Breakdown of microcreep in heavily doped silicon and germanium

Scripta METALLURGICA

Vol. 14, pp. 601-603, 1980 Printed in the U.S.A.

Pergamon Press Ltd. All rights reserved.

BREAKDOWN OF MICROCREEP IN HEAVILY DOPEDSILICON AND GERMANIUM

H. Siethoff Physikalisches I n s t i t u t der Universit~t WUrzburg D-8700 WUrzburg, West-Germany

(Received February 21, 1980) (Revised April 7, 1980)

Introduction Recently, Mohamed (I) analysed creep data of metal solid solutions of the so-called alloy type, i . e . of those deforming by a microcreep mechanism (2). He compared two models for the process of deformation, where dislocations dragging along solute atoms by diffusion, are rate controlling: the viscous-glide model (3,4) and the line-tension-assisted diffusion model (5). Mohamed emphasized the conditions for a breakdown of microcreep at high stresses, which have been suggested by Weertmann (6) to occur when the dislocations tear away from the solute atoms. Mohamed arrived at the following expressions for the breakdown stress o in case of the viscousglide model o/G = 0.1 e2c (Gb3/kT)

... (i)

and in case of the line-tension-assisted diffusion model o/G = (2kT/Gb3)c exp(W/kT)

...

(2)

(G shear modulus, k Boltzmann's constant, b Burgers vector, c atomic solute concentration, e m i s f i t parameter, Wdislocation-solute binding energy, T absolute temperature.) In the viscousglide model the interaction energy between dislocations and solute atoms is smaller than kT, and the solute atoms form an extended atmosphere (Cottrell cloud) around the dislocations. In this case only the long-range elastic interaction between dislocations and solute atoms has to be taken into account for the breakdown stress (Equation ( I ) ) . In the line-tension-assisted diffusion model, which is not restricted to a small interaction energy, most of the solute atoms are at a minimum distance from the dislocations and the breakdown stress is controlled by the binding energy W according to Equation (2). A comparison of the above models with the relevant creep data showed (1) that the viscous-glide model can quantitatively explain the breakdown of microcreep at high stresses of metal solid solutions. The situation is different in silicon and germanium with foreign atom additions of 0.02 to 0.2 atomic percent (which correspond to doping concentrations of 1019 to 1020 cm-3). These dilute solid solutions are characterized by a strong short-range electrostatic interaction between dislocations and solute atoms besides the normal elastic interaction (7,8). The total i n t e r action energies have been found (see below) to be 0.2 eV and 0.36 eV for arsenic in germanium and for phosphorus in s i l i c o n , respectively. These energies are higher than kT in the investigated temperature regions and, consequently, a model based on weak dislocation-solute i n t e r action seems not to be appropriate for the description of the measurements under consideration. I t is the aim of the present paper to show that the line-tension-assisted diffusion model is in accordance with the results on silicon and germanium. Discussion of the data for silicon and germanium Heavily doped s i l i c o n and germanium single crystals were deformed dynamically, and the stress at the lower yield point Zly was recorded as a function of the strain rate A at d i f f e r e n t

601 0036-9748/80/060601-03502.00/0 Copyright (c) 1980 Pergamon Press Ltd.

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temperatures and solute concentrations (8,9). Though the models of microcreep as described in the introduction refer to static deformation, i t seems not to be unrealistic to compare dynamic and static deformation in the case, where the rate-controlling process, i . e . the diffusion-controlled dragging of solute atoms by dislocation, is the same for both modes of deformation. This w i l l be confirmed in the following. Figure I shows results for germanium doped with 1.3x1019 As/cm3 at different temperatures (8). Three regimes of deformation can be distinguished: Regime A is characterized by a stress Tlv which is proportional to the cube root of the strain rate and which depends exponentially on temperature. From this temperature dependence, an activation energy is derived which can be identified with the activation energy of arsenic diffusion in germanium (8). I t was further shown that regime A can be quantitatively described by a microcreep model originally developed by Haasen (10). In regime B, the stress ~ly is independent of strain rate, at least at not too high temperatures, though there remains an ~xponential temperature dependence with an activation energy UD = 0.2 eV. This strain-rate independent region B was more thoroughly investigated in silicon doped with phosphorus and boron (9), especially with respect to i t s dependence on solute concentration c. A linear relationship between Tly and c was found. Consequently, the results on silicon and germanium follow the relationship B Zly

N

c exp (uB/kT)

. . . (3)

with an activation energy UB = 0.36 eV for silicon. UB and T~v were identified as dislocationsolute binding energy and stress for unpinning dislocations From solute atoms, respectively. The following break-away condition was deduced (8) Z~y = (kT/b3) c exp (uB/kT)

. . . (4)

o"500°C

2

/

/o

+o'600°C

o/

/

t~

800oc

E

_ _ o o ~ °," --o o

Z

%

o~ °~

B

w

P 0.5

~ /o j ~o / `°/

--0~0

0/0 ~,0~0"0f

oO..-0 " ~

°

o/900oc

/

0~0~0

O~

0.2 "° /

Ge+ 1.3 ~ 1019 A s / c m 3

0.1 I

l

10"s

10-~

I

10 -3

I

10 -2 G/s'l

FIG. I Stress at the lower yield point as a function of strain rate at different temperatures for n-doped germanium (n=1.3x1019 As/cm3); region A: microcreep, region B: break-down of microcreep, region C: free dislocation motion (Brion, Haasen, and Siethoff ( 8 ) ) .

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R

which differs from equation (2) only by a factor 2. This interpretation of UB and Tyv in silicon and germanium is strongly supported by the occurence of deformation inhomogeneities:-There are serrations in the stress strain curve indicating a Portevin-LeChetalier effect (7-9) and coarse LUders bands near the lower yield point (7,11,12). Relation (4) compares very well with experiments in the case of phosphorus in silicon. This is shown in Table 1. For germanium the agreement is poorer. We assume that the concentration of arsenic in solid solution at high temperatures (where the deformation experiments were performed) may be higher than at room temperature (where the impurity content was measured) for the following reasons: Arsenic shows l i k e other impurities in germanium and silicon a retrograde s o l u b i l i t y , and the maximums o l u b i l i t y (13,14) is close to the concentration investigated in Ref. 8. Such a situation may lead to the precipitation of a certain amount of impurities below the s o l u b i l i t y line, and these e l e c t r i c a l l y inactive precipitates do not contribute to the arsenic content measured at room temperature by electrical methods. On the other hand, the maximum s o l u b i l i t y of phosphorus in silicon (15) is much higher than the concentration investigated in Ref. 9 and similar problems are not l i k e l y to occur. TABLE 1 Comparison of Equation (4) with the Experiments Material

T/°C

uB/ev

Si 0.2 at %P

I000

0.36

1.7 x 10-4

2.9 x 10-4

9

600

0.20

1.7 x 10-4

1.6 x 10-5

8

Ge 0.03 at %As

T~y/G

kT c

exp (UB) kT

Ref.

In regime C (Figure 1) which has also been observed in silicon, the stress is high enough for the dislocations to move freely, i . e . without dragging solute atoms. This has been verified by experiments (8,9) which show regime C to be controlled by dislocation movement and interaction. The temperature dependence of Zlv is then characterized by an activation energy of dislocation motion which is typical for diamond structure materials. Conclusion I t is demonstrated that the semiconductors silicon and germanium containing small amounts of foreign atoms show microcreep phenomena at high temperatures on account of a strong shortrange electrostatic interaction between dislocations and solute atoms besides the normal elastic interaction. The breakdown stress, where the dislocations are depinned from the solute atoms, has been found to depend on temperature and solute concentration in the same way as was derived for the so-called line-tension-assisted diffusion model. Acknowledgements The author is indebted to Prof. W. Schr~ter and Prof. P. Haasen for valuable comments. References I. 2. 3. 4. 5. 6.

F.A. Mohamed, Mater. Sci. Eng. 38, 73 (1979). A.H. C o t t r e l l , Dislocations and'-I~lastic Flow in Crystals, p. 138, Oxford Univ. Press (1953). J. Weertman, J. Appl. Phys. 28, 1185 (1957). S. Takeuchi and A.S. Argon, E t a Met. 24, 883 (1976). J. Friedel, Dislocations, p.409, Perga~n Press, Oxford (1964). J. Weertman, in: Rate Processes in Plastic Deformation of Materials, J.C.M. Li and A.K. Mukherjee, eds., p.315, American Society for Metals, Ohio (1975). 7. H. Siethoff, Acta Met. 17, 793 (1969). 3. H.G. Brion, P. Haasen, ~ d H. Siethoff, Acta Met 19, 283 (1971). 9. H. Siethoff, phys. star. sol. 40, 153 (1970). 10. P. Haasen, in: Alloying Beha~our and Effects in Concentrated Solid Solutions, T.B. Massalski, ed., p.270, Gordon and Breach (1965). 11. H. Steinhardt and H. Siethoff, Z. Metallkunde 6__11,832 (1970). 12. H. Siethoff, Acta Met. 21, 1523 (1973). 13. F.A. Trumbore, W.G. Spi~er, RoA. Logan, and C.L. Luke, J.Electrochem. Soc. 109, 734 (1962). 14. V.I. F i s t u ] ' , P.M. Grinshtein, and N.S. Rytova, Sov. Phys.-Semicond. 4, 67 (-I~170). 15. G. Masetti, D. Nobili, and S. Solmi, in: Semiconductor Silicon 1977, H.R. Huff and E. S i r t l , eds., p.648, The Electrochemical Society, Princeton (1977).