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High-field properties of n-InP under high pressure
HIGH-FIELD PROPERTIES OF n-InP UNDER HIGH PRESSURE T. KOBAYASHI, K. TAKAHARA. T. KIMURA,K. YAMAMUTD and K. ABE
Department of Electrical and Electronic Engineering, Faculty of Engineering. Kobe University, 657, Japan
Rokko, Nada, Kobe
A&et-The hi electric field properties of n-InP at 300K have been studied as a function of pressure. Hydrostatic measurements are made in a piston and cylinder apparatus, using a liquid pressure-transmitting medium. The threshold fields (ET) for transferred electron instabilitiesrange from 7.5 to 8.5kV/cm at atmospheric pressure. The resistivity of the samples increases with increasing pressure. The most reliabk results show that ET increases sliitly with pressure be-low 40 kbar. This behavior can be explained qualitatively in terms of possible band structurechanges. BY using known variations of parameters such as effective mass and sub-band energy gaps, detailed theoretical calculations are carried out to fit the data and to determine the correct mode of operation (twoor three-level operation). The results are also compared with analogous experiments on GaAs.
1. INTRODUCTION It is well known that the microwave
voltage characteristics under hydrostatic pressures up to 40 kbar in order to determine whether & changes in this pressure range. A Teflon cell technique with a liquid pressure-transmitting medium[6] has been used, which ensures a truly hydrostatic pressure in the course of experiments. Monte Carlo calculations using the most reliable values of parameters and their variations with pressure have also been carried out in order to explain the experimental results. We expect to obtain information on the exact mode of operation and the coupling constants involved in the electron transfer process.
oscillations
in ntype GaAs and InP at high electric fields are caused by the transfer of electrons from high- to low-mobility valleys in the conduction band. In GaAs, this effect was verified by the high-pressure measurements of Hutson et al.[ll and Wasse et ai.121. They found that, as the sub-band energy gap between the r and X valleys decreased with pressure, the threshold field ET for oscillations decreased rapidly from its atmospheric pressure value. However, recent measurements of Pickering er a1.[3] have shown an initial increase in ET to 15kbar, contrary to the previous data. Subsequently, theoretical calculations have indicated that the results cannot be explained with only the X valleys as satellite valleys, but agreement is obtained by assuming the L valleys are below the X valleys and weakly coupled to the r vaUey[4]. In InP, the measurement of variations in the threshold field with pressure was first presented by Pitt et aL[S]. The most reliable results ‘show no change in & to 40 kbar. This was qualitatively explained in terms of possible band structure changes. Figure 1 shows a schematic diagram of the conduction band structure in InP in the vicinity of the conduction band edges. Under high pressure, the r valley moves away from the valence band maximum. This results in an increase in the effective mass in the r valley (a decrease in the mobility for polar optical mode scattering). The L valleysmove slowly away from the valence band maximum, while the X valleys move towards the valence band maximum. Therefore, the sub-band energy gaps in the conduction band decrease with pressure. The increase in the effective mass in the r valley and the decrease in the sub-band energy gaps could naturally affect the value of & but these effects oppose each other. At atmospheric pressure, the dominant electron transfer process in InP is presently expected to be from the r to L vdeys. However, because of the uncertainties in the theoretically determined band structure and in the experimental data, a detailed quantitative understanding of electron transfer process in InP is still lacking. In this paper, we have repeated measurements of the current-
Z.-AL
The samples are cut from an n-type InP single crystal with a low-field resistivity 0.32 Qcm. The electron concentration is 6.7 x 10’”cm-” and the mobility is about 3OOOcm*V-‘s-l. The samples are prepared by sculpturing and have large contact regions, so as to isolate the active region from the infIuence of the contacts. The active region length of the samples was typically 200 pm. Contacts were formed by evaporating AgSn or Sn and alloying at 4ML5oo”C. Current-voltage characteristics were measured by a sampling oscilloscope and an X-Y recorder. A highvoltage d.c. pulse whose duration time was 5 or 1Onsec and repetition rate was 60 Hz, was supplied to the sample by a 500 coaxial cable.
-ZXlC?Wba 2--3x Io-@M?a
L-5
I
_& L
-qlav
r
X
Fig. I. Schematic diagram &owing conduction band structure of indium phospbide. 79
80
T. KOBAYASHI eta/.
c
Truly hydrostatic measurements to 40 kbar were made in the piston and cylinder apparatus. The 12.5mm diameter pressure chamber is made of tungsten carbide, in which a Teflon cell is used as a sample container. The cell was filled with the pressure-transmitting liquid, a mixture of ethanol and methanol in the ratio of 1:l by volume. A detail of the sample assembly is shown in Fig. 2. Prior to the experiments, we had calibrated the highpressure system by using the Bir_rrtransition at 25.4 kbar and the manganin gauge. All measurements were made at room temperature. 0
3.RFmLTs
Figure 3 shows typical current-voltage curves at various pressures. It is clear that the slope of currentvoltage curve gradually decreases with pressure. The threshold’ voltage increases slightly and the threshold current decreases with pressure. These variations with pressure are analogous to those found by Pickering et al. [3] for GaAs in the pressure range O-15 kbar. Figure.4 shows the low-field resistivity as a function of pressure. The resistivity increases by about 27% at 25 kbar. This increase in low-field resistivity can be explained by considering the increase in the effective
CERAMC INSULATOR
PyROfHYLLlTE ALUNDUM CEMENT
FLUID
+I24
-i
Fig. 2. Teflon cell assembly for the 12.5mm diameterpressure chamber.
I t
I InP
SAV-6
k?
6-
‘J’; 34
(kbor)
3 s4 Y
APPLIED
,
VOLTAGE
(VI
Fig. 3. Typical current-voltagecurves at various pressures.The tikeshold voltage for instabilitiesis indicatedby the small vertical line at the end of each curve.
IO
,
.
20 PRESSURE
, 30
,
, 40
(kbar)
Fig. 4. Normalizedlow-fieldresistivityas a functionof pressure. Solid line is the calculated result for polar optical mode scattering.
mass ntc in the P valley with pressure. At low fields and 300 K, polar optical mode scattering is dominant in InP. When the P valley moves away from the valence band maximum, the electron mobility of the P valley will decrease, since it is proportional to rni-“* for polar optical mode scattering. Following the simple k*p relation, the increase in m$ is about 16% at 25 kbar. This leads to an increase in resistivity about 25% at 25 kbar, which is in reasonable agreement with our experimental results. But at pressures above 25 kbar, slight differences between the experimental data and the calculated curve are observed. The sub-band energy gaps are not so small as to cause appreciable thermal excitation of electrons to the higher valleys at low fields. Although the defect responsible for the deep donor is unknown in this material, these differences may, in part, reflect the presence of carrier freeze-out when the conduction band edge moves with a large pressure coefficient, while the deep donor state stays fixed relative to the valence band edge[6,7]. There is still a considerable spread in the exact threshold field ET in InP. Results vary from 6 to 12kV/cm[8-131, depending to some extent on the experimental methods. The threshold fields in our experiments range from 7.5 to 8.5 kV/cm at atmospheric pressure, and are much lower than those determined by microwave techniques (-12 kV/cm)[l I-131. The threshold field as estimated from the average field for the onset of instabilities could be significantly less than the true threshold, due to premature nucleation of instabilities through material non-uniformity and contact effects. Figure 5 shows the typical threshold field as a function of pressure. There is no doubt that ET, although its variation is not large, increases with increasing pressure. This is in contrast to the behaviour found by Pitt et al. (51 for InP where there is no change in ET to 40 kbar, but is similar to the recent data obtained by Pickering et a/.[31 for GaAs which showed an initial increase in ET to 15kbar. In the following, we attempt to theoretically explain the present data considering the variations of the effective mass and the sub-band energy gaps with pressure.
High-fieldpropertiesof n-InP underhigh pressure
InP 2.5 2.0 -
I
9 :I PY #” lbi II3t3 1.0_T_17__% ..._.._... - ,_,_. r.r.,,-_;---- -- ---- L’, ,I: -... ..____“_,
E
O,L-_+--l 0
IO
20
30
PRESSURE
40
30
60
(kbar)
Fig. 5. Normalizedthresholdfield as a function of pressure.All results are normalizedto their respective values at atmospheric pressure.0: presentresults;dashedline: Pitt et 01.[5];solii line: theoretical curve, includingthe variations of the effective mass and the sub-band energy gaps with pressure; dotted line:
theoretical curve, including the variations of the sub-band energy gaps with pressurealone.
4. COMPARISON WITA TIIJDItI?dTICAL CAI.CUL.ATIONS Monte Carlo calculations of the velocity-field characteristic in InP based on the three-level model[l4, 151 were made, including the pressure variations of several parameters. In our calculations, it is assumed that the P valley has an effective mass rnfof 0.078mo and moves away from the valence band maximum at a rate of 9.5 x 10d eV bar-’ with pressure[l6]. This results in an increase of rn$at a rate of about 0.6% kbar-‘[161. Accordingly, the variation of rn$with pressure is taken into consideration to discuss the influence on the threshold field. Due to the uncertainties in the exact band structure of InP, an effective mass of 0.4m, was used for both the L and X valleys and these valleys were placed 0.55 and 0.8 eV respectively above the I valley at atmospheric pressure. It is assumed that the I_. valleys move away from the valence band maximum at a rate of 3 x 10M6eVbar-‘, while the X valleys move slowly towards the valence band maximum at a rate of -2x 10e6eV bar-’ [ 171. At 40 kbar, we can estimate that the T-L sub-band energy gap is reduced by about half. The intervalley coupling constants and the phonon energies were the same values used by Herbert et a!.( IS] for screened electron-phonon interaction. Calculated results for the threshold field are shown in Fii. 5 as a function of pressure to 50 kbar, in good agreement with our experimental results. At atmospheric pressure, the calculated threshold field for the onset of negative differential mobility is about 9.5 kV/cm and is larger than those obtained in our experiments. The variation of the effective mass rn$withpressure has direct effects on the threshold field. When rn$ is taken to be a value of O.O78m, and its variation with pressure is not included in the calcplations, the threshold field decreases with increasing pressure due to the decrease in the sub-band energy gaps as shown in Fig. 5 (dotted line). This tendency is not in agreement with our experimental results, and also not in agreement with the results of Pitt
81
et al.]51 showing no change in ET to 40 kbar. Therefore, the increase in threshold field in our experiments proves that the increase in effective mass rn$is probably the dominant effect at pressures below 40 kbar rather than the decrease in the sub-band energy gaps. At atmospheric pressure, the number of electrons transferred to the L valleys was calculated to be about 4 to 5% of the total electron population at 9 kV/cm and it increases gradually with pressure. On the other hand, the number of electrons transferred to the X valleys at atmospheric pressure was negligible even at a field of 20 kV/cm. At 30 kbar, we find that about 1% of the electrons occupy the X valleys and these contribute only slightly to the average drift velocity. It is to be noted that although the X valleys were included in the calculations and placed 0.25 eV above the L valleys at atmospheric pressure, their role in determining the average drift velocity at pressures below 40 kbar was insignificant until extremely high fields were applied. At higher pressures, beyond 35 kbar, the theoretical curve for & (solid line) decreases again after passing through a maximum. This behaviour is somewhat similar to that found by Pickering et al.[3] for GaAs in the pressure range 15-20 kbar, but does not agree with the data obtained by Pitt et ~I.[51 for InP, where beyond 40 kbar & gradually rose. It is probable that for the L and X valleys, now being close together in energy, the effective coupling constants involving the P valley could be modified and raise E,, In spite of the uncertainties in some of the parameters used in the present calculations, theoretical results agree well with the experimental values. For a more rigorous comparison, more reliable information on the band structure in InP, the correct mode of operation and the effective coupling constants and their variations with pressure are required. 5. CONCLUSION The measurements of current-voltage characteristics in n-InP have been made under truly hydrostatic pressure to 40 kbar. It is shown that the low-field resistivity increases with increasing pressure. This tendency can be explained in terms of the increase in effective mass in the P valley. The threshold field shows a small increase. Theoretical calculations based on the three-level model have been carried out including the variation of the effective mass and the sub-band energy gaps with pressure. Calculated results for ET arein good agreement with the experimental results. It is suggested that in the pressure range O-40kbar the T-L electron transfer process is responsible for determining E7 (two-level operation), and the increase in effective mass in the P valley is the dominant effect on ET as compared with a decrease in the sub-band energy gaps. These results should further our understanding of high-field transport properties in InP. Acknowledgements-The authors wish to thank Prof. K. Ito of Faculty of Science, Kobe University for his kind offer of highpressureapparatusand for useful discussions. The authorsalso wish to thank Mr. A. Nakaue of the Asada Fundamental
82
T. KOBAYASHI etiai.
Research Laboratory, Kobe. Steel. Ltd., for allowing us to use high-pressure apparatus and for helpful discussions. This work was part&By supported by the Grant-in-Aid for SciintiBc Research from the Ministry of Education. RWIUWCES I. A. R. Hutson, A. Jayaraman, A. G. Chynoweth, A. S. Coriell and W. L. Feldman, Phys. Rev. Lett. 14,639 (1%5). 2. hf. P. Wasse, J. Lees and G. King, So&d-St. Electron. 9,601 w66). 3. C. Pickering, A. R. Adams, G. D. Pitt and hf. K. R. Vyas, 1. Phys. C: Solid State Phys. 8, 129(1975). 4. P. I. Vinson, C. Pickering. A. R. Adams, W. Fawcett and G. D. Pitt, Prof. 13th Int. Coaf. on Pltys. of ~icoadacta~. Rome, p. 1243(1976). 5. G. D. Pitt and M. K. R. Vyas. 1. Phys. C: Solid StatePhys. 8, 138(1975).
6. A. Jayaraman, A. R. Hutson, J. If. &Fee, A. S. Coriell and R. G. Maines. Reu. Sci. Instrum. 38,44 (I%?). 7. R. J. Siadek, P!rys. Reu. lSg, 1345(l%S). 8. B. A. Prew, Electron. Left. 7,584 (1971). 9. B. A. Prew. Electron. Let!. 8, 592 (1972). IO. R. Kaul, H. L. Grubin, G. 0. Ladd, Jr. and J. M. Berak, IEEE Tmn. Electron &I. ED19.988 (1972). 11.Ii. ‘T Lam and G. A. Acket, Electmn. Lett.7,722(1971). 12. G. H. Clover, A@. Phys. L&t. 2@,224 (1972). 13. L. D. Nielsen, Phys. Letf. 38A. 221 (1972). 14. W. Fawcett and 0. C. Herbert, 1. Phys. C: Solid State Phys. 7, 1641(1974). IS. D. C. Herbert, W. Fawcett and C. H&urn, 1. Phys. C: Solid State Phys. 9,3%9 (1976). 16. G. D. Pitt, J. Lees, R. A. Hoult and R. A. Stradling, J. Phys. C: Solid State Phys. 6, 3282(1973). 17. G. D. Pitt, J. Phys. C: So/id State Phys. 6, 1586(1973).
Department of Electrical and Electronic Engineering, Faculty of Engineering. Kobe University, 657, Japan
Rokko, Nada, Kobe
A&et-The hi electric field properties of n-InP at 300K have been studied as a function of pressure. Hydrostatic measurements are made in a piston and cylinder apparatus, using a liquid pressure-transmitting medium. The threshold fields (ET) for transferred electron instabilitiesrange from 7.5 to 8.5kV/cm at atmospheric pressure. The resistivity of the samples increases with increasing pressure. The most reliabk results show that ET increases sliitly with pressure be-low 40 kbar. This behavior can be explained qualitatively in terms of possible band structurechanges. BY using known variations of parameters such as effective mass and sub-band energy gaps, detailed theoretical calculations are carried out to fit the data and to determine the correct mode of operation (twoor three-level operation). The results are also compared with analogous experiments on GaAs.
1. INTRODUCTION It is well known that the microwave
voltage characteristics under hydrostatic pressures up to 40 kbar in order to determine whether & changes in this pressure range. A Teflon cell technique with a liquid pressure-transmitting medium[6] has been used, which ensures a truly hydrostatic pressure in the course of experiments. Monte Carlo calculations using the most reliable values of parameters and their variations with pressure have also been carried out in order to explain the experimental results. We expect to obtain information on the exact mode of operation and the coupling constants involved in the electron transfer process.
oscillations
in ntype GaAs and InP at high electric fields are caused by the transfer of electrons from high- to low-mobility valleys in the conduction band. In GaAs, this effect was verified by the high-pressure measurements of Hutson et al.[ll and Wasse et ai.121. They found that, as the sub-band energy gap between the r and X valleys decreased with pressure, the threshold field ET for oscillations decreased rapidly from its atmospheric pressure value. However, recent measurements of Pickering er a1.[3] have shown an initial increase in ET to 15kbar, contrary to the previous data. Subsequently, theoretical calculations have indicated that the results cannot be explained with only the X valleys as satellite valleys, but agreement is obtained by assuming the L valleys are below the X valleys and weakly coupled to the r vaUey[4]. In InP, the measurement of variations in the threshold field with pressure was first presented by Pitt et aL[S]. The most reliable results ‘show no change in & to 40 kbar. This was qualitatively explained in terms of possible band structure changes. Figure 1 shows a schematic diagram of the conduction band structure in InP in the vicinity of the conduction band edges. Under high pressure, the r valley moves away from the valence band maximum. This results in an increase in the effective mass in the r valley (a decrease in the mobility for polar optical mode scattering). The L valleysmove slowly away from the valence band maximum, while the X valleys move towards the valence band maximum. Therefore, the sub-band energy gaps in the conduction band decrease with pressure. The increase in the effective mass in the r valley and the decrease in the sub-band energy gaps could naturally affect the value of & but these effects oppose each other. At atmospheric pressure, the dominant electron transfer process in InP is presently expected to be from the r to L vdeys. However, because of the uncertainties in the theoretically determined band structure and in the experimental data, a detailed quantitative understanding of electron transfer process in InP is still lacking. In this paper, we have repeated measurements of the current-
Z.-AL
The samples are cut from an n-type InP single crystal with a low-field resistivity 0.32 Qcm. The electron concentration is 6.7 x 10’”cm-” and the mobility is about 3OOOcm*V-‘s-l. The samples are prepared by sculpturing and have large contact regions, so as to isolate the active region from the infIuence of the contacts. The active region length of the samples was typically 200 pm. Contacts were formed by evaporating AgSn or Sn and alloying at 4ML5oo”C. Current-voltage characteristics were measured by a sampling oscilloscope and an X-Y recorder. A highvoltage d.c. pulse whose duration time was 5 or 1Onsec and repetition rate was 60 Hz, was supplied to the sample by a 500 coaxial cable.
-ZXlC?Wba 2--3x Io-@M?a
L-5
I
_& L
-qlav
r
X
Fig. I. Schematic diagram &owing conduction band structure of indium phospbide. 79
80
T. KOBAYASHI eta/.
c
Truly hydrostatic measurements to 40 kbar were made in the piston and cylinder apparatus. The 12.5mm diameter pressure chamber is made of tungsten carbide, in which a Teflon cell is used as a sample container. The cell was filled with the pressure-transmitting liquid, a mixture of ethanol and methanol in the ratio of 1:l by volume. A detail of the sample assembly is shown in Fig. 2. Prior to the experiments, we had calibrated the highpressure system by using the Bir_rrtransition at 25.4 kbar and the manganin gauge. All measurements were made at room temperature. 0
3.RFmLTs
Figure 3 shows typical current-voltage curves at various pressures. It is clear that the slope of currentvoltage curve gradually decreases with pressure. The threshold’ voltage increases slightly and the threshold current decreases with pressure. These variations with pressure are analogous to those found by Pickering et al. [3] for GaAs in the pressure range O-15 kbar. Figure.4 shows the low-field resistivity as a function of pressure. The resistivity increases by about 27% at 25 kbar. This increase in low-field resistivity can be explained by considering the increase in the effective
CERAMC INSULATOR
PyROfHYLLlTE ALUNDUM CEMENT
FLUID
+I24
-i
Fig. 2. Teflon cell assembly for the 12.5mm diameterpressure chamber.
I t
I InP
SAV-6
k?
6-
‘J’; 34
(kbor)
3 s4 Y
APPLIED
,
VOLTAGE
(VI
Fig. 3. Typical current-voltagecurves at various pressures.The tikeshold voltage for instabilitiesis indicatedby the small vertical line at the end of each curve.
IO
,
.
20 PRESSURE
, 30
,
, 40
(kbar)
Fig. 4. Normalizedlow-fieldresistivityas a functionof pressure. Solid line is the calculated result for polar optical mode scattering.
mass ntc in the P valley with pressure. At low fields and 300 K, polar optical mode scattering is dominant in InP. When the P valley moves away from the valence band maximum, the electron mobility of the P valley will decrease, since it is proportional to rni-“* for polar optical mode scattering. Following the simple k*p relation, the increase in m$ is about 16% at 25 kbar. This leads to an increase in resistivity about 25% at 25 kbar, which is in reasonable agreement with our experimental results. But at pressures above 25 kbar, slight differences between the experimental data and the calculated curve are observed. The sub-band energy gaps are not so small as to cause appreciable thermal excitation of electrons to the higher valleys at low fields. Although the defect responsible for the deep donor is unknown in this material, these differences may, in part, reflect the presence of carrier freeze-out when the conduction band edge moves with a large pressure coefficient, while the deep donor state stays fixed relative to the valence band edge[6,7]. There is still a considerable spread in the exact threshold field ET in InP. Results vary from 6 to 12kV/cm[8-131, depending to some extent on the experimental methods. The threshold fields in our experiments range from 7.5 to 8.5 kV/cm at atmospheric pressure, and are much lower than those determined by microwave techniques (-12 kV/cm)[l I-131. The threshold field as estimated from the average field for the onset of instabilities could be significantly less than the true threshold, due to premature nucleation of instabilities through material non-uniformity and contact effects. Figure 5 shows the typical threshold field as a function of pressure. There is no doubt that ET, although its variation is not large, increases with increasing pressure. This is in contrast to the behaviour found by Pitt et al. (51 for InP where there is no change in ET to 40 kbar, but is similar to the recent data obtained by Pickering et a/.[31 for GaAs which showed an initial increase in ET to 15kbar. In the following, we attempt to theoretically explain the present data considering the variations of the effective mass and the sub-band energy gaps with pressure.
High-fieldpropertiesof n-InP underhigh pressure
InP 2.5 2.0 -
I
9 :I PY #” lbi II3t3 1.0_T_17__% ..._.._... - ,_,_. r.r.,,-_;---- -- ---- L’, ,I: -... ..____“_,
E
O,L-_+--l 0
IO
20
30
PRESSURE
40
30
60
(kbar)
Fig. 5. Normalizedthresholdfield as a function of pressure.All results are normalizedto their respective values at atmospheric pressure.0: presentresults;dashedline: Pitt et 01.[5];solii line: theoretical curve, includingthe variations of the effective mass and the sub-band energy gaps with pressure; dotted line:
theoretical curve, including the variations of the sub-band energy gaps with pressurealone.
4. COMPARISON WITA TIIJDItI?dTICAL CAI.CUL.ATIONS Monte Carlo calculations of the velocity-field characteristic in InP based on the three-level model[l4, 151 were made, including the pressure variations of several parameters. In our calculations, it is assumed that the P valley has an effective mass rnfof 0.078mo and moves away from the valence band maximum at a rate of 9.5 x 10d eV bar-’ with pressure[l6]. This results in an increase of rn$at a rate of about 0.6% kbar-‘[161. Accordingly, the variation of rn$with pressure is taken into consideration to discuss the influence on the threshold field. Due to the uncertainties in the exact band structure of InP, an effective mass of 0.4m, was used for both the L and X valleys and these valleys were placed 0.55 and 0.8 eV respectively above the I valley at atmospheric pressure. It is assumed that the I_. valleys move away from the valence band maximum at a rate of 3 x 10M6eVbar-‘, while the X valleys move slowly towards the valence band maximum at a rate of -2x 10e6eV bar-’ [ 171. At 40 kbar, we can estimate that the T-L sub-band energy gap is reduced by about half. The intervalley coupling constants and the phonon energies were the same values used by Herbert et a!.( IS] for screened electron-phonon interaction. Calculated results for the threshold field are shown in Fii. 5 as a function of pressure to 50 kbar, in good agreement with our experimental results. At atmospheric pressure, the calculated threshold field for the onset of negative differential mobility is about 9.5 kV/cm and is larger than those obtained in our experiments. The variation of the effective mass rn$withpressure has direct effects on the threshold field. When rn$ is taken to be a value of O.O78m, and its variation with pressure is not included in the calcplations, the threshold field decreases with increasing pressure due to the decrease in the sub-band energy gaps as shown in Fig. 5 (dotted line). This tendency is not in agreement with our experimental results, and also not in agreement with the results of Pitt
81
et al.]51 showing no change in ET to 40 kbar. Therefore, the increase in threshold field in our experiments proves that the increase in effective mass rn$is probably the dominant effect at pressures below 40 kbar rather than the decrease in the sub-band energy gaps. At atmospheric pressure, the number of electrons transferred to the L valleys was calculated to be about 4 to 5% of the total electron population at 9 kV/cm and it increases gradually with pressure. On the other hand, the number of electrons transferred to the X valleys at atmospheric pressure was negligible even at a field of 20 kV/cm. At 30 kbar, we find that about 1% of the electrons occupy the X valleys and these contribute only slightly to the average drift velocity. It is to be noted that although the X valleys were included in the calculations and placed 0.25 eV above the L valleys at atmospheric pressure, their role in determining the average drift velocity at pressures below 40 kbar was insignificant until extremely high fields were applied. At higher pressures, beyond 35 kbar, the theoretical curve for & (solid line) decreases again after passing through a maximum. This behaviour is somewhat similar to that found by Pickering et al.[3] for GaAs in the pressure range 15-20 kbar, but does not agree with the data obtained by Pitt et ~I.[51 for InP, where beyond 40 kbar & gradually rose. It is probable that for the L and X valleys, now being close together in energy, the effective coupling constants involving the P valley could be modified and raise E,, In spite of the uncertainties in some of the parameters used in the present calculations, theoretical results agree well with the experimental values. For a more rigorous comparison, more reliable information on the band structure in InP, the correct mode of operation and the effective coupling constants and their variations with pressure are required. 5. CONCLUSION The measurements of current-voltage characteristics in n-InP have been made under truly hydrostatic pressure to 40 kbar. It is shown that the low-field resistivity increases with increasing pressure. This tendency can be explained in terms of the increase in effective mass in the P valley. The threshold field shows a small increase. Theoretical calculations based on the three-level model have been carried out including the variation of the effective mass and the sub-band energy gaps with pressure. Calculated results for ET arein good agreement with the experimental results. It is suggested that in the pressure range O-40kbar the T-L electron transfer process is responsible for determining E7 (two-level operation), and the increase in effective mass in the P valley is the dominant effect on ET as compared with a decrease in the sub-band energy gaps. These results should further our understanding of high-field transport properties in InP. Acknowledgements-The authors wish to thank Prof. K. Ito of Faculty of Science, Kobe University for his kind offer of highpressureapparatusand for useful discussions. The authorsalso wish to thank Mr. A. Nakaue of the Asada Fundamental
82
T. KOBAYASHI etiai.
Research Laboratory, Kobe. Steel. Ltd., for allowing us to use high-pressure apparatus and for helpful discussions. This work was part&By supported by the Grant-in-Aid for SciintiBc Research from the Ministry of Education. RWIUWCES I. A. R. Hutson, A. Jayaraman, A. G. Chynoweth, A. S. Coriell and W. L. Feldman, Phys. Rev. Lett. 14,639 (1%5). 2. hf. P. Wasse, J. Lees and G. King, So&d-St. Electron. 9,601 w66). 3. C. Pickering, A. R. Adams, G. D. Pitt and hf. K. R. Vyas, 1. Phys. C: Solid State Phys. 8, 129(1975). 4. P. I. Vinson, C. Pickering. A. R. Adams, W. Fawcett and G. D. Pitt, Prof. 13th Int. Coaf. on Pltys. of ~icoadacta~. Rome, p. 1243(1976). 5. G. D. Pitt and M. K. R. Vyas. 1. Phys. C: Solid StatePhys. 8, 138(1975).
6. A. Jayaraman, A. R. Hutson, J. If. &Fee, A. S. Coriell and R. G. Maines. Reu. Sci. Instrum. 38,44 (I%?). 7. R. J. Siadek, P!rys. Reu. lSg, 1345(l%S). 8. B. A. Prew, Electron. Left. 7,584 (1971). 9. B. A. Prew. Electron. Let!. 8, 592 (1972). IO. R. Kaul, H. L. Grubin, G. 0. Ladd, Jr. and J. M. Berak, IEEE Tmn. Electron &I. ED19.988 (1972). 11.Ii. ‘T Lam and G. A. Acket, Electmn. Lett.7,722(1971). 12. G. H. Clover, A@. Phys. L&t. 2@,224 (1972). 13. L. D. Nielsen, Phys. Letf. 38A. 221 (1972). 14. W. Fawcett and 0. C. Herbert, 1. Phys. C: Solid State Phys. 7, 1641(1974). IS. D. C. Herbert, W. Fawcett and C. H&urn, 1. Phys. C: Solid State Phys. 9,3%9 (1976). 16. G. D. Pitt, J. Lees, R. A. Hoult and R. A. Stradling, J. Phys. C: Solid State Phys. 6, 3282(1973). 17. G. D. Pitt, J. Phys. C: So/id State Phys. 6, 1586(1973).