Dislocation-assisted complex scattering mobility of electrons in plastically deformed n-GaAs single crystals

Journal of Alloys and Compounds, 204 (1994) 37-45 JALCOM 886

37

Dislocation-assisted complex scattering mobility of electrons in plastically deformed n-GaAs single crystals C. V e e r e n d e r , M. N a g a b h u s h a n a m

and V. Haribabu

Department of Physics, University College of Technology, Osmania University, Hyderabad 500 007 (India)

(Received July 3, 1993)

Abstract DC conductivity and Hall effect measurements are made in undeformed and plastically deformed (by indentation) n-type GaAs samples between 77 and 300 K. The studies show that the dislocation-assisted vacancy complexes of activation energy 0.015-0.010 eV are present in deformed samples. The electron mobility of these samples is explained by considering different scattering processes. In plastically deformed samples an additional scattering mobility due to dislocation-assisted vacancy complexes is suggested to explain the experimental mobilities. The centres responsible for this scattering are associated with native vacancy complexes segregated at the dislocation sites. The fresh dislocation motion, mainly ce-dislocations (with higher mobility than /3-dislocations) help the creation and movement of acceptor vacancies and their segregation as complexes at the dislocation sites. The complex scattering mobility of electrons has been found to vary linearly with temperature in all the deformed samples. These complexes are also found to be temperature-insensitive throughout the extrinsic region of the sample.

1. Introduction Semiconductor crystals undergo a considerable degree of mechanical deformation during the fabrication of electronic devices [1, 2]. In the process, a number of defects such as surface damage, cracks, microtwins and dislocations are generated [3, 4]. Some of these defects can be avoided and others can be removed by carefully polishing and chemically etching the crystal; the exceptions are dislocations created inside the crystal due to sub-surface damage. These defects degrade the electrical properties of the semiconductors since the lifetime of the electronic carriers is reduced [5]. Moreover, fresh dislocations introduced via any damage may become the sources of segregation centres for impurity or dopant elements, and initiate brittle catastrophic failure of the device [6]. Therefore, the study of fresh dislocations, their interaction with point defects and their effect on the electrical properties of semiconductors are important. Fresh dislocations, which are 60 ° edge dislocations in a semiconductor, are known to introduce electronic levels in the forbidden gap associated with a dangling bond at the core [7]. Investigations on the electronic states of these dangling bonds have been made extensively on Ge and Si by measuring the Hall effect, mobility and photoconductivity [8-11]. Similar studies on binary semiconducting compounds such as InSb

Elsevier Sequoia SSD1 0925-8388(93 )00886-4

[12-14] and CdTe [15-17] have also been made. The general conclusions of these studies are: (i) c~- and/3-type dislocations, i.e. dislocations ending with indium and antimony atoms respectively in InSb crystals, and likewise in CdTe, introduce acceptor and donor levels respectively, (ii) the number of a- and/3-dislocations are introduced equally in InSb, (iii) s-dislocations move faster than /3-dislocations and thereby excess tellurium dislocations (donors) remain in CdTe. The authors have also studied the effect of dislocations on the galvanomagnetic properties of InSb single crystals, dislocations being created during the vacuum thermal annealing process [18]. So far only a few reports exist about the effects of dislocation on the electrical transport properties of GaAs [19-21]. Moreover, the studies concentrated on the formation of energy levels assisted by dislocations in the forbidden gap but the effect of fresh dislocations on charge carrier mobility and a comparison of experimental mobilities with theoretical ones were not attempted. Therefore, electrical conductivity, Hall coefficient and Hall mobility studies were performed from 77 to 300 K on uniaxially deformed GaAs using the indentation technique and the experimental mobilities were compared with mobilities arising from different scattering mechanisms. The discrepancy between the experimental and theoretical values of

38

C. Veerender et aL / Dislocation-assisted

mobilities are explained in terms of the effects of c~and /3-dislocations introduced during the process of deformation, their velocity and their interaction with the native defects of GaAs. A new scattering mechanism due to the complexes is also suggested to account for the experimental mobilities.

2. Experimental details

2.1. Sample preparation Single crystals of n-type GaAs were obtained from the Department of Physics, Federal University of Parana, Brazil. Slices perpendicular to the (111) axis were cut from the bulk, then from these slices, samples of rectangular bar geometry measuring about 4 x 1.5 x 1 mm 3 were cut. Work damage at the surface caused during sawing and lapping was removed by chemical etching. The etchant comprised HzSO4:H202:H20 in the ratio of 4:1:1 and was applied for about 2 rain. Five ohmic contacts (two current and three voltage contacts) are then made with spots of high purity indium at 200 °C in the presence of a nitrogen atmosphere. The voltage contacts were spread over the entire crosssection of the sample. The ohmic nature of the contacts was verified from the I - V characteristics throughout the temperature range under investigation (77-300 K). 2.2. Transport studies The Hall coefficient (RH) and conductivity (or) of the samples were measured using the standard five-probe technique. Measurements were taken from liquid nitrogen temperature (77 K) to room temperature (300 K) by mounting the sample in a double-walled vacuum cryostat, which has been described elsewhere [22]. The cryostat was placed exactly at the centre of tapered polecaps (5 cm diameter) of an electromagnet such that the sample is acted on by a uniform magnetic field. The uniformity and the strength of the magnetic field was measured with a differential gaussmeter. The current through the sample was tapped from the Keithley constant current source model No. 224. The Hall voltage and the voltage across the conductivity leads were measured using a Keithley nanovoltmeter model No. 181 for different currents through the sample. The output of the temperature sensor was measured through Keithley DMM 196. The three instruments were interfaced with PC (XT) through an IEEE-488 bus cable such that both the Hall and conductivity voltages were measured immediately one after the other at every 0.05 mV temperature difference. After the cryostat attained liquid nitrogen temperature, it was allowed to take the natural rise of temperature. Several measurements were taken to determine the correct Hall coefficient and conductivity values by changing the direction of the

complex scattering of electrons

current through sample and the magnetic field. A copper constantan thermocouple, with one of itsjunction's kept at 0 °C, was used as temperature sensor. The Hall voltage was measured to an accuracy of 0.3%. Taking into account the errors involved in the measurements of the magnetic field and the sample current, the error in RH is estimated to be about 1%. The conductivity is measured to an accuracy of 0.3%. The total error in the mobility measurement (RH X o') is therefore expected to be about 1.3%.

2.3. Plastic deformation After completing the Hall and conductivity measurements of the pure GaAs sample (referred to as G000) from 77 to 300 K, the sample was removed from the cryostat without disturbing the ohmic contacts. Then the sample was deformed by indenting with a diamond pointer attached to an NU-2 microscope. After every 40, 80 and 120 indentations (these samples are referred to as G040, G080 and G120) computer runs were made to measure the RH and ~r values at different temperatures. Care was taken to ensure that the indentations were distributed uniformly throughout the two large surfaces of the sample. This method of plastic deformation avoided the removal of ohmic contacts during the deformation process.

3. Results and discussion

3.1. Conductivity Figure 1 shows the variation in conductivity with temperature (log or vs. 103/T) for pure (G000) and deformed (G040, G080, G120) GaAs samples. The conductivity curves show that: (i) the pure sample has extrinsic conduction below 265 K (identified with the minimum of the conductivity curve), (ii) the starting temperatures for the extrinsic conduction of deformed samples (G040, G080 and G120) 0.98 Pure GO00

0.96

~

G040

E

~ o.9z b ~

0.9 0.88 103

_~

T(K )

)

Fig. ]. Temperature variation of the DC conductivity (log ~, v s . 1/7) for four samples of pure (G000) and deformed (G040, G080 and O120) n-type GaAs.

39

C. Veerender et al. / Dislocation-assisted complex scattering of electrons

shift gradually towards lower temperatures, nearly 240 K in G120 sample, (iii) the conductivity of the deformed samples at any given temperature is lower than that of the pure sample, (iv) though the conductivity values of all the samples are the same in the intrinsic region, they decrease gradually with the increase in deformation. These observations indicate that the deformation process creates defects that have a trapping nature (i.e. acceptor nature) towards the charge carriers (here these are electrons). These acceptor defects may be formed due to the higher velocity of o~-dislocations over /3dislocations where both are introduced during the deformation process. This observation is, respectively, unlike and like the observations made for InSb and CdTe [13, 17]. Also, a relatively steep rise observed in pure GaAs changes to a gradual one with an increase in deformation. This change may be a result of the formation of complex defects relating defect migration towards dislocations as a result of the motion of fresh dislocations.

3.2. Hall coefficient

The temperature variation in the Hall coefficient RH (in a magnetic field of 7.5 kG) for pure and deformed GaAs samples is shown in Fig. 2. The extrinsic region starts almost at 250 K in all the samples. This may be due to the high energy gap of the compound. RH is observed to be negative in all the samples showing the n-type nature of the samples. At every temperature, RH of the deformed sample decreases slightly from that of the pure sample, though a considerable change in conductivity is observed. As this change is small, overlapping of the curves is seen in Fig. 2. However, on sufficient magnification, the RH values are found to decrease with deformation.

3.3. Charge carrier concentration

The experimental values of the electron concentration n is taken as 3,/RH e, where e is the electronic charge and 3' is the Hall scattering factor which is equal to (T2)/(T) 2. To a fairly good approximation 3' is taken as unity in calculating n. A plot of n vs. T (log n vs. 103/T) is shown in Fig. 3. The temperature variation of the free charge carrier concentration n in the extrinsic region for compensated semiconductors (one-centre-one-level model) is given by:

n(n +NA) (No --NA--n)

=

N---sexp( - E D ) / k B T 2

(1)

where ND and Na represent the donor and acceptor concentrations respectively; Arc, the effective density of states in the conduction band, is given by Nc = 2(2mckB T/h2) 3;z

(2)

where me is the mass of the density of states, g is the degeneracy factor, kB is the Boltzmann constant and ED is the donor ionization energy. Equation (1) is fitted with the data given in Fig. 3 in order to determine NA, ND and ED for pure and deformed samples. The best fit values of NA and ND for the pure and deformed

1612

1608 I

E

0

g

o 6.6

,~ kc~o0°~

GI20 GOB0

16.04 5.8

~

~

o

6000

d

%

% 5,0 x l0 2

I03/T (K L)

)

Fig. 2. Temperature variation of DC Hall coefficient (log RH against l/T) for four samples of pure (G000) and deformed (G040, G080 and GI20) n-type GaAs.

0---~ I (K-') T

>

Fig. 3. Temperature variation of carrier concentration (log n vs. I/T) for four samples of pure (G000) and deformed (G040, G080 and G120) n-type GaAs.

40

C. Veerender et al. / Dislocation-assisted complex scattering o f electrons

TABLE 1. Calculated parameters for samples Sample

N^/N D

ED (eV)

ND (cm 3)

NA (cm 3)

N, (cm 3)

G000 G040 G080 G120

0.49 0.53 0.58 0.99

0.0172 0.0153 0.0122 0.0103

2.818x1016 2.531×10 ~6 1.854 × 10 '6 1.019× 1016

1.378×1016 1.351 × 10 I6 1.083 × 10 '6 1.017× 10 I6

4.196×1016 3.881x 10 '6 2.937× 1016 2.036x 1016

GO~00~

6.0

T I

/0 S

5.5

I

5.0

0.$

(/)

samples along with the donor ionization energies ED are given in Table 1. It is noted from this table that the values of ED for deformed samples are less than that of the pure one and ED decreases gradually with the increase in deformation. This indicates that the defects become shallower with deformation. It is also noted from Table 1 that the compensation ratio (NA/ No) increases with the deformation keeping their values higher than that of pure sample. This may be due to: (i) the creation of charged aeceptor centres during the formation and motion of a- and /3-dislocations introduced during the deformation, and (ii) the higher mobility of a-dislocations over /3dislocations helping the creation of acceptor centres and in turn reducing the electron concentration. As a result NA should increase with the increase in deformation, but the observed values of NA show a decreasing trend with the deformation. This contrary result may be due to some of the a-dislocations ending up (by virtue of their higher velocity over/3-dislocations) on the surface of the sample. At the same time, the possibility of acceptor complexes forming as a result of the interaction between fresh dislocations and native impurities, suggested by Gorodrichenko et al. [23] in GaAs, also cannot be ruled out. Thus the acceptor centres introduced during deformation and native impurities may segregate at slow moving dislocations (/3dislocations) and thereby cause a reduction in No. The same reduction in the values of ND may be observed from Table 1. In the present sample of n-GaAs, the reduction in No is such that NA/ND increases with deformation. However, the effective increase in compensation ratio (NA/ND) with the increase in deformation decreases the Charge carrier concentration.

3.4. Hall mobility The variation in Hall mobility ( # ~ = R n X a ) with temperature (log /x vs. log T) is shown in Fig. 4. It can be seen from the figure that the electron mobility decreases with deformation and that the mobility curves converge at higher temperatures. From the nearly equal mobilities of the samples near room temperature and from their increases with decreasing temperature, it appear s that carrier mobility is determined by both intrinsic properties and crystal defect centres. This figure

:

104 7>

T ~E >- 4.5 I-

I---

O

m O

_J

4.0

103

x I03 i

i

i

2Z3

i

£5

i

z.7

Log T (K) Fig. 4. Temperature dependence of observed Hall electron mobility (log p. vs. log T) for four samples of pure (G000) and deformed (0040, 0080 and O120) n-type GaAs. Temperature variation of calculated mobilities due tO deformation potential, optical phonon scattering and mobilities due to ionized impurities of deformed samples as indicated. TABLE 2. Peak temperature,/3 and estimated dislocation density for deformed samples Sample No.

Peak temperature T(K)

/3 (cm - i V - 1 s -~ K - ' )

N (cm 3 at 300 K)

G040 G080 G120

94 99 106

1528 1062 660

2.093 × 101° 3.012 × 10 '° 4.841 × 10 '°

also shows that the observed mobility of a deformed sample increases with a decrease in temperature and forms a peak depending on the strength of deformation, whereas within the observed temperature range (77-300 K) such a peak is not observed in the pure sample. The peak temperatures of different samples are noted against the sample numbers in Table 2. It is seen clearly from Table 2 that the peak temperature increases with an increase in the strength of deformation. To account for the observed mobility, scattering effects as a result of different defect centres have been considered and analysed. The mobility analysis adopted here is similar to that used by Ehrenreich [24, 25] for GaAs and InSb. Various scattering mechanisms were taken into account in these analyses. It was shown that the polar nature of the compound has a major effect

C. Veerender et al. / Dislocation-assisted complex scattering of electrons

41

TABLE 3. Values of parameters used in calculations Parameters

Value taken

me* =me/rno = effective mass of electron a=lattice parameter (cm) Ed=dislocation energy (eV) u= Poisson's ratio C~= p(#2) = average longitudinal elastic constant e~=static dielectric constant e= = high frequency dielectric constant w~=longitudinal optical phonon frequency ep~=piezoelectric coupling constant (A s cm -2) ~ = acoustical deformation potential (eV) C4 = coupling constant (eV)

0.068 5 . 6 5 3 2 x 10 - 8 6.942 0.31 1.19x1012 12.85

10.88 5 . 3 7 2 × t 0 t3 9 . 0 4 5 2 × 1 0 - t~ 22.6 15

Values of all the parameters are taken from the review articles of J.S. Blakemore [49] and D.E. Aspnes [50].

on the transport properties. As GaAs is one such compound, different scattering mechanisms need to be considered. The possible intrinsic scattering mechanisms are deformation potential (acoustic) scattering, piezoelectric scattering and polar and non-polar scattering associated with the optic modes. Ionized impurities, well-known defect centres, will also contribute to the above scattering phenomena. In all four scattering processes the mobility drops off with increasing temperature. Since we want to determine which of these mechanisms makes an appreciable contribution to the observed mobility we will consider each of these separately in some detail. Unless indicated otherwise, the complications arising from the degenerate energy bands are approximated to simple bands.

3.4.1. Piezoelectric scattering Scattering by piezoelectrically active acoustic modes [26, 27] results from a small component of non-vanishing polarization present in the long-wavelength acoustic modes. The mobility of carriers in a simple band with this interaction is l'05p(p~12) es2 /ZPES ----

e142(me/mo)3/2Tl/2

cm 2

V_I s-1

(3)

where e, is the static dielectric constant, e14 is the piezoelectric constant (in e.s.u, cm-2); p is density; (tz~2) is the square of the longitudinal sound velocity averaged over direction; and me/mo is the effective mass of electrons. Substituting the various parameters (given in Table 3) into eqn. (3), the resulting mobility is: JI'LPES ~--- (1.087 × 1 0 6 ) ( 3 0 0 / T )

1/2 c m 2 V - 1

s -1

3.4.2. Deformation potential scattering Atomic vibration deforms the potential energy configuration of the cation and leads to small vibrations in the energy gap. The variation in the energies of the conduction and valence band edges resulting from the vibrational motion is localized; these changes in potential energy of the carriers are only effected at the expense of changes in the kinetic energy of the carriers. Hence the mobility of the carriers is modified by the effects of deformation potentials caused by lattice vibrations. The deformation potential scattering mobility can be expressed as: /"~DPS--

2(2~-) m 3

eh4o(U~)2 7 eao2m*5/2(kuT) 3/2 cm2 V - 1

s-I

(5)

where e,c denotes the acoustic deformation potential in electron volts for the relevant band edge. Different values for eac have been suggested in the literature, but the commonly used value (22.6 eV) [28] is taken in our calculations. 3' is the Hall factor (tzH/t*) which has been evaluated for GaAs at various temperatures and for various scattering mechanisms by Ehrenreich [29]. For this scattering mode y = 1.01, with these values the calculated deformation potential scattering mobilities are given by: /ZDes = 5.912 × 107/Tz5 cm 2 V 1 s - 1

(6)

Since these values are approximately 30 and 10 times larger than the measured values at liquid nitrogen temperature and room temperature respectively, this scattering method is taken into account and its temperature variation is shown in Fig. 4.

(4)

The mobility values calculated using eqn. (4) turn out to be 400 times larger than the measured mobilities, indicating that this mechanism does not play an important role in determining Ize.

3.4.3. Non-polar optical mode scattering The expression for the mobility of holes in degenerate conduction bands scattered by non-polar interaction with optical phonons, tZNpo, can be written as:

C. Veerender et al. I Dislocation-assisted complex scattering of electrons

42

~ L N p 0 '~"

3.4.5. Polar optical phonon scattering

(1.35 X 10'7)pa203 [m*5/Z(m,~/2+ m21/2)1/2] C42T5/2 (rn, 3/2+ m23/z) ×

exp(- 0./T) 6(l/x)

(7)

with ~b(t)-n(1 +t)l/2+(n + 1)(1 - - t ) 1/2 =n(1 +t) '/z

for t< 1 for t> 1

Here n is an optical phonon occupation number given by [exp(O/7)-l) -1, O=hto,/kB is the Debye temperature, m I and m2 are the masses of the light and heavy holes respectively, a is the lattice constant (in centimetres) and C4 is the coupling constant in electron volts, about which little is known. Its upper limit in InSb was roughly estimated to be 15 eV [30]. Using the value of 15 eV for GaAs, we found that/ZNpo has values many times larger than those observed. With significantly larger values for the mass and C4 than estimated, /ZNpo could yield values comparable with the observed values. However, it is important to note that /ZNpo increases too rapidly as the temperature decreases, which is not in agreement with the temperature dependence of the observed mobility. Thus, at present we cannot rule out the possibility that this type of scattering contributes significantly to the total, but we suggest that it does not dominate the scattering.

3.4.4. Space charge scattering In highly compensated semiconductors an intrinsic region occurs in the materials owing to local compensation of the donors or acceptors. The intrinsic region is surrounded by space charge owing to the difference in Fermi level between the bulk of the materials and the intrinsic region. The potential difference thus created acts as an infinite well for the carriers. Treating these scattering centres as large impenetrable spheres of density ns and cross-sectional area G, the space charge scattering mobility is estimated to be: IZscs =el(nstrhkB)

(8)

This scattering plays quite an important role below a critical temperature for highly doped materials. For highly compensated materials this temperature may be near to room temperature. The diameter of the space charge was determined by Conwell and Vassel [30] to be 20 nm for a free carrier concentration of 10a5 cm -3. Although the highly deformed sample has a compensation ratio of nearly 0.99, with the values given above, it is observed to be 80 to 90 times larger than the experimental values. It is therefore not considered to be of importance.

This is the important scattering mechanism in III-V semiconducting compounds. It arises from the scattering of carriers by the electric polarization associated with induced electrostatic potential by the longitudinal optical phonons. The lattice polarization inducing the potential is a measure of the ionization of the bond, and consideration of the polarization at high and low frequencies gives a measure of the influence of ionization on the static dielectric constant. The expression for the dependence of mobility on the polar longitudinal optical mode scattering is:

1

e

8

(e2-')G(z) e-e-/

/*DPS-- 2aw, mr* 3~/2

(z '/z)

(9)

where z=ho~l/kT, o~1 is the angular frequency of the longitudinal optical phonons at the centre of the Brillouin zone. G(z)e -~ is a function which has been evaluated by Howarth and Sondheimer [31] and expanded by Ehrenreich [32] to include carrier screening effects and a is a polar coupling constant which is given by:

a = (melmo)'/2(Rylhto,)'/2(1/¢=

-

lies)

(10)

where Ry is Rydberg energy, and e= and es are the high and low frequency dielectric constants respectively. An implicit assumption in the derivation of the optical phonon scattering probability is that the phonon field and the carriers interact only weakly (i.e. a small coupling constant). The strong or weak coupling of the carriers depends on whether a is greater or less than unity. It is not clear up to which limit is reasonable for the magnitude of weak coupling. Aven and Segall [33] pointed out that the factor which reflects the relative magnitude of the succeeding terms for the weak coupling case is a/6. Since od6 is only 0.1 for GaAs, the weak coupling approach is adequate. In the limit of weak coupling the polaron mass mp replaces rn* in eqn. (9) through the relation mp = rn*(1 + a)/6

(11)

Usually IZoPs is calculated under the assumption that the parameters Es, e and hto I are independent of temperature. Thus the calculated /ZoPs is shown in Fig. 4. It should be noted that these corrections lead to values of/-~oes that are closer to the observed mobilities in the intrinsic range.

3.4. 6. Ionized impurity scattering Of all the lattice imperfections in a material, the scattering of a charge carrier in the coulomb field as a result of ionized impurities is of greatest importance. Calculations of the scattering rate of the charge carriers have been made by many workers for ionized impurities, but that of Brooks [34] is the most widely used. They

C. Veerender et aL / Dislocation-assisted complex scattering of electrons

applied the Debye screening term to limit the scattering for large impact parameters and calculate the transition probability for a parabolic band. For a non-parabolic band, having spherical constant energy surfaces, the scattering mobility can be written as: 27/2(47resEo)2

(kB T)3/2T

/LIIS= ~r3/2z2e3m~* ~/2N, [ln(1 + b) - b/(1 - b)]

(12)

where Ze is the charge of the ionized impurity atom; N~ is the total concentration of ionized impurities and is equal to NA+ND; G is the dielectric constant; eo is the permittivity of free space; h is Planck's constant and b is given by b = 24 me*(kBT)2~Sseo/(hae2n)

(13)

Substituting the proper values of the parameters as given in Table 2, the expressions are 3.95 × 10~ST3/2 ×y ~bIIS= N[ln(1 + b ) - b / ( 1 +b)]

(14)

b = 1.14 x 10~3T2/n

(15)

Here the Hall factor y = 1.93 [35]. The values of P-~s calculated using eqns. (14) and (15) at low temperatures were found to be not very much higher than the observed values. Therefore the ionized impurity scattering mobility is an important one among the others. Moreover it depends strongly on the concentration of ionized impurities. As this concentration changes for pure and deformed samples the tXHs is computed differently for different samples. The variation of/Xns with temperature for all the samples are shown in Fig. 4.

equation for /3 at the peak temperature (To) as -- ~/2

/3= T 2 ( d ~ T ) T-To

(18)

Hence,/3 values for the three deformed samples G040, G080 and G120 are calculated by substituting /x and d~/dT of the pure sample G000 taken at the corresponding peak temperatures of the deformed samples in eqn. (18). The calculated values of/3 along with the peak temperatures of the deformed samples are tabulated in Table 2. Each of the mobilities considered was computed using its respective expression. The individual temperature variation of tXops, tXDPSand /Xns are shown in Fig. 4. Dislocation mobility ~D of deformed samples are calculated using eqns. (16) and (18), and are plotted (log tXD VS. log 7) in Fig. 5. Following Rode [37] the total mobility 0XT, where the subscript T stands for theoretically calculated) is related to the intrinsic mobilities IX~ through I//.ZT = ~ 1 / ~ ,

(19)

1//J,T = I/~DPS + l/IXOPS + 1/~itS "b 1//3. D

(20)

The variation of /XT with temperature is shown in Fig. 4 as a solid line. At all the temperatures, the /XT curve deviates from the tx¢ curves of the deformed samples. Similar results have also been observed by different authors in binary semiconductor samples treated differently [38-40]. Mathur et al. [39] have studied the

ixl06

3.4. 7. Dislocation scattering

The temperature dependence of the dislocation scattering mobility of electrons in deformed samples will be interpreted by using the model proposed by Dexter and Seitz [36], according to which scattering of charge carriers by deformation potential associated with stationary edge dislocation is possible in samples possessing a dislocation concentration of more than 1 ×108 per cubic centimetre. The dislocation scattering according to them is characterized by the mobility tx and is given by #r~=flT

43

(16)

7u 4x10 5

Y, T

2>

~e (.) >b-.._1

o z; ixl05

where /3 = (32(1 - p)2kBhe)/(3fr(l - 2v)2Eo2AZNm *)

(17)

The parameter Ea represents the energy associated with dislocation, A is the lattice parameter and N the dislocation density. The other parameters are the usual ones. The mobility due to dislocation scattering of deformed samples is deduced using a differential method described earlier [17]. This method finally gives an

4 x 104 1.9

2.1

2.5 2.5 Log T K > Fig. 5. T e m p e r a t u r e variation of mobilities (log Iz vs. log T) due to eslimated dislocation and complex scattering.

44

C. Veerender et aL / Dislocation-assisted complex scattering of electrons

effects of high temperature anneal of n-CdS single crystals in cadmium on the electrical transport properties. It was found that the mobility values measured experimentally were lower than those calculated theoretically using a method based on the Brooks-Herring formula. The discrepancy was explained in terms of the effect of the carrier-carrier scattering correction applied to the Brooks-Herring mobility values. We have also studied ionized impurity scattering (IIS) in CdTe:Cd:In samples [40]. In these samples complexes such as [CdTe+-CII] or [Vc~-In]-~ were supposed to contribute somehow to lower the value of the carrier-carrier scattering correction to the IIS. Larsen et al. [38] have studied the electrical transport and photoelectronic properties on ZnTe:AI crystals. The most important results of their investigations are the evidence for significant contributions of the [Vz,A1] complex centre (an impurity-vacancy acceptor) and the dominance of this defect centre in many electronic properties such as electrical conductivity, photoconductivity and thermally stimulated current studies. Recently two of the authors have also studied IR-photoexcited p-type ZnTe and suggested that scattering mobility due to vacancy complexes segregated at the dislocation sites [40]. A relation between /x and T was also established (in the case of ZnTe) a s i z = A T S e BIT. In several other II-VI compounds the incorporation of donor impurities led to the formation of impurity-vacancy acceptors [41-43]. Likewise, photoluminescence studies of n-GaAs have suggested the presence of complexes containing both structure defects and impurity atoms: (VAsVGa) and (VasCuoa); (TeA.,VG,); (SnAsVGa); (SiG,CuG~) and so on [44-46]. Antisite defects, ASGa, formed during plastic deformation of GaAs are also identified by electron paramagnetic resonance measurements [47]. It is therefore known that GaAs crystals contain both gallium and arsenic vacancies, as well as gallium, arsenic and impurity interstitial atoms [45]. In the case of ntype GaAs the gallium vacancies VGa readily form complexes with donor impurity atoms [45, 46]. Interaction among these defects is active due to the motion of dislocations created during plastic deformation. This helps the formation of complexes with donor impurity atoms and acceptor centres created from the motion of a-dislocations either at native or relatively stationary dislocations (/3-type). EPMA studies of the original samples of GaAs have shown evidence of a very small amount of Fe impurities. Therefore, dislocations introduced during the deformation process may help the formation of complexes with Fe impurity atoms and acceptor vacancies at dislocation sites. In turn these complexes may scatter charge carriers (electrons) and give rise to a difference between the theoretical and experimental values of mobilities.

As the e--e scattering correction to ionized impurity scattering suggested by Bate et al. [48] cannot account for the difference in experimental and theoretical mobilities, it leads one to consider a scattering process as a result of dislocation-assisted complexes. The scattering mobility resulting from the complexes (/Xc) in deformed samples is thus calculated using 1/IZc = 1//z -

(21)

1//z T

The variation of/Xc with T for all the deformed samples is shown in Fig. 5. It can be seen that the complex scattering mobility varies linearly with T in all the deformed samples. (This linear variation is unlike the variation observed in IR-photoexcited ZnTe [37]. The reason may be because of the temperature insensitivity (within the temperature range observed) of complexes formed in GaAs, whereas the complexes are temperature sensitive in ZnTe). Figure 5 also shows that the number of complexes increases with an increase in the number of dislocations. The dislocation density introduced in each deformed sample is also calculated using eqn. (22) 32(1 p)2kBThe N = 37r(1 - 21j)2e~a)t2/ZD m * -

(22)

A plot between dislocation density and the strength of deformation (number of indentations) (Fig. 6) shows that N varies nonlinearly with deformation. This may be because of multiplication of dislocations and creation of vacancies during the motion of fresh dislocations. The excess dislocations and vacancies are therefore bound to form strong complexes which cannot be dissociated at temperatures below 260 K, i.e. in the temperature range corresponding to the extrinsic region.

v

4

g 8 O

i:5 2 x 101°

0

4 '0

d0 120 ' Tndenfation number Fig. 6. N o n l i n e a r variation o f dislocation density vs. t h e n u m b e r of i n d e n t a t i o n s .

C. Veerender et al. / Dislocation-assisted

4. Conclusions Hall mobility and DC conductivity of deformed nGaAs single crystals are found to be less than those of an underformed sample and, further, they decrease with the strength of deformation. Electrical conduction of the carriers is attributed to different scattering mechanisms. The electron mobilities as a result of scattering processes like piezoelectric, optical, ionized and dislocation scattering could not explain the experimental mobilities of deformed samples; additional scattering mobility resulting from a dislocation-assisted vacancy complex is suggested to explain mobility in the deformed samples. The activation energies of these complexes in the deformed samples range from 0.015 to 0.01 cV. The complexes are insensitive to the temperature in the extrinsic region.

Acknowledgments The authors CV and MNB thank the Head of the Department of Physics, Osmania University and the Principal of the College of Technology, Osmania University for their constant encouragement. One of the authors (CV) thanks the CSIR, New Delhi, India for providing a Senior Research Fellowship.

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