Iron precipitation in float zone grown siliconWorth B. Henley and Deepak A. Ramappa Citation: Journal of Applied Physics 82, 589 (1997); doi: 10.1063/1.365861 View online: http://dx.doi.org/10.1063/1.365861 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/82/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Competitive gettering of iron in silicon photovoltaics: Oxide precipitates versus phosphorus diffusion J. Appl. Phys. 116, 053514 (2014); 10.1063/1.4892015 Effects of crystal defects and their interactions with impurities on electrical properties of multicrystalline Si J. Appl. Phys. 113, 133503 (2013); 10.1063/1.4798600 The impact of Ge codoping on the enhancement of photovoltaic characteristics of B-doped Czochralski grown Sicrystal J. Appl. Phys. 111, 043707 (2012); 10.1063/1.3687935 The effect of oxide precipitates on minority carrier lifetime in p-type silicon J. Appl. Phys. 110, 053713 (2011); 10.1063/1.3632067 Surface photovoltage analysis of copper in p -type silicon Appl. Phys. Lett. 72, 2298 (1998); 10.1063/1.121341

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Iron precipitation in float zone grown siliconWorth B. Henleya) and Deepak A. RamappaCenter for Microelectronics Research, University of South Florida, Tampa, Florida 33620

~Received 13 February 1997; accepted for publication 8 April 1997!

Temperature dependent iron precipitation in float zone grown silicon wafers has beenexperimentally investigated. Results of iron precipitation experiments over a wide thermal processtemperature range and time are presented. Precipitation of iron in silicon was analyzed by aquantitative assessment of change in interstitial iron using a surface photovoltage minority carrierlifetime analysis technique. Contamination levels of iron in the range 1011–1013 atoms/cm3 areinvestigated. It is concluded that maximum iron precipitation occurs in the temperature range of500–600 °C. Iron precipitation is rapid in this region where more than 90% of the interstitial ironprecipitates in a period of 30 min. ©1997 American Institute of Physics.@S0021-8979~97!01714-3#

INTRODUCTION

Metallic transition elements are prevalent contaminantsin Si which can degrade device performance either by form-ing metal silicides or/and by acting as recombination centers.Iron is one of the primary heavy metal impurities in silicon.This is most probably due to the prevalence of stainless steelequipment in the fabrication line. Commonly reportedsources of iron contamination include ion implanters, con-taminated chemicals, and wafer handling tools. Iron diffusesrapidly through the silicon matrix by interstitial diffusion.Because of the high diffusivity~;1026 cm2/s at 900 °C!1

iron contaminates introduced from the wafer surface duringthermal processing diffuse throughout the bulk of the wafer.The steep, retrograde temperature dependence of iron solu-bility in Si ~Ref. 1! results in supersaturation during wafercooling from high process temperatures. This supersaturationis responsible for localized precipitation.

Iron plays an important role in the decoration of defectsin silicon.2–5This can be very detrimental to device region ofthe wafer, as strain fields and process induced defects canlocalize the Fe impurities in this sensitive area.6 It is wellaccepted that iron contamination degrades gate oxide integ-rity and decreases yield as devices are scaled to sub-microndimensions.7 Unprecipitated iron remains as the interstitialdeep level impurity Fei or as Fe–B pairs inp-type silicon. Itreduces minority carrier lifetime and increases diffused junc-tion leakage.

Generally for contamination levels of practical concern,at temperatures below 800 °C the Fe–Si system is metastableand thermodynamically favors iron-silicide precipitation.The iron solubility limit in silicon at 500 °C is about 23107 atoms/cm3. Since the best commercially available wa-fers today typically contain 53109 atoms/cm3 of iron, thefact that iron supersaturation and precipitation can occur area matter of general concern to the technologist.

The tendency for iron precipitation to occur is influencedby the amount of time for nucleation and embryo growthbefore the lower silicide reaction~formation! temperature isreached. This is illustrated in Fig. 1, which shows the tem-

perature cycle of a typical anneal or oxidation process. Pre-viously reported lower silicide temperatures vary between300 and 500 °C.8,9 Iron-silicide (FeSi2) precipitation favorsheterogeneous nucleation.10 This can be useful for some in-ternal gettering procedures as oxygen precipitates may serveas favored precipitating sites. It has also been shown that theinternally gettered iron is often not the precipitate phase.11

Redissolution of the FeSi2 phase or release of getteredatomic iron11 remains hazardous to the surface device area.

Fe precipitation in Si has been previously studied inhighly contaminated silicon @1014–1016 Fe atoms/cm3#10,12–15 and in the lower temperature range of100–300 °C.8,16 In this article we present an experimentwhich, quantitatively evaluates Fe precipitation in lightlycontaminated Si~1011–1013 Fe atoms/cm3! which is morerelevant to present day industrial standards. Low oxygencontent, float zone~FZ! grown silicon crystals were used inexperimentation, so as to avoid the uncertainties introducedby O2 precipitation and the consequent gettering uncertain-ties. Precipitation over the entire temperature range of 300–900 °C over different process times have been experimen-tally evaluated.

To analyze precipitation of iron in silicon, quantitativeinterstitial iron (Fei) concentration measurements were per-formed using the technique of surface photovoltage~SPV!minority carrier lifetime analysis. The SPV method has verygood sensitivity in detecting low concentrations of bulk Fei

in the silicon wafer.7 Interstitial Fe concentrations are mea-sured before and after a precipitation anneal. Any decrease inFei is assumed to be due to formation of the FeSi2 precipitatephase. This change in interstitial Fe (DFei) is used to ana-lyze the iron precipitation quantitatively with respect to timeand temperature. A characteristic relationship between theprecipitating iron and annealing time over the entire processtemperature range is deduced.

EXPERIMENT

The experiment can be broadly analyzed in two stages.First iron was diffused from a surface source into the wafer,to obtain a stable and uniform Fei concentration in the wafer.Following the in-diffusion, the iron rich surface region wasa!Electronic mail: henley@cmd.usf.edu

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chemically removed and various anneals were performed.Iron precipitation was monitored by comparing the change ininterstitial iron after the thermal anneal process.

The experimentation was performed using 3 in. 1–2V cm, p-type FZ grown ^100& wafers ~Wacker–Chemitronic!. Starting wafer background iron concentrationwas determined to be 431010 atoms/cm3. The samples werecleaned in the order HF–SC1–HF–SO2–HF where the HFwas diluted with water in the ratio 1:50. SC1 was a 1:2:10solution mixture of ammonium hydroxide, hydrogen perox-ide, and water heated to a temperature of 65 °C. SC2 was a1:1:5 solution mixture of hydrochloric acid, hydrogen perox-ide, and water maintained at 65 °C. The background level ofiron contamination from the starting wafers, cleaning proce-dure, and subsequent furnace processing was established tobe about 631010 atoms/cm3 at 900 °C. Thus the wafer pro-cessing procedure introduced about 231010 atoms/cm3 ofFei into the samples. This is typical after a high temperaturethermal process.

Selected samples were intentionally doped with iron byimmersion in a 100 ppm solution of ferric chloride (FeCl3)for 10 min and then nitrogen blowdried. By coating thesample this way, a source of Fe on both surfaces of thesample was established.

Iron concentration in the doped samples was set usingknown iron solubility relationships.1 To obtain a target Feiconcentration of 231013 atoms/cm3 a diffusion temperatureof 900 °C was used according to Fe solubility data.1,15 Theiron in-diffusion was performed in a horizontal diffusion fur-nace. The wafers were slowly ramped up to minimize latticedeformations and defect sites. The wafers were diffused for40 min in a nitrogen ambient. After the in-diffusion heattreatment the samples were quench cooled by blowing coolnitrogen vapors onto the surface during withdrawal from thefurnace. Other techniques and materials of quench coolingsuch as oil immersion, di-ethylene glycol, and water wereevaluated but dismissed as they caused a significant amountof thermally induced lattice damage, which disrupted minor-ity carrier lifetime measurements. The nitrogen cooling

cooled the sample down from 900 °C to room temperature inabout 2 min. Such rapid cooling was performed to preventany unwanted precipitation and to ensure most of the ironremained in an interstitial state.

The surface of the samples was chemically etched toremove any Fe rich areas on the surface. The etchant was aconcentrated reagent mixture of nitric acid (HNO3), glacialacetic acid (CH3COOH), and hydrofluoric acid~HF! in theratio 6:1:1 @Dash etch17#. They were etched for 3 min toremove a surface layer of about 60mm.

Interstitial iron concentration (Fei) and the change inFei was monitored using a SPV minority carrier lifetimeanalysis technique. The SPV method is an analytical tech-nique for the measurement of minority carrier diffusionlength and thus lifetime of carriers in semiconductors. It pro-vides a fast, noncontact, noninvasive measurement. Iron con-centration was determined from the lifetime measurementsusing well known Fe–B pairing relationships outlined below.

Interstitial iron is a very effective minority carrier re-combination center, with an energy level1,18 of Ev10.4 eV(Fei). In p-type silicon, interstitial iron electrostatically pairswith boron dopant atoms to form weakly bonded Fe–B pairs.The donor-acceptor pair Fe–B has an energy levelEv10.1 eV and an electron capture coefficient of approxi-mately 1/12 that of Fei . The Fe–B pair is a weak complexand is easily dissociated by brief thermal or opticalactivation.13,19Optical activation was adopted to alleviate theambiguity problem in distinguishing between contaminantsFe and Cr.18,19,20 The samples were placed on a steel slabmaintained at 0 °C, and exposed to high intensity white light.The lamp was placed 12 cm s above the sample and care wastaken so as to keep the temperature of the wafer below50 °C. The energy level and electron capture cross-sectiondisparity between the Fe–B pair and Fei is used to determineiron concentration indirectly, by the well known Fei /Fe–Bpairing/lifetime relationships.20–22 Quantitative assessmentof iron concentration was determined by the relative changein diffusion length measured before and after optical disso-ciation by the empirical formula19,20

@Fei #~cm23!51.0531016@~1/L2

2!2~1/L12!#,

whereL2 andL1 are the diffusion lengths inmm, after andprior to optical dissociation respectively. The measurementwas made at 10 points across the wafer and care was taken tomeasure the same sites on the sample.

For the precipitation studies the measured samples wereannealed for different times and temperatures. The speci-mens were annealed in a nitrogen ambient over the tempera-ture range of 300–900 °C, for times of 5–90 min. All theexperimental specimens were cooled at a similar rate to keepthe cooling rate constraint as a nonvariant. Quantitative mea-surement of Fei of each sample was performed by the SPVtechnique. By comparing the pre-anneal interstitial iron con-centration to that following the anneal, the precipitated frac-tion was easily calculated.

RESULTS

The amount of Fe diffused into the silicon wafer fromthe surface contamination was chiefly a function of the

FIG. 1. Typical siliconI /C fabrication thermal cycle showing where nucle-ation and precipitation is most likely to occur.

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drive-in temperature and independent of the drive-in durationfor a drive-in time of greater than 15 min. Since both thedrive-in and anneal were performed in nitrogen ambients,oxide growth was avoided and thus prevented Fe from outdiffusing into the oxide.7 This was verified by ellipsometryon processed samples. For the 900 °C drive-in temperatureused here, the described intentional contamination procedureroutinely yielded silicon wafers with;231013 atoms/cm3

interstitial iron concentration in agreement with solubilityconsiderations.1 Wafer mapping showed the iron concentra-tion uniformity to be to be610%. The wafer etchback andpolish following the contaminate drive-in had no discernibleeffect on the measured diffusion lengths.

Noncontaminated control Si wafer samples processedwith the Fe doped wafers showed some degradation in dif-fusion length following the thermal drive-in process. This

was most likely due to the rapid quenching from the 900 °Cprocess resulting in a thermally induced native defect struc-ture. Typical diffusion lengths and the corresponding Fei

concentrations measured on the iron doped Si samples areshown in Table I. The Fei concentrations of all the iron con-taminated samples, averaged around 2.731013 Featoms/cm3. Iron concentration on the noncontaminated con-trol samples was typically 6.6231010 atoms/cm3.

The precipitation anneal experiments showed the changein post anneal interstitial iron concentration to be highly de-pendent upon the annealing temperature and time. Figure 2clearly shows that significant precipitation occurs over thetemperature range of 400–800 °C. The greatest loss of inter-stitial iron was seen in the range of 500–600 °C. Our abilityto discern changes in interstitial iron was limited to about the1011 atoms/cm3 range due to the background wafer defectstructure effects on the SPV measured carrier lifetime. Thus,we have been unable to clearly asses what occurs beyond the90 min annealing. It is evident that significant precipitationcan occur in the 500–600 °C process regime. A loss of morethan two orders of magnitude in interstitial iron is noted.Above a temperature of 800 °C, precipitation is much re-duced and redissolution of pre-existing precipitates or releaseof some previously gettered iron is observed which can resultin an increase in the final Fei concentration.

Figure 3 further illustrates the time/temperature precipi-tation tendencies of the iron-silicon system. Here the dra-matic effect of the process temperature is seen clearly. Fortemperatures above 700 °C, there is less effective solute su-persaturation and the chemical thermodynamics still supportthe combined presence of both interstitial iron and the pre-cipitate phase. Indeed, as mentioned above, our work showsthat at temperatures exceeding 900 °C, precipitate redissolu-tion can occur. This finding was confirmed by subjectingheavily precipitated samples to a 900 °C anneal. SubsequentSPV measurements always revealed an increase of the inter-

FIG. 2. Iso thermal precipitation anneal results. Annealing temperatures~a!300–500 °C and~b! 500–800 °C. Decrease in interstitial iron concentrationwith annealing indicates iron precipitation.

FIG. 3. Iso thermal precipitation curves shown as a function of temperature.Maximum precipitation occurs in the temperature interval of 500–600 °C.Average initial interstitial iron concentration measured on all samples was;2.631013 atoms/cm3.

TABLE I. Typical minority carrier diffusion lengths and interstitial ironconcentrations measured on clean and iron doped silicon after annealing andquench cooling.

SampleDiffusion length

~mm!Fei concentration(atoms/cm3)

Fe doped 44.2 3.863 1013

Uncontaminatedwafer

112.4 6.623 1010

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stitial iron of these re-annealed samples indicating precipitateredissolution.

Figure 3 also indicates that below 500 °C, conversion tothe precipitate phase is drastically reduced. At such lowertemperatures, although the degree of supersaturation is quitehigh, not enough thermal energy is available to support thechemical conversion to the precipitate phase. It is also pos-sible that the reaction becomes diffusion limited at lowertemperatures. Thus the silicon is left in the highly meta-stable, supersaturated condition. It is also observed that in-creased time at a given annealing temperature providesample time for the nucleating precipitate to grow and leadsto increase in precipitation. This is more so in the criticaltemperature interval of 500–600 °C, as is evident fromFig. 3.

ANALYSIS

From a closer observation of the results of the 500 °Cprecipitation anneal, shown in Fig. 4, it is clear that ironprecipitation in silicon can be differentiated into two distinctregimes. There is a steep loss of interstitial iron in the first 30min which is ascribed to simultaneous nucleation and growthof the iron precipitate phase~regime 1!. The second regime~regime 2! is a growth zone characterized by slower decreasein interstitial iron as a function of annealing time. Over aprocess duration of 90 min under the critical annealing tem-peratures of 500 and 600 °C, about 99% and 96% of theinterstitial iron, respectively, is converted to the precipitatephase.

Rapid precipitation in the first 45 min of annealing,~re-gime 1 of Fig. 4! can also be analyzed by the growth ofprecipitates unhindered by the interference between growingparticles due to the abundance of solute atoms. This regimedisplays a distinct transient characteristic. There is a notablechange of slope in regime 2 of the curve in Fig. 4. Thischange is because of the general depletion of solute atoms bythe precipitation reaction. Therefore there is an overall de-cline in the precipitation rate. This transition can also be

postulated to be due to the preferential growth of bigger pre-cipitates at the cost of smaller precipitate nuclei which redis-solve.

From general precipitation theory, a mathematical rela-tion used by Turnbull23 is adopted to quantitatively analyzethe relationship of precipitation of iron as a function of tem-perature and time to provide a better understanding of theprocess characteristics. The kinetic law of a diffusion limitedprecipitating system can be mathematically represented23–27

by the following equation for the initial phase of precipita-tion

x512exp@2~ t/t!n#, ~1!

wherex is the precipitated fraction of iron in timet, t is thecharacteristic decay constant, and the powern is the growthexponent. The numerical value of the exponentn has beencorrelated by Ham24,25 to the shape of the formed precipi-tates. It is 3/2 for diffusion limited grown spherical precipi-tates. A powern of 2 and 5/2 has been proposed for rod andplate shaped precipitates respectively.24,25

The loss of Fei concentration after an annealing processindicates iron precipitation. The difference in the measuredFei concentrations before and after the anneal is the concen-tration of precipitated iron@Cp#. Applying Eq. ~1! for thehomogeneous nucleation of precipitates,23–25 iron precipita-tion in silicon as a function of annealing time can be quan-titatively represented as:

C~ t !/C05exp@2~ t/t!n#, ~2!

whereC(t) is the SPV measured interstitial iron after smalltime t, C0 is the initial concentration andC(t)/C0 is theunprecipitated fraction of interstitial iron. The equation is

FIG. 4. Iron precipitation characteristic of the 500 °C anneal showing twodistinct regimes of precipitation.

FIG. 5. The concentration of precipitated iron is proportional to the decreasein the interstitial iron concentration.Cpa@C02C(t)#.

TABLE II. The slopes (n) and the decay constants~t! for the differentexperimental curves.

Annealing temperature~°C! 300 400 500 600 700@t# Decay Constant~min! 269.5 77.7 17.3 23.0 70.0@n# Growth exp.~slope! ••• 1.328 1.791 1.543 1.196

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subject to the validity of the assumption that the amount ofprecipitated iron,Cp is proportional toC02C(t) as is illus-trated in Fig. 5.

The value of the characteristic decay constantt for theiron silicide precipitation curve in Fig. 4, can be determinedby equating the annealing time t to the decay time constant inEq. ~2!. The calculated values oft for the different ironprecipitation anneals are listed in Table II.

Regime 2 of the curve in Fig. 4 represents the precipitategrowth regime. The numerical value of this slope@thegrowth exponentn in Eq. ~2!# has been correlated byHam24,25 to the shape of the growing precipitates. The char-acteristic slopesn ~growth exponent! of the various iron pre-cipitation curves are listed in Table II. The calculated slopesrange between 1.2 and 1.8 suggesting the formation ofspherical precipitates. This is reasonable considering thevery small nature of the embryo precipitates.

Iron precipitation experimental data compared to the the-oretical curves described by the characteristic precipitationequation~2! is shown in Fig. 6. According to Ham,24,25 Eq.~2! is valid for the initial phase~small t! of a diffusion lim-ited precipitation process. From the figure it is clear that theexperimental values agree with the theoretical representationuntil the completion of 50% of the reaction, thus satisfyingHam’s condition. Further the precipitating system is also ingood agreement with theory until about 90% of the intersti-tial iron precipitates.

CONCLUSION

From the results of the precipitation annealing experi-ment, it is concluded that maximum iron precipitation occursin the critical temperature interval of 500–600 °C. Iron pre-cipitation is rapid in this region where more than 90% of theinterstitial iron precipitates in a period of 30 min. It is alsoconcluded that the cooling rate of a thermal process over theinterval of 500–600 °C is critical and should be acceleratedin this region to hinder iron precipitation.

Iron is proposed to have precipitated in the form of het-erogeneously distributed, spherical iron silicide precipitates.

This is because of the lattice defect structure created duringthe quenching procedure of our experiment which providespreferred nucleation sites.b-FeSi2 is expected to be thephase of the silicide since it is formed at low temperatures~,900 °C!. During the initial precipitation phase, the rapidconversion of interstitial iron to the precipitate phase causesa transient behavior in the precipitation curve. The exponen-tial decay constant is a function of the system temperature.The precipitate formation is predominantly a precipitate in-terface reaction limited process. With the gradual depletionof interstitial iron in silicon the precipitation rate of iron insilicon decreases with annealing time. This is postulated tobe due to preferential and competitive precipitate growth.The precipitating fraction of interstitial iron for any giventemperature is independent of initial concentration of inter-stitial iron.

The solubility limit of iron at 550 °C maximum precipi-tation temperature! is ;53107 atoms/cm3. Thus it can beestimated accordingly, that even at small iron contaminationlevels like 109 atoms/cm3 ~present day industrial standards!about 95% of the interstitial iron will supersaturate and thusbe subject to precipitation. Iron precipitation in the deviceregion of silicon wafers often proves detrimental to deviceyield. It can be concluded from the above experiment that thecooling rate in the interval of 500–600 °C is critical for in-tegrated circuit manufacture. Cooling rapidly through thiscritical regime will decrease the overall amount of iron pre-cipitation. The implications for iron gettering processes arealso apparent. Gettering implies capture of isolated Fe atomsand conversion to some other form at the getter site. If theiron precipitates before it is gettered, gettering capture effec-tiveness is reduced. So iron precipitation should be avoided.

ACKNOWLEDGMENTS

The authors wish to thank Dr. Eicke Weber and Dr.Lubek Jastrzebski for numerous helpful suggestions andtechnical comment. This work is supported by the WaferEngineering and Defect Science Consortium.

1E. R. Weber, Appl. Phys. A30, 1 ~1983!.2Y. H. Lee, R. L. Kleinhenz, and S. W. Corbett, Appl. Phys. Lett.31, 142~1977!.

3E. R. Weber and H. G. Riotte, Appl. Phys. Lett.33, 433 ~1978!.4H. Fleichtinger, J. Waltl, and A. Gscwandtner, Solid State Commun.27,867 ~1978!.

5H. Fleichtinger, J. Waltl, and A. Gscwandtner, Phys. Status Solidi A53,K71 ~1979!.

6A. Goetzberger and W. Shockley, J. Appl. Phys.31, 1821~1960!.7W. B. Henley, Ph.D. dissertation, University of South Florida, Tampa,1993.

8D. Gilles, E. R. Weber, and S. K. Hahn, Phys. Rev. Lett.64, 196 ~1990!.9J. M. Gallego and R. Miranda, J. Appl. Phys.69, 1377~1991!.10K. Graff, Mater. Sci. Eng. B4, 63 ~1989!.11M. Nakamura and T. Kato, Jpn. J. Appl. Phys.7, 512 ~1968!.12Scott A. McHugo, E. R. Weber, M. Mizuno, and F. G. Kirscht, Appl.Phys. Lett.66, 2840~1995!.

13K. Graff and H. Pieper, J. Electrochem. Soc.128, 669 ~1981!.14K. Honda, A. Ohsawa, and N. Toyokura, Appl. Phys. Lett.46, 582~1985!.15E. Weber and H. G. Riotte, J. Appl. Phys.51, 1484~1980!.16W. H. Shepherd and J. A. Turner, J. Phys. Chem. Solids23, 1697~1962!.17S. Wolf and R. N. Tauber, inSilicon Processing in the VLSI Era~Lattice,California, 1986!, Vol. 1, p. 531.

18C. B. Collins and R. O. Carlson, Phys. Rev.108, 1409~1957!.

FIG. 6. Precipitated fraction iron vs annealing time.~Annealing tempera-tures 600 and 700 °C!. The values ofn andt are previously calculated andare listed in Table II.

593J. Appl. Phys., Vol. 82, No. 2, 15 July 1997 W. B. Henley and D. A. Ramappa [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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19J. Lagowski, P. Edelman, A. M. Kontkiewich, O. Milic, W. Henley, M.Dexter, L. Jastrzebski, and A. M. Hoff, Appl. Phys. Lett.63, 3043~1993!.

20J. Lagowski, P. Edelman, M. Dexter, and W. Henley, Semicond. Sci.Technol.7, A185 ~1992!.

21G. Zoth and W. Bergholz, J. Appl. Phys.67, 6764~1990!.22L. Jastrzebski, W. Henley, and C. Neuse, Solid State Technol.12, 27

~1992!.

23D. Turnbull, in Solid State Physics, edited by F. Seitz and D. Turnbull~Academic, New York, 1956!, Vol. 3, p. 225.

24F. S. Ham, J. Appl. Phys.30, 1518~1959!.25F. S. Ham, J. Phys. Chem. Solids6, 335 ~1958!.26H. Reiss, J. Chem. Phys.19, 482 ~1951!.27C. A. Wert, J. Appl. Phys.20, 943 ~1949!.

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