IMPURITY BAND CONDUCTION STUDY BY PIEZORESISTANCE MEASUREMENTS

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IMPURITY BAND CONDUCTION STUDY BY

PIEZORESISTANCE MEASUREMENTS

M. Averous, J. Calas, C. Fau

To cite this version:

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IMPURITY BAND CONDUCTION STUDY

BY PIEZORESISTANCE MEASUREMENTS

M. AVEROUS, J. CALAS and C. FAU Centre d'Etudes d'Electronique des Solides (*)

UniversitB des Sciences et Techniques du Languedoc, P1. E. Bataillon, 34060 Montpellier Cedex, France

R6sumB.

-

En utilisant une technique de modulation de la contrainte uniaxe, nous Btudions la piezorksistance correspondant aux processus de conduction par bande d'impuretks et par hopping. Dans la conduction par bande d'impuretk la pikzorksistance est interpretbe par la variation de l'knergie d'activation 62 avec la contrainte. E2 est relik B 81, l'knergie d'ionisation, par la distance moyenne entre les impuretks R et a* le rayon effectif de Bohr. Le principal inter& de la piezorksistance dans cette &ion est de mettre en Bvidence l'existence de ce processus de conduction. D'autre part, cela nous permet de determiner avec precision les tempkratures entre lesquelles nous avons ce processus. Dans la conduction par hopping, quand elle existe, la pi~zor~sistance est relike a la variation de 8s avec la contrainte ; c'est-a-dire a la diminution de l'extension spatiale des fonctions d'onde de l'impuretk avec la contrainte.

Abstract. - By using a modulation technic of the uniaxial strain, when a static strain is applied, we study the piezoresistance corresponding to impurity band and hopping conduction processes. In impurity band conduction process, piezoresistance data are explained by the strain-induced variation of the activation energy 82 of the impurity band. 82 is related to 81, the ionization energy, through R, the average impurity separation, and a*, the effective Bohr radius. The main interest of piezoresistance measurements in this region is to show the existence of this conduction process. On the other hand, they enable us to accurately determine the range of temperature where this type of conduction takes place. In hopping conduction process, when it exists, we relate our results with the strain-induced variation of 63, which is the activation energy of the hopping process. Piezoresistance data can been explained by the decrease of the spatial extension of impurity wave functions under strain, i. e. by the decrease of the overlap of the wave functions.

Since the discovery of impurity conduction by Busch and Labhart [I] in S i c and by Hung and Gliessman [2] in Ge, a large effect has been devoted to the under- standing of this conduction mechanism [3,4]. Impurity conduction exhibits quite different properties for different impurity concentrations. Namely, at low concentration when R/a*

>

5, where

R

is the average separation of majority impurities and a * is their effectif Bohr radius, the impurity conduction exhibits an activation energy named 8,. In the range of intermediate concentration defined by 3

<

R/a*

<

5 the conduction process is least understood. The resistivity exhibits two activation energies 8, and. 8, a t low temperature. At high impurity concentration a transition to

metallic conduction is observed, and may be explained in the scheme of a degenerate semiconductor. In this work. we study with the help of piezoresistance measurements, the intermediate concentration on p type Gallin Antinionide. Since Tufte and Seltzer's paper no work has been done on the piezoresistance in p type GaSb. Their results are limited to 77 K-300 K, and the concentration range was reduced, so they were rather incomplete. Since this -first paper, galvanamagnetic

(*) Associk au C. N. R. S.

effects have been examined in p-GaSb using uniaxial compressionnal stresses by Metzler and Becker [6]. A study of activation energies with uniaxial static stress has been presented recently by Averous et al. [7]. In all

cases the range corresponding to intermediate concentration is very difficult to understand because the region where G , appears, may be considered like a n intermediate region between conduction by Hopping. By using a modulation of the stress we can show by the study of the derivate of the activation energies with the strain, that G, is not a superposition of two conduction processes, but really a n other process.

1. Experimental results.

-

Figure 1 shows the resistivity as a fonction of 103/T for all samples. The samples 2,3,4, are in (100) direction, and the samples 1 and 5 are in (111) direction. We see very clearly two parts where log p is linear with 103/T. For the samples 1 2 and 3, in the intermediate temperature range we cannot speak without ambiguity of a linearity with 103/T.

Figure 2 shows the Hall constant versus 1 0 3 / ~ f o r all samples. We can see that R, increases reaches a maxi- mum then decreases. For the samples 1, 2 and 3,

RH

disappears at low temperature, so we conclude that in

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C4-334 M. AVEROUS, J. CALAS AND C. FAU

FIG. 3.

-

Longitudinal'piezoresistance coefficients obtained by a modulation of the stress as a function of IO3lTfor all samples.

this range the conduction is made by bound carriers. For the samples 4 and 5

RH

becomes flat at low temperature.

From figures 2 and 3, we may make the following comments. If we consider the samples 1 , 2 and 3 which present three parts in piezoresistance,

R,

disappears in the range corresponding to the third part. So we can attribute this piezoresistance effect to the bound carriers. If we compare the Hall constant and the piezo-

107 K-I),

T resistance coefficient for the sample 4 and 5 we can FIG. I. - ReSiStivity as a function of 103/T for all samples. conclude that we have only two conduction processes :

conduction by valence band at high temperatures, conduction by impurity band a t low temperatures.

FIG. 4.

-

FOI resistivity and

sample 3 (100 direction) a superimposition of the the piezoresistance coefficient in arbitrary units

as a function of 103IT. 105

i

-

₀

,+

-

_I: a '03- 1 0 '

Figure 5 and figure 6 give piezoresistance data for different values of the static strain, respectively for the samples 3 and 1. The main remark is that, when the strain increases, the range of temperature corresponding to G , increases to.

-

,!'I

A ' A 2

1

-

lo

&,/o 3

Ejy"

Y

i

:rr

A o

Ty'

*y:\a5*- 4

. f

-...

_-.

_' ₅ _I ' ' ' ' 0 50 100 150

Figure 4 shows a superimposition of the resistivity and the piezoresistance coefficient .rill as a function of

1 0 3 / ~ for the sample 3, we can see the correspondence between the three parts in piezoresistance and in resistivity. ?'

-

lo3( K-I)

-

T ' ' A A)AM A+?* ' A_\ & . A ' p 4 1 A

\

< + / A , *

\$

1 .

"%

51

/"

/

[ F l

A ~ ~ . . ~ l s s n s ~ n c t . t ~ ~ a ~ 0 100 200

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FIG. 5.

-

Piezoresistance coefficients for sample 3 at different uniaxial compressional static stresses versus lO3/T.

'03(K-1 )-

T

FIG. 6. - The same for sample 1.

2. Interpretation.

-

We don't speak about high temperature region because we have previously published this study in two different ways : at first by using the acceptor binding energy method for the determination of b and d deformation potential constant values [7] and secondly in the point of view of the scattering processes 191. In this paper we speak only about the two regions corresponding to conduction by impurity band and hopping respectively.

The piezoresistance coefficients n,,,,, are generally 1 ap

defined like

-

,

when a static strain e is applied. In

E 0

our case we ap;?ly a static strain and we superimposed a modulated strain for making the n,,,,, measurements. So we can write our piezoresistance coefficients

1

a~

--where is the amplitude of the strain modu-

P

lation, p the resistivity at a given strain. If we have a pure conduction process,

and the slope of our piezoresistance curves as a function of l / k T gives the value of a6,/ae at a given strain. Figure 3 shows the piezoresistance coefficients zI,, for all samples as a function of 103/T.

nlmn is the piezoresistance in the (1, m, n) direction. It is to be borne in mind that when the current J is parallel to the field strengh X and to the (1 11) direction,

where S is the surface of the sample, p its resistivity. I f J / / X / / (100)

nij are the piezoresistance coefficients in the Smith no- tation 181. One can see two different behaviours if one compares the samples 1, 2 and 3 on the one hand, 4 and 5 on the other. The first three exhibit three parts :

n(1, m, n) decreases linearly with 103/T, passes through a minimum, then increases when 103/T increases. Part 111 shows a difference between the samples 1 and 2, and the sample 3 ; for samples 3 I1 increases. With 1 0 3 / ~ the principal interest of this figure is to show the existence without ambiguity of three regions. For samples 4 and 5 we have only clearly two parts. First n(1, m, n) decreases when 103/T increases, exhibits a minimum between 20 to 24 K and then increases. This is well verified for El because it is rather large and the measurements without modulation are signifi- cative so we can compared with our piezoresistance data.

This enable us, to show that the region I1 is very well defined, and it is not an intermediate region, but a region which corresponds to a characteristic conduction process. We deduce from the curves of figures 5 and 6 that dE,/de is always positive, eg that 6, increases in all cases with the strain. This fact is consistent with the decreasing of 6, with the strain as shown previously [7]. Let us remind, that at low temperature most

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C4-336 M. AVEROUS, J. CALAS AND C. FAU

Under some assumptions, Mikoshiba [lo] shows that equal to the separation between the Fermi Ievel and the 8, = Gl - p, where

p

is the exchange interaction ; level of isolated impurities

he found that : _{El = E + E , .}

-*

(1

+

$)

exp(-

$1

When the compensation is weak, E3 is given by an

Xa* expression of the form

where s is the screening parameter deduced from Slater's rule,

x

dielectric constant,

R the average impurities separation calculated from

a* the effective Bohr Radius calculated from

*

* 2 113

a* = (a/, a.L

1

with

//and

I

to the strain direction n, is an ajustable parameter which is a function of neighbourhouds. So we see that

p

varies like

sR

eap - ( h ( 2 m * ~ 1 ) 1 1 2

varies more quikly than any power of El ; this fact explains that G2 decreases when GI increases, and so explains that dE,/ds is positive when dEl/ds is negative. The variation of R with s is very small before the variation of a*.

For region 111, we have three different behaviours. For sample 4 and 5, we cannot speak of conduction by Hopping process. These samples are degenerated and their Hall constant is flat with 103/T(Fig. 2).

For sample 1 in one hand, and samples 2 and 3 in other hand dE3/de is positive and negative respectively. These appears in figure 2. When a static strain is apply for sample 1, dE3/ds increases with s and for sample 3, dG3/ds decreases with s (Fig. 5 and 6) This is explain.ed if the compensation are strongly different ; when the compensation is large the activation energy 8, remains

with

C1 = 0.66 C, = 1.35 a = 1 for Abrahams and Miller [l 11.

for Shklovskii [12].

K is the compensation = ND/NA.

So at the first order when a sample is strongly compensated, E, varies with the strain like

El

thus dE3/dE is negative.

For a weakly compensated sample, when N, increases the activation energy E3 deviates from the above equation because at low values of K the levels of most of acceptors are very little perturbated and their energies are very close to one another. Therefore the overly of the wave functions of the resonant states leads to the formation of an in~purity band. When we applied a strain, the spatial extension of the wave function decreases through a* and thus the overlap between the neighbouring acceptor states decreases too. So 8, increases with the strain and dE3/dE is positive. 3. Conclusion.

-

By using a modulation technic of the uniaxial strain, when a static strain is applied we made piezoresistance measurements on p type GaSb. In the low temperature region, we show clearly that the intermediate part corresponds to a well defined conduction process which is an impurity band conduction. The piezoresistance data are explained i n term of change of E,, the activation energy, of the impurity band, with the strain in the middle region and in term of variation of G3, the activation energy of the Hopping process, with the stress, in the lowest region : the behaviour of piezoresistance with the strain in the last case is different when K the compensation varies.

References

[l] B u s c ~ , G. and LABHART, H., Helv. Phys. Acta 19 (1946) 463. [7] AVEROUS, M., CALAS, J. and FAU, C., Proceeding of the 12th HUNG, C. S. and GLIESSMAN, J. R., Phys. Rev. 79 (1950) 726.

Mom, N. F. and twos^, W. D., Adv. Phys. edited by N. F. Mott 10 (1961) 107.

F~ITZSCHE, H., Phys. Rev. 125 (1962) 1552.

TUFTE, 0. N. and STELZER, E. L., Phys. Rev. 133 (1954) 1450.

international conference on the Phys. of Semicond. Stuttgart 223 (1974).

[8] SMITH, C., Phys. Rev. 94 (1954) 42.

191 AVEROUS, M., BONNAFE, J., CALAS, J. and FAN, C., Phys.

Stat. Sol. (a) 31 (1975) 227.

[lo] MIKOSHIBA, N., Phys. Rev. 187 (1962) 1960. . .