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Observation of transverse negative magnetoresistance in heteroepitaxial films of InSb on GaAs
Solid State Communications, Printed in Great Britain.
OBSERVATION
Vol. 71, No. 10, pp. 871-874,
OF TRANSVERSE HETEROEPITAXTAL J.B. Webb,
Laboratory
0038-1098/89 $3.00 + .OO Pergamon Press plc
1989.
NEGATIVE MAGNETORESISTANCE FILMS OF InSb ON GaAs
M. Paiment
and T. Sudersena
Rao*
for Microstructural Sciences, Division of Physics, National Research 100 Sussex Drive, Ottawa KlA 0R6, Canada (Received
27 February
IN
Council
Canada,
1989 by M.F. Collins)
The transverse magnetoresistance of InSb layers deposited epitaxially on (1OO)GaAs is reported. The magnetoresistance shows two components, a positive one for sufficiently thick layers, and a negative component that is revealed when the thickness of the layer is reduced. The negative magnetoresistance appears to arise from weak localisation of charge carriers at defects near the InSb/GaAs interface, since regions of low defect density show no negative component, while regions of high defect density show a predominantly negative component. The magnetoresistance can be accounted for using the model proposed by Shmartsev et al., in which the negative magnetoresistance arises from scattering of conduction electrons from localised impurity magnetic moments. The electron g-factor deduced from the model agrees closely with the predicted value for bulk InSb having similar levels of impurities. 1. INTRODUCTION THE OBSERVATION of negative magnetoresistance in heavily n and p doped InSb has been reported in a number of publications [l-6]. The effect has also been observed in doped Ge, manganese doped InAs [7] and in a number of metallic systems [S]. Although negative magnetoresistance has been primarily observed in doped semiconductors, there are some data reported by Broom [2] on mechanically deformed bulk crystals of InSb indicating that defect induced localisation effects can also give rise to this phenomenom. Broom found that negative magnetoresistance could be induced in bulk crystals of InSb by either grinding the surface of the crystal with an abrasive, which was believed to create microcracks, or by physically bending the sample. It was concluded that the phenomenon was not a bulk property of the material but was largely due to the method of specimen preparation. Since then, no further observations of negative magnetoresistance arising from the formation of lattice defects, have been reported. Recent advances in the quantum theory of Anderson localisation in disordered systems have provided a qualitative description of the negative magnetoresistante observed in n-InSb at low fields near 1OmK’ * Present address: Waterloo Scientific, Waterloo, Ont. Canada N2L 3X2.
419 Phillip
although a complete description of the phenomenon is not yet available. On the other hand, Shmartsev et al. [l] proposed a simple physical model a number of years ago, which has since been used to provide an empirical description of many of the results [9] reported in the literature. The model predicts the amplitude dependence of magnetoresistance on impurity concentration, as well as the magnetic moment of the localised site and field dependence of the magnetic moment in samples with high impurity concentration. In this study it is found that the model can also be used to describe the observed behaviour of the transverse negative magnetoresistance in heteroepitaxial layers of InSb on GaAs.
St. 871
2. RESULTS
AND DISCUSSION
The epitaxial layers used in this study were grown on semi-insulating (lOO)GaAs using the technique of metalorganic magnetron sputtering. A discussion of the growth technique and of the structural properties of the layers have been described in an earlier work [9]. The films selected for this study were n-type with a measured room temperature carrier concentration and mobility, based on a single carrier model of n = 1 x IO” cme3, p = 4 x lo3 cm2/V.s and n = 4 x 10”cmm3, p = 950cm2/V.s. for the 1.67pm and 0.17 pm thick films respectively. For all film thicknesses, the carrier concentration was only weakly dependent on temperature,
872
TRANSVERSE
Table 1. Summary given in the text.
Sample
NEGATIVE
of epilayer properties
Temp. 6)
and calculated values of mobility and electron g-factor based on the model
n
Pmeas
J%,k
(cmm3)
(cm’/V.s)
(cm’/V.s)
1.4 x 10” 1.4 x 10”
4400 4200
1900 1600
RT 77
1.67
NJ253
RT
0.26
77 RT 77
Vol. 71, No. 10
Thickness (microns)
NJ254
NJ256
MAGNETORESISTANCE
0.17
g
-
3.0 x 10”
1600
1400
-
3.3 x 10”
870
980
- 29
4.1 x 10” 4.2 x 10”
950 530
760 450
- 18 - 22
however the mobility decreased markedly with decreasing temperature for the thinner films. The reduced value of mobility for the thicker layers results from both increased scattering from defects near the interface and from compensation [lo]. A summary of the electrical properties of the layers used in this study is given in Table 1. The transverse magnetoresistance at 77 and 300 K was measured on 0.5 cm square samples in a Van der Pauw configuration. The results for three films, (1.67, 0.26 and 0.17 pm in thickness) are shown in Figs. 1 and 2. As shown in Fig. 1, at 300 K the magnetoresistance for the three films is positive for all the values of field up to 20 kG, but decreases in magnitude for decreasing film thickness and for decreasing temperature. The decrease with temperature is indicated in Fig. 2, where the measured magnetoresistance at 77 K is shown. However, unlike the results shown in Fig. 1,
the magnetoresistance for the thinnest film is negative for all values of the applied field. For this film, there is an initial decrease in magnetoresistance at low fields, followed by an increase at higher fields with a magnetoresistive minimum of - 1.2% at 12 kG. A similar behaviour is observed for film NJ253, however, the minimum is shifted to lower fields and the magnetoresistance changes sign and becomes positive at about 13 kG. No minimum is observed in the case of NJ254 which again shows only a positive magnetoresistance at all fields. It may be pointed out here that a similar dependence on magnetic field and temperature has been observed by several workers, in non-magnetic metals doped with magnetic impurities. This phenomenon has often been attributed to the scattering of conduction electrons by localised impurity magnetic moments. Toyozawa [1 1] proposed that magnetic states could also occur in semiconductors doped with non-magnetic
100
60
\
2
8 NJ256
t
60
-
Calc
^o ;‘ 2
4o
0
-20
L++-++-+-t 0 5
Magnetic
-20
-+--I 10
Field
15
20
(kGauss)
Fig. 1. Field dependence of the transverse sistance at 300 K, for samples of various
I 0
5
Magnetic magnetorethicknesses.
10
Field
15
0
(kGauss)
Fig. 2. Field dependence of the transverse sistance at 77K, for samples of various
magnetorethicknesses.
Vol. 71, No. 10
TRANSVERSE
NEGATIVE
impurities. Although Toyozawa’s model has been invoked by a number of researchers to explain the observed negative magnetoresistance in these semiconductors, the model fails to predict the experimentally observed magnetic field and temperature dependence of negative magnetoresistance. On the other hand, Shmartsev et al. [l] proposed a simple physical model based on Toyozawa’s results and previously reported results in doped semiconductors. Shmartsev noted that the onset of negative magnetoresistance usually occurs when the density of dopant atoms lies in the range 0.1 < N”3a, < 1 (near the Mott transition limit for metallic conduction), where N is the impurity density and uB is the Bohr radius of the impurity atom. For these levels of doping the degree of overlap between impurity states will be sufficient for the formation of an impurity band. In the case of InSb, the very small effective mass of the electrons means that the Bohr radius of a localised electron is very large. As a result, the formation of an impurity band will occur even at relatively low doping densities. Conduction will then occur by thermally assisted tunnelling between impurity states or by variable range hopping at lower temperatures. At sufficiently high impurity densities (above the Mott transition [12]), the donor band merges with the conduction band giving rise to metallic-like conduction. In this instance the electrons are delocalised with a magnetic susceptiblity that is temperature independent. However, since the donor levels are randomly distributed, some sites will be sufficiently separated from their nearest neighbours to form a localised centre at low temperature. These centres will have a corresponding magnetic moment and will give rise to a negative component of magnetoresistance through scattering of the conduction electrons. The negative magnetoresistance associated with such a scattering mechanism is given by AR/R,
-
(M)*
=
N;B;,
(1)
where M_ is the magnetic moment of the impurity site, N,, the number of impurities, and B, is the Brillouin function. For a localised magnetic moment in an sstate, the Brillouin function becomes B,
=
-a
tanh’(u*H/kT)
(2)
and u* = gu, where uII is the Bohr magnetron and h is the applied magnetic field. However, since the total observed magnetoresistance is the sum of a negative and one or more positive components, Shmartsev proposed the following empirical equation to explain the observed behaviour. R/&
=
- oB,’ + hH” + (exponential
where the first term is the negative
term),
component
(3) given
MAGNETORESISTANCE
873
by equation (2) and the second term is the commonly observed dependence of magnetoresistance for two band conduction [13]. For CL,,$ pPLp, the second term becomes = A’& Hz where A’ is a constant that depends on the carrier scattering mechanism and sample geometry. From the HZ term, the relative change in carrier mobility as a function of sample thickness can be deduced. Using equations (2) and (3) the various components of the magnetoresistance can be analytically separated. The solid lines in Figs. 1 and 2 are fits to the data based on the above equations. Deviations from the H* dependence is observed at high magnetic fields in the thicker layers, although no evidence for an exponential term is indicated. Thus, this term has been excluded from the calculations. The results of this calculation are given in Table 1. Several observations can be made from these results. Firstly, the negative component of magnetoresistante is essentially independent of thickness, but shows a decrease with increasing temperature in accordance with the temperature dependence of the Brillouin function. The calculated g values are given in Table 1. Within the accuracy of the three parameter fit, the g factor is essentially constant with an average value of -23. g values for the conduction electrons at this impurity concentration can be estimated from the known values of band gap and spin orbit splitting using the equation [14] g
=
2{1 -
[m&l*
-
11[A/3((&+ -%I + 2)1)> (4)
where m* is the electron effective mass at the Fermi energy, m, the free elecron mass and A the spin orbit splitting. For a carrier concentration of N IO” cmm3 the g value is estimated to be - 25. Unlike the results reported for doped Ge, the g values obtained in this study are close to those estimated for bulk InSb having similar levels of impurity doping. Secondly, the H* positive term increases with increasing layer thickness. This would be expected on the basis of the higher mobilities of the thicker samples. The closer agreement between the measured mobility and that of flp,,,, for the thinner films may result from a change in scattering of the carriers with decreasing film thickness. This would be consistent with the increased defect density observed for the thinner layers. Finally, for sufficiently thick layers, the negative component of magnetoresistance is completely masked by the positive term. Charge localisation in these epilayers can arise through a number of mechanisms related to lattice defects. The samples measured in this study show a continuous change in defect density with thickness. The large 14.6% lattice mismatch between the GaAs substrate and the InSb epilayer results in a high
874
TRANSVERSE
NEGATIVE
number (- IO” cm-*) of dislocations in the interface region [9]. This decreases to near lo9 cm-* at a distance of 3pm from the interface. In addition, epitaxy of InSb on GaAs proceeds by a 3-D island growth process which can introduce reduced dimensional localisation for sufficiently thin layers. For instance, for a layer thickness of 1700 A (NJ256), one observes a high density of interconnected rectangular islands, having an average width of 850 A, aligned in the ( 110) direction [9]. The width of these islands is similar to the Bohr radius of a localised electron in InSb (642 A) [l]. These defects are likely to contribute to carrier trapping in regions near the InSb/GaAs interface, although the exact mechanisms are not as yet clear. The correlation of defects with localisation is clearly indicated in sample NJ254, which is a continuous layer with lower overall defect density. Only positive magnetoresistance is observed within the temperature range studied. 3. SUMMARY (1) Regions of low defect density show no negative magnetoresistance within the temperature range studied. Localisation of carriers does not appear to be important at these temperatures and impurity densities for low defect InSb. (2) Regions of sufficiently high defect density show only a negative component indicating that weak localisation of charge carriers can arise from defects induced by lattice mismatch. (3) The observed field dependence of the magnet-
MAGNETORESISTANCE
Vol. 71, No. 10
oresistance can be described by the model proposed by Shmartsev [l]. The calculated g values deduced from this model are consistent with those predicted from ESR studies [14]. REFERENCES 1. 2. 3.
4. 5. 6. 7.
8. 9. 10.
11. 12. 13.
14.
Yu.V. Shmartsev, E.F. Shender & T.A. Polyanskaya, Sov. Phys.-Semicond. 4, 1990 (1971). R.F. Broom, Proc. Phys. Sot. 71, 470 (1958). S. Morita, T. Fukase, Y. Isawa, S. Ishida, Y. Takeuti &N. Mikoshiba, Proc. 15th Znt. conf. Phys. Semicond. Kyoto (1980). B.R. Sethi, P.K. Goyal, O.P. Sharma & P.C. Mathur, Phys. Status Solidi (b) 119,721 (1983). V.V. Galavanov & Z.A. Parimbekov, Sov. Phys. Semicond. 13, 69 (1979). M.M. Kechiev & O.N. Filatov, Sov. Phys. Semicond. 6, 1689 (1973). D.G. Andrianov, V.V. Karataev, G.V. Lazareva, Yu.B. Muravlev & A.S. Savel’ev, Sov. Phys. Semicond. 11, 738 (1977). R.C. Dynes, Proc. 16th Zntl. Conf. on Low Temp. Phys. (Los Angeles, 1981) Physica lOSA, (1982). T. Sudersena Rao, C. Halpin, J.B. Webb & J. Noad, Thin Sol. Films 163, 399 (1988). T. Sudersena Rao, C. Halpin, J.B. Webb, J. Noad & J. McCaffrey, J. Appl. Phys. 65, 585 (1989). Y. Toyozawa, J. Phys. Sot. Jap. 17,986 (1962). N.F. Mott, Phil. Msg. 6, 287 (1961). See for instance S.M. Sze, in Physics of Semiconductor Devices, Wiley-Interscience, New York (1969). R.A. Issacson, Phys. Rev. 169, 312 (1968).
OBSERVATION
Vol. 71, No. 10, pp. 871-874,
OF TRANSVERSE HETEROEPITAXTAL J.B. Webb,
Laboratory
0038-1098/89 $3.00 + .OO Pergamon Press plc
1989.
NEGATIVE MAGNETORESISTANCE FILMS OF InSb ON GaAs
M. Paiment
and T. Sudersena
Rao*
for Microstructural Sciences, Division of Physics, National Research 100 Sussex Drive, Ottawa KlA 0R6, Canada (Received
27 February
IN
Council
Canada,
1989 by M.F. Collins)
The transverse magnetoresistance of InSb layers deposited epitaxially on (1OO)GaAs is reported. The magnetoresistance shows two components, a positive one for sufficiently thick layers, and a negative component that is revealed when the thickness of the layer is reduced. The negative magnetoresistance appears to arise from weak localisation of charge carriers at defects near the InSb/GaAs interface, since regions of low defect density show no negative component, while regions of high defect density show a predominantly negative component. The magnetoresistance can be accounted for using the model proposed by Shmartsev et al., in which the negative magnetoresistance arises from scattering of conduction electrons from localised impurity magnetic moments. The electron g-factor deduced from the model agrees closely with the predicted value for bulk InSb having similar levels of impurities. 1. INTRODUCTION THE OBSERVATION of negative magnetoresistance in heavily n and p doped InSb has been reported in a number of publications [l-6]. The effect has also been observed in doped Ge, manganese doped InAs [7] and in a number of metallic systems [S]. Although negative magnetoresistance has been primarily observed in doped semiconductors, there are some data reported by Broom [2] on mechanically deformed bulk crystals of InSb indicating that defect induced localisation effects can also give rise to this phenomenom. Broom found that negative magnetoresistance could be induced in bulk crystals of InSb by either grinding the surface of the crystal with an abrasive, which was believed to create microcracks, or by physically bending the sample. It was concluded that the phenomenon was not a bulk property of the material but was largely due to the method of specimen preparation. Since then, no further observations of negative magnetoresistance arising from the formation of lattice defects, have been reported. Recent advances in the quantum theory of Anderson localisation in disordered systems have provided a qualitative description of the negative magnetoresistante observed in n-InSb at low fields near 1OmK’ * Present address: Waterloo Scientific, Waterloo, Ont. Canada N2L 3X2.
419 Phillip
although a complete description of the phenomenon is not yet available. On the other hand, Shmartsev et al. [l] proposed a simple physical model a number of years ago, which has since been used to provide an empirical description of many of the results [9] reported in the literature. The model predicts the amplitude dependence of magnetoresistance on impurity concentration, as well as the magnetic moment of the localised site and field dependence of the magnetic moment in samples with high impurity concentration. In this study it is found that the model can also be used to describe the observed behaviour of the transverse negative magnetoresistance in heteroepitaxial layers of InSb on GaAs.
St. 871
2. RESULTS
AND DISCUSSION
The epitaxial layers used in this study were grown on semi-insulating (lOO)GaAs using the technique of metalorganic magnetron sputtering. A discussion of the growth technique and of the structural properties of the layers have been described in an earlier work [9]. The films selected for this study were n-type with a measured room temperature carrier concentration and mobility, based on a single carrier model of n = 1 x IO” cme3, p = 4 x lo3 cm2/V.s and n = 4 x 10”cmm3, p = 950cm2/V.s. for the 1.67pm and 0.17 pm thick films respectively. For all film thicknesses, the carrier concentration was only weakly dependent on temperature,
872
TRANSVERSE
Table 1. Summary given in the text.
Sample
NEGATIVE
of epilayer properties
Temp. 6)
and calculated values of mobility and electron g-factor based on the model
n
Pmeas
J%,k
(cmm3)
(cm’/V.s)
(cm’/V.s)
1.4 x 10” 1.4 x 10”
4400 4200
1900 1600
RT 77
1.67
NJ253
RT
0.26
77 RT 77
Vol. 71, No. 10
Thickness (microns)
NJ254
NJ256
MAGNETORESISTANCE
0.17
g
-
3.0 x 10”
1600
1400
-
3.3 x 10”
870
980
- 29
4.1 x 10” 4.2 x 10”
950 530
760 450
- 18 - 22
however the mobility decreased markedly with decreasing temperature for the thinner films. The reduced value of mobility for the thicker layers results from both increased scattering from defects near the interface and from compensation [lo]. A summary of the electrical properties of the layers used in this study is given in Table 1. The transverse magnetoresistance at 77 and 300 K was measured on 0.5 cm square samples in a Van der Pauw configuration. The results for three films, (1.67, 0.26 and 0.17 pm in thickness) are shown in Figs. 1 and 2. As shown in Fig. 1, at 300 K the magnetoresistance for the three films is positive for all the values of field up to 20 kG, but decreases in magnitude for decreasing film thickness and for decreasing temperature. The decrease with temperature is indicated in Fig. 2, where the measured magnetoresistance at 77 K is shown. However, unlike the results shown in Fig. 1,
the magnetoresistance for the thinnest film is negative for all values of the applied field. For this film, there is an initial decrease in magnetoresistance at low fields, followed by an increase at higher fields with a magnetoresistive minimum of - 1.2% at 12 kG. A similar behaviour is observed for film NJ253, however, the minimum is shifted to lower fields and the magnetoresistance changes sign and becomes positive at about 13 kG. No minimum is observed in the case of NJ254 which again shows only a positive magnetoresistance at all fields. It may be pointed out here that a similar dependence on magnetic field and temperature has been observed by several workers, in non-magnetic metals doped with magnetic impurities. This phenomenon has often been attributed to the scattering of conduction electrons by localised impurity magnetic moments. Toyozawa [1 1] proposed that magnetic states could also occur in semiconductors doped with non-magnetic
100
60
\
2
8 NJ256
t
60
-
Calc
^o ;‘ 2
4o
0
-20
L++-++-+-t 0 5
Magnetic
-20
-+--I 10
Field
15
20
(kGauss)
Fig. 1. Field dependence of the transverse sistance at 300 K, for samples of various
I 0
5
Magnetic magnetorethicknesses.
10
Field
15
0
(kGauss)
Fig. 2. Field dependence of the transverse sistance at 77K, for samples of various
magnetorethicknesses.
Vol. 71, No. 10
TRANSVERSE
NEGATIVE
impurities. Although Toyozawa’s model has been invoked by a number of researchers to explain the observed negative magnetoresistance in these semiconductors, the model fails to predict the experimentally observed magnetic field and temperature dependence of negative magnetoresistance. On the other hand, Shmartsev et al. [l] proposed a simple physical model based on Toyozawa’s results and previously reported results in doped semiconductors. Shmartsev noted that the onset of negative magnetoresistance usually occurs when the density of dopant atoms lies in the range 0.1 < N”3a, < 1 (near the Mott transition limit for metallic conduction), where N is the impurity density and uB is the Bohr radius of the impurity atom. For these levels of doping the degree of overlap between impurity states will be sufficient for the formation of an impurity band. In the case of InSb, the very small effective mass of the electrons means that the Bohr radius of a localised electron is very large. As a result, the formation of an impurity band will occur even at relatively low doping densities. Conduction will then occur by thermally assisted tunnelling between impurity states or by variable range hopping at lower temperatures. At sufficiently high impurity densities (above the Mott transition [12]), the donor band merges with the conduction band giving rise to metallic-like conduction. In this instance the electrons are delocalised with a magnetic susceptiblity that is temperature independent. However, since the donor levels are randomly distributed, some sites will be sufficiently separated from their nearest neighbours to form a localised centre at low temperature. These centres will have a corresponding magnetic moment and will give rise to a negative component of magnetoresistance through scattering of the conduction electrons. The negative magnetoresistance associated with such a scattering mechanism is given by AR/R,
-
(M)*
=
N;B;,
(1)
where M_ is the magnetic moment of the impurity site, N,, the number of impurities, and B, is the Brillouin function. For a localised magnetic moment in an sstate, the Brillouin function becomes B,
=
-a
tanh’(u*H/kT)
(2)
and u* = gu, where uII is the Bohr magnetron and h is the applied magnetic field. However, since the total observed magnetoresistance is the sum of a negative and one or more positive components, Shmartsev proposed the following empirical equation to explain the observed behaviour. R/&
=
- oB,’ + hH” + (exponential
where the first term is the negative
term),
component
(3) given
MAGNETORESISTANCE
873
by equation (2) and the second term is the commonly observed dependence of magnetoresistance for two band conduction [13]. For CL,,$ pPLp, the second term becomes = A’& Hz where A’ is a constant that depends on the carrier scattering mechanism and sample geometry. From the HZ term, the relative change in carrier mobility as a function of sample thickness can be deduced. Using equations (2) and (3) the various components of the magnetoresistance can be analytically separated. The solid lines in Figs. 1 and 2 are fits to the data based on the above equations. Deviations from the H* dependence is observed at high magnetic fields in the thicker layers, although no evidence for an exponential term is indicated. Thus, this term has been excluded from the calculations. The results of this calculation are given in Table 1. Several observations can be made from these results. Firstly, the negative component of magnetoresistante is essentially independent of thickness, but shows a decrease with increasing temperature in accordance with the temperature dependence of the Brillouin function. The calculated g values are given in Table 1. Within the accuracy of the three parameter fit, the g factor is essentially constant with an average value of -23. g values for the conduction electrons at this impurity concentration can be estimated from the known values of band gap and spin orbit splitting using the equation [14] g
=
2{1 -
[m&l*
-
11[A/3((&+ -%I + 2)1)> (4)
where m* is the electron effective mass at the Fermi energy, m, the free elecron mass and A the spin orbit splitting. For a carrier concentration of N IO” cmm3 the g value is estimated to be - 25. Unlike the results reported for doped Ge, the g values obtained in this study are close to those estimated for bulk InSb having similar levels of impurity doping. Secondly, the H* positive term increases with increasing layer thickness. This would be expected on the basis of the higher mobilities of the thicker samples. The closer agreement between the measured mobility and that of flp,,,, for the thinner films may result from a change in scattering of the carriers with decreasing film thickness. This would be consistent with the increased defect density observed for the thinner layers. Finally, for sufficiently thick layers, the negative component of magnetoresistance is completely masked by the positive term. Charge localisation in these epilayers can arise through a number of mechanisms related to lattice defects. The samples measured in this study show a continuous change in defect density with thickness. The large 14.6% lattice mismatch between the GaAs substrate and the InSb epilayer results in a high
874
TRANSVERSE
NEGATIVE
number (- IO” cm-*) of dislocations in the interface region [9]. This decreases to near lo9 cm-* at a distance of 3pm from the interface. In addition, epitaxy of InSb on GaAs proceeds by a 3-D island growth process which can introduce reduced dimensional localisation for sufficiently thin layers. For instance, for a layer thickness of 1700 A (NJ256), one observes a high density of interconnected rectangular islands, having an average width of 850 A, aligned in the ( 110) direction [9]. The width of these islands is similar to the Bohr radius of a localised electron in InSb (642 A) [l]. These defects are likely to contribute to carrier trapping in regions near the InSb/GaAs interface, although the exact mechanisms are not as yet clear. The correlation of defects with localisation is clearly indicated in sample NJ254, which is a continuous layer with lower overall defect density. Only positive magnetoresistance is observed within the temperature range studied. 3. SUMMARY (1) Regions of low defect density show no negative magnetoresistance within the temperature range studied. Localisation of carriers does not appear to be important at these temperatures and impurity densities for low defect InSb. (2) Regions of sufficiently high defect density show only a negative component indicating that weak localisation of charge carriers can arise from defects induced by lattice mismatch. (3) The observed field dependence of the magnet-
MAGNETORESISTANCE
Vol. 71, No. 10
oresistance can be described by the model proposed by Shmartsev [l]. The calculated g values deduced from this model are consistent with those predicted from ESR studies [14]. REFERENCES 1. 2. 3.
4. 5. 6. 7.
8. 9. 10.
11. 12. 13.
14.
Yu.V. Shmartsev, E.F. Shender & T.A. Polyanskaya, Sov. Phys.-Semicond. 4, 1990 (1971). R.F. Broom, Proc. Phys. Sot. 71, 470 (1958). S. Morita, T. Fukase, Y. Isawa, S. Ishida, Y. Takeuti &N. Mikoshiba, Proc. 15th Znt. conf. Phys. Semicond. Kyoto (1980). B.R. Sethi, P.K. Goyal, O.P. Sharma & P.C. Mathur, Phys. Status Solidi (b) 119,721 (1983). V.V. Galavanov & Z.A. Parimbekov, Sov. Phys. Semicond. 13, 69 (1979). M.M. Kechiev & O.N. Filatov, Sov. Phys. Semicond. 6, 1689 (1973). D.G. Andrianov, V.V. Karataev, G.V. Lazareva, Yu.B. Muravlev & A.S. Savel’ev, Sov. Phys. Semicond. 11, 738 (1977). R.C. Dynes, Proc. 16th Zntl. Conf. on Low Temp. Phys. (Los Angeles, 1981) Physica lOSA, (1982). T. Sudersena Rao, C. Halpin, J.B. Webb & J. Noad, Thin Sol. Films 163, 399 (1988). T. Sudersena Rao, C. Halpin, J.B. Webb, J. Noad & J. McCaffrey, J. Appl. Phys. 65, 585 (1989). Y. Toyozawa, J. Phys. Sot. Jap. 17,986 (1962). N.F. Mott, Phil. Msg. 6, 287 (1961). See for instance S.M. Sze, in Physics of Semiconductor Devices, Wiley-Interscience, New York (1969). R.A. Issacson, Phys. Rev. 169, 312 (1968).