is understandable due to much smaller volumes. Furthermore, MEMS does not require the very small linewidths that process tools for large diameter wafers are designed for and which add significant cost to those tools, unnecessary cost from the

FIGURE 2.20 DF 450 mm CZ silicon crystal, out of a relatively small sized charge. The charge size was less than 300 kg. Courtesy of Silfex Inc., A Division of LAM Research.

MEMS perspective. However, the trend in MEMS is somewhat similar to that in the ICs as larger wafers do offer better volumes and economy, once the shift has happened, for those products and processes that display sufficient volumes. The following discussion concerns mainly silicon crystals intended for the IC market, as virtually any challenges that MEMS crystal sizes may face have already been resolved years earlier, because of the needs of semiconductor wafers. However, a look into the growth of very large silicon crystals helps better understand CZ growth of silicon as a whole. Figure 2.20 displays a 450 mm diameter crystal, grown out of a relatively small sized crucible and charge. A short ingot like this is suited for small scale production, but it is not a very attractive proposition once costeffective volume manufacturing is really needed. Only a tiny share of the total process time is used to grow the body, which is the only part of the crystal with real value. Almost 50% of the charge gets effectively wasted, as significant weight needs to be used for the crown, tail and the residual melt; the crown and the tail can usually be recycled back to the process, though, to improve silicon usage. Furthermore, there are significant quality challenges with short ingots, as the process is in a continuous state of transition. The thermal environment seen by the growing crystal does not even get properly stabilized before the tail mode has to be triggered. It is much more demanding to ensure that the material properties of the crystal are uniform in the early part of the body than at body lengths larger than about half or one full diameter. In this respect, the charge weight should increase to nearly the third power of the diameter. This would require batch sizes approaching 1 ton, for 450 mm crystals. Correspondingly, the process time would also be multiplied by a factor close to two, compared to good sized 300 mm crystals. This is, of course, not feasible as a single quantum leap, but 450 mm crystals are first grown out of

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PART | I Silicon as MEMS Material

charge sizes, which are close to the largest ones presently used to make 300 mm crystals. This helps push some issues to a little later, but there are still others to tackle. The very large diameter makes it more difficult to control the shape of the freezing interface, as the melt flow patterns and thermal distributions play a more major role. Especially the melt flows are more challenging, as there is space for more complex flow structures under the large crystal; thermal distributions inside the HZ and the crystal still behave fairly predictably. Furthermore, thermal stresses are significantly larger, which results in an increased probability of the loss of single crystalline structure. At the same time, as these large crystals will eventually be used for more advanced IC processes, many of the quality requirements, over the usable crystal length and diameter, will likely be tougher than for the present silicon materials. There is a need for significant learning to deliver not only the wafers to a competitive price, but ensuring that the necessary quality parameters are there, as well.

2.10.1 Neck Growth for Large Crystals The crystal diameter poses additional challenges to the growth of DF neck through three separate mechanisms. First, the larger melt is naturally more unstable, and therefore more efficient means of steadying the melt flows are needed. Secondly, the weight that the neck needs to carry increases rapidly with the diameter, though the charge size is, of course, more relevant here. And lastly, the larger opening in the thermal shield (Figure 2.21) makes it harder to maintain low thermal gradients in the neck, a critical requirement for growth of DF neck (Section 2.2.2). The challenge of a heavier weight pulling on the neck would be straightforward to address just by increasing the neck diameter. And that is something that does allow us to increase the charge size to some extent. However, a thicker neck also makes the conditions less favorable for the growth of a DF neck, and the circumstances need to be improved elsewhere. Refer to Section 2.2.2 for a short discussion on the topic of Dash neck. Temperature gradients near the melt surface can be made smaller by increasing the external temperature as seen by the neck surface. For example, an increase in the crucible rotation rate would cut down heat transfer in the melt and therefore, higher wall temperature will be required, which results in more heat radiated towards the neck. Lower bottom heater power makes an impact in the same direction, increase of side heater power. Magnetic field can be played with, to reduce heat transfer through the melt further. However, there are also risks to the high crucible wall temperature, if pushed extensively, see Section 2.10.4. Melt position can be lowered relative to the thermal shield above the melt, to reduce the impact

FIGURE 2.21 Crown of a 450 mm crystal growing in a transverse magnetic field, approaching the final diameter. The melt is very stable, thanks to the large field, and the surface of the crown is quite smooth. The visible shallow ridge is one of four similar features on the crown that tell about the 90 symmetry of the crystal. The shape of the ridge is also indicative of large transverse field. In the right hand corners, the shadows are created by a conical thermal shield that helps control gas flows and thermal distributions. Courtesy of Silfex, Inc., A Division of LAM Research.

of heat loss through the opening in that shield. Some additional, more complex mechanisms can be devised to bring down the upward heat loss. The lower end of the neck can be heated using some auxiliary power sources, for example, relatively intensive, radiative sources above the HZ, or lower intensity, radiative or inductive power generating elements closer to the melt. Magnetic fields can also be utilized to calm the melt to a great extent, which allows better diameter control and faster pull rate for the neck growth. The improved diameter control helps avoid weak points, where the diameter would be significantly smaller than the target, and therefore, the strength of the neck is higher, for the same target diameter, out of stable melt. A transverse field usually results automatically to a more stable melt than weaker cusp field (see Sections 2.7 and 2.10.8, Figure 2.21). However, a cusp field can also be modified during the neck, to a shape with more of an axial component, and thereby improve the melt stability significantly, for the growth of the thin section of the neck. Note that the reasons why axial fields are not used for the body growth do not apply while in neck. Heavily boron doped crystals can be grown somewhat more easily than lightly doped ones, as that dopant interferes with dislocation movements during the neck growth [33]. Therefore, somewhat thicker necks are feasible in otherwise identical growth conditions. A combination of actions, like those mentioned above that aim to reduce temperature gradients and help increase the seed lift, can add to the feasible neck thickness for heavily doped

Czochralski Growth of Silicon Crystals Chapter | 2

crystals to such an extent that it is able to carry several hundreds of kilograms safely. Additionally, intentional diameter variations can be introduced during the neck growth. If the melt is very stable, it is less challenging to control the profiles of these variations. The dislocations tend to grow out of the neck while the diameter is shrinking, which, based on simple geometrical considerations, is quite easy to understand. In addition, during the time the diameter is spreading out significantly, the dislocations tend to drift farther away from the neck centerline [34], making the removal during the diameter drop more effective. Done properly, this should allow us to increase the minimum diameter and thereby add to the neck’s ability to bear weight. However, this is a somewhat challenging proposition, and there are techniques that probably offer better rewards, as it comes to additional load carrying capacity. The growth of the DF neck and the requirement of carrying a large weight can be separated using additional mechanical devices. In this approach, a regular thin neck is first grown until DF. Then the diameter is increased substantially, after which the diameter is made to cut in again, by a fair amount. Then another length of the neck follows, well thicker than the original DF neck, enough to carry the full crystal safely. At some point, before excessive weight is accumulated, a separate mechanical system is deployed that makes a physical contact above the thick part of the neck, locking into the earlier mentioned tapered section [35]. This approach has the advantage of being conceptually very straightforward, but it is mechanically quite challenging; the environment where it needs to operate is hot and anything used there has also to be highly vibration and contamination free. A smart approach is to get away from the thin neck completely. This method relies on the fact that practically all the seed crystals today are DF anyway, when first dipped; the situation was greatly different more than 50 years ago when the Dash neck was first introduced. The challenge then becomes keeping the seed that way, from generating any dislocations during the dip. That is, the thermal shock that usually destroys the DF structure of the seed, when bringing it into contact with the melt, has to be mitigated to the extent that the DF structure is maintained, with a margin. There are two parts to consider here. The first one is the means of bringing heat into the tip of the seed crystal to the extent that its temperature is very close to the melting point before the dip. The thermal gradients created by the quick temperature change, as the seed makes the contact with the melt, will therefore be minimized. All of the above mentioned methods to reduce thermal gradients during neck growth can be utilized for this purpose, as well as in various combinations. The other part to consider is the impact that the abrupt melt contact may cause to the thermal stresses in the lower end of the seed. If we

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make the lower portion quite thin, even pointed, the first contact will take place at a small diameter and cross sectional area, and the amount of heat conducted up is minor, and the thermal stresses related to the gradients are small. And then there is the somewhat separate but equally important aspect of, how large those thermal stresses are allowed to be before the seed material develops dislocations. Heavily boron doped seeds tend to be significantly better in this respect than regular lightly doped ones [33]. Once the first contact has been made without creating dislocations, preferably at a small diameter, the seed can be brought gradually down and partially melted, until the right diameter has been reached for the start of the growth, that is, a safe diameter for the targeted weight. At that point, process conditions will be changed slightly, to effectively cool down the melt, and a length of thick neck pulled. This neck-like section is not really mandatory, but it helps establish stable conditions before the crown gets started. This approach avoids growth of the Dash neck completely, as there is no need to get rid of dislocations, as they never existed. There is also an additional advantage to this approach, as it comes to growth of crystals in other orientations; it does not really matter if the seed is cut into (100) or (110) orientation, it works for both. There are naturally some drawbacks to this method of growing DF crystals without necking. The seed can, as a rule, be used once only. The seed needs to be changed after every attempt, in case the DF structure is lost at some point, not only between different growth runs, though there are ways around this limitation. However, the expense of changing the seed is, in general, less of a concern for these heavy crystals, as there is so much value in the charge, compared to smaller crystal sizes. The melt temperature control before the dip is much more critical. One can no longer easily test the melt surface temperature using a section of the neck from the previous grow, but the melt temperature has to be on the mark. This requires better instrumentation, process stability, and/or procedures to get the grow started. Heavily boron doped seed crystals, or otherwise precipitation or solution strengthened DF seeds, which can tolerate substantially larger thermals stresses during the dip, can be used to pull lightly doped crystals as well. In combination with other means of reducing thermal shock, this makes neck-free growth significantly easier than by just using lightly doped seeds. However, care has to be exercised when growing high resistivity material, as the introduction of the seed into contact with the melt must not bring an excessive amount of dopant or contaminant into the charge. For a large and heavy crystal, the consequences of a potential neck breakage risk being significantly more perilous than in case of smaller charges. In addition to the more expensive crystal and charge that may be

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completely lost, the HZ components carry much more value. The potential melt spill is substantially more challenging to contain, and the risk of serious damage to the grower and environment is more severe. That is why, the risk of a neck breakage has to be taken down even though the load to be carried has increased.

2.10.2 Neck Extension Assuming that Dash neck is grown, there are other important variables than just the thickness of the neck and the weight it needs to carry. In case of large diameter crystals, the crown is heavy and the load increases further, very quickly as the body of the ingot starts to grow. That is why, the lower part of the neck, closest to the crown, is exposed to higher load than for smaller diameter crystals, even for similar charge sizes. At the same time, the large diameter means more heat escaping through the open space between the thermal shield and the crystal. This adds to the heat load experienced by the neck. It is advantageous to take the thin part of the DF neck much higher up, whilst leaving a thicker and stronger section near the crown, where the temperature is higher. This is straightforward to accomplish simply by growing another length of the neck, after the DF situation has been achieved, to a significantly larger diameter, by at least some tens of percent. The section needs to be long enough to take the thin section sufficiently high that the heat has only a minor impact to its strength. This does require additional process time, but this phase can also be used to stabilize the melt properly, before continuing to crown growth. Furthermore, there is a supplementary benefit to this thicker neck section: A crown always grows slightly onesided, due to various deficiencies in the symmetry of the setup and the off-orientation of the seed. A large diameter crown tends to develop more of this asymmetry, and due to the heavy weight and the large radius, there are substantially more bending stresses to the neck. The stiffness of a rod increases very quickly with the diameter, to the fourth power. Therefore, use of a suitable thicker section in the lower neck will help prevent that weight imbalance from getting worse during the crown as more mass is accumulated. In the worst case, this imbalance risks such bending stresses in the low end of the neck that dislocations are created there, which then bring in the possibility that they propagate into the growing crown. A thicker section in the neck, near the crown, will also be useful during the potential melt-back of the crystal, in case of loss of structure. During the melt-back, more heat needs to be introduced and, typically, the melt surface would be at a lower position. There is a risk, especially in the case of low dopant concentration material, that a thin neck softens extensively. At that point, it may no longer be

able to carry the weight that the hanging crystal, only partially immersed into the hot melt, would exert on the neck.

2.10.3 Additional Stresses on Neck A DF neck can stand very large tensile stresses, but it is brittle when cool and therefore it can also be easily broken, if the surface gets impaired. One mechanism to create such damage is oxidation, nitridation or carbide formation of the surface, which incurs considerable local stresses. Vacuum leaks or impurities in the argon supply can cause this additional damage, which is critical to avoid in case of large diameter, heavy crystals, beyond just curbing contamination levels. The control of the gas atmosphere around the neck is therefore vital, if Dash neck is grown without additional means to supporting the weight of the boule. Torsional stress on the neck due to viscous drag of the melt will still be quite small, thanks to the low value of viscosity, compared to the strength of even quite thin a neck, in the 5 mm range. The maximum torsional shear stress caused by the viscous drag remains at a fraction of 1 MPa, in the neck, that is, 12 orders of magnitude below the stresses caused by the weight of the crown of the crystal, alone. However, the magnetic braking moment by a transverse magnet is significantly larger. A 450 mm crystal rotating at 8 rpm in 0.4 T horizontal field may generate several tens of megapascals of additional shear stress, which is already a significant fraction of the stresses created by the weight of the full crystal. A further point, there is a significant rotational inertia in a heavy, large diameter ingot. This risks breaking the neck in case something goes wrong in the seed rotation system, if an abrupt change in the rotation rate ensues. Proper safety features need to be included in the grower design.

2.10.4 Crucible Wall Temperature The highest heater temperatures are required during the melt, meltback, stabilization, neck and towards the end of the tail. There are means to lower the heater temperature for the other parts of the process except the neck and the tail, without other really significant process implications. Therefore, the critical steps, in which the highest crucible wall temperatures are reached, are the neck and the late tail. During those stages, the temperature of the crucible outer wall risks soaring to the extent that there is significant wear to the susceptor, due to the chemical reaction between graphite and silicon dioxide (see Section 2.3.3), as well as production of substantial quantities of silicon and carbon monoxides. The former creates lightweight particles at lower temperatures, higher up in the HZ, and particle as well as additional carbon contamination to the melt may occur.

Czochralski Growth of Silicon Crystals Chapter | 2

The crucible wall thickness tends to increase faster than the crucible diameter, for the commercially readily available crucibles. What is more, amorphous silica is fairly good thermal insulator, and the wall is full of small bubbles and cavities, too (see Figure 2.15). Therefore, the temperature at the interface between the crucible outer surface and that of the susceptor risks being significantly higher than in smaller HZs. Furthermore, the larger distance that the heat has to travel through the melt to make it all the way to the growing neck, there is an additional temperature drop there. Use of effective melt stabilization methods risks adding significantly to this temperature difference. This very high temperature of the crucible outer edge is therefore much more of an issue for large crucible sizes and high level of melt stabilization, through, for example, strong transverse magnetic field. Significant mitigation can be achieved using crucibles that display a high level of transparency, in which case a substantial share of the heat is carried by radiation through the wall, and the wall thickness becomes less of a key factor for the heat transfer. Crucibles in which the bubble free layer extends through the entire wall are also available. Some of the additional power sources, mentioned above in Section 2.10.1, for the purpose of growing thicker DF necks or easier dipping for neckless growth, can also be utilized in other parts of the process, to ease the burden to the crucible. Furthermore, such heaters could be utilized for better process control, like diameter or pull rate control during the neck through tail, to adjust thermal distributions in the crystal and above the melt, as well as to reduce thermal stresses in the growing crystal. However, a fairly significant added complexity needs to be introduced into the grower to achieve such reduced strain for the crucible and enhanced options for the process control.

2.10.5 Double Layered Crucible Structure The inner surface of a high purity crucible is made out of synthetic silica powder, for the large sized crucibles (see also Section 2.8.3). This is also available for smaller crucible sizes, if certain stringent quality requirements are needed for the grown crystals. The final thickness of that synthetic layer is larger than the expected wear during the CZ grow. The outer layer is typically made starting with naturally occurring, more affordable pure quartz rock/ sand, which has higher concentrations of metallic elements than the synthetic powder. Both layers are fused into amorphous silica at high temperature, during the manufacturing process of the crucible. In addition to mitigating cost, natural sand is usually better suited for the outer layer thanks to its usually superior high temperature viscosity, compared to high purity

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synthetic silica. Some impurities, notably aluminum, make the material stiffer, furthermore, the typically higher hydroxyl ion concentration of fused silica lowers its viscosity. For these reasons, a crucible that has a thick outer layer made out of natural sand, especially if the aluminum content is on the high side, is more resistant against sagging (see Figure 2.7). At the same time, the inner layer, made out of lower viscosity synthetic silica, is easier to process to a virtually bubble free condition, see Figure 2.15.

2.10.6 Crucible Deformations Long hot hours and high surface temperatures tend to create problems at the crucible inner wall, if process conditions are conducive to high fluid shear there and, at the same time, the bubble free layer has become excessively soft. Use of silica grade with low viscosity would be a contributing factor here. From the process point of view, high temperature would play a part, as well as anything that would create that high shear stress. Without any magnetic field or crystal in contact with the liquid, the melt would rotate almost like a solid body, together with the crucible, and any fluid shear would be small at the crucible interface. A large sized crystal that spins at a fast rate against the rotation of the melt will also slow down the liquid, as will any significant deviation of the magnetic fields from axi-symmetry, too. This kind of deviation in symmetry is common in resistive cusp magnets, as there is usually quite a large vertical slot cut into the otherwise cylindrical iron shield, for the electrical and cooling water connections to run through, into the copper coils (see also Figure 2.1). The field may be 10% lower in that direction. At a high magnet power level, this asymmetry introduces a significant braking force that slows down the rotation of the melt, and therefore it also introduces shear stress to the fluid, next to the crucible wall. This melt shear will cause flow patterns that erode the wall in a non-uniform fashion. The melt eddies tend to create pressure distributions that, if the viscosity value of the silica material is on the low side, gradually result into a surface full of shallow ripples. This phenomenon is not unlike the ripples that waves and water create into the sand on a shallow beach, and the wind can also create similar formations (Figure 2.22). There is this interaction between the shapes in the crucible inner surface and the vortices in the melt, which causes these eddies to park themselves for extended periods of time at the same locations. Viscosity of the synthetic layer should therefore kept high, if significant shear is expected, even though this may pose additional challenges for the quality of the bubble free layer. In case of low rotations, small crystal size and good rotational symmetry of the magnet, this

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FIGURE 2.22 Ripples created by wind on a beach in Western Finland. Wavy structures of similar nature, though much more shallow, may be observed inside large crucibles in a process that exposes the crucible inner wall to significant fluid shear, if the temperature is high and silica viscosity relatively low. Comparable ripples can also be seen as created by water on shallow beaches.

deformation of the crucible inner wall is not expected. Furthermore, if transverse magnet is used, in combination with nearly zero crucible rotation, this will effectively eliminate any fluid shear at the interface. However, there are other risks related to crucible deformation if transverse magnet is employed. The absence of crucible rotation also removes any centrifugal force that would otherwise help keep the crucible wall erect. That is why, the risk of sagging of the crucible is somewhat higher. The larger stabilizing effect to the melt also tends to increase the maximum temperature of the crucible, which high value is usually reached at the low outer corner, in what is often called “R2” area (“R1” being the curvature of the bottom of the crucible). The wall above this portion of the crucible exerts a significant weight to this area. That load risks gradually deforming the R2 area, making it effectively thicker, if the silica material is too soft to support the weight above, for extensive periods of time. This causes changes in the expected melt position and temperature distributions. In an extreme case, the deformation may be so severe that the crucible wall makes a premature contact with the thermal shield around the crystal, during the tail. During that step, the temperature is very high and the support given by the hydrostatic pressure of the melt is gone; significant material loss may occur.

2.10.7 Intentional Devitrification There are some coatings or additives that can be used to homogenize wear at the crucible inner wall. They usually initiate crystallization of amorphous silica (devitrification) in a controlled fashion, which helps avoid local nucleation, non-uniform wear, and eventual particle releases; see a typical wear pattern in Figure 2.2. The first additive that became commercially available was barium, and

some others have also been researched. However, these substances bring some additional contamination into the melt, with the associated risk of deterioration of the crystal quality. The strict purity requirements of large semiconductor grade crystals seriously limit the use of potential additives. In contrast, on the outside of the crucible, utilization of these modifiers is easier, the benefit being a significant improvement to the stiffness of the material: crystalline silicon dioxide resists plastic deformation much better than amorphous silica in the pertinent temperatures. Use of the additives on the inner surface of the crucible above the melt level, to improve stiffness, also includes fewer contamination risks than under the melt level.

2.10.8 Transverse or Cusp Field for Very Large Crystals The trend in the IC industry has long been towards lower oxygen, and this is what a transverse magnet naturally delivers. A cusp magnet can also give low oxygen concentrations, but more typically, it results into concentrations that are close to those without any external magnetic field. The main advantage, however, of the transverse magnet over cusp is the lower wear rate and longer crucible lifetime. Due to slower erosion, there is also less silicon monoxide formation and evaporation from the melt, and therefore fewer related contamination and particle issues. As a side benefit, argon exhausts inside the HZ and to the grower do not get clogged as quickly, by silicon monoxide containing gases, which allows for longer maintenance intervals for those components. There are further advantages to the transverse field: It is more forgiving to the crucible in regard to a potentially low viscosity layer in the inner crucible wall (Section 2.10.6). There is also a more significant calming effect to the melt. But this is also somewhat of a doubleedged sword: As the heat transfer from the crucible to the center of the melt is reduced, the temperature at the crucible wall goes up, during the neck. This enhances the reaction between the crucible and the susceptor. At the same time, however, it also improves thermal conditions for DF neck. Low dopant gradients are easier to reach as the flow patterns under crystal are more straightforward, suited for small gradients. Lower seed rotations suffice to achieve those flat distributions, and this helps keep the crystal round, which allows for slightly higher pull rates in the body, provided other quality factors do not necessitate otherwise. But on the negative side, a transverse magnet is more costly and heavier, and it requires more radial space around the vacuum chamber. Crucible sag may be a more prominent issue with transverse magnets. That said, it is the author’s view that the winner, concerning CZ

Czochralski Growth of Silicon Crystals Chapter | 2

growth of very large diameter silicon crystals, will be the transverse magnet over cusp. Concerning time dependent fields like rotating magnetic field (RMF) [36] and traveling magnetic field [37], they may have some limited applicability for the growth of small and medium sized crystals. The used frequency is typically fairly high, for example, 50 Hz, and the actual field only a few milliTeslas or less; the high frequency field will penetrate to the melt only superficially. The aim is to create forces in such locations within the melt that the resulting flows would take care of heat, oxygen and dopant transfer in ways that rotations, natural convection and static magnetic fields cannot. For instance, the heater may be shaped in a suitable fashion and high AC currents there can be used to create the desired forces to the melt, those forces then help create advantageous melt flows. This kind of integrated approach seems reasonably practicable, though the field strength remains low. However, vis-a`-vis large melts, where very significant stabilizing effects are needed, the prospects look grim, to the author. These magnets, if built outside of the vacuum chamber, are relatively complicated, some additional considerations are required in the structure of the grower, to prevent, for example, eddy currents, generated in the vacuum chamber walls and the HZ, from interfering with the desired process, and the available stabilizing effect to the melt will very likely not suffice. There would be some serious challenges in combining one of these methods of forced convection with cusp or transverse magnetic field. If built outside of the grower, it gets very crowded there, furthermore, these AC fields tend to weaken quite quickly with the distance from the coils. On the other hand, built inside the grower, for example, if it is the heater than produces these fields, serious vibration issues should be expected, as the DC and AC fields would interact. However, static axial field, which usually cannot be used during the body growth (see Section 2.7), could benefit from a suitable time-dependent field: static axial field tends to bring very high oxygen melt from the bottom of the crucible to the crystal, and there may be a slim chance that this flow could be deviated through use of a practicable AC field. More modeling work and basic research is, however, needed. A further point, use of these AC magnetic fields will risk increasing the fluid shear at the crucible wall. Care has to be exercised, if the wall temperature is high, process hours long and there is no intentional devitrification to the silica material, otherwise, the additional shear may result into increased and more nonuniform crucible wear. Another time-dependent field that would very probably fail miserably is the thought of relatively slowly rotating transverse field at high intensity. At first glance, such a construction would combine the possibility of large, highly stabilizing field, to the other major effect that also

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calms the melt, the fluid rotation. However, the added mechanical complexity would be very significant, and highly likely, to no avail: If the rotation of the melt would be forced upon it by something like a powerful RMF that passes through the melt, and not only on the edges, it would also eliminate the very same physical phenomena that are responsible for the stabilizing effect of the melt rotation. The detailed analysis is beyond the scope of this text, but the message is clear, based on the author’s understanding: You cannot combine the stabilizing effects of the transverse magnetic field and that of melt rotation.

2.10.9 Boosting Crystal Weight This far, we have addressed challenges how to carry the heavy crystals, the need to control the melt flows and the heavy burden to the crucible. However, there are other options than simply to use a larger crucible size to increase the weight of the crystal. Some approaches like hot recharging and CCZ, already in use in the semiconductor and especially solar production, were tackled in Section 2.8. Here we will touch the topic from the perspective of very large diameter crystals. The challenges will be many and it may prove beneficial not to increase the initial charge size as quickly as the diameter change would suggest. Charge topping is quite straightforward, but it can add to the batch size by only a fairly limited amount. 3040% is already a quite good number, though the added amount in the hopper or feeder may be larger; it is just easier not to push the original charge size to its maximum, if more silicon will be added a little later anyway. Charge topping is a good intermediate measure, available to boost the charge size reasonably close to what can be reached using one size larger crucible. Hot recharging has serious shortcomings when it comes to very large diameter crystals: The crystal will still remain quite short anyway; a lot of time will be used for the neck, crown and tail growth; in case of loss of DF structure in tail, material losses will be more significant, relatively speaking, than in case of a longer body. However, the hardest challenge will be with the crucible: it will take a lot of heat during the tail growth, and that strain poses a clear threat to the success of the subsequent crystals from the same crucible. The CCZ approach looks more promising, at least on the surface. It relies on growing one tail only, out of one batch and crucible. In theory, the crystal manufacturers for the semiconductor industry could try to adopt the same approaches already in use within the PV industry. Certainly, some significant refinements would be required to ensure that the contamination in the melt would stay at a very low level. However, the present commercial approaches in PV, to the author’s knowledge, feed new

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silicon in solid form into specialized crucibles, or ones equipped with additional silica ware, and the crucible OD is relatively large compared with the crystal diameter. This is not very well suited for the purposes of trying to keep the HZ and the crucible size moderately small, in comparison with the crystal diameter, and to use well established, high quality crucible production technologies. A liquid feed would probably be more suited for this purpose, however, also a clearly more challenging process to develop. The “beating” that the crucible takes during the tail could be eased greatly through use of active heating above the melt. However, this would add significantly to the complexity of the equipment and process. On the other hand, there may well be some synergy between liquid silicon feed, for the purposes of CCZ, and active heating to reduce the temperature difference over the crucible wall. Yet, significant technological challenges will need to be resolved to make this happen. The proposed approach is not and probably should not be pure CCZ, but rather a process, in which a significant portion, but well less than 100%, of silicon consumed by the growing crystal would be replenished through the feed of new polysilicon. That way, the crystal size could be effectively increased, by hundreds of kilograms, and very long 450 mm crystals could be grown out of a puller, whose chamber diameter is no larger than some already in the marketplace. The crucible properties need to be developed further from what is presently available for the largest sizes. But that effort may well be significantly less than what would be required to increase the crucible size by another 8 in. or so, and then improving the quality. With continuous feed, the potential is there to pull longer 450 mm crystals out of 3236 in. crucibles than out of 4044 in. crucibles, without that feed. The availability of high quality 36 in. crucibles is presently quite low, and the development and manufacturing costs of even larger crucibles are probably quite high. There is also the additional bonus that the lesser amount of melt in the grower, at any given time, will have a positive effect on melt stability, to the weight that the crucible lift system is required to handle, as well as to the risks associated with melt spills.

2.10.10 Seed Chuck The crystal support assembly, the seed chuck, has to be redesigned for heavy loads, as well. For crystals that weigh less than about 150 kg, the seed is typically a simple cylindrical silicon rod of about 0.5 in. diameter, with a notch; the surface of the seed has been etched to remove any mechanical damage and to fine tune the diameter. The seed chuck includes a vertical hole to seat the rod, and a horizontal pin to lock the seed in place. The seed

and the chuck can be made easily to a sufficiently good orientation accuracy, for the neck and crystal to grow in a quite symmetric fashion. However, virtually all the load is carried by a small surface area at the pin and the notch. The pin pushes the seed against the opposite, vertical wall in the chuck, aligning it to the chuck, and at the same time, some load gets transferred to the chuck on the opposing side, where friction helps carry the weight. The seed can be made stronger simply by making it thicker, but the strength of the assembly improves only slowly with the thickness of the seed, and the contact at the notch remains a weak point. There are two relatively easy solutions to improve the load carrying capacity, both of which involve a “head” to the seed. If the bottom surface of the head is made flat and a corresponding planar, horizontal surface machined to the chuck, the weight pulls the seed against that flat surface of the chuck, minimizing the force acting on both surfaces. The contact surface area can be made quite large, as well. This is the most suited approach, if the seed’s ability to carry weight is the only concern. On the other hand, this is a rather poor design as it comes to accuracy of the seed orientation. The contact surface at the seed must be perpendicular to the desired orientation to good precision, and the pertinent dimension is small, only of the order of 0.751 in. In addition, the mating surface in the seed chuck assembly must also be made horizontal, to very good accuracy. This requirement is mechanically clearly more demanding than in case of a chuck for the rod-like, cylindrical seed. On the other hand, if one would like to ensure the orientation through use of tight tolerances for the shaft part of the seed, a risk of premature failure of the seed would be high. The chances are that the deviations from the ideal dimensions, that is, the mechanical tolerances, make the seed carry the weight primarily on one side of the head only, and resulting bending stresses will appear. That is why, sufficient clearance is needed between the shank section of the seed and the chuck, in this design, to carry the weight safely. The other, probably better performing approach is to use conical shape in the head of the seed, the angle of the cone being fairly blunt; the head diameter needs to be significantly larger than that of the shank and, at the same time, a small cone angle would create a wedge effect and increase the surface pressure at the contact. A simple matching cone in the seed chuck will not, however, work properly, mainly due to mechanical tolerances, again. This makes the design more complicated than what was described above. Additional components are needed to accommodate those deviations from perfect shapes. Ideally, the orientation of the seed is dictated by its shank, which can be oriented quite accurately, and by the mating hole in the seed chuck, where the seed needs to fit with little clearance. At the same time, the load needs to be

Czochralski Growth of Silicon Crystals Chapter | 2

carried by the conical head in a uniform fashion, with very little bending stress. The design needs to be robust in a sense that it distributes the forces over sufficiently large contact areas, and uniformly around the seed, even when the mechanical dimensions are as unfavorable as the machining tolerance windows permit. The materials in contact with the seed have to be chosen well, as well, due to cyclic loads, thermal cycles, the hardness and brittleness of silicon, and its readiness to react chemically with other materials, at high temperatures. At some point of time, molybdenum was used to build seed chucks, but it has, in addition to its cost and machining challenges, other disadvantages, too. It is quite hard, and the contact pressure on the brittle silicon side soars with crystal weight. On top of that, molybdenum and silicon react readily, which creates additional point-like stresses, which risk to weaken the silicon seed very significantly. Graphite has been less problematic, it is easily machined to desired shapes, and it is quite soft, which means that the pressure will be distributed more evenly. However, it is such lightweight material that a piece made out of molybdenum, tungsten, or other such material needs to be added, to stabilize the chuck. Graphite also reacts with silicon, but relatively slowly. The challenge with making the seed chuck out of graphite, for heavy crystals, is that it tends to be mechanically too weak to handle the large contact stresses, unless made quite massive. Graphite may be supported by stronger material, like fiber reinforced graphite, ceramic material like SiC, or high temperature metal like molybdenum, to add to its load carrying capacity. With the different materials, consideration is also required how the different CTEs (coefficient of thermal expansion) can be accommodated.

2.10.11 Additional Challenges The larger growers tend to create more open, continuous spaces above the HZ, as there is more volume in the vacuum chamber. The risk is that the gas flows easily create eddies in those uninterrupted volumes, bringing particles and contamination to the crystal surface and the melt. That is why, better control is required to ensure desired, laminar and non-contaminating flow patterns. Narrower channels and baffles may be needed, where open space once was legitimate. The process times are longer, quality requirements more stringent, and at the same time, potential of lost material bears more cost. Because of all this, deposition of contamination needs to be brought down considerably per unit time, which is opposite to what would be the natural tendency for the larger system. Lower seed lift of the large diameter crystals creates more challenging conditions for the diameter control. The optical measurement, based on measuring light levels at the meniscus, introduces a time delay before a change in

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the diameter becomes detectable. If the seed lift is low, a similar temporal rate of change in the diameter results into a more pronounced trend, that is, the diameter is changing at a steeper angle than for faster pull speeds. At the same time, the diameter behavior is unstable in the sense that if a diameter trend has been born, it first tends to get more pronounced and to go on for quite some time, unless quick corrective actions are employed promptly, as described in Section 2.3.1. The challenge here is, with slow pull speed, that the trend tends to collect more steam before the control system is able to take those counter measures. The average seed lift is also somewhat more challenging to maintain steady. There is significantly more thermal inertia in a large batch of silicon, inside of a well insulated HZ, than what is typical for smaller sized HZs. A related topic is the dwindling seed lift while the body grows longer, as the radiative heat transfer from the surface of the crystal gets gradually less effective. Active cooling elements around the crystal are helpful here. Different approaches are utilized in both IC and PV industry today, and some of them can be adopted to boost the pull speed of these large diameter crystals (see also Section 2.9.4). However, one needs to be more careful with potentially excessive thermal stresses, especially in the early part of the body, as the large diameter material is more predisposed to those stresses. In the late body and tail, the risk of thermal stresses killing the crystal is less plausible, and fairly significant productivity enhancements can be achieved with use of proper additional cooling of the growing crystal. A further challenge in the growth of large crystals is the heavy mass and long time required to grow the tail, and the squandered material in the body, in case of loss of DF structure in the tail. The value of the unusable material, because of a L/S in the tail, increases very significantly with the diameter. Modern HZs do not leave a lot of visibility to the bottom of the crystal and the melt, and typically, the meniscus can only be seen from a quite steep angle. Once in tail, the chances are that there is no direct visibility to how quickly the diameter may be tapering in. There are mainly three options here: (i) One can tune the process for the diameter to decrease so gradually that there is still some visible curvature on the melt surface to be seen, behind the full diameter of the body. This will, however, require additional silicon mass and process time, and therefore, it is not recommended, but maybe early in the process development. (ii) The process can be learned by simple trial and error, by running a predetermined recipe and then changing the conditions for the next grow, based on the results of the previous one. This is a straightforward and a fairly viable approach, once the overall profiles are close to where they should be. At that

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point, relatively small changes can be applied to fine tune the process further. However, there are some major challenges, too, as the conditions in the end of the body do vary some, and those differences from run-to-run tend to amplify during the long tail. Furthermore, the growth behavior in the tail tends so be somewhat unstable, just like in the body, and some information about what is going on during the tail is highly desirable. (iii) One can use whatever instrumentation is already available and develop new ones, to help define the status of the grow, frequently enough. Oftentimes, there is access to the crystal weight and melt level information. For a large diameter crystal, these two parameters are fairly sensitive to how the tail diameter is behaving, and deviations from target curves will indicate if a control action may be required. However, these two pieces of information can give a dependable estimate of the actual diameter, if integrated over a lengthy period of time, only, typically starting from 10 min to more than 1 h. Faster and more direct measurements of the actual diameter would be highly desirable. Optical or other systems that allow measurement of the tail diameter, while a direct optical path is not there, will be essential for good process control of the tail growth. Today, 450 mm silicon CZ crystals are grown in small scale industrial volumes. While the shift to this wafer size within the IC industry will eventually, probably happen several years from now, the question is not if the required crystal material can be generated or not, but rather, what the best approaches may be to produce it in an efficient and economically sustainable manner.

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FURTHER READING R. Uecker, The historical development of the Czochralski method, J. Cryst. Growth 401 (2014) 7. J. Friedrich, L. Stockmeier, G. Mu¨ller, Constitutional supercooling in Czochralski growth of heavily doped silicon crystals, Acta Phys. Pol. A 124 (2013) 219. M.E. Glicksman, Principles of Solidification, Springer, New York, 2011. G. Dhanaraj, K. Byrappa, V. Prasad, M. Dudley (Eds.), Springer Handbook of Crystal Growth, Springer, Berlin-Heidelberg, 2010. W. Lin, H. Huff, Silicon Materials, in: R. Doering, Y. Nishi (Eds.), Handbook of Semiconductor Manufacturing Technology, second ed., Taylor & Frances, Boca Raton, FL, 2008. G. Mu¨ller, J. Me´tois, P. Rudolph (Eds.), Crystal Growth—From Fundamentals to Technology, Elsevier, Amsterdam, 2004. R.S. Feigelson (Ed.), 50 Years Progress in Crystal Growth—A Reprint Collection, Elsevier, Amsterdam, 2004. H. Scheel, T. Fukuda (Eds.), Crystal Growth Technology, John Wiley & Sons, Chichester, UK, 2003. J. Evers, P. Klu¨fers, R. Staudigl, P. Stallhofer, Czochralski’s creative mistake: a milestone on the way to the gigabit era, Angew. Chem. Int. Ed. 42 (2003) 5684.