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Galvanomagnetic effects in n-InSb at low temperatures in strong magnetic fields
518
SESSION
S:
GALVANOMAGNETIC
EFFECTS
Table 1. The activation energy, CA, for the mobility of electrons in. donor levels localized by a strong jield and the ratio of EAto the donor ionization energy, 61,for three n-type InSb samples.
magnetic
(k = Boltzmann’s constant)
n, = 3.3 x 1Ol4 cm-s es/k 10
15 20 24 28
-
EAIEI :
-
4.5”K
0.29 0.34 0.33 0.32
B-l n, = 1.4 X lOi crnm3 CA/k
j
-
CA/El
O-l n = 1.04 X lOi crne3 i
:aik
~
8.O”K 9.8
-
7.3”K 8.7 9.4 9.8
0.38 0.39 0.39 0.37
1 i
-
I is the jump frequency given by the exchange integral.) According to equation (2), an explicit temperature dependence of Tpi is contained in the bracketed factor, which represents the probability of donor levels being empty and thus providing sites into which electrons can jump. In the absence of compensation (or if only excess donors provide bound levels) this factor decreases approximately exponentially as the temperature is lowered and thus could account for the observed temperature dependence of TM. (See Fig. 3, for example.) However, we believe that our samples are rather highly compensated. In this case the bracketed factor would be almost independent of temperature. Thus D itself would have to be a thermally activated function of temperature to account for the observed
J. Phys. Chem. Solids
s.4
Pergamon
i
lA/c1 0.49 0.51
-
I I
1
temperature dependence of Tpt. This could occur, for example, if electrons need to be raised to excited donor levels in order for them to conduct. Such a hypothesis is consistent with the fact that the ratio of the activation energy to the donor ionization energy is constant in a given sample. (See Table 1.) Acknowledgments-Thanks are due to E. N. R. W. KEYES for helpful discussions.
ADAMS
and
REFERENCES 1. SLADEK R. J. J. Phys. Chem. Solids 5, 157 (1958).
Y., KEYES R. W., and ADAMS E. N. r. Phys. Chem. Solids 1, 137 (1956). 3. HUNG C. S. Phys. Rev. 79, 727 (1950). 4. GREENE R. F. and ADAMS E. N. Westinghouse Research Laboratories Scientific Paper 6-94760-2P14. 2.
YAFET
Press 1959. Vol. 8. pp. 518-523.
Printed in Great Britain
GALVANOMAGNETIC EFFECTS IN a--InSb AT LOW TEMPERATURES IN STRONG MAGNETIC FIELDS* J. C. HASLETT and W. F. LOVE Physics Department,
University of Colorado, Boulder, Colorado
1. INTRODUCTION
AS a result of the low effective mass in the conduction band of n-InSb, the magnetic quantum of energy Lo (WC = cyclotron frequency) is quite * This work was supported by the United States Atomic Energy Commission and the Council on Research and Creative Work of the University of Colorado.
large even in moderate magnetic fields. Under the condition that fiwc$ E and kT, where E is the electron energy, all electrons will occupy the ground oscillator state of their motion transverse to the field. This extreme case has been designated as the “quantum limit” by ARGYRES and ADAMS.(~) The purpose of these experiments was to provide
SESSION
S:
GALVANOMAGNETIC
519
EFFECTS
25 24
16
I OO
I
I
20
40
I
60
I 60
I 100
I 120
I 140
I
160
I
,
H (Kilogauss)
FIG. 1. Longitudinal magnetoresistance ratio of I&b 2712 vs. magnetic field strength at 78“K, 14”K, and 3.9°K.
experimental data on InSb in the quantum limit. At liquid-helium temperatures a single band picture no longer applies to ta-InSb. In a magnetic field impurity levels split off from the conduction band to form an impurity band. This leads to “freeze out” effects in the galvanomagnetic properties.c2-4) 2. ~~~~ REXWB The technique for producing pulsed magnetic fields is described adequately in the literature.(5-‘) In these experiments the original data are taken
with a Tektronix 535 oscilloscope and Polaroid Land Camera. The horizontal sweep is driven by a signal proportional to the magnetic field and the vertical sweep by the sample voltage. Data from three separate ingots of n-InSb having different purities have been taken. The ingots have been labeled 27, 28, and 29 with excess donor concentrations of 1.2 x 1015, 1.4 x 1015, and 2.8 X 101” cm-a respectively. The authors are indebted to Dr: E. N. ADAMS for providing the indium antimonide used in these experiments. The samples had dimensions of the order of 1 mm x
520
SESSION
S:
GALVANOMAGNETIC
1 mm x 5 mm. Separate current and potential or Hall Ieads were soldered to the samples with indium solder. Fig, 1 shows data on the longitudinal magnetoresistance ratio as a function of magnetic field strength of InSb 27A taken with the sample immersed in baths of liquid nitrogen, hydrogen, and heiium. The measuring current density was 8.7 A/cm2. No dependence of the magnetoresistance ratio on current was observed at 78°K. The variation is linear with field strength at the highest iields. A.RGYRESand ADAM@ predict such
j =04
amp/cm2
” T= 2.1” K
v
j=
EFFECTS
the lowest current densities (-0.003 A/ems) the magnetoresistance ratio varies exponentiaily with magnetic field strength. At intermediate current densities (N 0.1 A/ems) a combination of both types of behavior accompanied by a peculiar form of noise at the highest field strengths is found. The transition between the two types of behavior is rather abrupt. Fig. 2 shows three schematic drawings of the original data on InSb 28D. The upper picture was taken at an inte~ediate current density and shows the exponential low field behavior and abrupt transition to a linear behavior accompanied by noise. The smeared out region at higher field strengths represents high frequency oscillations which have a noise-like character. A detailed examination of the oscillations showed that they had an irregular sawtooth character and a frequency of around 200 kc/s. The middle picture shows the behavior at higher current densities where the oscillations have disappeared. The lower picture shows the results for two successive pulses with the magnetic field in opposite directions. Some typical data on InSb 28D, taken after the specimen had been etched and the leads resoldered, are shown in the schematic of Fig. 3. Results similar
2 omp’cmZ
T* 3.9"K
j =0.0033amp/cm2 T =
3-S”K
FIG. 2. Schematic drawings of typical longitudinal magnetoresistance data on InSb 28D at 4°K.
a linear variation for a non-degenerate semiconductor in the Iattice scattering range. The results at 78°K do not agree quantitatively with their theory, possibly because lattice scattering is not predominant in InSb at this temperature. An unusual feature of these results is the decrease in the magnetoresistance ratio with decreasing temperature. The results at liquid-helium temperatures are complicated by a strong dependence on measuring current density, magnetic field strength, temperature, and the nature of the soldered leads. At high current densities (- 10 Afcm2) a linear variation of the longitudinal magnetoresistance ratio with magnetic field strength is generally observed. At
j = OQ033omp/cm* T: I+’
K
FIG. 3. Schematic drawings showing typical Iongitudinal magnetoresistance data on InSb 28D after sample had been etched and leads resoldered.
SESSION
S:
GALVANO
to those in Fig. 2 are obtained except that the character of the noise has changed considerably. The upper picture shows the exponential behavior at all field strengths for a sufficiently low measuring current density. The middle picture was taken at the same current density but at a lower temperature to illustrate the temperature dependence of these effects. The noise now appears “clipped”. In the third picture the noise has almost disappeared except for a few steps in the curve. The initial exponential behavior of sample
InSb
29
n=2+2
MAGNETIC
EFFECTS
voltage is interpreted as a “freeze-out” effect. The abrupt changes in sample voltage with magnetic field strength are interpreted as electrical breakdown due to impact ionization of bound electrons. The noise is similar in character to that found by MCKAY(~) associated with breakdown in silicon p-n junctions. Fig. 4 supports the notion of electric breakdown occurring at high measuring current densities. The current density is plotted vs. electric field strength for InSb 29A at different values of the applied
A ~10’~ cm-3
T=40°K I
10’4
II H
I
IO.'
521
I lo-
I
100 E (V/cm)
FIG. 4. Plot of current density vs. electric field strength at vkious values of magnetic field strength for InSb 29A.
522
SESSION
S:
GALVANOMAGNETIC
EFFECTS
InSb 28 F T = 3.9’K
II 0
I
I
25
50
I I 75 100 H(K~logaur.)
I
I
125
I50
FIG. 5. Hall coefficient in InSb 28D vs. magnetic field strength for various measuring current densities.
magnetic field. These curves were obtained by an analysis of a series of pictures taken at different current densities. Note that the sample was nonohmic even at zero magnetic field. This is probably a “hot electron” effect. The breakdown is clearly indicated by the vertical portions of the curves. It was found that the. breakdown electric field increases with increasing concentration of excess donors. Measurements of the Hall coefficient have been
made to check the idea of breakdown, and the results are shown in Fig. 5. The constant Hall coefficient at high current densities indicates that complete ionization of donor impurities is maintained at all field strengths. The initial rise observed at low current densities is the “freeze-out” effect and the dropping off of the Hall coefficient at high magnetic fields is assumed to be charge multiplication by impact ionization which accompanies the breakdown.
SESSION
S:
GALVANOMAGNETIC 4.
REFERENCES
s.5
Pergamon
FREDERIK~EH. P. R. and HOSLER W. R. Phys. Rev.
108. 1136 (1957).
1. ARGYRES P. N. and ADAMS E. N. Phys. Rev. 104, 900 (1956). 2. KEYES R. W. and SLADEK R. J. r. Phys. Chem. Solids 1, 143 (1956). 3. SLADEK R. J, Westinghouse Laboratories Scientific Paper 8-1038-p28 (1957). To be published in J. Phys Chem. Solids.
J. Phys. Chem. Solids
523
EFFECTS
5. FURT~ H. P.‘ and .WAYXEK R. W. Rev. Sci. Instrum. 27, 195 (1956). 6. FURTH H. P., LEVINE M. A., and WANIEK R. W. Rev. Sci. Instrum. 28, 949 (1957). 7. FONER S. and KOLM H. H. Rev. Sci. Instrum. 27,‘547 (1956). 8. MCKAY K. G. Phys. Rev. 94, 877 (1953).
Press 1959. Vol. 8. pp. 523-525.
Printed in Great Britain
ELECTRONIC PROPERTIES OF GRAY TIN SINGLE CRYSTALS* A. W. EWALD Department
THE growth of gray tin single crystals from mercury solution has recently been reported.“) Because these crystals are grown from a liquid phase they should be relatively free of the physical imperfections present in all previous specimens of gray tin prepared by the solid-solid phase transformation. Growth at a reduced temperature (-20 to -30°C) and at a low rate (N 1 cm per month) should also favor a high degree of crystalline perfection. Despite their growth from an amalgam the best crystals appear to be as pure as the tin from which they are grown. These crystals of highest purity are grown at temperatures between -2.5 and -30°C and contain approximately 10” n-type impurities per cm3. Growth above -20°C produces p-type crystals due to mercury alloying. The single crystal data presented here were obtained on two specimens typical of a number of n-type samples investigated. The samples were cut to dimensions of approximately O-2 x 0.4 x 5.0 mm using an “Airbraisive” sandblast unit. Sample A was used primarily for a comparison of the electronic properties of a single crystal with those of a filament obtained by the phase transformation. The
* This work was supported Research.
and 0. N. TUFTE
of Physics, Northwestern
by the Office of Naval
University,
Evanston,
Ill.
filament was prepared from Vulcan tin of the same purity (99.999 per cent) as that used in growing the crystals. Also the same electrode arrangement was used for the single-crystal specimen as for the filament and consisted of current and potential leads attached to the sample ends with Hall probes at the mid-point. Sample B was used to study the field dependence of the magnetoresistance at nitrogen and helium temperatures. For this purpose separate potential probes consisting of 0.003 in. diameter wire were attached to one edge of the sample. A comparison of the conductivities of the single crystal and transformed filament is shown in Fig. 1. The good agreement in intrinsic slopes indicates equal purity since in gray tin of this order of purity the temperature dependence of the intrinsic conductivity is sensitive to impurity content.? The higher extrinsic conductivity of the single crystal may therefore be attributed to the higher mobility characteristic of the more perfect crystal structure. The magnetoresistance coefficients plotted in Fig. 2 also reflect the higher mobility in the single crystal t This effect which was first observed in transformed filaments (EWALD A. W. and KOHNKE E. E. Phys. Rev. 97, 607 (1955)) has also been found in mercury-alloyed single crystals.
SESSION
S:
GALVANOMAGNETIC
EFFECTS
Table 1. The activation energy, CA, for the mobility of electrons in. donor levels localized by a strong jield and the ratio of EAto the donor ionization energy, 61,for three n-type InSb samples.
magnetic
(k = Boltzmann’s constant)
n, = 3.3 x 1Ol4 cm-s es/k 10
15 20 24 28
-
EAIEI :
-
4.5”K
0.29 0.34 0.33 0.32
B-l n, = 1.4 X lOi crnm3 CA/k
j
-
CA/El
O-l n = 1.04 X lOi crne3 i
:aik
~
8.O”K 9.8
-
7.3”K 8.7 9.4 9.8
0.38 0.39 0.39 0.37
1 i
-
I is the jump frequency given by the exchange integral.) According to equation (2), an explicit temperature dependence of Tpi is contained in the bracketed factor, which represents the probability of donor levels being empty and thus providing sites into which electrons can jump. In the absence of compensation (or if only excess donors provide bound levels) this factor decreases approximately exponentially as the temperature is lowered and thus could account for the observed temperature dependence of TM. (See Fig. 3, for example.) However, we believe that our samples are rather highly compensated. In this case the bracketed factor would be almost independent of temperature. Thus D itself would have to be a thermally activated function of temperature to account for the observed
J. Phys. Chem. Solids
s.4
Pergamon
i
lA/c1 0.49 0.51
-
I I
1
temperature dependence of Tpt. This could occur, for example, if electrons need to be raised to excited donor levels in order for them to conduct. Such a hypothesis is consistent with the fact that the ratio of the activation energy to the donor ionization energy is constant in a given sample. (See Table 1.) Acknowledgments-Thanks are due to E. N. R. W. KEYES for helpful discussions.
ADAMS
and
REFERENCES 1. SLADEK R. J. J. Phys. Chem. Solids 5, 157 (1958).
Y., KEYES R. W., and ADAMS E. N. r. Phys. Chem. Solids 1, 137 (1956). 3. HUNG C. S. Phys. Rev. 79, 727 (1950). 4. GREENE R. F. and ADAMS E. N. Westinghouse Research Laboratories Scientific Paper 6-94760-2P14. 2.
YAFET
Press 1959. Vol. 8. pp. 518-523.
Printed in Great Britain
GALVANOMAGNETIC EFFECTS IN a--InSb AT LOW TEMPERATURES IN STRONG MAGNETIC FIELDS* J. C. HASLETT and W. F. LOVE Physics Department,
University of Colorado, Boulder, Colorado
1. INTRODUCTION
AS a result of the low effective mass in the conduction band of n-InSb, the magnetic quantum of energy Lo (WC = cyclotron frequency) is quite * This work was supported by the United States Atomic Energy Commission and the Council on Research and Creative Work of the University of Colorado.
large even in moderate magnetic fields. Under the condition that fiwc$ E and kT, where E is the electron energy, all electrons will occupy the ground oscillator state of their motion transverse to the field. This extreme case has been designated as the “quantum limit” by ARGYRES and ADAMS.(~) The purpose of these experiments was to provide
SESSION
S:
GALVANOMAGNETIC
519
EFFECTS
25 24
16
I OO
I
I
20
40
I
60
I 60
I 100
I 120
I 140
I
160
I
,
H (Kilogauss)
FIG. 1. Longitudinal magnetoresistance ratio of I&b 2712 vs. magnetic field strength at 78“K, 14”K, and 3.9°K.
experimental data on InSb in the quantum limit. At liquid-helium temperatures a single band picture no longer applies to ta-InSb. In a magnetic field impurity levels split off from the conduction band to form an impurity band. This leads to “freeze out” effects in the galvanomagnetic properties.c2-4) 2. ~~~~ REXWB The technique for producing pulsed magnetic fields is described adequately in the literature.(5-‘) In these experiments the original data are taken
with a Tektronix 535 oscilloscope and Polaroid Land Camera. The horizontal sweep is driven by a signal proportional to the magnetic field and the vertical sweep by the sample voltage. Data from three separate ingots of n-InSb having different purities have been taken. The ingots have been labeled 27, 28, and 29 with excess donor concentrations of 1.2 x 1015, 1.4 x 1015, and 2.8 X 101” cm-a respectively. The authors are indebted to Dr: E. N. ADAMS for providing the indium antimonide used in these experiments. The samples had dimensions of the order of 1 mm x
520
SESSION
S:
GALVANOMAGNETIC
1 mm x 5 mm. Separate current and potential or Hall Ieads were soldered to the samples with indium solder. Fig, 1 shows data on the longitudinal magnetoresistance ratio as a function of magnetic field strength of InSb 27A taken with the sample immersed in baths of liquid nitrogen, hydrogen, and heiium. The measuring current density was 8.7 A/cm2. No dependence of the magnetoresistance ratio on current was observed at 78°K. The variation is linear with field strength at the highest iields. A.RGYRESand ADAM@ predict such
j =04
amp/cm2
” T= 2.1” K
v
j=
EFFECTS
the lowest current densities (-0.003 A/ems) the magnetoresistance ratio varies exponentiaily with magnetic field strength. At intermediate current densities (N 0.1 A/ems) a combination of both types of behavior accompanied by a peculiar form of noise at the highest field strengths is found. The transition between the two types of behavior is rather abrupt. Fig. 2 shows three schematic drawings of the original data on InSb 28D. The upper picture was taken at an inte~ediate current density and shows the exponential low field behavior and abrupt transition to a linear behavior accompanied by noise. The smeared out region at higher field strengths represents high frequency oscillations which have a noise-like character. A detailed examination of the oscillations showed that they had an irregular sawtooth character and a frequency of around 200 kc/s. The middle picture shows the behavior at higher current densities where the oscillations have disappeared. The lower picture shows the results for two successive pulses with the magnetic field in opposite directions. Some typical data on InSb 28D, taken after the specimen had been etched and the leads resoldered, are shown in the schematic of Fig. 3. Results similar
2 omp’cmZ
T* 3.9"K
j =0.0033amp/cm2 T =
3-S”K
FIG. 2. Schematic drawings of typical longitudinal magnetoresistance data on InSb 28D at 4°K.
a linear variation for a non-degenerate semiconductor in the Iattice scattering range. The results at 78°K do not agree quantitatively with their theory, possibly because lattice scattering is not predominant in InSb at this temperature. An unusual feature of these results is the decrease in the magnetoresistance ratio with decreasing temperature. The results at liquid-helium temperatures are complicated by a strong dependence on measuring current density, magnetic field strength, temperature, and the nature of the soldered leads. At high current densities (- 10 Afcm2) a linear variation of the longitudinal magnetoresistance ratio with magnetic field strength is generally observed. At
j = OQ033omp/cm* T: I+’
K
FIG. 3. Schematic drawings showing typical Iongitudinal magnetoresistance data on InSb 28D after sample had been etched and leads resoldered.
SESSION
S:
GALVANO
to those in Fig. 2 are obtained except that the character of the noise has changed considerably. The upper picture shows the exponential behavior at all field strengths for a sufficiently low measuring current density. The middle picture was taken at the same current density but at a lower temperature to illustrate the temperature dependence of these effects. The noise now appears “clipped”. In the third picture the noise has almost disappeared except for a few steps in the curve. The initial exponential behavior of sample
InSb
29
n=2+2
MAGNETIC
EFFECTS
voltage is interpreted as a “freeze-out” effect. The abrupt changes in sample voltage with magnetic field strength are interpreted as electrical breakdown due to impact ionization of bound electrons. The noise is similar in character to that found by MCKAY(~) associated with breakdown in silicon p-n junctions. Fig. 4 supports the notion of electric breakdown occurring at high measuring current densities. The current density is plotted vs. electric field strength for InSb 29A at different values of the applied
A ~10’~ cm-3
T=40°K I
10’4
II H
I
IO.'
521
I lo-
I
100 E (V/cm)
FIG. 4. Plot of current density vs. electric field strength at vkious values of magnetic field strength for InSb 29A.
522
SESSION
S:
GALVANOMAGNETIC
EFFECTS
InSb 28 F T = 3.9’K
II 0
I
I
25
50
I I 75 100 H(K~logaur.)
I
I
125
I50
FIG. 5. Hall coefficient in InSb 28D vs. magnetic field strength for various measuring current densities.
magnetic field. These curves were obtained by an analysis of a series of pictures taken at different current densities. Note that the sample was nonohmic even at zero magnetic field. This is probably a “hot electron” effect. The breakdown is clearly indicated by the vertical portions of the curves. It was found that the. breakdown electric field increases with increasing concentration of excess donors. Measurements of the Hall coefficient have been
made to check the idea of breakdown, and the results are shown in Fig. 5. The constant Hall coefficient at high current densities indicates that complete ionization of donor impurities is maintained at all field strengths. The initial rise observed at low current densities is the “freeze-out” effect and the dropping off of the Hall coefficient at high magnetic fields is assumed to be charge multiplication by impact ionization which accompanies the breakdown.
SESSION
S:
GALVANOMAGNETIC 4.
REFERENCES
s.5
Pergamon
FREDERIK~EH. P. R. and HOSLER W. R. Phys. Rev.
108. 1136 (1957).
1. ARGYRES P. N. and ADAMS E. N. Phys. Rev. 104, 900 (1956). 2. KEYES R. W. and SLADEK R. J. r. Phys. Chem. Solids 1, 143 (1956). 3. SLADEK R. J, Westinghouse Laboratories Scientific Paper 8-1038-p28 (1957). To be published in J. Phys Chem. Solids.
J. Phys. Chem. Solids
523
EFFECTS
5. FURT~ H. P.‘ and .WAYXEK R. W. Rev. Sci. Instrum. 27, 195 (1956). 6. FURTH H. P., LEVINE M. A., and WANIEK R. W. Rev. Sci. Instrum. 28, 949 (1957). 7. FONER S. and KOLM H. H. Rev. Sci. Instrum. 27,‘547 (1956). 8. MCKAY K. G. Phys. Rev. 94, 877 (1953).
Press 1959. Vol. 8. pp. 523-525.
Printed in Great Britain
ELECTRONIC PROPERTIES OF GRAY TIN SINGLE CRYSTALS* A. W. EWALD Department
THE growth of gray tin single crystals from mercury solution has recently been reported.“) Because these crystals are grown from a liquid phase they should be relatively free of the physical imperfections present in all previous specimens of gray tin prepared by the solid-solid phase transformation. Growth at a reduced temperature (-20 to -30°C) and at a low rate (N 1 cm per month) should also favor a high degree of crystalline perfection. Despite their growth from an amalgam the best crystals appear to be as pure as the tin from which they are grown. These crystals of highest purity are grown at temperatures between -2.5 and -30°C and contain approximately 10” n-type impurities per cm3. Growth above -20°C produces p-type crystals due to mercury alloying. The single crystal data presented here were obtained on two specimens typical of a number of n-type samples investigated. The samples were cut to dimensions of approximately O-2 x 0.4 x 5.0 mm using an “Airbraisive” sandblast unit. Sample A was used primarily for a comparison of the electronic properties of a single crystal with those of a filament obtained by the phase transformation. The
* This work was supported Research.
and 0. N. TUFTE
of Physics, Northwestern
by the Office of Naval
University,
Evanston,
Ill.
filament was prepared from Vulcan tin of the same purity (99.999 per cent) as that used in growing the crystals. Also the same electrode arrangement was used for the single-crystal specimen as for the filament and consisted of current and potential leads attached to the sample ends with Hall probes at the mid-point. Sample B was used to study the field dependence of the magnetoresistance at nitrogen and helium temperatures. For this purpose separate potential probes consisting of 0.003 in. diameter wire were attached to one edge of the sample. A comparison of the conductivities of the single crystal and transformed filament is shown in Fig. 1. The good agreement in intrinsic slopes indicates equal purity since in gray tin of this order of purity the temperature dependence of the intrinsic conductivity is sensitive to impurity content.? The higher extrinsic conductivity of the single crystal may therefore be attributed to the higher mobility characteristic of the more perfect crystal structure. The magnetoresistance coefficients plotted in Fig. 2 also reflect the higher mobility in the single crystal t This effect which was first observed in transformed filaments (EWALD A. W. and KOHNKE E. E. Phys. Rev. 97, 607 (1955)) has also been found in mercury-alloyed single crystals.