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Electron-hole pair production and gunn effect in InSb
Solid State Communications,
Vol. 7, pp. 905—908, 1969.
Pergamon Press.
Printed in Great Britain
ELECTRON—HOLE PAIR PRODUCTION AND GUNN EFFECT IN InSb* Syiwester Porowski and William Paul Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts 02138 and J.C. McGroddy, Marshall I. Nathan and J.E. Smith, Jr. IBM Watson Research Center, Yorktown Heights, New York 10598 (Received 29 April 1969 by J.A. Knsmhansl)
A study of the low and high field transport properties, the Gunn effect and avalanche breakdown as a function of pressure in n-InSb has been used to obtain information about the properties of higher conduction band minima and impurity levels associated with them.
AT ATMOSPHERIC pressure the lowest conduction band minimum of InSb has I~symmetry and
germanium-family semiconductors, lowers the energies of the conduction band minima at X1
the energetic distance to the higher L1 and X1 minima is somewhat greater than the direct energy gap to the F15 valence band of about 0.2 eV. Therefore a uniform electric field of a few hundred V/cm applied to n-type InSb causes the creation of electron—hole pairs by hot electrons rather than electron transfer between the small mass, high mobility I~minimum and the high mass, low mobility X or L minima. We have found, however, that the application of hydrostatic pressure permits such transfer and the consequent observation of the Gunn effect. Study of this effect and of resistivity data at high pressure give information the properties the higher minima and about the appropriate band of structure conditions for observation of the Gunn effect.
and L1 relative to that at F, Thus, the application of pressure provides a band structure more favorable to the observation of the Gunn effect. A rough calculation using the Kane two band model gives 1.1 E0 as the threshold energy E~ for electrons for electron—hole pair production. The observation of the Gunn effect at pressure P shows that the L1 or X1 minima may be lower and are unlikely to be much higher in energy above the F1 minimum than 1.1 E9 (P). .
The crystals used came from several different sources, and typically had of carrier t4cm3and mobilities aboutdensities of about lO 600,000 cm2/V-sec at 77°K. The samples were rectangular bars 1.2 mm long with transverse dimensions of 0.2 x 0.2 mm. The contacts were formed by evaporating Sn (2% Te) alloy on the
Hydrostatic pressure increases the direct energy gap E 9 at the rate dE9 (P) / a~ = 15 x 10-6 eV/bar, and by analogy with other
faces of a polished slice and flash alloying the surface, which was subsequently plated with gold. The samples were mounted in a copper sample holder in the pressure apparatus, which uses He gas as transmitting medium. n-ger-
*The part of this work carried out at Harvard University was supported by the Office of Naval Research under Contract N00014-67-A-0298-0012 and by the ARPA under Contract SD-88.
.
manium resistors were used to lower the source 905
906
ELECTRON—HOLE PAIR PRODUCTION AND GUNN EFFECT IN lnSb
Vol. 7, No. 13
1~/çbors
Time (nsecs)
FIG. 1. Typical waveform of current vs. time in the high pressure
range where Gunn effect is observed. impedance and for monitoring the sample current which was measured with 10—20 ns pulses. At the lowest pressures, for fields below our maximum of 700 V/cm, the behavior of the current vs. time is characteristic of a bulk avalanche, while at high pressures the behavior is characteristic of materials exhibiting the Gurin effect. A typical current waveform is shown in Fig. 1 for the high pressure range. At intermediate pressures, several types of behavior are observed. Toward the low pressure end of this range, the dependence of sample current on field first shows the normal saturation due to carrier heating in one band, then a régime of rapid current increase caused by pair production, and finally a régime of current instability associated with Gunn effect. Figure 2 shows a typical curve of current vs. field illustrating these regimes; it was taken at a time of 5 ns after the application of the field pulse. As the pressure is increased, the threshold field for Gunn effect decreases until the field region of impact ionization of pairs is unobservable. In the Gunn effect régime, the sample current at fixed bias at first decreases rapidly for a short time and then remains constant indicating the formation and transit across the sample of a high field dorriain. Thereafter the current increases in step wise fashion, the width of the steps being approximately equal to the domain transit time at higher pressures. The current increase
at the end of each step is believed to be due to the production of electron—hole pairs within the high field domains, subsequent trapping of the holes, and release of the electrons as high mobility carriers after the domain has traversed the sample. The exact dependence of the threshold field on pressure depends on the sample measured, but there are two clearly distinguished classes of behavior. In the first, type A, which occurs in 800—
600—
I / / 0300 200 00— 0 0
g~ G~n~ ~
on0nre9fm~me1 200 400
régme 600
FIELD(VOLTS/CM) FIG. 2. Dependence of current on field in the
intermediate pressure range, showing three regimes of behavior.
Vol. 7, No. 13
ELECTRON—HOLE PAIR PRODUCTION AND GUNN EFFECT IN InSb
907
band structure model of F
samples which exhibit the carrier freeze-out
1 and L, conduction band extrema separated by 0.45 eV at atmospheric pressure and having pressure coefficients appropriate for germanium-like semiconductors. Relevant parameters of this model for several pressures
effect discussed below, the curve exhibits a minimum at about 9 kbars, and the oscillations disappear at the highest pressures attained, about 13 kbars. In the second kind of behavior, type B, the threshold field decreases monotonically with increasing pressure and the oscillations do not weaken up to the highest pressure.
in the range of observed Gunn effect are shown in Table 1. From the Table it appears that Gunn effect oscillations occur even when E~ is substantially less than EL, — Er-,. Evidently the rate of pair production is not high enough to prevent a sufficient density of carriers from reaching the higher minima and causing Gunn effect. It should be added immediately that this is not in accord with current ideas on impact ionization and its relation to Gunn effect, and may mean that the tentative band structure model or its pressure coefficients are incorrect.
From the results of measurements of the pressure dependence of the resistivity, Paul’ concluded that for pressures up to 27 kbars at T = 300°K no subsidiary minima are appreciably occupied. Assumption of reasonable values for effective masses of F, and L, minima indicates that Paul’s resistivity vs. pressure determination at room temperature would have shown up interband carrier transfer effects if EL, — E1-, at 27 kbars had been less than about 0.15 eV. It is also known from measurements on In~Ga,~Sb alloys that the L, minima, which have been proved to be only about 0.08 eV above the F, minimum in GaSb, remain the second lowest set 2 The of minima the of series andtoin L, InSb. most recentthrough estimate the F, separation
The dependence of the Gunn effect threshold field on pressure and the disappearance of the effect at high pressures of great and is partly understood. At isthese high interest pressures
(~12 kbars) the energy separation
by Woolley’s group2 is between 0.45 and 0.5 eV. If we now assume’ that c9/aP (EL — Er,) = —1 x lO~eV/bar, we would predic’t (EL — Er,) to be 0.18—0.23 eV at 27 lcbars. In view of these two pieces of evidence, we therefore choose to examine the Gunn effect results in terms of a
(EL,—
Er,),
according to our tentative model, is approximately 033 eV, which is over 40 kT, and therefore the disappearance of the effect cannot be due to sharing of the carriers between bands at zero field. Also, this energetic separation is much greater than the interband separation at which the
Table 1 P
Eg(P)
1.1E~(P)
EL,(P)
(bars)
(eV)
(eV)
(eV)
4000 6000 8000 10,000 12,000
0.28 0.31 0.34 0.37 0.40
0.31 0.34 0.37 0.41 0.44
0.41 0.39 0.37 0.35 0.33
—
Er,(P)
Parameters based on InSb model with an energy gap at 77°K of 0.22 eV, an energetic separation between F, and L, conduction band minima of 0.45 eV, and pressure coefficients 9E /aP = 1.5 x 10~ eV/bar and a/3P (EL—Er, )= — 1 x i0~ eV/bar. E~ is the ~hreshold energy for ionization by an electron.
908
ELECTRON—HOLE PAIR PRODUCTION AND GUNN EFFECT IN InSb
Guns effect disappears in GaAs3 or uniaxially
strained Ge.4 It has been determined from resistivity and Hall effect measurements at high pressures and low temperature that in samples of type A there is a rapid drop of free carrier density which starts in the same pressure range as the Gunn threshold field increases. It is supposed that de-ionization into impurity levels associated with the higher-lying L, minima is responsible.5 On the other hand, samples of type B show no such drop in carrier density in this pressure range. Thus there appears to be a direct correlation of the increase in threshold and disappearance of Gunn effect with the rapid decrease in carrier density. Current work is in three areas. (1) Verification of the existence of these impurity levels and the nature of the responsible
Vol. 7, No. 13
defect, and quantitative investigation of the functional dependence of Gunn threshold field on carrier density. (2) Careful measurements of electron—hole generation rate below the threshold field for Gunn effect which should give additional information about the energy separation of the minima and the conditions for observation of the Gunn effect. (3) Study of the pair generation at low pressures where the Gunn effect is not observed, which will give the energy gap dependence of the generation rate. Acknowledgements — We take this opportunity to acknowledge the assistance of F.R. Fiegel, Jr. in the fabrication of the samples, and of James Inglis and David McLeod for assistance in some of the measurements.
REFERENCES 1.
PAUL W., J. Appi. Phys. 32, 2082 (1961). See also Demchuk, Tsidilkovskii and Radionov, Soviet Phys. Solid State 7, 1257 (1965).
2.
WOOLLEY and CODERRE, to be published. One of us (W.P.) is much indebted to Professor Woolley for the opportunity to examine his data before publication.
3.
WASSE, M.P., LEESJ., and KING G., Solid State Electronics 9, 601 (1966).
4.
SMITH J.E., Appi. Phys. Lett. 12, 233 (1968).
5.
See PAUL W., Proceedings of the Ninth International Conference on Semiconductors, Moscow, 1968, to be published.
Das Untersuchen der Schwach- und Starkfeldtransporteigenschaften, des Gunn-Effekts, und der Lawinen-Durchbruch, als Funktionen des Druckes, in n-Typ-InSb hat Informationen iiber die Eigenschaften höheren Leitungsband-Minima und der diesigen Störstellen-Niveaus gegeben.
Vol. 7, pp. 905—908, 1969.
Pergamon Press.
Printed in Great Britain
ELECTRON—HOLE PAIR PRODUCTION AND GUNN EFFECT IN InSb* Syiwester Porowski and William Paul Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts 02138 and J.C. McGroddy, Marshall I. Nathan and J.E. Smith, Jr. IBM Watson Research Center, Yorktown Heights, New York 10598 (Received 29 April 1969 by J.A. Knsmhansl)
A study of the low and high field transport properties, the Gunn effect and avalanche breakdown as a function of pressure in n-InSb has been used to obtain information about the properties of higher conduction band minima and impurity levels associated with them.
AT ATMOSPHERIC pressure the lowest conduction band minimum of InSb has I~symmetry and
germanium-family semiconductors, lowers the energies of the conduction band minima at X1
the energetic distance to the higher L1 and X1 minima is somewhat greater than the direct energy gap to the F15 valence band of about 0.2 eV. Therefore a uniform electric field of a few hundred V/cm applied to n-type InSb causes the creation of electron—hole pairs by hot electrons rather than electron transfer between the small mass, high mobility I~minimum and the high mass, low mobility X or L minima. We have found, however, that the application of hydrostatic pressure permits such transfer and the consequent observation of the Gunn effect. Study of this effect and of resistivity data at high pressure give information the properties the higher minima and about the appropriate band of structure conditions for observation of the Gunn effect.
and L1 relative to that at F, Thus, the application of pressure provides a band structure more favorable to the observation of the Gunn effect. A rough calculation using the Kane two band model gives 1.1 E0 as the threshold energy E~ for electrons for electron—hole pair production. The observation of the Gunn effect at pressure P shows that the L1 or X1 minima may be lower and are unlikely to be much higher in energy above the F1 minimum than 1.1 E9 (P). .
The crystals used came from several different sources, and typically had of carrier t4cm3and mobilities aboutdensities of about lO 600,000 cm2/V-sec at 77°K. The samples were rectangular bars 1.2 mm long with transverse dimensions of 0.2 x 0.2 mm. The contacts were formed by evaporating Sn (2% Te) alloy on the
Hydrostatic pressure increases the direct energy gap E 9 at the rate dE9 (P) / a~ = 15 x 10-6 eV/bar, and by analogy with other
faces of a polished slice and flash alloying the surface, which was subsequently plated with gold. The samples were mounted in a copper sample holder in the pressure apparatus, which uses He gas as transmitting medium. n-ger-
*The part of this work carried out at Harvard University was supported by the Office of Naval Research under Contract N00014-67-A-0298-0012 and by the ARPA under Contract SD-88.
.
manium resistors were used to lower the source 905
906
ELECTRON—HOLE PAIR PRODUCTION AND GUNN EFFECT IN lnSb
Vol. 7, No. 13
1~/çbors
Time (nsecs)
FIG. 1. Typical waveform of current vs. time in the high pressure
range where Gunn effect is observed. impedance and for monitoring the sample current which was measured with 10—20 ns pulses. At the lowest pressures, for fields below our maximum of 700 V/cm, the behavior of the current vs. time is characteristic of a bulk avalanche, while at high pressures the behavior is characteristic of materials exhibiting the Gurin effect. A typical current waveform is shown in Fig. 1 for the high pressure range. At intermediate pressures, several types of behavior are observed. Toward the low pressure end of this range, the dependence of sample current on field first shows the normal saturation due to carrier heating in one band, then a régime of rapid current increase caused by pair production, and finally a régime of current instability associated with Gunn effect. Figure 2 shows a typical curve of current vs. field illustrating these regimes; it was taken at a time of 5 ns after the application of the field pulse. As the pressure is increased, the threshold field for Gunn effect decreases until the field region of impact ionization of pairs is unobservable. In the Gunn effect régime, the sample current at fixed bias at first decreases rapidly for a short time and then remains constant indicating the formation and transit across the sample of a high field dorriain. Thereafter the current increases in step wise fashion, the width of the steps being approximately equal to the domain transit time at higher pressures. The current increase
at the end of each step is believed to be due to the production of electron—hole pairs within the high field domains, subsequent trapping of the holes, and release of the electrons as high mobility carriers after the domain has traversed the sample. The exact dependence of the threshold field on pressure depends on the sample measured, but there are two clearly distinguished classes of behavior. In the first, type A, which occurs in 800—
600—
I / / 0300 200 00— 0 0
g~ G~n~ ~
on0nre9fm~me1 200 400
régme 600
FIELD(VOLTS/CM) FIG. 2. Dependence of current on field in the
intermediate pressure range, showing three regimes of behavior.
Vol. 7, No. 13
ELECTRON—HOLE PAIR PRODUCTION AND GUNN EFFECT IN InSb
907
band structure model of F
samples which exhibit the carrier freeze-out
1 and L, conduction band extrema separated by 0.45 eV at atmospheric pressure and having pressure coefficients appropriate for germanium-like semiconductors. Relevant parameters of this model for several pressures
effect discussed below, the curve exhibits a minimum at about 9 kbars, and the oscillations disappear at the highest pressures attained, about 13 kbars. In the second kind of behavior, type B, the threshold field decreases monotonically with increasing pressure and the oscillations do not weaken up to the highest pressure.
in the range of observed Gunn effect are shown in Table 1. From the Table it appears that Gunn effect oscillations occur even when E~ is substantially less than EL, — Er-,. Evidently the rate of pair production is not high enough to prevent a sufficient density of carriers from reaching the higher minima and causing Gunn effect. It should be added immediately that this is not in accord with current ideas on impact ionization and its relation to Gunn effect, and may mean that the tentative band structure model or its pressure coefficients are incorrect.
From the results of measurements of the pressure dependence of the resistivity, Paul’ concluded that for pressures up to 27 kbars at T = 300°K no subsidiary minima are appreciably occupied. Assumption of reasonable values for effective masses of F, and L, minima indicates that Paul’s resistivity vs. pressure determination at room temperature would have shown up interband carrier transfer effects if EL, — E1-, at 27 kbars had been less than about 0.15 eV. It is also known from measurements on In~Ga,~Sb alloys that the L, minima, which have been proved to be only about 0.08 eV above the F, minimum in GaSb, remain the second lowest set 2 The of minima the of series andtoin L, InSb. most recentthrough estimate the F, separation
The dependence of the Gunn effect threshold field on pressure and the disappearance of the effect at high pressures of great and is partly understood. At isthese high interest pressures
(~12 kbars) the energy separation
by Woolley’s group2 is between 0.45 and 0.5 eV. If we now assume’ that c9/aP (EL — Er,) = —1 x lO~eV/bar, we would predic’t (EL — Er,) to be 0.18—0.23 eV at 27 lcbars. In view of these two pieces of evidence, we therefore choose to examine the Gunn effect results in terms of a
(EL,—
Er,),
according to our tentative model, is approximately 033 eV, which is over 40 kT, and therefore the disappearance of the effect cannot be due to sharing of the carriers between bands at zero field. Also, this energetic separation is much greater than the interband separation at which the
Table 1 P
Eg(P)
1.1E~(P)
EL,(P)
(bars)
(eV)
(eV)
(eV)
4000 6000 8000 10,000 12,000
0.28 0.31 0.34 0.37 0.40
0.31 0.34 0.37 0.41 0.44
0.41 0.39 0.37 0.35 0.33
—
Er,(P)
Parameters based on InSb model with an energy gap at 77°K of 0.22 eV, an energetic separation between F, and L, conduction band minima of 0.45 eV, and pressure coefficients 9E /aP = 1.5 x 10~ eV/bar and a/3P (EL—Er, )= — 1 x i0~ eV/bar. E~ is the ~hreshold energy for ionization by an electron.
908
ELECTRON—HOLE PAIR PRODUCTION AND GUNN EFFECT IN InSb
Guns effect disappears in GaAs3 or uniaxially
strained Ge.4 It has been determined from resistivity and Hall effect measurements at high pressures and low temperature that in samples of type A there is a rapid drop of free carrier density which starts in the same pressure range as the Gunn threshold field increases. It is supposed that de-ionization into impurity levels associated with the higher-lying L, minima is responsible.5 On the other hand, samples of type B show no such drop in carrier density in this pressure range. Thus there appears to be a direct correlation of the increase in threshold and disappearance of Gunn effect with the rapid decrease in carrier density. Current work is in three areas. (1) Verification of the existence of these impurity levels and the nature of the responsible
Vol. 7, No. 13
defect, and quantitative investigation of the functional dependence of Gunn threshold field on carrier density. (2) Careful measurements of electron—hole generation rate below the threshold field for Gunn effect which should give additional information about the energy separation of the minima and the conditions for observation of the Gunn effect. (3) Study of the pair generation at low pressures where the Gunn effect is not observed, which will give the energy gap dependence of the generation rate. Acknowledgements — We take this opportunity to acknowledge the assistance of F.R. Fiegel, Jr. in the fabrication of the samples, and of James Inglis and David McLeod for assistance in some of the measurements.
REFERENCES 1.
PAUL W., J. Appi. Phys. 32, 2082 (1961). See also Demchuk, Tsidilkovskii and Radionov, Soviet Phys. Solid State 7, 1257 (1965).
2.
WOOLLEY and CODERRE, to be published. One of us (W.P.) is much indebted to Professor Woolley for the opportunity to examine his data before publication.
3.
WASSE, M.P., LEESJ., and KING G., Solid State Electronics 9, 601 (1966).
4.
SMITH J.E., Appi. Phys. Lett. 12, 233 (1968).
5.
See PAUL W., Proceedings of the Ninth International Conference on Semiconductors, Moscow, 1968, to be published.
Das Untersuchen der Schwach- und Starkfeldtransporteigenschaften, des Gunn-Effekts, und der Lawinen-Durchbruch, als Funktionen des Druckes, in n-Typ-InSb hat Informationen iiber die Eigenschaften höheren Leitungsband-Minima und der diesigen Störstellen-Niveaus gegeben.