- Email: [email protected]
Permittivity of β-Ga2O3 at low frequencies
NOTES
multiplication region is maintained either by sideways diffusion of carriers due to strong optical phonon scattering, or by generation due to recombination radiation. The entire multiplication region is therefore indirectly supported by the central avalanche. The net fractional leakage of carriers from the central avalanche will increase rapidly if the diameter of the avalanche region is decreased. Small changes of field in the avalanche region might therefore have a surprisingly large effect on the stability of the stable microplasma. In observations of the current-voltage characteristic at a temperature of approximately 125°K it was noted that, from the first appearance of the quasi-stable microplasma to the completely stable microplasma (resistance 100 a) there was a voltage increase of about 2 mV. This would correspond to a change in the maximum field of about 200 V cm-’ [see Ref. 71. In silicon this same field is generated at a distance of 600 A from a single electron charge. It is suggested that the re-distribution of field associated with the change in charge-state of a single trap in the avalanche region of a quasi-stable microplasma would be sufficient to cause the continuous avalanche condition to become unstable. This instability would lead to a period of continuous switching similar to that observed in Fig. 2(b). Thus the duration of the grouped ‘switch-off transients in Figs. 2(c) and (d) would correspond to the relaxation times of single traps in the microplasma avalanche region. This temporary return to the unstable state is, in effect, a reversal of Shockley’s ‘lock-on’ mechanism[3]. Previous mechanisms of microplasma switching are insufficient to explain the grouping of ‘switchoff’ transients. A model has been suggested that is compatable with previous observations and that will also explain the new observations described above. It is interesting to note that a similar discussion of the effects of trapping in microplasmas will explain the grouping of ‘switch-on’ transients. /Icknowledgement-Thanks are due to Professor J. H. Leek of this department for providing laboratory facilities. Department of Electrical Engineering and Electronics University of Liverpool England *NOW
England.
at International
Computers
M. ELMS* A. LOWE
Ltd., Kidsgrove,
1057 REFERENCES
1. 2. 3. 4. 5.
R. H. Hatiz,J. applPhys.36,3123,(1965). R. J. McIntyre, j.-appl: Phys. 32,982. (1961). W. Shocklev.Solid-St. Electron. 2.35, (1961). G. Keil, and I. Ruge, J. appl. Phys. 36, i600, (1965). K. L. Chiange, and P. 0. Lauritzen, Solid-St. Electron. 13,619,(1970). 6. G. Keil, and H. Bemt, Solid-St. Electron. 9, 321, (1966). 7. S. I. Miller, Phys. Rev. 105,1246 (1957).
Solid-Stare
Elecfronics
Pergamon Press 1971. Vol. 14. pp. 1057-1059. Printed in Great Britain
Permittivity of p-Ga,O, at low trequencies (Received28 January 1971; in revisedform 4 March 1971)
THE relative dielectric constant E,. of p-G&O, in the direction perpendicular to the (100) plane is found to be 10.2 +0.3. Within the measurement error el is the same at 297°K and at 77”K, and is independent of frequency from 5 kHz to 500 kHz. EXPERIMENTAL PROCEDURES We have measured the dielectric constant of pGhO,[ l] in the direction perpendicular to the (100) plane. This is the best cleavage plane of the crystal. Measurements were performed on platelets originating from three single crystals. Crystal A was flame-grown from G%O, powder. The single crystal so obtained is extrinsic and n-type. A possible explanation is that oxygen deficiencies act as donors; when thin platelets of this crystal are heated in oxygen at temperatures of the order of 1200°C their resistivity increases greatly. Crystal B was flux grown from a solution of G&O, in PbF2. Crystal C was also grown in this manner but the solution contained 1.2 per cent of T%05. Both crystals are of very high resistivity. Thin platelets were cleaved from crystals B and C. A platelet free of steps and cracks was selected and its thickness measured with a Carson Dice Electronic Micrometer. The platelet was then cleaned by dipping it in concentrated orthophosphoric acid for several minutes, then briefly in hydrochloric acid, and finally rinsed in distilled water. Next, a circular gold dot was evaporated on one side of the platelet in a vacuum below lo+ Torr. A back contact was then evaporated on the entire reverse side of the platelet, thus forming a parallel plate capacitor. The radius of the gold dot
1058
NOTES
was measured from calibrated microphotographs. Boonton 75 C and 74C-SS capacitance bridges were used to determine the capacitance of the sample. The value was found to be independent of illumination, of d.c. bias, and of frequency within the experimental error of 0.5 per cent and the accessible ranges of & 6.1 V and 5 kHz to 500 kHz. The capacitances found at room temperature (297°K) and at liquid nitrogen temperature (77°K) differ by less than the experimental uncertainty of 1.5 per cent. After capacitance measurements, the gold electrodes were removed by a brief dip in ‘aqua regia’ and the platelet thickness was remeasured. Platelets cleaved from crystal A were first heated in a diffusion furnace to 1180°C for 9.5 hr in an atmosphere of pure oxygen to increase their resistivity. After this treatment the capacitance of the thinnest samples became independent of d.c. bias, of frequency and of illumination. Except for this heat treatment, samples of crystal A were prepared and measured as outlined earlier.
II.0
-
--10.0 Er
where l0 = 8.854 X 1O-12 F/m is the permittivity of free space. The results are reported in Fig. 1. One-sigma errors are indicated for each measurement. The final average value is E, = 10.2 +0.3. Within the measurement error, the dielectric constant is the same at 297°K and at 77”K, and is independent of frequency in the range from 5 kHz
-
obtain an estimate of the dielectric constant independent method, the resistivity and Hall were measured on a platelet of the flame crystal A without previous heat treatment Table 1. Experimental
--P
-
P
I
I
I
I
I
Al
El
82
83
C1
Fig. 1. Relative dielectric constant of p-G&O, perpendicular to the (100) plane, obtained from five different samples originated from three different single crystals A,BandC. in oxygen.
tronic. was
The conduction
was found
to be elec-
At 4056 G and 297”K, the Hall mobility /lo = 89.6 &’
15%
and the average donor concentration
was
Nd = 3.3 * 1017.cLHcm-3* 10% pd
where ,.&dis the drift mobility. The Hall pattern was then removed with nitric acid and circular gold dots where evaporated on one side of the platelet. An ohmic contact was made over the whole back side by vacuum evaporating Mg and then Al without breaking vacuum during the process. The capacitance C as a function of bias voltage V was measured and straight lines were obtained in the l/C2 vs. V plot. The relative dielectric constant derived from the slope of these lines according to 2
dV
ErNd =Qqd(l/C2)
to 500 kHz.
To by an effect grown
--P
1
RESULTS AND DISCUSSION
Experimental values obtained on two typical samples are summarized in Table 1. The relative dielectric constant E, is calculated with these data from [21
---
-
I;,f 10.5 9.5
---
(where S is the surface area of the gold dot and q is the electronic charge) is E, = 12.7 -+ 2.5 assuming c%r= pd. A scatter of *20% in crNd for the different gold dots indicates that significant
values of two typical samples
Sample
B3
Cl
Radius R of circular dot Thickness A of sample Capacitance C
0.2066mm-c 1% 46.5 kO.7 pm 0.3201 -t-O.0018 pF
0.2670 mm 2 0.4% .51.4&0.6pm 0.4773 kO.0025 pF
1059
NOTES
variations in doping concentration exists across the platelet. This uncertainty in the doping underlies the error indicated previously for lr and for pH. The result of this experiment, although less accurate than the direct determination of Ed described first, is compatible with 4 = 10.2 2 0.3. Acknowledgement - Dr. Richard E. Marsh kindly performed the X-ray analysis which confirmed the pmodification of the crystals and identified the cleavage pianes of our platelets. We thank him for this contribution.
California Institufe of Technology, Pasadena, California 9 1109
netic field of an air coil c. The coil was supplied by a sine-wave generator with variable frequency. The magnitude of magnetic induction was kept constant by controlling the coil current, which was measured by a thermal milliampermeter. The alternating signal on the sample was measured by a selective millivoltmeter (input impedance > 300 kR).
B. HOENEISEN C. A. MEAD M-A.
NICOLET
U.S.A. Fig. 1. Measurement REFERENCES
1. S. Geller, J. them. Phys. 33,676 (1960). 2. C. H. Sequin, Solid-St. Electron. 14,417 (1971).
Solid-Stare Electronics
On
Pergamon Press 1971. Vol. 14, pp. 1059-1060. Printed in Great Britain
thefrequency response of Ge-magnetodiodes (Received
FREQUENCY responses
25 January
197 1)
of Ge-magnetodiodes were measured with d.c. currents in an alternating magnetic field. Dependence of frequency response characteristics on loading resistance was found. Frequency characteristics of magnetodiodes give important information relative to their application in alternative or pulse magnetic fields. There is relatively little information on this problem. The Sony Corporation has given the frequency characteristics of Sony-magnetodiodes [ 1,2], where the frequency responses are flat from steady magnetic field up to about 10 kHz in commercial samples. Flat response up to 100 kHz has been obtained in smaller samples. In this work the frequency characteristic of Gemagnetodiodes at various loading resistances are presented and compared with characteristic of magnetoresistances with a magnetic depletion layer [3,43. Experimental samples were prepared in our institute. The measurement arrangement is shown in Fig. 1. The forward biased sample M was in the mag-
arrangement.
Measured samples were approximately of the same geometry, similar to Sony magnetodiodes. Typical results at the magnitude of the magnetic field B = 10 G are shown in Figs. 2 and 3, for the magnetodiode as well as for a magnetoresistance, signed as MD and MR, respectively. Influence of the magnetic induction magnitude on the frequency response in the range of the above mentioned value was not observed. Of interest was the fact that the frequency responses of the magnetodiodes depended on the loading resistance. The higher the loading resistance, the higher the frequency of the flat response, as can be seen in Figs. 2 and 3. With high loading resistance in the circuit the magnetodiode works in a regime with constant current. Thus, the voltage across the pn-junction is practically constant, so that the injection from electrodes does not change under the influence of the magnetic field [5]. Therefore, the magnetodiode in a circuit with high loading resistance behaves analogously to a magnetoresistance with a magnetic depletion layer. In a circuit with small loading resistance there is a constant voltage across the magnetodiode and under the influence of the magnetic field, when the resistance of the central part of the magnetodiode rises, comes to the redistribution of the voltages in such a way, that the pn-junction voltage decreases. As a result the magnetic field changes the injection from the electrodes in this case. This fact can be the reason for the poorer frequency response at lower loading resistance. These suggestions are also proved by the frequency responses of
multiplication region is maintained either by sideways diffusion of carriers due to strong optical phonon scattering, or by generation due to recombination radiation. The entire multiplication region is therefore indirectly supported by the central avalanche. The net fractional leakage of carriers from the central avalanche will increase rapidly if the diameter of the avalanche region is decreased. Small changes of field in the avalanche region might therefore have a surprisingly large effect on the stability of the stable microplasma. In observations of the current-voltage characteristic at a temperature of approximately 125°K it was noted that, from the first appearance of the quasi-stable microplasma to the completely stable microplasma (resistance 100 a) there was a voltage increase of about 2 mV. This would correspond to a change in the maximum field of about 200 V cm-’ [see Ref. 71. In silicon this same field is generated at a distance of 600 A from a single electron charge. It is suggested that the re-distribution of field associated with the change in charge-state of a single trap in the avalanche region of a quasi-stable microplasma would be sufficient to cause the continuous avalanche condition to become unstable. This instability would lead to a period of continuous switching similar to that observed in Fig. 2(b). Thus the duration of the grouped ‘switch-off transients in Figs. 2(c) and (d) would correspond to the relaxation times of single traps in the microplasma avalanche region. This temporary return to the unstable state is, in effect, a reversal of Shockley’s ‘lock-on’ mechanism[3]. Previous mechanisms of microplasma switching are insufficient to explain the grouping of ‘switchoff’ transients. A model has been suggested that is compatable with previous observations and that will also explain the new observations described above. It is interesting to note that a similar discussion of the effects of trapping in microplasmas will explain the grouping of ‘switch-on’ transients. /Icknowledgement-Thanks are due to Professor J. H. Leek of this department for providing laboratory facilities. Department of Electrical Engineering and Electronics University of Liverpool England *NOW
England.
at International
Computers
M. ELMS* A. LOWE
Ltd., Kidsgrove,
1057 REFERENCES
1. 2. 3. 4. 5.
R. H. Hatiz,J. applPhys.36,3123,(1965). R. J. McIntyre, j.-appl: Phys. 32,982. (1961). W. Shocklev.Solid-St. Electron. 2.35, (1961). G. Keil, and I. Ruge, J. appl. Phys. 36, i600, (1965). K. L. Chiange, and P. 0. Lauritzen, Solid-St. Electron. 13,619,(1970). 6. G. Keil, and H. Bemt, Solid-St. Electron. 9, 321, (1966). 7. S. I. Miller, Phys. Rev. 105,1246 (1957).
Solid-Stare
Elecfronics
Pergamon Press 1971. Vol. 14. pp. 1057-1059. Printed in Great Britain
Permittivity of p-Ga,O, at low trequencies (Received28 January 1971; in revisedform 4 March 1971)
THE relative dielectric constant E,. of p-G&O, in the direction perpendicular to the (100) plane is found to be 10.2 +0.3. Within the measurement error el is the same at 297°K and at 77”K, and is independent of frequency from 5 kHz to 500 kHz. EXPERIMENTAL PROCEDURES We have measured the dielectric constant of pGhO,[ l] in the direction perpendicular to the (100) plane. This is the best cleavage plane of the crystal. Measurements were performed on platelets originating from three single crystals. Crystal A was flame-grown from G%O, powder. The single crystal so obtained is extrinsic and n-type. A possible explanation is that oxygen deficiencies act as donors; when thin platelets of this crystal are heated in oxygen at temperatures of the order of 1200°C their resistivity increases greatly. Crystal B was flux grown from a solution of G&O, in PbF2. Crystal C was also grown in this manner but the solution contained 1.2 per cent of T%05. Both crystals are of very high resistivity. Thin platelets were cleaved from crystals B and C. A platelet free of steps and cracks was selected and its thickness measured with a Carson Dice Electronic Micrometer. The platelet was then cleaned by dipping it in concentrated orthophosphoric acid for several minutes, then briefly in hydrochloric acid, and finally rinsed in distilled water. Next, a circular gold dot was evaporated on one side of the platelet in a vacuum below lo+ Torr. A back contact was then evaporated on the entire reverse side of the platelet, thus forming a parallel plate capacitor. The radius of the gold dot
1058
NOTES
was measured from calibrated microphotographs. Boonton 75 C and 74C-SS capacitance bridges were used to determine the capacitance of the sample. The value was found to be independent of illumination, of d.c. bias, and of frequency within the experimental error of 0.5 per cent and the accessible ranges of & 6.1 V and 5 kHz to 500 kHz. The capacitances found at room temperature (297°K) and at liquid nitrogen temperature (77°K) differ by less than the experimental uncertainty of 1.5 per cent. After capacitance measurements, the gold electrodes were removed by a brief dip in ‘aqua regia’ and the platelet thickness was remeasured. Platelets cleaved from crystal A were first heated in a diffusion furnace to 1180°C for 9.5 hr in an atmosphere of pure oxygen to increase their resistivity. After this treatment the capacitance of the thinnest samples became independent of d.c. bias, of frequency and of illumination. Except for this heat treatment, samples of crystal A were prepared and measured as outlined earlier.
II.0
-
--10.0 Er
where l0 = 8.854 X 1O-12 F/m is the permittivity of free space. The results are reported in Fig. 1. One-sigma errors are indicated for each measurement. The final average value is E, = 10.2 +0.3. Within the measurement error, the dielectric constant is the same at 297°K and at 77”K, and is independent of frequency in the range from 5 kHz
-
obtain an estimate of the dielectric constant independent method, the resistivity and Hall were measured on a platelet of the flame crystal A without previous heat treatment Table 1. Experimental
--P
-
P
I
I
I
I
I
Al
El
82
83
C1
Fig. 1. Relative dielectric constant of p-G&O, perpendicular to the (100) plane, obtained from five different samples originated from three different single crystals A,BandC. in oxygen.
tronic. was
The conduction
was found
to be elec-
At 4056 G and 297”K, the Hall mobility /lo = 89.6 &’
15%
and the average donor concentration
was
Nd = 3.3 * 1017.cLHcm-3* 10% pd
where ,.&dis the drift mobility. The Hall pattern was then removed with nitric acid and circular gold dots where evaporated on one side of the platelet. An ohmic contact was made over the whole back side by vacuum evaporating Mg and then Al without breaking vacuum during the process. The capacitance C as a function of bias voltage V was measured and straight lines were obtained in the l/C2 vs. V plot. The relative dielectric constant derived from the slope of these lines according to 2
dV
ErNd =Qqd(l/C2)
to 500 kHz.
To by an effect grown
--P
1
RESULTS AND DISCUSSION
Experimental values obtained on two typical samples are summarized in Table 1. The relative dielectric constant E, is calculated with these data from [21
---
-
I;,f 10.5 9.5
---
(where S is the surface area of the gold dot and q is the electronic charge) is E, = 12.7 -+ 2.5 assuming c%r= pd. A scatter of *20% in crNd for the different gold dots indicates that significant
values of two typical samples
Sample
B3
Cl
Radius R of circular dot Thickness A of sample Capacitance C
0.2066mm-c 1% 46.5 kO.7 pm 0.3201 -t-O.0018 pF
0.2670 mm 2 0.4% .51.4&0.6pm 0.4773 kO.0025 pF
1059
NOTES
variations in doping concentration exists across the platelet. This uncertainty in the doping underlies the error indicated previously for lr and for pH. The result of this experiment, although less accurate than the direct determination of Ed described first, is compatible with 4 = 10.2 2 0.3. Acknowledgement - Dr. Richard E. Marsh kindly performed the X-ray analysis which confirmed the pmodification of the crystals and identified the cleavage pianes of our platelets. We thank him for this contribution.
California Institufe of Technology, Pasadena, California 9 1109
netic field of an air coil c. The coil was supplied by a sine-wave generator with variable frequency. The magnitude of magnetic induction was kept constant by controlling the coil current, which was measured by a thermal milliampermeter. The alternating signal on the sample was measured by a selective millivoltmeter (input impedance > 300 kR).
B. HOENEISEN C. A. MEAD M-A.
NICOLET
U.S.A. Fig. 1. Measurement REFERENCES
1. S. Geller, J. them. Phys. 33,676 (1960). 2. C. H. Sequin, Solid-St. Electron. 14,417 (1971).
Solid-Stare Electronics
On
Pergamon Press 1971. Vol. 14, pp. 1059-1060. Printed in Great Britain
thefrequency response of Ge-magnetodiodes (Received
FREQUENCY responses
25 January
197 1)
of Ge-magnetodiodes were measured with d.c. currents in an alternating magnetic field. Dependence of frequency response characteristics on loading resistance was found. Frequency characteristics of magnetodiodes give important information relative to their application in alternative or pulse magnetic fields. There is relatively little information on this problem. The Sony Corporation has given the frequency characteristics of Sony-magnetodiodes [ 1,2], where the frequency responses are flat from steady magnetic field up to about 10 kHz in commercial samples. Flat response up to 100 kHz has been obtained in smaller samples. In this work the frequency characteristic of Gemagnetodiodes at various loading resistances are presented and compared with characteristic of magnetoresistances with a magnetic depletion layer [3,43. Experimental samples were prepared in our institute. The measurement arrangement is shown in Fig. 1. The forward biased sample M was in the mag-
arrangement.
Measured samples were approximately of the same geometry, similar to Sony magnetodiodes. Typical results at the magnitude of the magnetic field B = 10 G are shown in Figs. 2 and 3, for the magnetodiode as well as for a magnetoresistance, signed as MD and MR, respectively. Influence of the magnetic induction magnitude on the frequency response in the range of the above mentioned value was not observed. Of interest was the fact that the frequency responses of the magnetodiodes depended on the loading resistance. The higher the loading resistance, the higher the frequency of the flat response, as can be seen in Figs. 2 and 3. With high loading resistance in the circuit the magnetodiode works in a regime with constant current. Thus, the voltage across the pn-junction is practically constant, so that the injection from electrodes does not change under the influence of the magnetic field [5]. Therefore, the magnetodiode in a circuit with high loading resistance behaves analogously to a magnetoresistance with a magnetic depletion layer. In a circuit with small loading resistance there is a constant voltage across the magnetodiode and under the influence of the magnetic field, when the resistance of the central part of the magnetodiode rises, comes to the redistribution of the voltages in such a way, that the pn-junction voltage decreases. As a result the magnetic field changes the injection from the electrodes in this case. This fact can be the reason for the poorer frequency response at lower loading resistance. These suggestions are also proved by the frequency responses of