Czochralski Growth of Silicon Crystals

Czochralski Growth of Silicon Crystals

2 Chapter Two Czochralski Growth of Silicon Crystals Olli Anttila Silfex Incorporated—A Division of Lam Research Corporation, Eaton, OH, USA Czochr...

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Chapter Two

Czochralski Growth of Silicon Crystals Olli Anttila Silfex Incorporated—A Division of Lam Research Corporation, Eaton, OH, USA

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 [2–4]. The differences in the method devel­ oped by Teal and Little were so large compared with the original method by Czochralski that it would prob­ ably be more just to call it the Teal–Little method [4]. The existence of another method, zone refining, that was originally used to purify germanium polycrystal­ line 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 form now 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 tech­ niques also allow growth of high-resistivity silicon, and all commercial crystal sizes can be made with CZ tech­ nique. Only if very high-resistivity silicon (2–3 kΩcm) or silicon without dissolved oxygen is needed, FZ material should be used. Still today, the availability of the highest-purity FZ crystals in 200 mm diameter is limited. Those interested in learning more about the FZ technique should consult, for example, reviews of Dietze [5], Zulehner [6], or Mühlbauer [7]. In late 1950s, Dash significantly improved the method of growing silicon crystals by adding a neck­ ing 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, almost 50 years after its introduction. Major evolutionary steps have been made; for example, maximum crystal weights are several hundreds of kilograms, magnetic fields are applied for better control of the melt behavior, all imag­ inable 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 rotat­ ing system, growth chamber that houses the hot zone (HZ), vacuum interlock, receiving chamber for the grown crystal, and crystal rotating and lifting sys­ tem. For more details, see Ref. [9], Figure 81 a and b. Modern CZ systems are able to grow crystals up to 450 mm in diameter, with charge sizes close to 500 kg. In MEMS applications, however, the maximum size of the crystal is 200 mm in diameter, and charge size may exceed 100 kg.

2.1.1 Crucible An essential part of CZ growth is that the single semi­ conductor crystal is pulled out of melt that is contained

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Silicon as MEMS Material

in a refractory crucible. No solvent is used; that is, the melt consists of the same elements as the growing crys­ tal. In the case of silicon, the melt is almost pure ele­ mental 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. 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 state, silica. A glimpse at the periodic table of the ele­ ments and the knowledge of the deleterious impact that most elements have on silicon material quality, even in very minute quantities, lead to only a few candidates. Almost all metals are excluded because the allowed concentrations are only in parts-per-trillion atomic (ppta) range. Group III and group V elements are elec­ trically active dopants that often may be tolerated to 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 inten­ tionally 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 allowed in the crystal in a fairly large concen­ tration, typically in 10 parts-per-million atomic (ppma) range; and in most applications for silicon wafers, oxy­ gen 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 is close to unity [10], 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]. In practice, the vast majority (98–99%) of oxygen that is being dissolved 20

from the silica crucible wall by the highly reactive sili­ con melt will be evaporated into the grower atmosphere and purged away by the inert gas flow that is mandatory for successful growth. Only 1–2% of the dissolved oxy­ gen ends up in the growing crystal itself. 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 cru­ cible 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 oxy­ gen released into the gas flow over one growth may be in the range of hundreds of grams in today’s large furnaces.

2.1.2 Hot-Zone Materials The basic building material for a HZ for silicon CZ crys­ tal 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 crys­ tal grower, which parts are essential in creating a proper temperature distribution around the semiconductor melt and the growing crystal. Furthermore, HZ design largely defines purge gas flow patterns inside the grower. Graphite is the material of choice because of its good availability as 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 mate­ rial 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 transported from the heater(s) to the crucible and elsewhere inside the HZ. However, radia­ tion is typically the dominant mode of heat transfer at these high temperatures, especially over long distances. The most commonly used insulator material is graph­ ite 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 per­ formance of the material. Oftentimes, the outer surfaces of rigid felt insulation are coated with a more continu­ ous 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,

Czochralski Growth of Silicon Crystals

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 carboneous particles that are mixed with a carbo­ neous binder to form a mass that can be molded either by extrusion or in an isostatic press. Higher-quality parts are typically isostatically pressed. The molded blocks are first carbonized and finally graphitized at very high tem­ perature, 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 contamina­ tion levels are several orders of magnitude higher than what is allowed for silicon single-crystal material. Care must therefore be taken in the hot-zone design to pre­ vent 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 remain­ ing metals deep inside to reach the surfaces fairly eas­ ily. Furthermore, silicon monoxide that is present in the purge gas around the graphite surfaces is able to pene­ trate deep into the bulk of material and react there. Many other materials are used to create HZs. Carbon-fiber-reinforced graphite (CFC) is mechanically much stronger; but it is also more expensive and poses more limitations to the design. Silicon carbide (SiC) is in many respects a better-performing material than graph­ ite; but it has significantly higher cost, and large-sized components’ availability is poor. However, SiC is often used as a CVD coating to enhance the lifetime of graph­ ite 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 molybde­ num or ceramic materials that are compatible with the environment, may be used in locations where there is no risk of contamination to the melt. Molybdenum is often used because of its moderately high cost, as well as its low diffusivity into silicon crystal and its very low segregation coefficient of about 5*10-8 [11], which allows substantial molybdenum contamination in the melt before damaging concentration may enter into the crystal.

2.1.3 Hot-Zone Structure A traditional HZ, as shown in Figure 2.1, contains a

graphite susceptor around the silica crucible (which is

CHAPTER 2

Neck Graphite heater Crystal Silica crucible Meniscus Melt Graphite susceptor Heat shield Spill tray

Fig 2.1 ● Basic HZ structure. The melt is contained in a silica crucible, out of which the crystal is slowly pulled. Around the heater there are insulating elements to reduce heat losses, and a spill tray is located below the melt to collect the melt in case the crucible were to break. Modern HZs may be considerably more complex.

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 distrib­ ute heat around the silica crucible a little bit more uniformly. The heater is usually connected to two or four elec­ trodes at its lower edge, typically by some kind of sup­ porting elements also made of graphite. The electrodes deliver the required power, which is at least tens of kWs, but often well exceeds 100 kW. The heater is nor­ mally of picket type, which means that it has vertical slits cut into it in a manner that forces the electric cur­ rent flow up and down, in opposite directions in neigh­ boring pickets (see Figure 2.4). The voltage is quite low and amperage is high, mainly because of the high elec­ trical 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 insula­ tion around the HZ. The heat shield drastically reduces the power consumption, and it also helps create a more proper 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 through such struc­ tural 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 21

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the heater supports and any openings for gas flows. Structural parts stretching through the insulation may easily lead to several, or even more than ten kW’s, of additional power losses per such part, and more poorly controlled temperature distribution usually will result. 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 dangerous steam explosion. The role of the spill tray is to collect all mol­ ten silicon and stop it before it makes contact with the stainless surfaces of the chamber or damages the expen­ sive mechanisms lower in the grower that are respons­ ible 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 2.2. Considering the high tempera­ ture 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

low pressure argon gas

silica crucible

Si crystal

SiO

Si melt O from crucible

graphite heater

graphite support

Fig 2.2 ● 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.

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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 effi­ cient cooling is desirable, for example, to enhance cool­ ing of the grower after the power has been shut off. Typical gas pressure is in the15–50 mbar range, and gas flow is in the tens to more than 100 standardliters-per-minute (slpm) range. Lowered pressure is used to reduce gas consumption relative to atmos­ pheric growth. As an example, if the process is running at 60 slpm/25mbar and the receiving chamber of the grower has an inner diameter of 12 inches, the result­ ing gas velocity in that part of the grower would be 0.5–0.6 m/s, which is enough to ensure clean laminar flow. However, larger pressure would require also a larger mass flow of purge gas, to maintain a flow pattern that would not be overly influenced by temperature dif­ ferences in the gas and to avoid undesired thermal con­ vection. 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 practi­ cal 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, which space 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 hot­ ter 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 crystal. 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 mon­ oxide is strongly dependent on the gas temperature. As the monoxide containing gas travels upwards, it cools

Czochralski Growth of Silicon Crystals

down, and tiny monoxide particles are formed. (It is not clear whether these particles are really made of sili­ con monoxide or whether the composition is rather a very-fine-grained mixture of silicon dioxide and elemen­ tal silicon.) The poor control of gas flow allows a part of this cloud of tiny particles to go back down towards the melt, and some of them may survive the hotter con­ ditions until they make contact with the melt surface very close to the freezing interface. Marangoni convec­ tion (see Section 2.6.4) then takes the particles directly to the crystal, again with a chance of loss of structure.

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, about 5 kg in a bag, though larger contain­ ers may also be used. Double bags also make it possible to remove the outer bag separately before bringing the bags into the charging area, to reduce any contamination that could be transported into the crucible. The cruci­ ble 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 sepa­ rate area, after which the full crucible, with or without the graphite susceptor, is transported to the grower and lifted into place. Handling of a full crucible is challeng­ ing, as its weight varies from tens to hundreds of kgs, depending on hot-zone size; the material is hard and brittle, allowing no shocks or scratching; and contami­ nation is an eternal foe. The way in which different sizes of silicon pieces are stacked into the crucible is an art of its own kind. 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 less than 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 cruci­ ble 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 col­ umn of silicon chunks, which are fused together, often

CHAPTER 2

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. A crack in the crucible is always a serious situa­ tion, and its consequences must be taken into account in the design of the HZ as well as in the process con­ siderations. 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 there­ fore 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 evacu­ ated 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 contami­ nation, into the melt and the surroundings during the long process hours. Another policy is to perform a leak test after the growth. This kind of test may 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 is 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.

2.2.1 Melting 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. 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 23

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before the material is so worn that difficulties are cre­ ated 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 to close to the preferred temperature, 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 two-color pyrometer that senses the surface temperature close to where the seed will be dipped.

2.2.2 Neck At the right temperature, 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 Figure 2.3), and the same seed may be used over and over again without excessive concerns about whether the DF structure is maintained or not. The basic idea in the necking step, originally intro­ duced by Dash in the late 1950s [8], is that disloca­ tions 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 sili­ con have a preferred axis in a 110 direction. Should one try to grow a neck of uniform thickness to this crys­ tal orientation, some of the dislocations would have no difficulty in staying within the neck; they would simply

Fig 2.3 ● 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.

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grow in length together with the neck. The more the growth axis deviates from the nearest 110 direc­ tion, 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 ade­ quate, the thickness seldom much exceeds 4 mm, and a few cm’s in the proper speed/diameter range suffices. 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. Several approaches have been used to address this issue, such as enabling the use of a thicker neck, constructing an additional means to sup­ port the weight, or developing ways to grow DF crystals without any necking procedure at all. However, these approaches are beyond the scope of this book. There exists some confusion about the density of dislocations in CZ silicon crystals. Because of histori­ cal reasons, specifications often allow nonzero disloca­ tion 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 dis­ locations 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 cer­ tain 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 sen­ sor, better than the pyrometers used in the instrumen­ tation. As soon as the neck diameter and average growth

Czochralski Growth of Silicon Crystals

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 diam­ eter at a proper pace: Too slow results in an unnecessar­ ily long process time 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 growth rate results in structure loss, as the too-cool melt causes an uncontrollable growth rate in some crys­ tal orientations. The larger the diameter of the crown, the cooler must the melt also be, and that is why there is a con­ tinual decrease in the heater power/temperature. The typical 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 2.3), but there are also things tak­ ing place under the surface, which we cannot see. The freezing interface usually becomes increasingly con­ vex towards the melt, and that shape has a significant impact on the chances of success of the crown and sub­ sequent 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. However, the freezing interface then tends to be highly convex, and as it tends to be fairly straight or even con­ cave in the body, the shape of the freezing interface 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 dif­ ferent, and the loss of structure will be more probable than if those speeds are close 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 borondoped material), this change of interface shape may easily be fatal for the crystal. Why this should be so is, however, beyond the scope of this book. 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

CHAPTER 2

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 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 is sometimes called transition and some­ times 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 in the diameter over a relatively short distance, and ideally the growth turns vertical at the same diameter as is cho­ sen for the body. At that point, the pull speed is low­ ered again, to match that of the early body. If the pull speed of the transition 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 temperature drop is usually needed, but after a while, the temperature changes will be slow. 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.

2.2.5 Tail 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. A part of this remaining melt is used to form a so-called tail. This section of the crystal is needed for two purposes: First, there will be thermal shock that will almost inevitably introduce slip dislocations as the crystal is detached from the melt. This slip will proceed a shorter distance upwards than if the growth would 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 25

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to achieve a more uniform thermal history to the end of the body, more comparable to the other parts of the body. Should the crystal be detached at full diameter, the end portion would cool down much more rapidly than if a long tail is grown.

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 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 cms 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 crys­ tal 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 parts.

2.3 Issues of Crystal Growth In the following sections, diameter control, doping, and HZ lifetime are discussed.

2.3.1 Diameter Control 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 times thermal conductiv­ ity, on both sides of the interface. However, the solidifi­ cation process releases heat at a rate that is equal to the speed of crystallization times 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 26

least averaged over time. The time-dependent processes in the melt make temperature gradients at the melt side vary over time, which creates striations to the crystal (see Figure 2.5), 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 opti­ cally. The melting point of silicon is high enough to give ample intensity for optical measurements, and in prac­ tice, 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 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 the locations of two points at the meniscus, or several point locations that are iden­ tified and a best-fit calculation performed to get the diameter of the meniscus. The luminousness of the meniscus (Figure 2.3) 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 bound­ ary between solid and molten material is very difficult to distinguish. The diameter is then measured at some suitable location in that meniscus, a few mms outside of the crystal edge. The physical properties of elemental silicon define what is known as wetting angle, whose magnitude is 11°: This is the angle between the edge of the growing (verti­ cal) 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 freez­ ing interface is located as much as about 7 mm above the melt level, as measured a couple of cms outside the crystal. The balance between the surface tension of the melt and gravity dictates the shape of the interface 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 exter­ nal 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 immedi­ ately 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 pos­ sible: (1) Heat transfer at the crystal side of the inter­ face could be enhanced. However, if no changes take place there, this does not happen by itself. (2) Heat

Czochralski Growth of Silicon Crystals

transfer at the melt side could be lowered, but again, no intentional changes are made there. (3) 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. Should the average pull speed, after proper control of the diameter has been established, be off from the tar­ get, 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 crys­ tal allows larger growth rate), and quality issues. Some crystals are grown slowly to establish a suitable balance between growth rate and thermal gradients, which bal­ ance has an impact on very small vacancy-related defects, known as COPs, in dense IC circuits [12]. 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 to the average growth rate, the average taken over sev­ eral 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 delay. Another possibility is to change the heater power. There are a couple of other possibilities 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 [13]; by other means of introduc­ ing energy to the crystal; or by changing its thermal environment in a more passive way. At the melt side, transport of heat from crucible wall towards the freez­ ing 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 Ωcm. This corresponds to 1015–1016 dopant atoms/cm3, which translates to only mgs of elemental dopant to a charge of tens of kgs or more. A small quantity like this is very difficult to allot in a consistent manner, and therefore the dopant is usually introduced as-diluted to a larger amount of silicon. A suitable amount of dopant

CHAPTER 2

element may be melted together with silicon to make an alloy in which the dopant concentration is in the 0.01– 0.1% range. If this alloy is prepared carefully so that the concentration is uniform, a very convenient 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 heav­ ily 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 ele­ mental 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 prefer­ ably 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 phos­ phorus, 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 dopant will be needed; there will be more dirt in the system, adding to chances of particles and yield losses; and the repro­ ducibility 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 volatile n-type dopants normally reduce oxy­ gen concentration in the grown crystals, as oxygen in the melt is depleted more efficiently near the gas–melt interface. Volatile oxides of the dopant are carried away by the purge gas just as oxygen is carried as silicon mon­ oxide, 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 the useful lifetime of the crucible. These dopants have also some effect on surface tension and therefore to the melt flows near the melt surface (see Section 2.6.4).

2.3.3 HZ Lifetime HZ materials have only a limited lifetime, partly

because of high temperatures and partly because of the

27

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Silicon as MEMS Material

Fig 2.4 ● 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.

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 insulat­ ing 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 2.4), 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 through and around the heater. Further downstream, the reactivity of the gas has already been reduced. The lifetime of a heater may be as short as just twenty crystals, but with more sophisticated designs, it may be hundreds of crys­ tals 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 mate­ rial starts shrinking when the temperature goes down. However, the coefficient of the thermal expansion of the silica crucible is extremely small, only about onetenth 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 28

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 mms. 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 sections to move independently. However, in addition to reduced mechanical strength, 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 tempera­ ture, makes graphite and silica react to form carbon and silicon monoxides, which are both volatile. This reac­ tion 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 vicin­ ity of the cuts performed to allow susceptor sections to move relative to each other. Furthermore, the result­ ant 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 maxi­ mized, and the crystal quality is good and repeatable. 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, except for the first few cms of the crystal above the melt [18]. This allows for bet­ ter control of the temperature distribution in the crys­ tal. 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 HZs, where achievable growth rates decline towards the end of the body, as the hot crucible rises gradu­ ally. All this gives a better and more reproducible qual­ ity. 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 enhanced lifetimes of the HZ parts, as maximum tem­ peratures 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

Czochralski Growth of Silicon Crystals

fact that improved insulation results in a situation where 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 addi­ tion 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 cor­ rosive 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 diame­ ter of the growing crystal from the melt or even signifi­ cantly 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 independ­ ence between gas flows near the melt surface and ther­ mal 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 monox­ ide 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 hot-zone parts, it is preferable that the contact of the gas with these part be kept to a mini­ mum. Various approaches are available, which, however, all add to the complexity of the hot-zone design.

2.5 Heat Transfer There are three significant modes of heat transfer that operate during silicon crystal growth: conduction, con­ vection, and radiation. Radiation is of major significance between sur­ faces 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 effi­ ciently 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 Stefan–Boltzmann law tells us that the radiant power density is proportional to the fourth power of the tem­ perature. That is why, especially over longer distances,

CHAPTER 2

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 tem­ peratures, much better than, say, stainless steels. On the other hand, insulators are designed in such a man­ ner that conduction is made difficult. For example, the graphite fibers conduct only along the fibers, and as there is limited contact between fibers, it is difficult for the heat to be conducted through the thickness of an insulating layer. At the same time, the fibrous struc­ ture cuts the radiation repeatedly over a short distance, making radiation a much less effective means of heat transfer 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 cruci­ ble 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 large 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 made will be explained in Section 2.8), and radiation may pass freely. Sometimes, the bubble structure of the crucible has a significant impact on its temperature dis­ tribution, 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 the conduc­ tion 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 2 to 3 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 low in the silicon CZ process and argon is a poor ther­ mal 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 incom­ ing gas itself. Typically, the gas flow is in tens of slpm, and during the passage through the HZ, the temperature 29

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Silicon as MEMS Material

rises by well more than 1000°C. In most cases, a few, but no more than about 5, additional kW 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 addi­ tional, but local, heat loss is only in 1 kW range. The total upward directed heat transfer rates in, say, 150–200 mm crystals seldom exceed 2–3 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 hun­ dreds of kgs, 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 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 vis­ cosity does to slow down melt movements. That, com­ bined with the large volume of the melt, makes it very difficult to control the melt behavior properly. The crys­ tal sizes grown for MEMS applications are, fortunately, slightly smaller (the present charge sizes seldom exceed 100 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,

Growth axis

30

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 insuf­ ficient 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 (Figure 2.5) 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 com­ monly 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 men­ tioned 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 [14]. 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.

Sample cut

Fig 2.5 ● LPS (Lateral Photovoltage Scanning) [20] 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.

Czochralski Growth of Silicon Crystals

The second dimensionless number is known as the Rayleigh number (Ra), and it describes the ratio between 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 viscos­ ity 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 differ­ ent temperatures, and over cold spots the growth rate is greater than over hot spots, where the crystal may actu­ ally 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 2.5). As the crystal is rotated during growth, there is typically some component to the stri­ ations that is related to the rotation rate. In addition, there are longer-term variations that are related to the time that it takes a new larger hot spot to arrive under the crystal, after the previous one has gone. The tem­ perature disturbances may also result in the loss of the single crystalline structure; unstable melt behavior typi­ cally 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, oxy­ gen has much lower diffusivity in the melt than heat. 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 concen­ tration in the crystal do not follow too closely the resis­ tivity 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 rea­ son 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 convec­ tion is not the dominant convection mechanism, the inferences derived from these dimensionless numbers (Gr, Ra) may be grossly misleading.

CHAPTER 2

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, it may take a long time for the melt to adjust its rotation rate to that of the crucible, but this time is short anyway compared with the total proc­ ess 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 trans­ verse field exerts a strong decelerating force to a rotat­ ing body of electrically conducting fluid, and the melt will be almost nonrotational, independent of the cruci­ ble rotation rate. However, this case will be discussed in a little more detail in Section 2.7.1, and other cases will not be touched here at all. 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 push­ ing the melt on top sideways, towards the cooler crys­ tal. 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 cms inwards from the crucible wall. And correspond­ ingly, 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 upwardoriented 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 azimuthal velo­ city, 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 angu­ lar velocity would increase correspondingly. The same behavior may be seen in the case of tornadoes and hurri­ canes, where the wind approaching the eye of the storm rotates ever more rapidly. This phenomenon has a major

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Silicon as MEMS Material

impact on the centrifugal force that this fluid volume experiences, whereas the rest of the melt that is rotat­ ing approximately with the crucible is unaffected. The higher the crucible rotation is, the shorter the distance will be that the fluid volume is able 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 25000 N/m3), but in practice this difference in centrifugal force is very significant. Gravity itself does not cause free con­ vection, 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 signifi­ cant 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 relatively 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 2.6). 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 convec­ tion 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 balanc­ ing of temperatures would eliminate the driving force

0

32

0.01

0.02

for free convection, and free convection would no longer play a role in heat transfer. However, several tens of rev­ olutions per minute would be required, and in practice this would be very challenging to realize. Use of a suitable magnetic field to support the stabilizing effect of melt rotation would seem to make this approach to stabilizing melt behavior somewhat more realizable [15].

2.6.3 Crystal Rotation The most evident reason for the rotation of the grow­ ing 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 prac­ tice 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 [16]. The resulting flow pattern con­ tains an upward-directed component that is independ­ ent 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 rota­ tion 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 also pro­ portional 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

0.03

0.04

0.05

Fig 2.6 ● 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 perpendicular velocity component to the direction of rotation is shown, only. The velocity scale is in meters per second.

Czochralski Growth of Silicon Crystals

rotate in the first place prevent it from moving relative to the crystal. Far from the interface, the rotation rate is 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 dis­ tributing 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 some­ times prove to be more complicated than that. The cool melt from under the crystal tends to reduce thermal gradients outside of the meniscus. Any disturbance out of the cylindrical shape has a better chance of surviving and growing into a significant disturbance if the tem­ perature outside of the crystal increases only gradually. There are always such disturbances because of random fluctuations and because of the anisotropy of the grow­ ing single crystal. The most prominent anisotropic fea­ ture is the existence of four vertical growth nodes along the crystal, at 90° intervals, in case of (100) material. The nodes are caused by closed packed {111} planes that try to grow a little longer 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, three-dimensional flow patterns will develop near the periphery of the crystal, again at four-fold sym­ metry, that cause the relatively narrow growth nodes to widen and flatten, and finally the crystal changes its shape to become somewhat star-shaped. This simple and well-organized flow pattern by crys­ tal 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 rotation rates would again create a sim­ ple flow. In this case, the pattern would be identical to what was described previously, but the direction of the flow would be inversed [16]. This kind of configuration would create very large oxygen gradients over the radial dimension of the crystal, as well as a high dopant gradi­ ent 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 cru­ cible, most of the melt, also under the crystal, rotates

CHAPTER 2

in the same direction as the crucible; under the crys­ tal, at a lower rate than outside of the crystal radius. The melt immediately under the crystal rotates with it, but already, a few mms below, 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 melt-gas 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 par­ ticle 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 tem­ perature dependence of surface tension at the melt–gas 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 tem­ perature 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 magni­ tude 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 sig­ nificant part of it is directed close to the melt. At low pres­ sure, 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 oxy­ gen containing gases is needed in the vicinity of the meltgas interface, and this translates to high gas velocity. Oftentimes, if melt behavior during CZ growth is simulated computationally, oxygen is considered as 33

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Silicon as MEMS Material

not having an influence on melt flows. This makes the optimization of the growth process substantially easier, as the melt flows may be modeled on thermal con­ siderations and forced convections, only. After hav­ ing 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 sig­ nificant shear to the melt interface, or if the cooling effect of the gas flow changes the temperature distribu­ tion in the crystal and around the crucible by a consid­ erable amount, this approach is no longer valid. Then the melt flows should be recalculated, adding very sig­ nificantly 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, trans­ verse and cusp fields. Almost pure axial fields are poorly suited, as they tend to prevent transport of oxygen and dopant from under the crystal; and, therefore, the resulting oxygen concentration is high and variation of oxygen and dopant in the radial direction (radial gradi­ ents) is often large. Magnets weigh usually several tons, and the power may be well beyond 100 kW. However, more powerhungry magnets have been increasingly replaced with superconducting magnets. Sometimes, especially older growers have been modified to take more lightweight magnets, despite the cost of higher electric current den­ sity and larger power loss, as the space around the vac­ uum chamber has been in short supply and the grower frame has not allowed for significant excess weight. Furthermore, if low field is considered sufficient, mod­ ern permanent magnet materials together with iron yokes may be applicable. The movement of an electrically conducting fluid in a magnetic field causes an electromotive force that is per­ pendicular to both the field and the direction of move­ ment. This electromotive force tends to create electric currents that, in interaction with the external magnetic field, oppose the fluid motion. The field strengths typi­ cal for magnetic CZ (MCZ) processes are sufficient to slow down various flow patterns very significantly. This has implications to various 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, together with reduced crucible wear, results in better DF growth yields. 34

2.7.1 Transverse Field

A transverse magnetic field is created from conventional copper or superconducting coils that are located in the vertical position. Heavy iron yokes are used to shorten the magnetic path and to reduce the important stray fields. This type of field has the unpleasant character­ istic of breaking the otherwise almost perfect cylindri­ cal symmetry of the growth geometry. However, as the field impacts on melt behavior only, and the melt flows in the case of large crystals deviate from cylindri­ cal symmetry in a significant manner anyway, this loss of symmetry is not as serious a breach as it may first seem. The crucible (and melt) rotation is normally rela­ tively fast in 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 cre­ ate 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 melt rotation rate would be close to zero, essentially independent of the crucible rotation rate.

2.7.2 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 [17]. The cylindrical symmetry is maintained. A typical shape of cusp field is shown in Figure 2.7. This type of field also creates electromotive forces as the melt is rotated, but contrary to the transverse field, there is little force created that would try to stop the rotation. That is why an MCZ process utilizing the cusp field may be very similar to a normal CZ process. Far from the freezing interface, the magnetic field is strong­ est and its impact on reducing melt flows is also great­ est. 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 out­ side of the crystal radius the melt convection is largely suppressed. Oxygen concentration in an MCZ process is often con­ sidered to be substantially lower than in an otherwise sim­ ilar 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

Czochralski Growth of Silicon Crystals

0

0.2

0.4

of oxygen into the melt is diminished. However, it also has an impact on melt flows near the melt–gas 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, in gas flows may be utilized to remove oxygen from the melt, and that is why the use of a magnetic field does allow the reach­ ing of lower oxygen levels. However, a lower oxygen level 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. Such processes are normally not applied, as it would be quite difficult to control the radial uniformity of oxygen concentration.

2.7.3 Time-Dependent Fields Much more complex magnetic fields may be devised for better control of melt behavior, and the fields may also be time dependent. However, these possibilities are beyond the scope of this book.

2.8 Hot Recharging The CZ crystal growth process that has been described earlier 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. The easiest way of doing this is to use

0.6

0.8

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CHAPTER 2

Fig 2.7 ● 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) is attained at the crucible corner. Near freezing interface, there is almost no field. Solid lines depict the magnetic lines of force.

granular polysilicon, small spheres in the 1–4 mm diam­ eter range that flow easily, even through small-diameter tubes or other structures, to make the feed. However, because of the limited availability of this material and additional concerns, other types of materials may also be used: Small-sized chunks may be fed in a manner similar to granular material, using larger-sized chan­ nels. Or a vertical tube-like structure filled with small chunks 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 hang­ ing into the end of the seed cable/shaft and fed into the melt in a well-controlled manner. Or adding to the complexity in a significant manner, new silicon may be added as molten from outside of the crucible proper. In all of these cases, the main goal is to reduce cost and save time compared with growing a single crystal from the melt. The cost of the relatively expensive cru­ cible, 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 contamina­ tion 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 time savings, too, to the cycle time per produced kg of crys­ tals, 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 structure loss increases as the wear pro­ ceeds. The way the crucible wall has been fused makes 35

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Silicon as MEMS Material

the near inner surface of better quality than the deep bulk of the material. Over the years, various alterna­ tives 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 hot-zone design and the growth proc­ ess, 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 and other imperfections that would initiate nonuniform wear that may result in the release of small silica/quartz

particles into the melt. 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 uniformly than in the absence of this uniform devitri­ fied layer, and at the same time the crystal rejects those added elements so powerfully that the concentration in the crystal remains insignificant. It is recommend 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 solu­ bility and reduced intensity of the melt flow patterns, as well as to use various magnetic fields to stabilize the melt.

References 1. J. Czochralski, Ein neues Verfahren zur Messung der Kristallisations­ geschwindigkeit der Metalle, Z. Phys. Chem. 92 (1918) 219. 2. G.K. Teal, J.B. Little, Growth of germanium single crystals, Phys. Rev. 78 (1950) 647. 3. G.K. Teal, E. Buehler, Growth of silicon single crystals and single crystal silicon pn junctions, Phys. Rev. 87 (1952) 190. 4. H.R. Huff, From the lab to the fab,

transistors to integrated circuits, in:

C. Claeys, F. Gonzalez, R. Singh, J. Murota, P. Fazan (Eds.), ULSI Process Integration III, The Electrochemical Society Proceedings Series PV 2003– 06, 2003, p. 15. 5. W. Dietze, W. Keller, A. Mühlbauer, Floating zone silicon, in: J. Grabmaier (Ed.), Crystals: Growth, Properties and Applications, vol. 5, Silicon, SpringerVerlag, Berlin, 1981. 6. W. Zulehner, The growth of highly

pure silicon crystals, Metrologia 31

(1994) 255.

7. A. Mühlbauer, Innovative induction melting technologies: a historical review, International Scientific Colloqium in: Modelling for Materials Processing, Riga, June 8–9, 2006, p. 13. 8. W.C. Dash, Growth of silicon crystals free from dislocations, J. Appl. Phys. 30 (1959) 459.

9. W. Zulehner, D. Huber, Czochralski­ grown silicon, in: Crystals, vol. 8, SpringerVerlag, Berlin–Heidelberg, 1982. 10. W. Zulehner, Czochralski growth of silicon, J. Cryst. Growth 65 (1983) 189. 11. J. Davis, A. Rohatgi, R. Hopkins, P. Blais, P. Rai-Choudhury, J. McCormick, H. Mollenkopf, Impurities in silicon solar cells, IEEE Trans. Electron Dev. ED-27 (1980) 677. 12. E. Dornberger, W. von Ammon, The dependence of ring-like distributed stacking faults on the axial temperature gradient of growing Czochralski silicon crystals, J. Electrochem. Soc. 143 (1996) 1648. 13. U. Ekhult, T. Carlberg, M. Tilli, Infra­ red assisted Czochralski growth of silicon crystals, J. Cryst. Growth 98 (1989) 793. 14. M.G. Braunsfurth, A.C. Skeldon, A. Juel, T. Mullin, D.S. Riley, Free convection in liquid gallium, J. Fluid Mech. 342 (1997) 295. 15. O. Anttila, Some observations of growth of CZ silicon and dream of ideal growth, ECS Trans. 3 (4) (2006) 3. 16. H. Schlichting, K. Gersten, Boundary Layer Theory, eighth ed., Springer, 2000.

Further reading G. Müller, J. Métois, P. Rudolph (Eds.), Crystal Growth—From Fundamentals to Technology, Elsevier, 2004.

36

H. Scheel, T. Fukuda (Eds.), Crystal Growth Technology, John Wiley & Sons, 2003.

17. R.W. Series, Effect of shaped magnetic field on Czochralski silicon growth, J. Cryst. Growth 97 (1989) 92. 18. O.J. Anttila, M.V. Tilli, V.K. Lindroos, Computer modelling of the temperature distribution in the silicon single crystals during growth and the thermal history of the crystal, in: J.C. Mikkelsen, Jr., S.J. Pearton, J.W. Corbett, S.J. Pennycook, (Eds.), Oxygen, Carbon, Hydrogen and Nitrogen in Crystalline Silicon, vol. 59, Materials Research Society Proceedings Series, 1985, Vol. 59, p. 323. 19. O. Anttila, M. Laakso, J. Paloheimo, J. Heikonen, J. Ruokolainen, V. Savolainen, T. Zwinger, Simulation of silicon Cz growth: where we are now, in: C.L. Claeys, M. Watanabe, P. Rai-Choudhury, P. Stallhofer (Eds.), High Purity Silicon VII, vol. 200220, ECS Symposium Proceedings Series, Vol. 2002–20, p. 65. 20. A. Lüdge, H. Riemann, Doping inhomogeneities in silicon crystals detected by the lateral photovoltage scanning (LPS) method, in: J. Donecker, I. Rechenberg (Eds.), Defect Recognition and Image Processing in Semiconductors 1997, CRC Press, 1997, p. 145.