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Effect of a magnetic field upon the gunn effect in InSb
Solid State Communications,
Vol.8, PP. 855—858, 1970.
Pergamon Press.
Printed in Great Britain
EFFECT OF A MAGNETIC FIELD UPON THE GUNN EFFECT IN InSb E. Muller and D.K. Perry Department of Electrical Engineering, Texas Tech. University, Lubbock, Texas 79409 (Received 2 February 1970 by A.A. Maradudin)
For times less than 2.5 nsec after the application of an electric field pulse in n-type InSb at 77°K,a sharp drop in the current occurs for electric fields> 600 V/cm. This drop has been previously interpreted as the occurrence of the Gunn effect in InSb due to intervalley transfer. A transverse magnetic field produces an appreciable decrease in the threshold for the instability.
WHEN AN electric field of 600 V/cm or more is applied to n-type InSb at 77°K,an instability occurs, which is characterized by a sharp drop in the current density.’ This instability only exists for times less than 2.5nsec after the application of the electric field pulse, since impact ionization leads to large increases in the current for times longer than this. Smith et al.’ have interpreted the instability as an intervalley scattering of the electrons from the central <100> valley of the conduction band into the subsidiary <111> valleys leading to the Gunn effect.2 These subsidiary valleys lie approximately 0.45 eV1 above the central valley minimum. Sincethis value of i~ is considerably greater than the band gap, EG = 0.22 eV, it had previously been felt that the impact ionization and consequent carrier multiplication precluded the occurrence of the Gun effect in this material except when subjected to hydrostatic pressure.3 In this paper, the observation of a strong decrease of the threshold electric field for the occurrence of the negative differential conductivity (NDC) in a transverse magnetic field is reported. This sharp decrease is apparently inconsistent with the interpretation of the instability as an intervalley transfer mechanism, since the decrease would require a reduction of A. Such a reduction is not expected for purely magnetic effects.
Samples of n-type InSb with a carrier concentration of 2 x 10’~cm3 and a carrier mobility of 5 x 10~cm2/V-sec are mounted in a coaxial insertion unit in a constant voltage circuit. The samples are typically 0.015 x 0.015 x 0.135 cm. Rectangular electric field pulses are supplied from a coaxial cable discharge pulser and have a risetime of less than 0.35 nsec at the sample. The current and voltage are monitored by a sampling oscilloscope and the I—V curves are plotted for a time of 1.0 nsec after the start of the pulse. The instability is characterized by the sharp drop in the current at the threshold electric field. With the application of an external magnetic field, the threshold is observed to drop considerably. From an initial threshold of 600 V/cm, the threshold decreases to a value of 530 V/cm for a magnetic field of 3000 G parallel to the electric field. For a 3000 G magnetic field perpendicular to the electric field, the threshold electric field decreases to 220 V/cm. The behavior of the I—V characteristics are shown in Fig. 1 for several values of the magnetic field. For the largest transverse magnetic fields used, the threshold for the instability has dropped below the electric field required for impact ionization to occur for these short times, while for the lower magnetic fields the electric field threshold is such that impact ionization is a competing process. 855
856
EFFECT OF A MAGNETIC FIELD UPON THE GUNN EFFECT IN InSb
Vol.8, No. 11
I
U >
0G. 750G
—500 G 1000G.
~
I-
u
BIlE
.
OG
I-
000G G.
z
-‘
A
C -j
o U, U I
,):0 200
6b0
4b0
ELECTRIC FIELD
8 0
1000
(V/CM)
MAGNETIC
a
FIG.
C I-.
2
~-750
(GAUSS)
2. Variation of the threshold electric field
electric field for the instability by the applied magnetic field does not appear to be consistent with an intervalley transfer mechanism. Smith et a!.1 report a decrease of the threshold electric field when the sample is subjected to hydrostatic pressure. A pressure of 8.9kbar affects a reduction of about a third in the threshold field, i.e. to about 400 V/cm. For this pressure, the separation in the valleys, A, has decreased to 0.36eV. An equivalent threshold
,-500G
z
FIELD
3000
with the applied magnetic field. The observed reduction of the threshold
~0 G
U’
2000
G
0
“~IO0OG ,...1500 G
.3QOoG ~00G, 200 400 ELECTRIC
FIELD
600
800
(v/cM)
b 1. The J—E characteristics for n-type InSb for (a) a longitudinal magnetic field and (b) a transverse magnetic field, for various values of the magnetic field. The curves are taken at a time of 1.Onsec after application of the electric field pulse. The instability is characterized by the sharp drop in current at the threshold electric field. FIG.
field reduction of about is caused 1000 G.forAlthough a transverse this is magnetic a large magnetic field, CLcT> 1, the conduction band is not quantized since ~ < KT even at the lattice temperature. Further, the magnetic bandshift is insufficient to account for the apparent energy change of A. At most, the shift of the bands can be expected to be of the order of 1/2 ?iw~,which is of the order 1 meV. This is only a small fraction of the shift in A of 0.09 eV found from the hydrostatic measurements, so that the magnetic field could not be causing the threshold decrease due to a decrease of A. A decrease in threshold could occur if the competing ionization
Vol.8, No.11
EFFECT OF A MAGNETIC FIELD UPON THE GUNN EFFECT IN InSb
process is retarded in some manner. A magnetic field does affect the generation rate, but only slightly except at the highest electric fields involved.4 At these fields, the threshold of the the instability is moved by a small magnetic field, which is too small to measurably change the generation rate. At these higher electric fields, energy diffusion terms are becoming iniportañtin the distribution function. In this case, the magnetic field should also decrease the number of electrons with energy sufficient to make the intervalley transition, so that a reduction of the threshold due to a decrease of the generation rate is not likely. The large value of the transverse magnetic field leads to Hall electric fields which are considerably stronger than the longitudinal electric field. Even so, the higher energy electrons in the distribution could still see a transverse force comparable to that due to the electric field at the instability threshold in the absence of the magnetic field. Although these electrons could possibly have sufficient energy for the intervalley process, it is these same electrons which are involved in the impact ionization process, and nocarrier generation is observed at the strongest magnetic fields during the time in which the instability occurs, so that a transverse instability is not likely. It is also possible that the magnetic field tends to accentuate any inhomogeneity in the electric field and leads to strong high field domains near the contacts. Although the average electric field is lower, the electric field in these domains could be sufficient to cause the instability. Again, however, it would be expected that impact ionization could also occur in the domain. In this case, the ionization would propagate out from the domain until the carrier multiplication filled the sample. If this were the case, it would take longer for the avalanche breakdown to build up in the sample leading to a longer time duration of the instability, This is not observed experimentally. From these considerations, the effect of the magnetic field upon the short time instability occurring in InSb is such that it apparently contradicts the assumption of an intervalley type Guns instability, Smith et al. draw their conclusion for a Gunn instability from three measurements: (1) the
857
observation of the current drop, (2) the observance of travelling domains, and (3) the effect of pressure on the threshold. The first of these is in agreement with the present measurements. The second of these follows from the first, since the domains are not unique to the Gunn effect, but are possible for any negative differential conductivity mechanism as was pointed out by Ridley.5 Thus, it is the third measurement, the pressure dependence, which leads to the assumption of the Gunn effect. It is possible that the pressure affects the instability in a manner other than through the shift of the various valleys, as is apparently done by the magnetic field. Although the effect of the magnetic field does not conclusively rule out the intervalley transfer mechanism, it is apparently inconsistent with such an explanation. As a consequence, it is wor’thwhile to mention several other mechanisms which could lead to such an instability. Persky and Bartelink 6 have predicted a negative differential mobility (NDM) due to non-parabolicity of the energy bands. However, in this case, it is not likely that the magnetic field would lower the threshold electric field for the onset of NDM, although the predicted threshol.d of 550 V/cm is in qualitative agreement with the experimental value for this instability. G. Smith has considered the effect of the high electric field and consequent polar optical phonon emission driving the phonon distribution out of equilibrium.7 He predicts a NDM due to the build-up of the non-equilibrium phonons at high electric fields. Steele and Tosima have experimentally observed the existence of NDM in InSb in impact ionization due to the onset of strong electron-hole scattering in the avalanche produced plasma.8 It is qualitatively easy to understand the effect of the magnetic field in this case. The, magnetic field reduces the mobility, hence the number of excess carriers required for electron-hole scattering to dominate is reduced and a lower threshold electric field results. Similar effects could be caused by pressure. It is possible therefore, although not conclusive, that a mechanism other than intervalley transfer is involved in the instability.
858
EFFECT OF A MAGNETIC FIELD UPON THE GUNN EFFECT IN InSb
Vol.8, No. 11
1.
REFERENCES SMITH J.E., NATHAN MI., MCGRODDY J.C., POROWSKI S.A. and PAUL W., App. Phys. Len. 15, 242 (1969).
2.
FOYT A.G. and MCWHORTER A.L., IEEE Trans. Electron Devices ED—13, 79 (1966).
3. 4.
GUNN J.B., Solid State Commun. 1, 88 (1963). FERRY D.K. and HEINRICH H., Phys. Rev. 169, 670 (1968).
5. 6.
RIDLEY B.K., Proc. Phys. Soc. 82, 954 (1963). PERSKY G. and BARTELINK D.J., IBM Journal 13, 607 (1969).
7. 8.
SMITH G. and BEATTIE A.R., to be published; SMITH G., Bull. Am. Phys. Soc. 11—15, 304 (1970). STEELE M.C. and TOSIMA S., Jap. J. appi. Phys. 2, 381 (1963).
Im n-typ InSb bei 77°K,bei kurzen Zeiten (<2.Snsec), nach dem Anfang des Elektrischfeldpuls, kommt eine Stromabnahme bei Feldstarken von 600 V/cm vor. Diese Abnahme in InSb wurde vorher als ‘Guns Effekte’ erklärt. Das transversale Magnetfeld erzeugt eine grosse Abhahme der Elektrischfeld-Schwelle der Instabilitàt.
Vol.8, PP. 855—858, 1970.
Pergamon Press.
Printed in Great Britain
EFFECT OF A MAGNETIC FIELD UPON THE GUNN EFFECT IN InSb E. Muller and D.K. Perry Department of Electrical Engineering, Texas Tech. University, Lubbock, Texas 79409 (Received 2 February 1970 by A.A. Maradudin)
For times less than 2.5 nsec after the application of an electric field pulse in n-type InSb at 77°K,a sharp drop in the current occurs for electric fields> 600 V/cm. This drop has been previously interpreted as the occurrence of the Gunn effect in InSb due to intervalley transfer. A transverse magnetic field produces an appreciable decrease in the threshold for the instability.
WHEN AN electric field of 600 V/cm or more is applied to n-type InSb at 77°K,an instability occurs, which is characterized by a sharp drop in the current density.’ This instability only exists for times less than 2.5nsec after the application of the electric field pulse, since impact ionization leads to large increases in the current for times longer than this. Smith et al.’ have interpreted the instability as an intervalley scattering of the electrons from the central <100> valley of the conduction band into the subsidiary <111> valleys leading to the Gunn effect.2 These subsidiary valleys lie approximately 0.45 eV1 above the central valley minimum. Sincethis value of i~ is considerably greater than the band gap, EG = 0.22 eV, it had previously been felt that the impact ionization and consequent carrier multiplication precluded the occurrence of the Gun effect in this material except when subjected to hydrostatic pressure.3 In this paper, the observation of a strong decrease of the threshold electric field for the occurrence of the negative differential conductivity (NDC) in a transverse magnetic field is reported. This sharp decrease is apparently inconsistent with the interpretation of the instability as an intervalley transfer mechanism, since the decrease would require a reduction of A. Such a reduction is not expected for purely magnetic effects.
Samples of n-type InSb with a carrier concentration of 2 x 10’~cm3 and a carrier mobility of 5 x 10~cm2/V-sec are mounted in a coaxial insertion unit in a constant voltage circuit. The samples are typically 0.015 x 0.015 x 0.135 cm. Rectangular electric field pulses are supplied from a coaxial cable discharge pulser and have a risetime of less than 0.35 nsec at the sample. The current and voltage are monitored by a sampling oscilloscope and the I—V curves are plotted for a time of 1.0 nsec after the start of the pulse. The instability is characterized by the sharp drop in the current at the threshold electric field. With the application of an external magnetic field, the threshold is observed to drop considerably. From an initial threshold of 600 V/cm, the threshold decreases to a value of 530 V/cm for a magnetic field of 3000 G parallel to the electric field. For a 3000 G magnetic field perpendicular to the electric field, the threshold electric field decreases to 220 V/cm. The behavior of the I—V characteristics are shown in Fig. 1 for several values of the magnetic field. For the largest transverse magnetic fields used, the threshold for the instability has dropped below the electric field required for impact ionization to occur for these short times, while for the lower magnetic fields the electric field threshold is such that impact ionization is a competing process. 855
856
EFFECT OF A MAGNETIC FIELD UPON THE GUNN EFFECT IN InSb
Vol.8, No. 11
I
U >
0G. 750G
—500 G 1000G.
~
I-
u
BIlE
.
OG
I-
000G G.
z
-‘
A
C -j
o U, U I
,):0 200
6b0
4b0
ELECTRIC FIELD
8 0
1000
(V/CM)
MAGNETIC
a
FIG.
C I-.
2
~-750
(GAUSS)
2. Variation of the threshold electric field
electric field for the instability by the applied magnetic field does not appear to be consistent with an intervalley transfer mechanism. Smith et a!.1 report a decrease of the threshold electric field when the sample is subjected to hydrostatic pressure. A pressure of 8.9kbar affects a reduction of about a third in the threshold field, i.e. to about 400 V/cm. For this pressure, the separation in the valleys, A, has decreased to 0.36eV. An equivalent threshold
,-500G
z
FIELD
3000
with the applied magnetic field. The observed reduction of the threshold
~0 G
U’
2000
G
0
“~IO0OG ,...1500 G
.3QOoG ~00G, 200 400 ELECTRIC
FIELD
600
800
(v/cM)
b 1. The J—E characteristics for n-type InSb for (a) a longitudinal magnetic field and (b) a transverse magnetic field, for various values of the magnetic field. The curves are taken at a time of 1.Onsec after application of the electric field pulse. The instability is characterized by the sharp drop in current at the threshold electric field. FIG.
field reduction of about is caused 1000 G.forAlthough a transverse this is magnetic a large magnetic field, CLcT> 1, the conduction band is not quantized since ~ < KT even at the lattice temperature. Further, the magnetic bandshift is insufficient to account for the apparent energy change of A. At most, the shift of the bands can be expected to be of the order of 1/2 ?iw~,which is of the order 1 meV. This is only a small fraction of the shift in A of 0.09 eV found from the hydrostatic measurements, so that the magnetic field could not be causing the threshold decrease due to a decrease of A. A decrease in threshold could occur if the competing ionization
Vol.8, No.11
EFFECT OF A MAGNETIC FIELD UPON THE GUNN EFFECT IN InSb
process is retarded in some manner. A magnetic field does affect the generation rate, but only slightly except at the highest electric fields involved.4 At these fields, the threshold of the the instability is moved by a small magnetic field, which is too small to measurably change the generation rate. At these higher electric fields, energy diffusion terms are becoming iniportañtin the distribution function. In this case, the magnetic field should also decrease the number of electrons with energy sufficient to make the intervalley transition, so that a reduction of the threshold due to a decrease of the generation rate is not likely. The large value of the transverse magnetic field leads to Hall electric fields which are considerably stronger than the longitudinal electric field. Even so, the higher energy electrons in the distribution could still see a transverse force comparable to that due to the electric field at the instability threshold in the absence of the magnetic field. Although these electrons could possibly have sufficient energy for the intervalley process, it is these same electrons which are involved in the impact ionization process, and nocarrier generation is observed at the strongest magnetic fields during the time in which the instability occurs, so that a transverse instability is not likely. It is also possible that the magnetic field tends to accentuate any inhomogeneity in the electric field and leads to strong high field domains near the contacts. Although the average electric field is lower, the electric field in these domains could be sufficient to cause the instability. Again, however, it would be expected that impact ionization could also occur in the domain. In this case, the ionization would propagate out from the domain until the carrier multiplication filled the sample. If this were the case, it would take longer for the avalanche breakdown to build up in the sample leading to a longer time duration of the instability, This is not observed experimentally. From these considerations, the effect of the magnetic field upon the short time instability occurring in InSb is such that it apparently contradicts the assumption of an intervalley type Guns instability, Smith et al. draw their conclusion for a Gunn instability from three measurements: (1) the
857
observation of the current drop, (2) the observance of travelling domains, and (3) the effect of pressure on the threshold. The first of these is in agreement with the present measurements. The second of these follows from the first, since the domains are not unique to the Gunn effect, but are possible for any negative differential conductivity mechanism as was pointed out by Ridley.5 Thus, it is the third measurement, the pressure dependence, which leads to the assumption of the Gunn effect. It is possible that the pressure affects the instability in a manner other than through the shift of the various valleys, as is apparently done by the magnetic field. Although the effect of the magnetic field does not conclusively rule out the intervalley transfer mechanism, it is apparently inconsistent with such an explanation. As a consequence, it is wor’thwhile to mention several other mechanisms which could lead to such an instability. Persky and Bartelink 6 have predicted a negative differential mobility (NDM) due to non-parabolicity of the energy bands. However, in this case, it is not likely that the magnetic field would lower the threshold electric field for the onset of NDM, although the predicted threshol.d of 550 V/cm is in qualitative agreement with the experimental value for this instability. G. Smith has considered the effect of the high electric field and consequent polar optical phonon emission driving the phonon distribution out of equilibrium.7 He predicts a NDM due to the build-up of the non-equilibrium phonons at high electric fields. Steele and Tosima have experimentally observed the existence of NDM in InSb in impact ionization due to the onset of strong electron-hole scattering in the avalanche produced plasma.8 It is qualitatively easy to understand the effect of the magnetic field in this case. The, magnetic field reduces the mobility, hence the number of excess carriers required for electron-hole scattering to dominate is reduced and a lower threshold electric field results. Similar effects could be caused by pressure. It is possible therefore, although not conclusive, that a mechanism other than intervalley transfer is involved in the instability.
858
EFFECT OF A MAGNETIC FIELD UPON THE GUNN EFFECT IN InSb
Vol.8, No. 11
1.
REFERENCES SMITH J.E., NATHAN MI., MCGRODDY J.C., POROWSKI S.A. and PAUL W., App. Phys. Len. 15, 242 (1969).
2.
FOYT A.G. and MCWHORTER A.L., IEEE Trans. Electron Devices ED—13, 79 (1966).
3. 4.
GUNN J.B., Solid State Commun. 1, 88 (1963). FERRY D.K. and HEINRICH H., Phys. Rev. 169, 670 (1968).
5. 6.
RIDLEY B.K., Proc. Phys. Soc. 82, 954 (1963). PERSKY G. and BARTELINK D.J., IBM Journal 13, 607 (1969).
7. 8.
SMITH G. and BEATTIE A.R., to be published; SMITH G., Bull. Am. Phys. Soc. 11—15, 304 (1970). STEELE M.C. and TOSIMA S., Jap. J. appi. Phys. 2, 381 (1963).
Im n-typ InSb bei 77°K,bei kurzen Zeiten (<2.Snsec), nach dem Anfang des Elektrischfeldpuls, kommt eine Stromabnahme bei Feldstarken von 600 V/cm vor. Diese Abnahme in InSb wurde vorher als ‘Guns Effekte’ erklärt. Das transversale Magnetfeld erzeugt eine grosse Abhahme der Elektrischfeld-Schwelle der Instabilitàt.