A regime of the yield point of silicon at high temperaturesHans Siethoff, Hans Georg Brion, and Wolfgang Schröter Citation: Applied Physics Letters 75, 1234 (1999); doi: 10.1063/1.124652 View online: http://dx.doi.org/10.1063/1.124652 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/75/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Surface self-diffusion of silicon during high temperature annealing J. Appl. Phys. 115, 134903 (2014); 10.1063/1.4870476 Response of copper to shock-wave loading at temperatures up to the melting point J. Appl. Phys. 114, 083511 (2013); 10.1063/1.4819328 Dislocation density reduction in multicrystalline silicon solar cell material by high temperature annealing Appl. Phys. Lett. 93, 122108 (2008); 10.1063/1.2990644 Effects of Zn addition and thermal annealing on yield phenomena of CdTe and Cd 0.96 Zn 0.04 Te singlecrystals by nanoindentation Appl. Phys. Lett. 82, 1200 (2003); 10.1063/1.1556573 Transmission electron microscopy observation of deformation microstructure under spherical indentation insilicon Appl. Phys. Lett. 77, 3749 (2000); 10.1063/1.1332110

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A regime of the yield point of silicon at high temperaturesHans Siethoffa)

Physikalisches Institut, Universita¨t Wurzburg, Am Hubland, D-97074 Wu¨rzburg, Germany

Hans Georg BrionInstitut fur Materialphysik, Universita¨t Gottingen, D-37073 Go¨ttingen, Germany

Wolfgang SchroterIV. Physikalisches Institut, Universita¨t Gottingen, D-37073 Go¨ttingen, Germany

~Received 3 May 1999; accepted for publication 8 July 1999!

We present measurements of the lower yield point of undoped floating-zone silicon at temperaturesbetween 800 and 1300 °C. The knowledge of the defect structure in this temperature range is ofconsiderable importance for the numerical simulation of dislocation generation in various solarsilicon materials. Above about 1050 °C, we find marked deviations from the well-knownlow-temperature behavior, thus establishing a further deformation regime. It is characterized by anactivation energy of 4.1 eV. Comparison to preliminary work indicates that this effect depends onthe as-grown dislocation density, but not on the ambient during deformation. We tentatively assumethat it may reflect the change in the mechanism of self-diffusion typical for silicon at hightemperatures. ©1999 American Institute of Physics.@S0003-6951~99!03935-2#

For solar cell technology, multicrystalline silicon1 andrapidly grown silicon ribbons2 become increasinglyimportant.3 These materials contain extended defects likegrain boundaries, precipitates, and dislocations, which re-duce significantly the cell efficiency. A key role is played bydislocations, especially when decorated by impurities. Withgrowth of the material, dislocations are generated by thermalstresses, which form in the solid during cooling from themelt. To lower the dislocation density, numerical simulationsof the cooling process and of the plastic release of thermalstress are performed,4 which need as an input, data on thegeneration, multiplication, and motion of dislocations at hightemperatures. One method to obtain such data is to investi-gate the beginning of plastic deformation, i.e., to measure thetemperature and strain-rate dependence of the yield point.Reliable measurements and the understanding of the under-lying mechanisms are available only up to 1100 °C. There-fore, in present day numerical calculations of the plastic re-lease of thermal strain, those data are extrapolated into thehigh-temperature range. However, some hitherto not ex-plained results on lower yield point5–7 and dislocationvelocity8 for temperatures above about 1100 °C indicate sig-nificant deviations from the low-temperature behavior.Therefore, we decided to reinvestigate the yield stresses ofundoped silicon between 800 and 1300 °C with special em-phasis on temperatures above about 1050 °C. It turned out tobe necessary to also measure the strain-rate dependence foran adequate interpretation of the data.

The stresst ly at the lower yield point of silicon at tem-peratures below about 1100 °C has been found9,10 to obey alaw such as

t ly5Clye1/n exp~U/nkT!. ~1!

Here, T is the deformation temperature,e the strain rate,

and Cly a constant not depending onT and e; k is Boltz-mann’s constant. The analysis of the data yieldedU52.3 eV andn52.9. Relation~1! is compatible with Haas-en’s yield point theory.11 In this model,n225m andU areidentified with the stress exponent and activation energy, re-spectively, of the dislocation velocityv according to

v5v0tm exp~2U/kT!, ~2!

wherev0 is a rate constant. Stress and temperature depen-dence, as given by Eq.~2! have been experimentallyverified8,12,13at temperatures below about 800 °C with valuesfor U andm close to those drawn from the lower yield stress.Equivalently, Haasen’s model allows us to describe the stressand temperature dependence of the creep rateew at the in-flection point of the creep curve according to

ew5Cwtn exp~2U/kT!, ~3!

with Cw5Cly2n . This has been also verified by experiments

with U52.4 eV andn53.14 The whole subject has beendealt with in review papers.11,15,16

The material~n type, 60V cm! used in the present in-vestigation was FZ silicon from Wacker-Chemitronic,Burghausen; it was dislocation free. Specimens of dimension3.533.5315 mm3 were cut from the bars by a diamond saw,lapped, and chemically polished for 2 min in a solution of 2HNO3, 1 HF, and 1 CH3COOH. The orientation was123&,which is favorable for single slip. The deformation was car-ried out at constant strain rates in an Instron machine. Aprotecting atmosphere of purified argon was used. The re-sults were compared to those obtained in earliermeasurements9,10 at low temperatures on samples, whichwere treated in the same way as described above, but had anas-grown dislocation densityN05104 cm22, and which weredeformed under forming gas.

The results of the present investigation on dislocation-free silicon are given in Figs. 1 and 2 by the open symbols.In the log–log plot of Fig. 1, the lower yield stresst ly isa!Electronic mail: siethoff@physik.uni-wuerzburg.de

APPLIED PHYSICS LETTERS VOLUME 75, NUMBER 9 30 AUGUST 1999

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shown as a function of strain rate. The full points at 1300 °Cand the dashed lines are from our former work9,10 on mate-rial with an as-grown dislocation density ofN05104 cm22.The dotted curve and the dot-dash part at 900 °C representthe creep measurements of Reppich, Haasen, and Ilschner,14

the former obtained from dislocation-free silicon, the latterfrom material withN05104 cm22. It is noted that Reppich’sdata linearly extend ours to very small strain rates forN0

5104 cm22, actually they overlap between 1023 and1024 s21. This demonstrates the equivalence of the loweryield point in the stress–strain curve and the inflection pointof the creep curve.

Figure 1 further indicates that dislocation-free anddislocation-containing silicon show congruent behavior athigh strain rates and low temperatures. Here, the slope of thecurves is characterized byn53 @Eqs.~1! and~3!#, but at lowstrain rates marked deviations occur. These are observed in

the creep measurements~dotted line at 900 °C! and, in moredetail, in the present investigation~open symbols!. Figure 1shows that, with decreasing strain rate, the slope of thecurves becomes smaller below 1023 s21, but then again in-creases, indicating the existence of a new regime at very lowstrain rates. The data at 1300 °C from the formerinvestigation10 ~full points! apparently support this view.

This behavior is also reflected in the temperature depen-dence of the lower yield stress as shown in the Arrheniusplot of Fig. 2. Again, the dashed lines describe our earliermeasurements9,10 on silicon with N05104 cm22. The openpoints are from the dislocation-free material used in thepresent investigation, as also is the case with the few data ofReppich, Haasen, and Ilschner14 ~full points!. At highstresses~data above 7 MPa in Fig. 2! and high strain rates~data above 1023 s21 in Fig. 1!, the temperature dependenceof the lower yield point is characterized by an activationenergy U/n50.75 eV. According to Eq.~1! and togetherwith n53 ~see above!, one obtainsU52.25 eV. These val-ues are compatible with those found in earlier work~seeabove!. More distinctly than for the strain-rate dependence asshown in Fig. 1, the slope of the curves decreases at lowerstresses, but then again increases, corroborating the existenceof a new regime at temperatures above about 1050 °C andstresses below approximately 3 MPa. It is finally noted thatthe upper yield point could be observed up to 1250 °C, andthat it showed a temperature and strain-rate dependence simi-lar to that of the lower yield point.

Assuming that Eq.~1! may be also applied to the high-temperature regime, a fit~using data for stresses below 3MPa! leads to the following parameters:n53.260.3 andU5(4.160.3) eV. The exponentn is not much differentfrom that of the low-temperature regime~see above!; theactivation energy, however, is appreciably larger. In Fig. 2 afurther important result is manifested: Silicon withN0

5104 cm22 ~dashed line! shows qualitatively similar featuresas the dislocation-free material. The quantitative difference,however, is that the low-temperature regime extends tohigher temperatures, i.e., that the new high-temperature re-gime is shifted closer to the melting point for the dislocation-containing material. The reason for this different behavior isnot yet understood, and will be dealt with in a forthcomingpaper.

Our results on the lower yield stress of dislocation-freesilicon are qualitatively compatible with data obtained fromother works at high temperatures where, however, the strain-rate dependence was not measured. An important point, inthis context, is that the environment of the samples duringdeformation was different: Omri5 used a mixture of 90% Heand 10% H2 as a protecting atmosphere, in our work argonwas applied, while Yonenaga17 deformed his specimens in avacuum of 1023 Pa. In the latter case, few data were evalu-ated by us from published deformation curves. The compari-son of these results shows that the occurrence of the high-temperature regime of the yield point of silicon does notsignificantly depend on the ambient during deformation.

Furthermore, our results are compatible with the inves-tigation of Farber and Nikitenko,8 who measured the dislo-cation velocity of silicon between 550 and 1300 °C. Theyalso found two different regimes, with activation energiesU

FIG. 1. Lower yield stress as a function of strain rate at different tempera-tures in a log–log plot. Open symbols: present work, dislocation-free silicon^123&; full points and dashed lines: silicon123& with an as-grown disloca-tion density of approximately 104/cm2, taken from Refs. 9 and 10; dottedcurve and dot-dash line at 900 °C: equivalent creep measurements ondislocation-free and dislocation-containing silicon^145&, respectively, takenfrom Ref. 14.

FIG. 2. Arrhenius plot at different strain rates. Open symbols: lower yieldstress from the present work; full points: equivalent creep measurementsaccording to Ref. 14~both from dislocation-free silicon!; dashed lines: loweryield stress of material with an as-grown dislocation density of approxi-mately 104/cm2, taken from Refs. 9 and 10. Some points are interpolatedfrom Fig. 1.

1235Appl. Phys. Lett., Vol. 75, No. 9, 30 August 1999 Siethoff, Brion, and Schroter

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@Eq. ~2!# of 2.2 and 4.0 eV at low and high temperatures,respectively. They discuss changes in the point-defect struc-tural state at 1100 °C to be responsible for the high-temperature effect, but additionally note that also the transi-tion from vacancy to interstitial self-diffusion typical forsilicon18,19 could play a role.

We propose for several reasons that the latter effect maybe responsible for the occurrence of the high-temperatureregime of the lower yield stress. There is at first the sametemperature range where the transition occurs. Second, suchan effect is not observed for the yield point of germanium,10

where self-diffusion does not show any similar transition.18

Finally, and more important, we mention that the activationenergy underlying the lower yield stress in the low-temperature regime@Eq. ~1!# is correlated to a diffusion en-ergy, an effect that has been found for silicon, germanium,and various III–V compounds.16,20 This result consistentlyleads to the idea that a similar, though quantitatively differ-ent correlation could also exist at high temperatures in sili-con, where interstials dominate self-diffusion.

In summary, we have investigated the first stages of sili-con plasticity at high temperatures, for which so far onlypreliminary data exist. We have found strong evidence for ahigh-temperature deformation regime, with a considerablylarger activation energy of 4.1 eV compared to 2.3 eV for thelow-temperature regime. Our results will certainly have asignificant impact on numerical simulation of dislocationgeneration in various solar silicon materials. From a funda-mental point of view, the preliminary relation between plas-ticity and diffusion looks rather promising, but needs furtherinvestigation.

The authors are indebted to Dr. K. Ahlborn for a com-puter fit, and to U. Scha¨ufele for carefully preparing thesamples.

1D. Helmreich,Silicon Processing for Photovoltaics II~Elsevier, London,1987!, p. 97.

2H. Lange and I. Schwirtlich, J. Cryst. Growth104, 108 ~1990!.3J. Moller, in Handbook of Semiconductor Technology, edited by W.Schroter and K. Jackson~Wiley-VCH, Weinheim, 1999! ~in press!.

4C. Haßler, E. U. Reisner, W. Koch, A. Mu¨ller, D. Franke, and T. Rettel-bach, Solid State Phenom.67-68, 447 ~1999!.

5M. Omri, These de 3me Cyle, L’Institut National Polytechnique de Lor-raine, Nancy, 1981.

6M. Omri, C. Tete, J.-P. Michel, and A. George, Philos. Mag. A55, 601~1987!.

7H. Siethoff, Philos. Mag. Lett.58, 129 ~1988!.8B. Y. Farber and V. I. Nikitenko, Phys. Status Solidi A73, K141 ~1982!.9H. Siethoff and P. Haasen, inLattice Defects in Semiconductors, edited byR. R. Hasiguti~University of Tokyo, Tokyo, 1968!, p. 491.

10W. Schroter, H. G. Brion, and H. Siethoff, J. Appl. Phys.54, 1816~1983!.11H. Alexander and P. Haasen, Solid State Phys.22, 27 ~1968!.12A. George, C. Escaravage, G. Champier, and W. Schro¨ter, Phys. Status

Solidi B 53, 483 ~1972!.13M. Imai and K. Sumino, Philos. Mag. A47, 599 ~1983!.14B. Reppich, P. Haasen, and B. Ilschner, Acta Metall.12, 1283~1964!.15H. Alexander, inDislocations in Solids, edited by F. R. N. Nabarro

~North-Holland, Amsterdam, 1986!, Vol. 7, p. 113.16H. Siethoff, Semicond. Semimet.37, 143 ~1992!.17I. Yonenaga, J. Electrochem. Soc.143, L176 ~1996!.18W. Frank, U. Go¨sele, H. Mehrer, and A. Seeger, inDiffusion in Crystal-

line Solids, edited by G. E. Murch and A. S. Nowick~Academic, Orlando,FL, 1984!, p. 63.

19M. Tang, L. Colombo, J. Zhu, and T. Diaz de la Rubia, Phys. Rev. B55,14279~1999!.

20H. Siethoff, H. G. Brion, and W. Schro¨ter, Phys. Status Solidi A125, 191~1991!.

1236 Appl. Phys. Lett., Vol. 75, No. 9, 30 August 1999 Siethoff, Brion, and Schroter

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