Internal friction study on the mobility of screw dislocations in undoped InSb

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Internal friction study on the mobility of screw dislocations in undoped InSb

D. Quélard, P. Astié, J.L. Gauffier

To cite this version:

D. Quélard, P. Astié, J.L. Gauffier. Internal friction study on the mobility of screw dislocations in

undoped InSb. Revue de Physique Appliquée, Société française de physique / EDP, 1988, 23 (7),

pp.1291-1295. �10.1051/rphysap:019880023070129100�. �jpa-00245943�

Internal friction study ^{on the} mobility ^{of screw} dislocations in undoped

InSb

D. Quélard, P. Astié and J. L. Gauffier

Laboratoire de Physique ^des Solides, ^{associé au} CNRS, INSA, Avenue de Rangueil, 31077 Toulouse Cedex, France

(Reçu le 27 novembre 1987, révisé le 8 février 1988, accepté ^{le 22 mars} 1988)

Résumé.

La mobilité des dislocations a été étudiée dans InSb non dopé par frottement intérieur basse

fréquence (1 Hz) ^entre 0,1 ^et 0,98 Tm. ^{Avec une} sous-structure composée essentiellement de dislocations vis

engendrée par déformation plastique à ^{403 K, on a mis en} évidence deux pics d’amplitude importante ^{situés à}

570 K et 725 K. Le pic ^{à 570} K, ^d’allure symétrique, ^est interprété ^{comme un} pic de relaxation intrinsèque ^de

dislocations vis par nucléation de doubles décrochements, suivie de la propagation latérale de chaque

décrochement. L’analyse ^{de ce} pic ^{conduit à une} énergie d’activation de 1,27 ± 0,11 eV voisine de celle de la déformation plastique.

Abstract.

Dislocation mobility is studied by ^low frequency internal friction in undoped InSb between 0.1 and 0.98 Tm. Samples characterized by ^a mainly ^screw dislocations substructure generated by ^low temperature (403 K) deformation, ^{reveal two} high amplitude peaks ^{located at} 570 and 725 K. The 570 K-peak symmetrically shaped ^is explained ^{as an} intrinsic relaxation peak ^{of screw} dislocations moving by double kink nucleation followed by their lateral propagation. ^The peak analysis ^{leads to an} activation energy 1.27 ± 0.11 eV, ^{close to the} apparent activation energy of the InSb plastic deformation.

Classification

Physics ^Abstracts

46.30

61.70

62.40

1. Introduction.

The plasticity of semiconductor III-V compounds

has been intensely ^{studied for} several years in order to reduce the high density ^of grown-in dislocations in

crystals ^made by liquid encapsulation Czochralski

(LEC) technique [1].

At low temperature (T/Tm 0.4) ^the plastic

deformation of single crystals ^{deformed in} simple glide ^{seems to} be controlled by the motion of screw

dislocations [2]. ^At higher temperature, the mechan- isms involved are more complex ^{and the initial}

dislocation density ^{seems to} plan ^an important part in plastic deformation. In the case of GaAs [2-5],

InP [6], ^InSb [2], ^{it was} possible ^to determine the apparent activation energy between 0.3 and 0.6 Tm:

a rather important ^scatter appears through ^the

different results in the low stress range, where the stress relaxation technique ^{does not seem to be}

suitable. In order to get ^more informations about the different mechanisms involved in the dislocation

displacement, ^{and to} precise the values of the activation energies ^{in the low stress} range (i.e. ^shear

stress from 10-6 03BC ^to 10-5 03BC ; 03BC : ^shear modulus), ^it

was interesting ^{to use another} technique, ^{i.e. the}

intemal friction. With a linear rise in temperature, this technique ^{allows to} get ^a spectrum ^{of elastic} energy losses, ^{related to the} thermally ^activated displacement ^{of the different} structural defects _pre-

sent in the material [7]. ^The displacement ^{of the}

different types ^of dislocations moving ^{in the} sample give ^{rise to several} peaks ^{centered on different} temperatures Tp, Tp ^{being related to the activation}

energy of the displacement by ^{an Arrhenius law.}

Compared ^{to this} technique, plastic deformation tests give ^{a mean} estimation on the different types ^of mobile dislocations [8].

In undoped InSb, ^{Ohori and Sumino} [9] ^found

three low amplitude peaks ^of dislocations in the high frequency range (kHz) with activation energies ^0.05,

0.08 and 0.36 eV with activation energies ^{0.05, 0.08}

and 0.36 eV, ^{but none} of these values can be attributed to dislocation glide of any type.

The aim of this paper is to present ^low frequency (=1 Hz) measurements of intemal friction due to

screw dislocation displacement ⁱⁿ undoped ^InSb.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:019880023070129100

1292

2. Experimental.

In order to study ^the mobility ^{of a} given type ^of dislocations, ^{one has to be able to} introduce these dislocations selectively into the material. This has been done for screw dislocations by plastic ^defor-

mation of InSb at low temperature, i.e. below 430 K

[2].

The present experiments ^{were made on and} undoped ^InSb crystal supplied by ^MCP France,

which has the following characteristics :

The samples (20 ^{x 6 x 6} mm 3 ) has their compres- sion axis paralle ^to [123] with lateral faces of

(111 ) ^and (541 ) type, ^{in order to favour} single glide by activation of the primary glide system (111) [101 ]. ^{Moreover, the} preferential ^{abrasion of a}

lateral face (541 ) ^{favoured the} superficial ^activation

of fast a-type ^60° dislocations, ^{which can} easily generate ^screw dislocations (soft mode) [10]. ^The compression ^{tests were} made under helium atmos-

phere ^{at a constant strain rate} (1’

^{3.4 x 10-5} S- 1)@

with an apparatus previously ^described [3]. ^The

deformation was achieved in two stages : ^a predefor-

mation of 1.2 % at 523 K beyond the lower yield point, ^{then a} deformation of 1.4 % at 403 K. The

samples ^were then cooled down to room temperature under stress, in order to preserve the generated

dislocation substructure.

After plastic deformation, ^the samples ^{were cut}

with a wire saw. The internal friction samples (dimensions ^{20 x 2 x 0.8} mm3), ^with long ^axis paral-

le to [123 ] (large ^{lateral faces} parallel ^to (541 )) ^were

obtained after mechanical polishing. ^A subsequent

chemical polishing permitted ^{to remove the surface}

defects introduced by mechanical polishing.

The internal friction and elastic modulus measure- ments have been made with a torsion pendulum, especially adapted ^for brittle materials [11], working

in free decay ^{at a low} frequency (1 Hz) ^between

77 K and 790 K, ^the temperature rising ^{at a constant}

rate of 2 K/min. The measurements were made at

amplitudes (maximal ^shear strain) ranging ^from 2 x 10- 6 to 6.5 x 10- 6.

TEM observations made after plastic deformation allowed to observe the dislocation substructure

(Fig. 4).

Fig. ^1.

^{Internal friction} Q-1

and elastic modulus

f 2 curves versus temperature ^for undoped ^InSb crystals.

undef. : undeformed sample ; ^{def. :} sample ^deformed by

uniaxial compression : ^{1,2 % 523 K + 1,4 % 403 K.}

3. Results.

Figure ¹ shows the typical internal friction and elastic modulus as functions of temperature ^obtained during ^{a first rise in} temperature ^{from 300 K to} 790 K, ^{with a} measurement amplitude ^{of 6.5 x} 10- 6 (maximum ^shear deformation). ^For compari-

son, the curves related to an undeformed InSb single crystal ^{with same} orientation are shown on the same

figure. ^{The curves} for the deformed material show rather low values of intemal friction

(Q-l === 4 ^x 10- 6 ) ^{at low} temperatures. ^{It increases} slowly ^with temperature up ^to 500 K, ^{then a more} pronounced increase of Q-1 ^{occurs and two} peaks

appear superimposed ^{on a} high temperature background. ^This background ^{can be described} by ^a

law of the type QF A exp HF _{12]. The}

law of the type QF

^{A p} kT ^{[12]. Thé}

values of the two parameters ^{A and} HF ^deduced

from a plot ^of log (Q-1- QÕ 1) versus 1 T ^{(QÕ 1 :}

Fig. ^2.

a) ^{Internal friction} 0394Q-1 (after background substraction) ^{versus T-1.} b) Differentiated elastic modulus

d f2 _{versus T- 1.}

dT versus T-1.

apparatus background) ^{are A}

^{0.34 ;} HF

0.22 eV. Figure 2a shows the variation of the intemal friction 0394Q-1 obtained after substraction of the

background (QF 1 ⁺ Q-0 1) ^{as a function of T- 1. Two}

well-defined, separated, peaks appear centered ^on 570 K and 725 K, ^with respective heights ^{25 x 10- 4}

and 15 x 10-4.

Figure 2b shows the variation of the differentiated modulus df2 dT ^{versus T-1. Two minima of} df2 dT ^appear

at the temperature ^{of the} 0394Q-1 peaks ^{and a third}

one at 650 K. The symmetry ^{of the curve} 0394Q-1

versus T-1 observed for the peak ^{at 570 K} suggests ^a comparison ^{with a} Debye peak ^{of the} type à Q

0394 03C903C4 1+03C9203C4 where w is the frequency of the oscil-

lations, à the relaxation strength, ^{and T the relax-}

ation time related to the temperature by ^{an Ar-}

rhenius ^rhenius 1 ^{law : r} = 03C40 exp

To exp AH

kT

Figure 3 shows that the shape ^{of the} experimental peak ^{is close to that of a} Debye peak, ^{with a}

03C40 ranging ^from 10-13 s to 10- II s. The associated activation _energy, deduced from the peak tempera- ture, varies ^from 1.16 eV (for To

10-11 s) ^to

1.38 eV (for ^03C40

^10-13 s). ^{The same type of} analysis applied ^{to the} high temperature peak ^{leads to values}

of 1.47 eV for To

10- 11 s and 1.76 eV for _03C40

10-13 s.

Fig. ^3.

Fitting of the low temperature peak by ^a Debye peak. experimental peak ; - - - Debye peak (To

^{10- "} s) ; ;... Debye peak (03C40

^{10- 11} s).

4. Discussion.

In discussing ^the experimental ^results presented ⁱⁿ

the preceeding section, ^{we have to take into account}

the observed characteristics of the dislocation sub- structure induced by plastic deformation at 403 K.

The TEM observations (Fig. 4) ^{show a} majority (~ ⁹⁰ %) ^of straight ^screw dislocations parallel ^to

[101 ], ^{with some 60°} dislocations (~10 %), ^{the total} density being ^{about 1.2 x} 108 CM- 2.

The two peaks only observed after plastic ^defor-

mation are due to the dislocations induced by plastic

deformation. They ^are of relaxation types according

to the modulus defects observed at the peak ^tem- peratures ^on the elastic modulus curve (Fig. 2b).

i) ^The highest peak, ^{centered on 570 K, is} prob- ably ^{related to screw} dislocations. Indeed in most

published models, ^the height ^of peaks ^{due to the}

dislocation relaxation [13] ^is proportional ^to pLn (1 ⁿ 2 ) ^{where p is the} density ^{of mobile dislo-}

cations and L the mean free length ^{of these dislo-}

cations. This peak is very similar ^to the y-peak,

observed in BCC metals. As a matter of fact, ^while the peaks of intemal friction related to dislocations

are generally ^{4 to 5 times} wider than a Debye peak (like ^Bordoni peaks ^{in FCC} crystals), ^{it has been}

observed that in BCC metals, long straight ^screw

dislocations introduced after plastic deformation at low temperature gave rise to the ypeak, very close to a Debye peak [14]. ^{So one} may ^assume that this

peak originates ^{from a} mechanism of double kink

generation ^{on screw} dislocations, ^as in BCC metals

([15], [7]).

The activation energy related ^to the mobility ^of

screw dislocations that is deduced from our exper- iments is 1.27 ± 0.11 eV ; ^{this value is} just ^{a little} higher ^than the value of 1.15 eV found with stress relaxation tests made during plastic deformation [2].

Besides, it has been shown that the plastic ^defor-

mation of 111-V compounds ^{at low} temperature ^was controlled by ^the displacement ^{of screw} dislocations

[2]. Moreover, individual dislocation velocity

measurements [16] gave ^a value of 1.1 eV related to the mobility ^{of screw} dislocations. The good agree- ment between the values of àH calculated with the different techniques thus confirms our interpretation

of the 570 K peak.

The lowest peak, ^{centered on 725} K, might origi-

nate from the same mechanism but acting ^{on the}

other type ^of dislocations observed in the material

(i.e. ^60° dislocations, probably ^of /3-type), ^{which are}

in lower density. Indeed, individual dislocation vel-

ocity measurements [16] gave ^an activation energy

Q/3 ^{greater than} Qscrew (Qp ^{~1.2 eV). Compared to}

these results and those of TEM in situ studies [17],

the activation energies Qscerw ^and Qf3 ^{should be close}

together, ^{while an} important gap (= ^0.3 eV) sepa- rates our two peaks, excluding ^{such an} hypothesis.

The 725 K peak ^takes place ^at high temperature

(0.89 Tm) : exodiffusion of the volatile element overcomes, favouring ^a process of dislocation climb characterized by ^an irreversible evolution of the microstructure. Such an evolution is traduced by ^the

modulus defect observed at 650 K without any

anomaly ^{on the} Q-1(T) ^curve. Some dislocation

loops and debris observed by ^{TEM after internal}

friction experiments support ^this hypothesis. ^The

two peaks ^still appear during ^{the 2nd and 3rd rises in}

temperature, ^{at the same} temperatures, ^{but with}

lower amplitudes.

1294

Fig. ^4.

Dislocation substructure after plastic deformation. TEM observations : majority (~ ⁹⁰ %) ^of straight ^screw dislocations, ^{with some 60°} dislocations (~10 %).

5. Conclusion.

The above presented ^{results are the first} results of low frequency (1 Hz) ^{intemal friction} experiments

on III-V compounds, ^{on a} large range of temperature (0.1 ^{to 0.98} Tm). ^{In the case of} undoped InSb, ^the

low temperature deformation gives ^{rise to two well-}

defined peaks : ^{the first one at 570 K} (= ^0.7 Tm ) ^is surely ^{due to} double kink generation ^{followed with}

lateral kink migration ^{on screw} dislocations. The second peak ^{at 725 K} (= ^0.9 Tm) ^{is more difficult to} explain. ^Further experiments ^are necessary, espe-

cially by changing ^the dislocation substructure intro- duced with other deformation conditions. ^{It seems} necessary ^{too to} take into account the effect of the

applied ^stress (amplitude ^{effects or static stress}

superimposed).

Acknowledgments.

The authors like to thank J. J. Couderc and P.

Chomel (Laboratoire ^de Physique ^{des Solides de}

Toulouse) ^{for TEM} observations, ^{D. Caillard and}

A. Couret (L.O.E. Toulouse), ^J. Woirgard ^{and P.}

Mazot (ENSMA Poitiers) for constructive dis- cussions.

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