Adsorption and desorption kinetics of In on Si(100)

Adsorption and desorption kinetics of In on Si(100)

314 Surface ADSORPTION J. KNALL, Department AND DESORPTION KINETICS Science 209 (1989) 314-334 North-Holland, Amsterdam OF In ON Si(100) S.A. B...

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Science 209 (1989) 314-334 North-Holland, Amsterdam

OF In ON Si(100)


of Physics, Linksping

University, S-58183 Linkiiping, Sweden

and J.E. GREENE Department Laboratory, Received

of Materials Science, The Coordinated Science Laboratory, and The Materials IIOI W. Springfield Avenue, University of Illinois, Urbana, IL 61801, USA

17 August

1988; accepted

for publication

14 October



The structure and surface morphology of In overlayers on Si(100) surfaces were investigated as a function of substrate temperature and surface coverage using low-energy and reflection high-energy electron diffraction as well as Auger electron spectroscopy. Desorption kinetics of adsorbed In was studied with modulated-beam desorption and temperature-programmed desorption spectroscopies. Indium was found to grow on Si(lO0) according to a Stranski-Krastanov mechanism with the initial formation of several two-dimensional phases preceding the nucleation and growth of three-dimensional In islands. Binding energies and frequency factors were extracted from the desorption measurements using a model based on first-order desorption from several interdependent surface phases. First-order and zeroth-order kinetics were observed for the total desorbing flux from coexisting surface phases.

1. Introduction Several of the dopants used for co-evaporative doping during silicon molecular beam epitaxial (Si MBE) growth (e.g. Sb [l], Ga [2], In [3,4], Al [4]) have been found to incorporate via a two-step process: the dopant atoms first adsorb in a surface overlayer and then either desorb or become incorporated into the growing crystal. This tendency to segregate at the surface introduces broadening of the dopant depth profiles and leads to low, and exponentially temperature-dependent, dopant incorporation probabilities u [l-3]. A number of procedures employing energetic particle-bombardment of the surface overlayer have been developed in order to overcome the deficiencies of thermal * Permanent address: Department of Materials sity, Evanston, IL 60208-9990, USA.


and Engineering,

0039-6028/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)



.I. &all et al. / Adsorptionand &sorptionkineticsofIn on Si(IO0)


doping and to improve control over dopant concentrations and depth distributions [4-71. Regardless of whether the incorporation is “spontaneous” or induced by particle bombardment, the dopant overlayer plays an important role in governing the dopant concentration in the growing film. Previous investigations have shown that In has a very low spontaneous incorporation probability during co-evaporative doping of MBE Si(a < 4 X lo-’ for T, > 550“ C) [4]. However, cIn was greatly enhanced by bombardment of the In overlayer with energetic Si+ ions, which caused secondary implantation of In. The incorporation probability in this latter case showed a rather complex dependence on substrate temperature and In flux [S]. A detailed knowledge of the structure, coverage, and binding energy of the dopant in the overlayer is necessary in order to understand this behavior. This paper addresses the adsorption and desorption behavior of In on Si(100) surfaces at substrate temperatures Ts between 300 and 750°C. The results are relevant to both the understanding of processes involved in the incorporation of dopants during MBE growth and the early stages of growth of metal films on Si. The investigation has resulted in a set of equations that describes the desorbing In flux as a function of temperature and coverage. Initial results, including a surface phase diagram, have previously been published in ref. [9]. The structure and coverage of the overlayers were investigated using low-energy electron diffraction (LEED), reflection high-energy electron diffraction (RHEED), and Auger electron spectroscopy (AES). The desorption kinetics of adsorbed In were studied with modulated-beam desorption spectroscopy (MBD) and temperature programmed desorption (TPD) using a linear temperature ramp. The experimental MBD and TPD spectra were analyzed by fitting them with model calculations based on first-order desorption from several interdependent surface phases. From the diffraction observations, AES m~surements, and desorption experiments it was concluded that In grows on Si(100) by a Stranski-Krastanov mechanism, with the formation of several two-dimensional (2D) phases preceding the nucleation and growth of three-dimensional (3D) In islands. The first 2D phase was disordered with a saturation surface coverage of = 0.07 monolayer (1 ML = 6.8 X 1014cm-* which corresponds to the number of sites on an unreconstructed Si(lO0) surface) and a binding energy of = 2.8 eV. Higher In coverages B led to the formation of areas with an ordered 3 x 4 reconstructed phase which progressively replaced the previous phase to completely cover the surface at 8 t: 0.5 ML. The binding energy of In in this phase was = 2.85 eV. At substrate temperatures T, above 450 o C, the completion of the 3 X 4 phase was followed by the formation of a second disordered two-dimensional phase with a lower binding energy, 2.45 eV. Saturation of this latter phase at 0 = 1.5 ML led to accumulation of additional In in three-dimensional islands. The binding energy of In in the 3 x 4 phase was found to


J. Km11 et al. / Adsorption

and desorption kinetics of In on Si(lO0)

be 2.85 eV while the In that adsorbed on top of the 3 X 4 phase had a binding energy of 2.45 eV. In a related paper, ref. [8], we have used the equations derived in this paper to describe the correlation between the In surface coverage and the In incorporation probability u during Si-MBE growth in combination with secondary implantation using Si+ ion bombardment induced by a negative substrate bias. It was found that the temperature and In flux dependence of u was determined premarily by the adsorption-desorption behavior of In on the Si surface.

2. Experimental Electron diffraction (RHEED and LEED) and AES measurements together with a few desorption measurements were performed in a Vacuum Generators V-80 Si MBE system which is described in detail in ref. [8]. However, most of the desorption (MBD and TPD) measurements were carried out in a smaller vacuum system, shown schematically in fig. 1. This system was used in order to increase the signal-to-noise ratio, since it allowed the mass spectrometer to be mounted closer to the sample than in the MBE system. The system pressure was < 10K9 Torr during measurements. The desorbing In flux I,, was measured at an angle of 45 o from the surface normal using a quadrupole mass spectrometer (VG SX 200) with line-of-sight view, defined by a pair of water-cooled apertures, to a small region (- 5 x 5 mm) near the center of the sample. II


i ks



Fig. 1. Schematic diagram of the system used for MBD and TPD spectroscopy measurements.

J. Knall et al. / Adsorption and desorprion kinetics of In on Si(IO0)


The substrates were 8 Q-cm phosphorous-doped Si(lO0) wafers that were cut into pieces 45 by 10 mm. Before insertion into the vacuum system, the samples were cleaned by a wet chemical oxide etch-regrowth procedure described in ref. [8]. Final cleaning was carried out in-situ and consisted of 5 min outgassing at 550° C followed by desorption of the surface oxide at 850” C for 5 min. The substrates were heated by passing current directly through the sample and the temperature was monitored by an infrared pyrometer. The pyrometer was calibrated versus a chromel-alumel thermocouple via the substrate resistivity as described in refs. [8,10]. The flux from the In effusion cell was indicent normal to the surface and was measured, both before and after desorption experiments, with a quartz crystal monitor placed at the sample position. The temperature of each sample was measured as a function of heating current. The data was then programmed into a computer and used to control the temperature during the desorption experiments. The computer was also used to control the effusion shutter and to record the mass spectrometer signal. Each desorption spectrum presented is the average of 5-10 spectra taken to improve the statistics of the data.

3. Experimental


3. I. Electron diffraction

and Auger electron spectroscopy

The growth characteristics of In deposited on clean Si(100) surfaces were observed using RHEED, LEED and AES. The RHEED patterns were obtained during growth, while the sample had to be transferred to the analytical chamber of the V-80 MBE system for LEED and AES analyses. The sample could also be heated in the latter position for observation at elevated temperatures. Indium layers with different thickness were grown at ambient temperature and Si Auger spectra were recorded sequentially at the following substrate temperatures: T, = - 20, 400, 20, and 530 o C. When recording Auger intensities from a resistively heated sample, the voltage across the sample broadens the Auger peaks and thus leads to a decrease in the peak-to-peak values in differentiated spectra. To alleviate this problem, we have normalized the intensities to those from the clean substrate at the appropriate temperatures. Auger peak-to-peak intensities of the differentiated Si 92 eV peak as a function of coverage are shown in fig. 2. The shape of the Auger intensity plots are all indicative of a Stranski-Krastanov growth mechanism. The initial decrease in the Si Auger signal occurs during the formation of a two-dimensional. In layer and the constant signal with increasing 8 occurs when In


J. GalI

et al. / Aahvption

and desorption kinetics of in on Si(lO0)

m As Deposited at TS= 20°C 0 Measured at TS = 20°C after Anneal at T,=400”% n Measured at TS q4OOoC o Measured at TS =53O”C -Calculated for Layer-by-Layer Is








Growth x



Fig. 2. Peak-to-peak intensities Isi of differentiated Si Auger spectra measured and 530 o C, as a function of In coverage 0 on Si(lO0) substrates. A calculated 0, assuming two-dimensional growth, is also shown.

at Ts = 20, 400, 20 curve of Zsi versus

accumulates in 3D islands. Calculated Si Auger intensities for layer-by-layer growth, also shown in fig. 2, were obtained from the following equation: Zsi=(1-8,)Zsoi


+0,Z,9 exp(-n/A),


where 1: is the intensity from clean Si, X the escape depth (in ML) of Si Auger electrons through the In overlayer, n the integer In layer number, and 6, the coverage of layer n. Each complete layer was taken to be 1 ML thick. X was determined to be 2.2 ML by fitting eq. (1) to the Auger intensities for 8 5 1 ML recorded at T’ = 20 o C directly after growth. Indium grew twodimensionally for coverages up to - 3 ML. However, when films grown at - 20 o C were annealed at 400 o C and then analyzed again at - 20 o C (or at the annealing temperature) the Auger signal leveled off at 0.5-0.7 ML. Since no significant desorption or in-diffusion of In occurs at 400 o C, this indicates that some In was removed from the 2D layer and accumulated into 3D islands during the anneal. However, when the surface temperature was raised to 530 ’ C during Auger analysis, we found that a thicker 2D layer was formed on the surface as indicated by the Si AES signal leveling off at 1.5-2 ML. We have not recorded Auger intensities for 0.5 < B < 4 ML at Ts = 53O*C since the desorption rate at B > 0.5 ML was - 0.02 ML s-l, which would lead to an increase in the Si signal during the 20 s it took to record the Auger spectrum. Finally, lowering the temperature below 400 o C again led to a lower coverage (0.5-0.7 ML) 2D layer. The Si Auger signal was also recorded during desorption of 5-10 ML thick films at Ts = 500-600 o C. A typical result, in this case Ts = 550 o C, is shown


J. Knoll et al. / Adsorption and desorption kinetics of In on Si(lO0)




80 Time,



t (s)

3. Peak-to-peak intensities of differentiated Si Auger spectra versus desorption Ts = 550 OC after deposition of - 5 ML In on a Si(100) surface.



fig. 3. The initial part of the desorption spectrum is characterized by a very slow increase in Si signal as In is lost primarily from 3D islands, either by direct desorption from the islands, or by diffusion onto the 2D layer and desorption from there. It will be shown in the following section that the latter process is dominant. When the 3D islands are gone, the 2D layer coverage begins to decrease leading to a much faster increase in the Si signal. The rate of change in the Si signal decreases again when it reaches a level correspondof an increase in the In ing to a coverage of - 0.5 ML. This is an indication binding energy at 0 I 0.5 ML. RHEED patterns were recorded as a function of 19for incident In fluxes Jr, at the substrate of between 0.01 and 0.5 ML s-l. For growth at T, > 300“ C, the RHEED pattern began to change from that characteristic of the initial Si(100)2 x 1 reconstruction to that of a Si(100)3 x 4-In reconstruction at a coverage 8 of - 0.1 ML. The quality of the 3 X 4 pattern was optimal (sharp spots with minimum diffuse background) at - 0.5 ML. At 300” C < T, < 450 o C, the intensity of the 3 x 4 pattern decreased very slowly with increasing 0 above 0.5 ML and was still visible at 1000 ML, the highest coverage used. This is consistent with the initial formation of a 2D layer at coverages up to 0.5-0.7 ML, followed by nucleation and growth of 3D islands, as deduced from the AES measurements. For Ts > 450” C, increases in 0 above 0.5 ML led to a more rapid degradation of the 3 X 4 pattern and only feint 1 x 1 streaks remained of the surface pattern at 8 > 1.5 ML. When the 1 x 1 pattern was observed using LEED, the spots were sharp, but weak, with a diffuse background indicating that the diffraction pattern emanated from the substrate, but that the intensity was reduced by a disordered overlayer. From the above observations we conclude that In atoms randomly occupy a fraction of the available surface sites and form a 2D gas at coverages up to slightly less than 0.1 ML at which areas with an ordered 3 x 4 structure start to form. The 3 X 4 structure is complete at 0.5 ML and then, at T, > 450 o C, in


J. Km11 et al. / Adsorption and desorption kinetics of In on Si(IO0)

gradually becomes replaced by a disordered phase at higher coverages or becomes decorated with 3D islands at Ts < 450 o C. The transition between the two morphologies, (3 X 4 + 3D islands and disordered 2D layer + 3D islands) occurred abruptly and reversibly for samples with B > 1.5 ML when T, was increased or decreased through - 450 o C. In addition, during growth at Ts > 550” C, a Si bulk diffraction pattern became visible at coverages above - 0.7 ML indicating that the Si surface had roughened. The roughness remained when the sample was cooled to ambient temperature and analyses of the LEED patterns from such surfaces showed the presence of (310) oriented Si facets [9]. After deposition, the bulk spots were visible together with either the 1 X 1 pattern at T, > 450 o C or the 3 X 4 pattern at T, -c 450 o C. However, the diffraction spots emanating from facets were always much weaker in intensity than the spots in the 3 x 4 pattern when observations were made at ambient temperature. Based on the intensities of the LEED spots, we estimate that the fraction of the substrate surface area that was faceted was less than 10%. 3.2. Modulated-beam


Modulated-beam desorption spectra were obtained over the temperature range from 530 to 710 o C by using a mass spectrometer to measure the time variation of the desorbing flux Jdes while the In flux from the effusion cell J,, was turned on and off with a magnetically-actuated shutter. The spectrum shown in fig. 4 was recorded at a substrate temperature T, of 680 o C and an incoming flux JI, of 0.025 ML s-‘. The In coverage 8 at any given time t can be obtained by integration between the curves corresponding to JI, and Jdes from the time t, at which the shutter is opened to t: e=

‘(J~~-J~_) J [II



For the spectrum in fig. 4, the saturation coverage 6’,,,, which is reached when the incoming flux equals the desorbing flux, was 0.04 ML. This spectrum could be fitted well (as shown) with the following equations which describe first-order desorption from a single phase: Jdes=Jln{l-exp[-k,(t-to)]}



for t > t,,


where t, is the time at which the shutter was closed and k, is the desorption rate constant. From plots of ln( J,, - Jdes) versus t for t < t, and ln( Jdes) versus t for t > t, (also shown in fig. 4), we obtain k, = 0.61 as the absolute value of the slope. According to transition-state theory for first-order rate processes [ll], k, can be related to T, as k, = v1 exp( -Q/kT,),


J. Km11 et al. / Adsorption

and desorption kinetics of In on Si(100)

Fig. 4. Desorbing in flux Jdes, from a Si(lO0) surface maintained at Ts = function of time t during a modulated-beam experiment. The dashed curve In flux J,,. A calculated curve based upon the model presented in section lower part of the diagram shows corresponding plots of ln( J,, - Jdes) and


680 o C, plotted as a shows the impinging 4 is also shown. The ln( Jdes) versus 1.

where v1 is a preexponential factor that depends on the entropy change associated with desorption and E, is the desorption activation energy. A series of MBD spectra were recorded at T, between 640 and 71O’C and k, was obtained from the part of the spectra corresponding to B < 0.07 ML. The results are plotted, as ln(k,) versus l/T,, in fig. 5 from which we obtain E, = 2.8 f 0.2 eV and ZJ,= 3 X lo’“*’ s-‘.


Fig. 5. Desorption

SubstrateTemperature,Ts PC) 680 I 1 660 ( 700 ,I ,

720 II

rate constant


for In on Si(lO0) versus coverages B < 0.07 ML.

640 I




at In


J. KnaN et al. / Adsorption

and desorption kinetics of In on Si(lO0)

Time, t (s)

Fig. 6. Desorbing In flux Jdes from a Si(lO0) surface, maintained at 7” = 650 ’ C, as a function of time t during a modulated beam experiment. The dashed curve shows the impinging In flux J,, and the arrows indicate points at which 6’ = 0.07 ML. A calculated curve based upon the model presented in section 4 is also shown. The lower part of the diagram shows corresponding plots of ln( J,, - Jdes) and ln( Jdes) versus t.

When T, was decreased and/or JI, increased to yield 0,,, > 0.07 ML, the full spectra could no longer be fitted with eqs. (3a) and (3b). The spectra exhibited an abrupt change in slope at 8 = 0.07 ML which was particularly noticeable in the plots of ln( Jdes) and ln( J,, - Jdes) as shown for a typical example in fig. 6. This behaviour is indicative of the formation of a second 2D phase, with a slightly lower desorption coefficient, which starts to nucleate at 8 = 0.07 ML and progressively replaces the first 2D phase as B increases. According to the electron diffraction observations, the formation of the second phase resulted in a 3 X 4-In surface reconstruction. The surface overlayer morphology is depicted schematically in fig. 7. Spectra similar to that shown in fig. 6 were obtained for all In deposition conditions leading to 0.07 < 8,,, < 0.5 ML. MBD spectra recorded under conditions corresponding to 0,,, > 0.5 ML exhibit a rapid increase in desorption rate as t9 exceeded 0.5 ML (see, for example, fig. 8). This is evidence of the accumulation of In in sites for which the In binding energy is significantly smaller than in the first two phases. As T, was decreased and/or J,, increased even further, conditions were reached for which the steady-state value of Jdes was lower than JI,. Thus there was a continuous accumulation of In and Jdes became independent of 8. By integration of spectra, obtained at T, = 530-560 “C and J,, 2 0.04 MLs-‘, such as the example shown in fig. 9, Jdes was found to saturate when 8 reached - 0.7 ML. The AES results presented in the previous section showed that In

J. Knall et al. / Adsorption In on Z-D

and desorption kinetics of In on Si(100)



C0ver0ge.e (ML)

In Gas (PJmse

1) t?
L,,,/,//,, 3x4


2-DInGas :

,/ /,,,,,,,,/, 3X4tPhase






In Gas 0.7<8<1.5


Disordered 1.5
Fig. 7. Schematic


of the morphology

of In overlayers

as a function

of coverage

0 on

Si(100) at Ts > 450 o C.

was present on the surface in a 2D layer up to coverages > 1.5 ML for T, > 450 o C. Combining the two results indicates that under these conditions, In desorption occurs with zeroth-order kinetics from a 2D adlayer. Zeroth-order desorption is generally associated with thick deposits consisting of bulk-like multilayers. However, zeroth-order desorption has also been reported for 2D sub-monolayer coverages of, for example, Au [12] and Ag [13] on Si as well as I












Fig. 8. Desorbing In flux Jdes from a Si(100) surface, maintained at Ts = 630 o C, as a function of time during a modulated beam experiment. The dashed curve shows the impinging In flux J,, and the arrows indicate points at which 0 = 0.07 and 0.5 ML. A calculated curve based upon the model presented in section 4 is also shown.


J. KnaNet al. / Adsorptionand desorptionkineticsof In on Si(lO0)

f”(5&30’ -G > 0.04










Measured _ Calculated



Fig. 9. Desorbing In flux Jdes from a Si(lO0) surface, maintained at Z’s = 540 ’ C, as a function of time during a modulated beam experiment. The dashed curve shows the impinging In flux J,, and the arrows indicate points at which ~9= 0.5 and 0.7 ML. A calculated curve based upon the model presented in section 4 is also shown.

of Xe on graphite [12]. The latter three results were explained by assuming that islands of one 2D phase coexist in equilibrium with a 2D gas and that most of the desorption occurs from the 2D gas which contains an essentially constant amount of adsorbed atoms. In the present case of In on Si(lOO), the diffraction experiments suggest that regions of a disordered In phase gradually replace the 3 x 4 phase at coverages between 0.5 and 1.5 ML. The rapid increase in Jdes at 8 = 0.5 ML thus indicates that a 2D gas (phase 3) with a lower binding energy is formed on top of the 3 X 4 structure before 2D islands of the more dense disordered phase are nucleated within the 3 X 4 structure at 8 = 0.7 ML. The 2D gas on the 3 X 4 structure then remains in equilibrium with the dense disordered phase while the latter replaces the 3 x 4 phase with increasing coverage leading to the observed zero&order desorption at coverages between 0.7 and 1.5 ML. This situation is illustrated schematically in fig. 7. At coverages exceeding - 1.5 ML and T, > 450” C, 3D islands were formed as indicated by the leveling off of the Auger signal. For the desorption spectrum in fig. 10, 0 reached - 2 ML before the In shutter was closed. Jdes increased slightly at 8 = 1.5 ML and then again became independent of 8. From the AES results, we conclude that the 3D islands occupy only a small fraction of the surface area and that the coverage between the islands remains essentially unchanged. The 3D islands are expected to be liquid as the temperatures in these experiments are well above the melting point of In (156OC). We interpret the zeroth-order desorption at 6 > 1.5 ML as corresponding to 3D In islands existing in equilibrium with the 2D In layer

J. KnaN et al. / Adsorption and desorption kinetics of In on Si(1 WI)








Fig. 10. Desorbing In flux Jaw from a Si(lO0) surface, maintained at T.. = 530 o C, as a function of time during a modulated beam experiment. The dashed curve shows the impinging In flux J,, and the arrows indicate points at which 0 = 0.5,0.7 and 1.5 ML.

surrounding the islands. The 3D islands act as a reservoir, supplying material to the 2D layer during desorption and maintaining the coverage in the 2D layer constant, while desorption occurs primarily from the 2D layer. We believe that the slight drop in Jdes which occurs when J,, is set equal to zero by closing the effusion cell shutter (see fig. 10) is due to a corresponding change in the coverage of the 2D layer. 3.3. Temperature programmed


TPD spectra were obtained by depositing an initial In coverage 8, at T, -c 300 o C and then increasing T, at a controlled constant rate. Fig. 11 shows typical TPD spectra recorded with dT,/dt = 10 o C/s for initial coverages between 0.25 and 3 ML. All spectra with 8, > 1.5 ML initially followed the same Jdes versus T, curve until 8 decreased to 1.5 ML where a small break occurred and the spectra shifted over to follow another common Jdes versus T, curve (indicated in the figure by a dotted line) with a lower desorption rate. Spectra with 0.7 < 0, < 1.5 ML followed the lower Jdes versus T, curve from the start. These results are consistent with the MBD and diffraction observations of zeroth-order kinetics due to the presence of 3D islands at 8 > 1.5 ML and zeroth-order desorption at a slightly lower Jdes at 0.7 < 8 < 1.5 ML. A plot of ln(J,,,) versus l/T, was obtained from the leading edge of the low temperature peak, for spectra with 13,> 1.5 ML. The slope of this plot gave an activation energy of 2.5 eV for desorption from a surface with 3D islands coexisting with a 2D layer.


J. KnaN et al. / Adsorption

and desorption kinetics of In on Si(100)

90.3 5 . 5 c 0.2 F 0 0.1 b 6 a 0 450










Fig. 11. Temperature-programmed desorption spectra obtained by increasing the substrate temperature Ts at a constant rate of dT,/dt = 10 o C after deposition of an initial In coverage 8, of between 0.25 and 3 ML on a Si(100) surface. The symbols indicate the points at which the In coverage has decreased to 1.5 and 0.7 ML.

When 6 decreased below 0.7 ML, the 2D gas on top of the 3 x 4 phase started to become depleted leading to a rapid decrease in .I+... Eventually, for B < 0.5 ML, desorption from the 3 x 4 phase (phase 2) and the low coverage 2D-gas (phase 1) became dominant. Desorption from phases 1 and 2 gave rise to the high temperature peak. The fact that this peak appeared at a considerably higher T, shows, in agreement with the MBD results, that these phases have significantly higher desorption energies than the phases that form at higher coverages.


-y-4 d 7 I c 2-6c

7 $

_ : * 3, 0


. .*


. : . *. *

k 15



t ‘?s)

Fig. 12. Desorbing In flux Jdes from a slightly contaminated Si(100) surface, maintained at Ts = 690 o C, as a function of time during a modulated beam experiment. The dashed curve shows the impinging In flux J,, and the arrows indicate the points at which 0 = 0.02 ML.

J. hall

et al. / Adsorption and desorption kinetics of In on Si(100)


3.4.Effects of surface contamination The first preliminary desorption experiments were carried out using a newly fabricated substrate holder which was not properly outgassed. Thus it was not possible to obtain clean sample surfaces. Plots of In{ J&) and ln( Jr, - J&) versus desorption time corresponding to MBD spectra from these surfaces exhibited a break at - 0.02 ML, as shown in fig. 12. The slope of these curves decreased at coverages less than 0.02 ML indicating a lower desorption rate constant. The effect of contamination was also observed in the TPD spectra as a small tail on the high temperature side of the high temperature peak. These features disappeared after proper system outgassing. We conclude that the presence of surface conta~nation increased the In binding energy for a small amount of surface In.

4. Desorption mode1 and calculations of desorption spectra From the results presented in the previous sections, it is possible to construct a model of the initial growth of In on Si(lO0). The various stages of growth at T, > 450” C are shown schematically in fig. 7. In this section, we describe the mathematical formulation of a model used to calculate desorption spectra which succesfully fit the experimental data. The desorption rate for adatoms that desorb independently of each other from a single type of binding state varies linearly with the coverage 8. This situation occurs for In on Si(100) at In coverages below 0.07 ML when only a 2D gas is present on the surface. In this case, the desorption flux can be written as Jdes = ok, = 8v, exp( - E,/KT,).


This leads directly to the expressions in eqs. (3a) and (3b) for J& versus t during an MBD experiment. The fit to experimental data is shown by the typical results in fig. 5 to be excellent. E, and v, were determined to be 2.8 rt 0.2 eV and 3 x 10i4*‘, s-l, respectively. For 8 > 0.07 ML, In is present on the surface in more than one phase. Assuming first-order desorption from each phase, the differential equation that governs the total surface coverage B can be written as [email protected]/dt = ~J&s,i i


= j&f~?~ + Jr,, i


where ki is the desorption constant for desorption from phase i and t9, is the amount of In, expressed in ML, in that phase. In order to use eq. (6) to calculate desorption spectra, it is necessary to also describe the exchange of


J. KnaN et al. / Adsorption

and desorption kinetics of In on Si(100)

material among the surface phases. The general situation when three surface phases coexist with the gas phase can be illustrated by the following scheme: -k3-

Phase 3


Gas Phase


Phase 2

Phase 1



From the data presented in sections 3.2 and 3.3, it appears that for coverages between 0.07 and 0.7 ML the relatively dense 3 x 4 phase coexists with less dense 2D gases on the surface surrounding the 3 X 4 islands and on top of the islands. We will first consider the general case in which phase 2 consists of 2D islands with relatively high density and phases 1 and 3 are less-dense 2D gases on the surface surrounding the islands and on top of the islands, respectively. Thereafter we will apply the resulting equations to the case of In on Si(100). The total surface coverage contained in phase i is given by 0, = p,Ai, where p, is the local surface coverage of phase i and A, is the fraction of the surface covered by phase i. It is assumed that phases 1 and 2 together cover the surface completely and that phase 3, the 2D gas on top of phase 2, covers the islands completely. The desorbing flux is then given by the following set of equations: A, =Aj,





+ PzA2

+ P3A3

Jiz?, = k,P,A,

Combining J

+ k,P,A,

+ k,p,

(7c) (74

+ k,P,A,.

these equations

= k,p, des

= 0,

- kpi

and solving 8 + P,Pz(k,



- kz) + P,Px(k,


P2 + P3 -






- k3)



To illustrate some general features of eq. (8) we consider the simplified case for which p3 is negligible. This leads to the following equation for desorption from dense 2D islands coexisting with a surrounding 2D gas, J



k,p, - k,p, P2 -




p,p2(k,- k2) Pz-Pl



If only one surface phase (e.g. the low-density

phase 1) is present



= 0,

J. KnaN et al. / Adsorption

and desorption kinetics

of In on Si(lO0)


eq. (9) reduces to Jdeb = k,B as required. When the islands of the higher-density phase 2 are nucleated at 8 = 19,, pZ will be introduced in eq. (9) with a value ~~(8~) > p,(f&). If the supersaturation required to nucleate phase 2 is negligible, A,, A,, and p, will be continous through f3, which implies that Jdes will also be continuous at 0,. When the exchange of material between the two surface phases occurs along the perimeter of the islands, the rate of material exchange will be governed by equations of the type J,2 = k,,p,A’; and J,, = k,,pzA; (x = l/2 when the islands grow isotropically and the number of islands is constant) for the flux from phase 1 to 2 and 2 to 1, respectively. The equation of mass balance for phase 1 then becomes d(piA,)/dt


J&I - Jdes.1 - Jn + JZI.

Since the activation energy than the desorption energy, will be much larger than experiment. Thus, we can and pZ will be independent order of the total desorption


for surface diffusion is generally significantly lower the rate of exchange between the surface phases the other terms in eq. (10) during a desorption make the approximation J12 = J,, and, hence, p1 of 8. With respect to eq. (9), this implies that the process will depend on the sign and magnitude of


(Q, - +,)/(p, - P,). When K is positive, eq. (9) leads to first-order desorption with the desorption rate constant K. Setting K = 0 (or K much smaller than the second term in eq. (9)) makes Jdes independent of 8, i.e. leads to zeroth-order desorption. A negative K results in Jdes decreasing with increasing 8. A situation in which K is negative (i.e. k,p, > k,p,) can only occur when p1 is maintained high by an incoming flux from the vapor phase and when k, > k, due to a strong adatom-adatom attraction. This type of situation has been observed for Au and Cu on graphite [14]. In the present case of In on Si(lOO), eq. (9) provides a good description of the desorption behavior at 8 < 0.5 ML assuming that only phase 1 is present at B < 0.07 ML and only phases 1 and 2 are present at 0.07 I 0 < 0.5 ML. At 0.5 < 8 < 0.7 ML Jdes could be qualitatively described by only accounting for the presence of phase 2 and 3. Jdes is then given by Jdes = 0.5k,

+ (0 - 0.5)k,.


However, a much better quantitative agreement between the experimental data and calculated curves over the entire range from 0.07 to 0.7 ML was obtained by taking into account that all three phases coexist at B > 0.07 ML and using the full equation set (7a)-(7d) (see, for example, fig. 8). At 0 2 0.07 ML, p, was taken to be constant at 0.07 ML, full coverage of phase 1, while p2 was set equal to 0.5 ML, which from electron diffraction results was found to be full coverage of phase 2. p3 was determined by the rates Jz3 and J32 at which In atoms are exchanged between phases 2 and 3. Jz3 is proportional to the


J. Knall et al. / Arlsorption and desorption kinetics

of In

on Si(IO0)

Table 1 Parameter values used in the model calculations E, = 2.8 f 0.2 eV E, = 2.85 f0.2 eV

E, = 2.45 to.2 eV

Y, = 3xlO’4*1 s-1 P,=3x10’4*‘s-’ v3=9x10’3*‘s-’

p, = 0.07 & 0.005 ML pz = 0.5 + 0.05 ML kz,/k,z = 0.0002

amount of In in phase 2, A+,,

while J32 is proportional to the product of the amount of In in phase 3, AZ+, and the number of free positions on the substrate which is, in turn, proportional to A,. Assuming that the rate of exchange of material between different phases on the surface is large compared to the desorption and deposition rates, we can, as discussed above, set JZ3 equal to J32, which leads to the following set of equations:

Jm = k,,p,& >

(124 (Qb)

J23 = J32-


The above expressions for Jx3 and J32 give a correct description when A, is small and lead to the observed rapid increase in p3 as A, aproaches zero at 0 = 0.5 ML. With the parameters used to fit our experimental data (see table l), the difference between Jdes values obtained using eqs. (7a)-(7d) and those obtained from eq. (9) in combination with eq. (11) is only important at coverages in the vicinity of 0 = 0.5 ML. This is due to that p3 is very small (< 4 x 10V4) at t9 < 0.4 ML and that A, is small (< 10e3) at ti > 0.6 ML. We have not accounted for the presence of phase 3 interfering with desorption from phase 2. However, since phase 3 has a much higher desorption rate coefficient, desorption from this phase will completely dominate the total flux by the time the coverage of phase 3 becomes large enough to affect to desorption rate from phase 2. Thus, including an interference of this type will not si~ific~tly alter the calculated desorption spectra. At higher coverages, 0.7 < 6 < 1.5 ML, zeroth-order desorption was observed from an overlayer consisting of a disordered 2D phase coexisting with a 2D gas (phase 3) on top of the 3 X 4 phase as shown schematically in fig. 7. At these total coverages, phase 3 has reached its saturation partial coverage, p3 = 0.2 ML, and the desorption rate from this phase is much higher than that from the 3 x 4 phase. Thus desorption from the 3 X 4 phase can be neglected and the situation corresponds to that described by eq. (9) with a K-value near zero. In our model calculations, the desorption rate for 0.7 -C8 < 1.5 ML was simply maintained constant at the value corresponding to 6 = 0.7 ML (see fig. 9). No attempts were made to fit spectra at 0 > 1.5 ML. All parameters used in fitting the MBD spectra are listed in table 1. The observed difference between k, and k, is, in general, expected to be due to

J. KnaN et al. / Adsorption and desorption kinetics of In on Si(lO0)


changes in both v and E. In fact, it has been observed in several studies that compensation occurs [15], i.e., a decrease in E is accompanied by a decrease in v, when one overlayer phase replaces another. However, since the difference between k, and k2 was rather small, it was not possible to separate out the contribution from changes in E and v by fitting MBD spectra over a limited range of temperatures (600-710” C). In analyzing the data, we therefore assumed that the preexponential factors were the same for phases 1 and 2. The temperature dependence of the ratio k,,/k,, could not be determined since the ratio itself is quite small and only provides a small correction to the part of the spectra that corresponds to coverages near 0.5 ML. The fact that k,,/k,, is small shows that the 3 X 4 layer is essentially complete before any significant amount of In is contained in the third phase. It was furthermore observed that MBD spectra with 19> 0.5 were slightly asymmetric (see, for example fig. 8) and that a better fit between experimental and calculated results on the rise part of the spectra near 8 = 0.5 ML could be obtained by increasing the ratio k,,/k,, when J,, # 0. We interpret this as an inaccuracy in the assumption that Jz3 = J3* in eq. (12~). That is, the coverage in phase 3, p3, is affected by the incoming and desorbing fluxes. A more correct approach would be to use an expression similar to eq. (10) for mass balance of phase 3. This, however, leads to greatly increased computational difficulties and k,, and ks2 become independent fitting parameters. TPD spectra were also calculated using the above model. An example of experimental and calculated spectra with 8 = 1.5 ML is shown in fig. 13. The parameter values given in table 1 were used for the calculation and the fit is remarkably good over the entire spectrum. The observed influence of a small amount of surface conamination was simulated by including desorption from a corresponding density pc of binding

dT /dt = lO”C/s

.****** Measured Calculated











Fig. 13. Temperature-programmed desorption spectrum obtained by raising the temperature linearly at a rate of 10 o C/s from 450 to 800 ’ C after deposition of 1.5 ML In on Si(100). A calculated spectrum based on the model presented in section 4 is also shown.


J. KnaN et al. / Aclsorption and desorption kinetics of In on Si(lO0)

sites with binding energy EC and preexponential factor v,. These sites were considered to be filled when 0 2 p,. Setting vc equal to v,, EC was found to be 0.05 eV higher than E,. The MBD spectrum shown in fig. 12 was calculated using p, = 0.02 ML. 5. Discussion Structural studies, using surface electron diffraction, of thin metal overlayers on Si have been performed for a large number of metals. However, only a very limited number of such studies have been combined with measurements of adatom binding energies. One reason for this is that the extraction of quantitative information from desorption experiments is not always straightforward. This is especially true when there are several coexisting phases. Early desorption investigations of gases on solids often relied on a spectrum-evaluation method which assumed no interaction among different overlayer phases [16-181. However, in the case of metals on semiconductors, interacting overlayer phases are often encountered. An early model for desorption from interacting phases was presented by Arthur [19] for Zn on GaAs. This concept has been further developed by Le Lay et al. [12] in studies of Au on Si and by Opila and Gomer [20] for Xe on W. Such analyses reveal important information about the kinetic processes that govern the structure and formation of overlayer phases. Present theoretical models predict that the film growth mode in a given desorption experiment depends on the ratio s2 OS the adatom/substrate to adatom/adatom interaction strengths [21-231, and the mismatch between bulk and film lattice constants [23]. Experimental results are generally classified into one of three categories [24]: (1) layer-by-layer growth (Frank-Van der Merwe, FM, or complete-wetting mode), (2) initial layer growth followed by 3D nucleation and growth (Stranski-Krastanov, SK, or incomplete-wetting mode), and (3) 3D nucleation and growth (Volmer-Weber, VW, or non-wetting mode). It has been observed in experiments involving noble and molecular gases on graphite [22], that complete-wetting occurs only over a narrow range in D with either incomplete-wetting or non-wetting occurring at lower D values and incomplete-wetting also occurring in systems with higher W values. In several cases, a transition from incomplete-wetting to complete wetting was observed at the bulk triple point of the adsorbate [25]. However, such a wetting transition has also been observed for CF, on graphite at a temperature far below the bulk triple point [26]. Most metal/Si systems studied up to now exhibit either a SK or VW behavior. The situation for Ga is somewhat unclear. Although convincing evidence of ordered 2D layers of Ga on both Si(100) and (111) surfaces have been presented [27,28], there are also reports of evidence for non-wetting of Ga on both Si(lO0) [29] and Si(ll1) [29,30].

J. KnaN et al. / Adsorption and desorption kinetics of In on Si(100)


Binding energies for In on Si(100) have not previously been measured. However, for In on Si(lll), E values between 2.55 and 2.7 eV [31,32] have been reported for coverages below 1 ML. Results from our previous work on the morphology of In/Si(lOO) [9] have shown that In grows according to a SK mode, both above and below the melting point of bulk In. The present work demonstrates that In in the initial 2D layer has a binding energy of - 2.8 eV which is a factor of 1.1 larger than the enthalphy of evaporation of bulk In, AH,, = 2.47 eV [33] (i.e. s2 > 1). However, for In desorption from a surface on which 3D islands coexist with a 2D layer (19> 1.5 ML), an activation energy of - 2.5 eV (see section 3.3) which is approximately equal to AH,,, was obtained. These relations between the binding energies and AH,, are consistent with the observation of SK growth mode. Moreover, the coexistence of several In surface phases at 0.7 < 0 < 1.5 ML leads to zeroth-order desorption while at 0.7 < 8 < 0.7 ML, the desorption kinetics are first-order. Apart from a fundamental interest in the kinetics of metal condensation on Si, a prime motive for this study was to obtain detailed information about the surface residence time, 7, of In on Si(100) versus 19 and T, in order to investigate the relationship between 7 and the incorporation probability of In during Si MBE growth. In ref. [8], r-values, calculated from the model presented here, have been used to interpret data for incorporation of In by recoil implantation during Si MBE growth and to calculate values of the effective cross-section of recoil implantation.

Acknowledgments The authors gratefully acknowledge the financial support of the Swedish Natural Science Research Council (NFR), the Joint Services Electronics Program (USA), and the Semiconductor Research Corporation (USA) during the course of this work.

References [l] R.A. Metzger and F.G. Allen, J. Appl. Phys. 55 (1984) 931. [2] G.E. Becker and J.C. Bean, J. Appl. Phys. 48 (1977) 3395. [3] J. Knall, J.-E. Sundgren, J.E. Greene, A. Rockett and S.A. Barnett, Appl. Phys. Letters 45 (1984) 689. [4] J. Knall, J.-E. Sundgren, L.C. Markert, A. Rockett and J.E. Greene, J. Vacuum Sci. Technol. B, in press. [S] R.A.A. Kubiak, W.Y. Leong and E.H.C. Parker, Appl. Phys. Letters 46 (1985) 565. [6] H. Jorke, H.-J. Herzog and H. Kibbel, Appl. Phys. Letters 47 (1985) 511. [7] S. Delage, Y. Campidelli, F. Amaud d‘Avitaya and S. Tatarenko, J. Appl. Phys. 61 (1987) 1404. [8] J. Knall, J.-E. Sundgren L.C. Markert and J.E. Greene, Surface Sci., in press.


J. KnaN et al. / Aabrption

and desorption kinetics of In on Si(IO0)

[9] J. KnaIl, J.-E. Sundgren, G.V. Hansson and J.E. Greene, Surface Sci. 166 (1986) 512. [lo] M.-A. Hasan, J. Knall, S.A. Barnett, A. Rockett, J.-E. Sundgren and J.E. Greene, J. Vacuum Sci. Technol. B 5 (1987) 1332. [ll] S. Glasstone, K.J. Laidler and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 1941). [12] G. Le Lay, M. Manneville and R. Kern, Surface Sci. 65 (1977) 261. [13] G. Le Lay, M. Manneville and R. Kern, Surface Sci. 72 (1978) 405. [14] J.R. Arthur and A.Y. Cho, Surface Sci. 36 (1973) 641. [15] P.J. Estrup, E.F. Greene, M.J. Cardillo and J.C. Tully, J. Phys. Chem. 90 (1986) 4099. [16] G. Carter, Vacuum 12 (1962) 245. [17] P.A. Redhead, Vacuum 12 (1962) 203. [18] G. Ehrlich, J. Appl. Phys. 32 (1961) 4. [19] J.R. Arthur, Surface Sci. 38 (1973) 394. [20] R. Opila and R. Gomer, Surface Sci. 112 (1981) 1. [21] R.J. Muirhead, J.G. Dash and J. Krim, Phys. Rev. 29 (1984) 5074. [22] M. Bienfait, J.L. Seguin, J. Suzanne, E. Lerner, J. Krim and J.G. Dash, Phys. Rev. 29 (1984) 983. [23] M.H. Grabow and G.H. Gilmer, Surface Sci. 194 (1988) 333. [24] R. Kern, G. Le Lay and J.J. Metois, in: Current Topics in Materials Science, Vol. 3, Ed. E. Kaldis (North-Holland, Amsterdam, 1979). [25] J. Krim, J.G. Dash and J. Suzanne, Phys. Rev. Letters 52 (1984) 640. [26] J. Suzanne, J.L. Seguin, M. Bienfait and E. Lerner, Phys. Rev. Letters 52 (1984) 637. [27] T. Sakamoto and H. Kawanami, Surface Sci. 111 (1981) 177. [28] D. Bolmont, P. Chen, C.A. Sebenne and F. Proix, Surface Sci. 137 (1984) 280. [29] M. Zinke-Allmang and L.C. Feldman, Surface Sci. 191 (1987) L749. [30] F.G. Allen, S.S. Iyer and R.A. Metzger, Appl. Surface Sci. 11/12 (1982) 517. [31] T.A. Nguyen Tan, Surface Sci. 43 (1974) 562. [32] S. Baba, M. Kawaji and A. Kinbara, Surface Sci. 85 (1979) 29. [33] R. Hultgren, R.L. Orr, P.D. Anderson and K.K. Kelley, Selected Values of Thermodynamic Properties of Metals and Aloys (Wiley, New York, 1963).