DISLOCATIONS IN SEMICONDUCTORS

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DISLOCATIONS IN SEMICONDUCTORS

P. Haasen

To cite this version:

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DISLOCATIONS IN SEMICONDUCTORS

(Institut fiir Metallphysik, Universitat Gottingen, Allemagne)

RBsum6.

-

L'auteur rksume les proprietks des dislocations dans les semiconducteurs, notamment leur vitesse de glissement et leur influence sur les proprKtCs de transport et donne quelques applications.

Abstract. - Properties of dislocations in semiconductors are reviewed, mainly dislocation velocities and influence on transport properties. Applications are described.

1. Introduction.

-

Since 1952 it is known that the elemental semiconductors Ge and Si lose their characteristic brittleness a t temperatures above two thirds of their melting temperatures and become as ductile as fcc metals [l]. Ge and Si crystals have a diamond cubic structure (the related 111-V compounds like InSb have a sphalerite structure) and slip on

(

l11

)

planes in 110 > directions as expected from their fcc translation symmetry. Slip occurs by the movement of dislocations. These defects can be made visible particularly easy in these materials by etching, infrared, X-ray, or electron transmission techniques, see [l]. In the studies which are described below dislocation intersections with a surface are etch pitted and dislocation densities are counted, up to N = 10' cmw2 by optical microscopy, and above that value by replica methods. Dislocation velocities are measured by Johnston and Gilman's [2] double etching technique outlined in figure 1. A dislocation ending in the surface a t A moves t o B between two etches by the action of a stress z in the slip plane during the time At. The

mean velocity v is then defined by the distance AB = Ax divided by At if Axis proportional to At. v depends

on the length I of the dislocation segment moving, on the angle between its Burgers vector b and its line

direction, and on other material parameters as will be shown below. If N and v are known from such

microscopic experiments, the macroscopic strain rate i follows for any fixed temperature and stress from

E

= bNv (1)

if all N dislocations are assumed to be moving with the same velocity v. E (E, z) is measured in a static

creep experiment at constant stress (or in a dynamic test at constant strain rate ; the latter yields the stress- strain curve z = Z(E, E)). We will discuss in the following how this dependence E(&, 7) is made up by that

of its constituents N(t, E ) and v(%,

R)

according t o theory and experiment. The relation between z and N determines work hardening, that between N and E

dislocation multiplication. These two processes are of general interest.

In a semiconductor the dislocation velocity may

/

,"i

depend on doping (As or Ga) as we will see. This is

/?'.Q/

l'

f

l I f

related to the core structure and the atomic mechanism of

calculate. motion On of the a dislocation, inverse effect which of dislocations we have tried affec- to ting semiconducting properties, some new facts have

l I

I 1

.

\' 0 ,

j!

become known recently which will briefly be mentioned below. Plastic deformation of semiconductors may

'C, A f have technical applications in the future, as is also

indicated in this report. This paper is based heavily on the work of members of the Gottingen Institut, particularly Dr. H. Alexander, Dr. E. Peissker, Dr. R. Labusch, Dipl. Phys. S. Schafer, W. Schroter, FIG. 1. - Measuring dislocation velocity and K. Berner, whose cooperation is gratefully acknow-

by double etching. ledged.

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DISLOCATIONS IN SEMICONDUCTORS C 3 - 3 1

2. Dislocation velocity and core structure.

-

The Johnston-Gilman technique for measuring v was first applied to semiconductors by Chaudhuri et al. [3]. These authors produced a linear dislocation array by scratching the side of a crystal at room temperature fol- lowed by heating. Then these dislocations were moved by bending the crystal between three wedges. This created an inhomogeneous stress distribution and

Shear stress T ( k g / m m 2 )

+

FIG. 2. - Dislocation velocity in Ge vs. stress according to [3].

yields the v(z) relation in a rough manner as shown in figure 2. It is described by

v = B(T)zm, where nz 1.5 f 0.2 and

B(T) = B, e-'IkT

,

(see figure 6)

.

( 2 ) For intrinsic Ge U = 1.6

+

0.05 eV, rather independent of z*. A similar relation holds for Si and

InSb such that U is proportional to their respective melting temperatures T,. Furthermore, U is about half the activation energy of self diffusion. m decreases in the order InSbjGelSi, 2

>

m

>

1. In metals, on the other hand, values of m 9 1 are measured and B is rather temperature independent. Thus dislocations in the diamond structure move in a quasi-viscous manner and rather slowly for T d TJ2.

Schafer [5] has recently repeated these measurements on Ge under improved experimental conditions. In his experiments a homogeneous stress acted on a few dislocation rings of known diameter I and of known dislocation character. He finds a similar z and T dependence of v (slightly larger m, smaller U at lower T ) as did Chaudhuri et al. [3] in addition to a definite dependence of v on the angle between b and

V r p SLW-'J S c r e w o/O--O 0- o / O '

FIG. 3. -Dislocation velocity in Ge vs.

loop length according to [5]

T = 440 "C, 7 = 0,466 kg/rnm2

line direction and on the loop size I, see figure 3. Screws move faster than edges, especially at higher temperatures, and long dislocations move faster than short ones due to the line tension.

The motion of a dislocation in the diamond structure, as characterized above, can be described atomistically by the formation of kink pairs in the Peierls potential, see figure 4. A calculation of the kink formation energy

<"l1 <110),

(*) A relation U

-

z -1 as has been proposed by Gilman 141, does not hold for Ge or Si up to stresses of G/100, G = shear

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by Labusch [6] is based on Peierls'model and on the known elastic properties of the diamond structure, His results for a screw dislocation in Ge are : Peierls potential 0,225 eV, Peierls force 212 kg/mm2, kink pair formation energy 1,75 eV, kink potential 0,M eV. The movement of the kink along the Peierls potential (in the kink potential) thus appears to be relatively easy and is little influenced by the mutual attraction of the double kink partners. The (almost) linear stress dependence of v probably stems from the difference in formation rates of forward and backward kink pairs. The increase in velocity with increasing dislocation length characterizes the back stress of the line tension. Screw dislocations are rarely found in electron transmission surveys of the slip plane of deformed Ge [7], probably because they move faster than edges. The latter appear to be responsible for work hardening. We will return to this point later.

Patel et al. [S] have recently measured dislocation velocities in otherwise dislocation-free crvstals of heavily doped Ge. Results obtained at 500 OC and z = 6 kg/mm2 are shown in figure 5 for additions of

IMPURITY CONCENTRATION/CM~

FIG. 5. -Dislocation velocity in Ge vs.

doping, T = 500 oC,

z = 6 kg mm -2, according to 181.

As, Ga, Sn. No effect of doping is seen on the intrinsic range while for concentrations c 2 10" cm-3, where the material becomes extrinsic at this temperature, As eases and Ga hinders dislocation movement. Sn (or Si) have no effect on v even at higher c. The velocity becomes again independent of c (As, Ga) at the highest c and thus depends on doping qualitatively as the Fermi level. In terms of eq. (2) both B, and U appear to be affected by c, but not m. Figure 6 shows the temperature dependence of v for a number of dopings. This diagram resembles that of the diffusion constant vs. temperature and doping plotted according to Valenta et al. [g] in figure 7. From this Patel et al. [8] propose that both dislocation velocity and diffusion may be influenced by the abundance and

FIG. 6. - Dislocation velocity vs. temperature

at z = 6 kg mm -2 according to [a].

RG. 7. -Diffusion coefficient in Ge

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DISLOCATIONS IN SEMICONDUCTORS C 3 - 3 3 mobility of vacancies. That is difficult to believe,

although the distorted dislocation core of a 600-dislocation may be assumed rather pictorially to move like a row of vacancies [101. True vacancies are, howe- ver, neither necessary nor helpful in dislocation movement over the slip plane. Another possible explanation for the influence of doping on velocity considers it a homogeneous effect on the Peierls potential and on the line energy of the dislocation via the shear modulus. According to Brunner and Keyes [l11 the modulus c,, of Ge decreases by 4.4

%

due to the addition of 3,5 X 10" As. The effect of p-doping is expected to be much smaller, as are the effects in Si [12], in qualitative agreement with velocity measurements [8]. Theoretically a shear strain changes the occupation of various energy valleys by electrons. A rather different approach to the v(c) results considers the dislocation itself charged as proposed by Read [l31 [l]. Figure 8a shows the core structure of a 600 dislocation in the diamond lattice.

Extra half plane

[iii]

\

FIG. 8. - 600 dislocation in InSb and effect of bending direction on sign of excess dislocations.

There is a row of dangling bonds (the density of which approaches zero for the screw orientation), some of which, according to Read, accept an electron to pair their spins. The acceptor level according to measurements of Pearson et al. [l41 lies 0.22 eV below the lower edge of the conduction band. There- fore it should be occupied in strongly n-doped Ge though not in intrinsic or in p-doped material. A

donor action of the dislocation was not observed, nor could the dangling bond in the dislocation core be found in ESR experiments. The latter has now been observed 1151 in silicon which has a smaller spin- orbit coupling than germanium. Later investigators [16, 171 have located the acceptor level of the dislocation in n-Ge in the middle of the forbidden band (width = 0.7 eV in Ge at T = 0) rather than in the upper one-third [14]. A level in the middle of the band could produce a change in the core structure of the dislocation with doping and possibly in the dislocation velocity, as shown in figure 5. Recently, and unexpectedly, Blick and Schroter [l81 have found an acceptor level due to dislocations in p-Ge, about 0,l eV above the valence band. Now it is most likely that the results of figure 5 could in principle be explained by the charge a dislocation carries.

In this connection it is appropriate to point out a difference in mobility of positive and negative 6O0-dislocations predicted for 111-V compounds like InSb 1101. Due to the polarity in the stacking of

{

11 1

)

planes with In and Sb atoms, figure 8a, a positive dislocation ends with a row of say In atoms, and a negative dislocation with a row of Sb atoms. Due to their different valencies in the atomic state these atoms should also produce different core structures in a crystal dislocation : In particular, the disturbance in the core of the In-dislocation should be smaller, its mobility higher than that of the Sb-dislocation. This effect has indeed been measured [l91 (though not on v directly) in bending creep experiments on InSb crystals of different orientation, as will be described below. This effect serves to show again that the friction determining the dislocation mobility in the diamond and related sphalerite structure is located in the very core of this dislocation.

3. Dislocation interaction and multiplication.

-

The second microscopic parameter determining the macroscopic plasticity of a crystal is the density N

of mobile dislocations. By the methods described above we can only count dislocations at rest which may for many reasons, give a number N, different from N. Only the success of the assumption N, = N at small deformations justifies it, as we will see. A

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interacting dislocations Ni, which determines the mean internal stress zi in the crystal. For elastic interaction of edge dislocations

v = Poisson's ratio. Berner and Alexander [20] have checked eq. (3) by counting dislocations (N,) in a crystal whose creep under a stress t has come to an

end because zi has approached z. The result is plotted in figure 9 as log N, vs. log z and exactly confirms the

lead the dislocation out of its slip plane in order to fill the crystal with dislocations in three dimensions. M, I,

6 may be functions of z (and N). For any reasonable choice of M(z), l(z) it is impossible to fit our experimental results to mechanism (a) while model (b) pro- vides a good description if

An inverse stress dependence of S-' is expected in a mechanism Iike the one shown in figure 10 in which

FIG. 9. - Limiting dislocation density vs. stress in Ge at 582 OC according to [20].

z = A

f i

relation, eq. (3), if Ni X Nt. The measured constant of proportionality is A = 6,6 X 10-3 kg cm- l

(for areas of maximum dislocation density) com- paredj to A = 4,5 X 10-3 kg cm-' calculated from eq. (3). Still better agreement in A is obtained from measurements [20] of local slip and dislocation distributions which will be described now.

We have so far determined only the limiting dislocation density Ni at various z.

Ni

is produced by a process of multiplication during straining from the (very small) initial dislocation density No in these crystals. Two types of multiplication mechanisms are discussed in the literature : (a) Multiplication from fixed (Frank-Read) sources [21] (length l, volume density M) and (b) exponential multiplication [4] [l91 [2]. They give different

I?(&)

relations as follows :

6 - l is the length of path after which a dislocation has created a new loop from itself by some at present

FIG. 10. - Forming a dislocation loop from a dipole. the partners of an edge dislocation dipole pass each other under the stress z after a sufficiently large super- jog has been built up. Such events have been observed by electron transmission, but never a Frank-Read source [23] [7]. Haasen [24] proposed that a stress z,,, instead of the applied stress z is to be used in eq. (5) as well as eq. (2) to take into account the internal (back) stress zi defined in eq. (3)

zeff = - c - zi = z

-

A @ . _{( 6 )} We will see that eq. (4b) well describes our experiments if and only if the stress z,,, eq. (6), rather than z [22] is used. The multiplication law following by integration from eq. (4b), (5) and (6) with N = No for E = 0

has been checked [20] by etch pit counts and local strain measurements on Ge crystals deformed under various z at 582 OC. It is important that strain is measured at the same element of the crystal where etch pits are counted because slip is never homogeneous over the length of the specimen. In this way data like those shown in figure 11 were obtained which are at variance with previous results [22] [25] but are well represented by eq. (7) with A = 5,5 X 10-3 kg cm-'

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DISLOCATIONS IN SEMICONDUCTORS

X local measurements

a v e r a g e

FIG. 11.

-

Dislocation density vs. local shear strain [20].

left in the deformed crystal. It is this concept of the elastic back stress which takes into account the non- linearity of E(N), figure 11, and which makes the assumption of an empirical work hardening coefficient [2] [26] [27] appear unnecessary and ambiguous. 4. Macroscopic creep curve. - The information obtained on the parameter N and v in eq. (l), see eq. (2), (6), (7), now is used to calculate macroscopic plastic strain vs. time (the creep curve) at constant .r and temperature T [l91 [28] from

where N (E) is the inversion of eq. (7). 0.0 I ' I 2 3 4 */*W

Qualitatively the solution of this eq. (8) can be visua- lized as follows (see Fig. 12) : At small E the dislo-

cation density and

i.

are small and the back stress A

JN

is negligible compared to z, therefore

N z ~ ) E for N > N ,

I Initibl weep period

and k~ B K ~ " + ' E for E 6 1 . (9) II S t a t i o ~ r ~ creep

m

hbrk-hanlenr;lg p4C;dd

This means that E rises exponentially with time with a time constant

, , P t . ?

te = e U ' k T / ~ o KT""

.

(10) 3 4 * / t w

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effect of back stress on velocity and multiplication (Direct velocity measurements on Si are scarce so rate. The maximum value of E at intermediate strains far L31 ; they yield U = 2.2 eV, m = 1 .4). In the

is obtained from eq. (8) creep experiments two types of silicon crystals were

used, one with No = 1.8 X 104 cm-' grown-in

kW

= ( ~ B ~ / A ' C) zmf e-"lkT _{(1 1)} dislocations and the other with No = 0. Both sets where C = (m

+

2)"+'/4 mm = 6.75 for m = 1

.

In a more complete solution, a finite No(ats = 0) can be taken into account [28].

E,

is calculated to be independent of No while the creep time t , to the inflexion point should decrease with increasing No as

give the same E',(z) (for not too small z), while they differ in t, at all z (see figure 16) as predicted by the theory. We don't know yet whether grown-in dislocations do move and multiply themselves or whether they just stimulate new sources. At least, the initial dislocation density seems to be proportional to the t , z t,(2.7

+

In z/A &)

,

₍₂₂₎ grown-in dislocation density. ~uithermore, evidence has been obtained by changing specimen dimensions (m w 1). The theory has been applied to creep expe- that volume, not surface sources, are important [19]. riments on Ge, Si, InSb and is found to be in remar- Other creep parameters are also found in good agree- kable agreement with the experimental results. Figu- ment with the theory [19, 28, 29, 201, with the para- res 13 and 14 show measured creep curves of Si toge- meters B,, A, K determined by independent experi-

FIG. 13 and FIG. 14. - Creep curves of silicon [29].

ther with the calculated normal curve [291. In figure 15 _merits,_see

₅

_2,_{3, At large strains the experimental}_E'_is and 16 the stress and temperature dependence of the _{smaller than the calculated one which may-indicate} creep Parameters E,, tw is ~lottedaccording to eqs (10) _{that now Ni}_>_{N, i. e. dislocations, whose long range} and (11). The activation energy found both for

E,

stresses (eq. (3)) are not compensated by dipole and t, is U = 2.4 eV ; the stress exponents for

E,

formation, are becoming immobile.

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DISLOCATIONS I N SEMICONDUCTORS C 3 - 3 7

FIG. 15 and Fig. 16. - Temperature and stress dependence of creep parameters in silicon [29].

Open symbols : No = 1.8 X 104 cm-', closed symbols : No = 0.

ments on InSb which prove the predicted difference in test at constant strain rate. In that case the elastic term mobility of 60° In- and Sb- dislocations [19]. As ?/Gmust be added on the right side of eq (1). The result shown in figure 8b, bending of an InSb crystal in of detailed calculations [24, 281 and experiments opposite directions introduces excess dislocations of ,

opposite sign. The sign of these dislocations, i. e. 8 - I O ~ E

the polarity of the crystal, may be determined by etching 1301. Crystals bent to produce In- dislocations in excess are found to creep faster than crystals with Sb-

dislocations, as shown in figure 17 for two thicknesses Tz300'C

h between the bending wedges. (The thickness effect at constant area of the stressed surface demonstrates volume sources as mentioned above). The stationary creep rate and the incubation time observed for opposite bending directions differ by 50

%

(and more at high temperatures), while the strain E , at the inflexion point

is the same in both cases. Since E , is independent of dislocation velocity [19, 281 while E',, t ,

'

are proportional to v, it is the velocity of In- and Sb- dislocations which must be different. The observed ratio V,, : V,,

may be interpreted by an activation energy for Sb- dislocations being 1-2

%

higher than for In-dislocations. Of course the measured creep anisotropy is dilu- ted by minority )) and screw dislocations.

0 50 100 750 200 250 3W

5. Resumee and applications.

-

The above theory FIG. 17.

-

Creep curves of InSb specimens of two heights h

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[31, 32, 331 is a quantitative explanation of the yield point phenomenon observed in semiconductors (and other crystals with small No and small m). Johnston and Gilman [2] have pointed out that a pronounced upper and lower yield stress must be observed if a certain overall strain rate is enforced on a specimen in which few dislocations move and multiply slowly. In that case E: is initially carried by an elastic rate of stress rise ; this speeds up dislocations which in turn multiply faster ; then the plastic contribution to E increases. Finally, work hardening balances the drop in stress due to increasing N a n d the stress starts rising again. The principles applied above to creep experiments also describe the yield point quantitatively for Ge, Si, InSb tested at various T, i, No [34] and dopings [8] although the yield instability introduces some complications [32, 351. Both sets of experiments are interpreted by the few basic assumptions of our theory, indicating that dislocations in semiconductors :

( a ) move quasi-viscously (parameters m, B),

(b) multiply exponentially (parameter K),

(c) interact elastically (parameter A).

There is an equation of state which allows dynamic experiments to be calculated from creep tests and VC. vs. The inhomogeniety of slip, even in the

gross form of Luders bands, has been taken into account quantitatively [20, 321.

The plasticity of semiconductors at intermediate temperatures can be used technically in producing layer devices by (( deformation welding u (S. Schafer, Gottingen, 1965, patent applied for). A piece of, say, n-Ge is placed on top of a piece of p-Ge of the same (easy slip) orientation. and both are compressed toge- ther a few

%

in a matter of minutes at 500 OC. The resulting weld shows area1 contact and the typical current-voltage characteristic of a rectifier. The n-p transition is very sharp ; there is, of course, some decrease in carrier lifetime due to the dislocations introduced. The method might be useful in producing semiconductor contacts, as well as in convincing sponsors that deforming semiconductors is not just another dislocation game (l).

(1) Prof. W. H. Robinson kindly helped in preparing the manus- cript. The work was supported by the Deutsche Foschungs-

genleinschaft.

[l] HAASEN (P.), SEEGER (A.), (c Halbleiterprobleme )), 1958, 4, p. 68, VieweglBraunschweig.

121 JOHNSTON (W. G.), GILMAN (J. J.), J. Appl. Physics,

1959, 30, 129.

[3] CHAUDHURI (A. R.), PATEL (J. R.), RUBIN (L. G.),

J. Appl. Physics, 1962, 33, 2736 ; 1963, 34, 240.

[4] GILMAN (J. J.), J. Appl. Physics, 1965, 36, 3195.

[5]

SCHAFER

(S.), Ph. D. Thesis Gottingen, 1966. [6] LABUSCH (R.), Phys. Stat. Sol., 1965, 10, 645. [7] ALEXANDER (H.), Habil. Thesis Gottingen, 1966. [S] PATEL (J. R.), CHAUDHURI (A. R.), J. Appl. Physics,

in press.

[g] VALENTA (W. M.) and RAMASASTRY (C.), Phys. Rev.,

1957, 106, 73.

rioi HAASEN (P.). Acta

et.

1957, 5, 598.

[l l

j

BRUNNER (L. J.), KEYES (R.. W.), Phys. Rev. Lett.,

1961, 7, 55.

[l21 KEYES (R. W.), IBM Jl., 1961, 5, 266.

[l31 READ (W. T.), Jr. Phil. Mug., 1954, 45, 775, 1119. [l41 PEARSON (G. L.), READ (W. T.), Jr., MORIN (F. J.),

Phys. Rev., 1953, 93, 666.

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[l61 BROUDY (R. M.), Adv. Phys., 1963, 12, 135. 1171 GIBSON (A. F.), PAIGE (E. G. S.), Phil. Mug., 1958,

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[20] BERNER (K.), ALEXANDER (H.), to be published. [21] VAN BUEREN (H. G.), Physica, 1959, 25, 775. [22] DEW-HUGHES (D.), IBM Jl., 1961, 5, 279. [23] ALEXANDER (H.), MADER (S.), Acta Met., 1962, 9,

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[25] ALEXANDER (B. H.), PATEL (J. R.), Acta Met., 1956.

4, 385.

[26] JOHNSTON (W. G.), J. Appl. Physics, 1962, 33, 2716.

[27] GOWORKOW (W. G.), INDENBOM (W. L.), PAPKOW (W. S.), REGEL (W. R.), Fiz. Tvevd. Tela, 1964,

6, 1039.

[28] HAASEN (P.), Festkorperprobleme, 1964, 3, 67, Vieweg/Braunschweig.

[29] REPPICH (B.), HAASEN (P.), ILSCHNER (B.), Acta Met.,

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[30] FAUST (J. W.), SAGAR (A.), J. Appl. Physics, 1960,

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[31] SCHAFER (S.), ALEXANDER (H.), HAASEN (P.), Phys.

Stat. Sol., 1964, 5, 247.

1321 SCHROTER (W.), ALEXANDER (H.), HAASEN (P.)

Phys. Stat. Sol., 1964, 7, 983.

[33] SIETHOFF (H.), Ph. D. Thesis, Gottingen, to be published.

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1963, 34, 2788.