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Trap-controlled bunching of electrons in acoustoelectric domains
Solid State Communications,
Vol. 7, pp. 1027—1029, 1969.
Pergamon Press.
Printed in Great Britain
TRAP-CONTROLLED BUNCHING OF ELECTRONS IN ACOUSTOELECTRIC DOMAINS M. Schulz*; B.K. Ridley Physics Department, University of Essex, Coichester, U.K.
(Received 2 .~1ay1969 by G. Leibfried)
For an acoustoelectric domain in GaAs the saturation current is found to be independent of the electron concentration. This result and incubation time measurements are in accord with a simple model of trap-controlled bunching of electrons in the domain.
IN n-TYPE GaAs at liquid nitrogen temperature and under strong illumination we have observed high-field domains which are clearly associated with the generation and propagation of acoustic flux. The invariance of the current in presence of the domain and the variation with illumination of the incubation time for the domain formation point to and can be interpreted by trap-controlled bunching of electrons in the acoustoelectric domain,
sample. The specimen current then was monitored on the oscilloscope. For fields higher than a threshold field 300—800 V/cm the same typical oscillations appeared in the current as they are known for acoustic domains. 1,2 The characteristics are the appearance of an incubation time ‘T and the period of the oscillation close to an acoustic transit time Ttransjt indpendent of the applied field. (A typical current oscillation giving the definitions is shown in the insert of Fig. 2.) Clear acoustic domains were observed tcm for coriductivities down to 0.2 ~2“
Specimens (0.5 x 0.5 ~ 8mm ~) were cut from a 0.2~lcm ‘undoped’ GaAs ingot from Monsanto with the long dimension in the [110] crystal direction for strong piezoelectric coupling
The current in presence of the domain ‘sat the field E 0 outside the domain and the incubation time ‘r~for domain formation have been measured with respect to the conductivity. If we assume a drift mobility independent of illumination the conductivity can be taken as a measurein for the1 free electron concentration. As shown Fig. we find the saturation current independent of conductivity. The field E
of shear acoustic waves. In ± 1 per cent Te pallets alloyed onto the end faces of the rod produced satisfactory ohmic contacts. At 77~K the conductivity of the sample could be varied by illumination in the range from tcm-, using Si-filtered light10~to from a pro0.6cr lamp in order to avoid excitation across jector
0 the energy gap of GaAs. Illumination with unfiltered white light showed the same results presumably because the generated holes recombined very quickly, so that effectively electrons were generated from traps only, Constant voltage pulses of Ca. 3~._sduration were applied across the long dimension of the *Now at Institut fuer Elektrowerkstoffe, Freiburg i.Br., Germany.
1027
outside the domain also shown in Fig. 1 therefore is inversely proportional to the conductivity. The invariance of the saturation current density and the variation with light of the field E0 is evidence that the total electron population, free and trapped, is bunched by the acoustic waves in the domains. To see this let the free electron concentration be n and the total electron concentration be N. If the traps are fast enough to respond to the sound waves the ratio n/N = f is always fixed for a particular illumination level
1028
ACOUSTOELECTRIC DOMAINS IN GaAs
Vol. 7, No. 14
/
.1
~-~—~1’\
1M1
r~r~& [rM] 0 / oturot,on ct.,TIflt (I sat.) [WJ [cm )4
E
T~.Curr~ 2000
500
400
\
72 ~
•
/
•0
/ ~ ,I/ ‘I
//
/1 0
__________________
01
02
03
0.4
/
/
f~~d E 0
o
t5 I
05
06
0
0
07
0
/ / ,/
f%.
/
/
~‘/ ii. I’ ~/ 200? ?400 ~ E
05
e / / /
to
~o
~00 —
E(V/cm)
FIG. 1. Saturation current ‘eat in presence of the domain, field E0 outside the domain and effective mobility ~ e~f = Vs/E0 in function of the conductivity varied by illumination of the sample.
Fic. 2. Reciprocal incubation time in function of the applied electric field. Parameter is the trapping factor f deduced from ~ ~ /~. The straight lines are calculated. The insert shows a typical current oscillation giving the definitions of ‘r~ and ‘sat’
and is known as the trapping factor. For small lattice loss, f~E0 must be close to the synchronous drift velocity ~E3 = V3 according 3 expression for zero gain.4 Thus we have to White’s
Using White’s linear theory for acoustic amplification which is applicable during the incubation time we can express the incubation time as —
T1 5
=
enp.E0
=
efNpE0
=
4 v Ignoring the lattice loss 3 /E0 = = ~ is a measure for the effective mobility which is also recorded in Fig. 1. Note that this mobility is proportional to the conductivity as expected from the trapping factor. From the ratio 3cm2/Vs at 77°K)we can evaluate the =trapping /~eff”~ (~ 8 x 10 factors involved for the four illumination levels used 7.2
i 8
i 10
—
2v3
[K2~
]
g
eNv5
independent of n, in accord with observation. In the case of fast trapping the total electron concentration is completely bunched by the acoustic flux in the domain,
f =
=
• 16
For these four population ratios the reciprocal incubation time 1/ri is recorded in Fig. 2.
where g is the overall gain necessary for thermal acoustic waves to cause nonlinear effects in the current and E0 = V5 /(f~i) again is the threshold field for acoustic amplification. Since g is only weakly dependent on the trapping factor f we notice that 1/T% is proportional to the electric field with a slope independent of f. The trapping causes a displacement of the straight lines giving an intersection with the field axis at E0. In Fig. 2 the slope of the straight lines is fitted for the line f = 1/7.2 to obtain the value for the gain g = 9 (= 78dB). The measured points then fit well to the whole set of lines. The presented experimental results therefore are consistent with the simple model of fast trapping for bunched electrons in the acoustic domain.
Vol. 7, No. 14
ACOUSTOELECTRIC DOMAINS IN GaAs
1029
REFERENCES 1.
SLIVA P.O., BRAY R., Phys. Rev. Lett. 14, 372 (1965).
2.
LEROUX-HUGON P., J. Phys. 28, Suppl. No. 2 Cl—65 (1967).
3.
WHITE D.L., J. appi. Phys. 33. 2547 (1962).
4.
The field outside the 5domain the synchronous E3 = Vs/p whichisisnot higher to overcome field the intrinsic loss.but If lattice loss is field not for the threshold acoustic amplification negligible we must replace V 3 by Vth (> V3 ). Since the loss is determined by the frequency for maximum gain, which is determined by N in the fast trapping case, V~ will be independent of illumination level so our main argument is unaffected, but the trapping factors will be increased by a factor Vth /V0.
5.
RIDLEY B.K., WILKINSON J., Brit. J. Phys. C (1969) to be published.
Der Sättigungsstrom für eine akustoelektrische Domäne in GaAs ist von der Elektronenkonzentration unabh’ángig gefunden w2rden. Dieses Ergebnis und auch Inkubationszeitmessungen stehen in Ubereinstimmung mit einem einfachen Modell für Trap-kontrollierte Bflndelung der Elektronen in der Domäne.
Vol. 7, pp. 1027—1029, 1969.
Pergamon Press.
Printed in Great Britain
TRAP-CONTROLLED BUNCHING OF ELECTRONS IN ACOUSTOELECTRIC DOMAINS M. Schulz*; B.K. Ridley Physics Department, University of Essex, Coichester, U.K.
(Received 2 .~1ay1969 by G. Leibfried)
For an acoustoelectric domain in GaAs the saturation current is found to be independent of the electron concentration. This result and incubation time measurements are in accord with a simple model of trap-controlled bunching of electrons in the domain.
IN n-TYPE GaAs at liquid nitrogen temperature and under strong illumination we have observed high-field domains which are clearly associated with the generation and propagation of acoustic flux. The invariance of the current in presence of the domain and the variation with illumination of the incubation time for the domain formation point to and can be interpreted by trap-controlled bunching of electrons in the acoustoelectric domain,
sample. The specimen current then was monitored on the oscilloscope. For fields higher than a threshold field 300—800 V/cm the same typical oscillations appeared in the current as they are known for acoustic domains. 1,2 The characteristics are the appearance of an incubation time ‘T and the period of the oscillation close to an acoustic transit time Ttransjt indpendent of the applied field. (A typical current oscillation giving the definitions is shown in the insert of Fig. 2.) Clear acoustic domains were observed tcm for coriductivities down to 0.2 ~2“
Specimens (0.5 x 0.5 ~ 8mm ~) were cut from a 0.2~lcm ‘undoped’ GaAs ingot from Monsanto with the long dimension in the [110] crystal direction for strong piezoelectric coupling
The current in presence of the domain ‘sat the field E 0 outside the domain and the incubation time ‘r~for domain formation have been measured with respect to the conductivity. If we assume a drift mobility independent of illumination the conductivity can be taken as a measurein for the1 free electron concentration. As shown Fig. we find the saturation current independent of conductivity. The field E
of shear acoustic waves. In ± 1 per cent Te pallets alloyed onto the end faces of the rod produced satisfactory ohmic contacts. At 77~K the conductivity of the sample could be varied by illumination in the range from tcm-, using Si-filtered light10~to from a pro0.6cr lamp in order to avoid excitation across jector
0 the energy gap of GaAs. Illumination with unfiltered white light showed the same results presumably because the generated holes recombined very quickly, so that effectively electrons were generated from traps only, Constant voltage pulses of Ca. 3~._sduration were applied across the long dimension of the *Now at Institut fuer Elektrowerkstoffe, Freiburg i.Br., Germany.
1027
outside the domain also shown in Fig. 1 therefore is inversely proportional to the conductivity. The invariance of the saturation current density and the variation with light of the field E0 is evidence that the total electron population, free and trapped, is bunched by the acoustic waves in the domains. To see this let the free electron concentration be n and the total electron concentration be N. If the traps are fast enough to respond to the sound waves the ratio n/N = f is always fixed for a particular illumination level
1028
ACOUSTOELECTRIC DOMAINS IN GaAs
Vol. 7, No. 14
/
.1
~-~—~1’\
1M1
r~r~& [rM] 0 / oturot,on ct.,TIflt (I sat.) [WJ [cm )4
E
T~.Curr~ 2000
500
400
\
72 ~
•
/
•0
/ ~ ,I/ ‘I
//
/1 0
__________________
01
02
03
0.4
/
/
f~~d E 0
o
t5 I
05
06
0
0
07
0
/ / ,/
f%.
/
/
~‘/ ii. I’ ~/ 200? ?400 ~ E
05
e / / /
to
~o
~00 —
E(V/cm)
FIG. 1. Saturation current ‘eat in presence of the domain, field E0 outside the domain and effective mobility ~ e~f = Vs/E0 in function of the conductivity varied by illumination of the sample.
Fic. 2. Reciprocal incubation time in function of the applied electric field. Parameter is the trapping factor f deduced from ~ ~ /~. The straight lines are calculated. The insert shows a typical current oscillation giving the definitions of ‘r~ and ‘sat’
and is known as the trapping factor. For small lattice loss, f~E0 must be close to the synchronous drift velocity ~E3 = V3 according 3 expression for zero gain.4 Thus we have to White’s
Using White’s linear theory for acoustic amplification which is applicable during the incubation time we can express the incubation time as —
T1 5
=
enp.E0
=
efNpE0
=
4 v Ignoring the lattice loss 3 /E0 = = ~ is a measure for the effective mobility which is also recorded in Fig. 1. Note that this mobility is proportional to the conductivity as expected from the trapping factor. From the ratio 3cm2/Vs at 77°K)we can evaluate the =trapping /~eff”~ (~ 8 x 10 factors involved for the four illumination levels used 7.2
i 8
i 10
—
2v3
[K2~
]
g
eNv5
independent of n, in accord with observation. In the case of fast trapping the total electron concentration is completely bunched by the acoustic flux in the domain,
f =
=
• 16
For these four population ratios the reciprocal incubation time 1/ri is recorded in Fig. 2.
where g is the overall gain necessary for thermal acoustic waves to cause nonlinear effects in the current and E0 = V5 /(f~i) again is the threshold field for acoustic amplification. Since g is only weakly dependent on the trapping factor f we notice that 1/T% is proportional to the electric field with a slope independent of f. The trapping causes a displacement of the straight lines giving an intersection with the field axis at E0. In Fig. 2 the slope of the straight lines is fitted for the line f = 1/7.2 to obtain the value for the gain g = 9 (= 78dB). The measured points then fit well to the whole set of lines. The presented experimental results therefore are consistent with the simple model of fast trapping for bunched electrons in the acoustic domain.
Vol. 7, No. 14
ACOUSTOELECTRIC DOMAINS IN GaAs
1029
REFERENCES 1.
SLIVA P.O., BRAY R., Phys. Rev. Lett. 14, 372 (1965).
2.
LEROUX-HUGON P., J. Phys. 28, Suppl. No. 2 Cl—65 (1967).
3.
WHITE D.L., J. appi. Phys. 33. 2547 (1962).
4.
The field outside the 5domain the synchronous E3 = Vs/p whichisisnot higher to overcome field the intrinsic loss.but If lattice loss is field not for the threshold acoustic amplification negligible we must replace V 3 by Vth (> V3 ). Since the loss is determined by the frequency for maximum gain, which is determined by N in the fast trapping case, V~ will be independent of illumination level so our main argument is unaffected, but the trapping factors will be increased by a factor Vth /V0.
5.
RIDLEY B.K., WILKINSON J., Brit. J. Phys. C (1969) to be published.
Der Sättigungsstrom für eine akustoelektrische Domäne in GaAs ist von der Elektronenkonzentration unabh’ángig gefunden w2rden. Dieses Ergebnis und auch Inkubationszeitmessungen stehen in Ubereinstimmung mit einem einfachen Modell für Trap-kontrollierte Bflndelung der Elektronen in der Domäne.