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Monte Carlo calculations of THz generation in wide gap semiconductors
Physica B 314 (2002) 171–175
Monte Carlo calculations of THz generation in wide gap semiconductors E. Starikova, P. Shiktorova, V. Gru$zinskisa, L. Reggianib, L. Varanic,*, J.C. Vaissie" rec, Jian H. Zhaod a Semiconductor Physics Institute, A. Go$stauto 11, 2600 Vilnius, Lithuania INFM – National Nanotechnology Laboratory, Dipartimento di Ingegneria dell’Innovazione, Universita" di Lecce, Via Arnesano s/n, 73100 Lecce, Italy c Centre d’Electronique et de Micro-optoelectronique de Montpellier, cc 084, (CNRS UMR 5507) Universit!e Montpellier II, Place E. Bataillon, 34095 Montpellier Cedex 5, France d SiCLAB, Department of Electrical and Computer Engineering, Rutgers University, Piscataway, NJ 08855, USA b
Abstract The high-frequency generation associated with the optical-phonon transit-time resonance in a constant electric field is analyzed by Monte Carlo simulations of different nitrides such as InN, GaN and AlN. Calculations show that the microwave power generation occurs in a wide frequency range covering practically the whole submillimeter range and persisting in the THz frequency range up to the liquid nitrogen temperature. r 2002 Elsevier Science B.V. All rights reserved. PACS: 72.20.Ht; 72.30.+q; 72.80.Ey Keywords: Terahertz generation; Monte Carlo calculations; Nitrides
1. Introduction An interesting possibility to obtain microwave generation is associated with the mechanism of optical-phonon transit-time resonance where a dynamic negative differential conductivity (DNDC) is connected only with the quasi-periodic dynamics of carriers inside the optical phonon sphere in momentum space [1]. Indeed, when accelerated by an applied electric field at low temperatures (lower than that equivalent to the optical-phonon one), a carrier moves quasiballis*Tel.: +33-467143822; fax: +33-467547134. E-mail address: [email protected] (L. Varani).
tically up to the optical phonon energy, then quickly emits an optical phonon and returns to the sphere centrum. Accordingly, the carrier dynamics takes an oscillating character and regions of DNDC can appear near the transit-time frequency and its harmonics. In conventional compound semiconductors, the maximum generation frequency is limited to the GHz region [2] while a relevant increase in the maximum value of generation frequency can be expected in nitrides as a consequence of a higher energy of the optical phonon and a stronger interaction between electrons and optical phonons [3,4]. In the present paper, the above expectations are investigated through a Monte Carlo calculations
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 3 7 4 - 6
E. Starikov et al. / Physica B 314 (2002) 171–175
172
of the amplification band and gain (linear analysis) and the maximum generated power (nonlinear anaysis) in InN, GaN and AlN.
2. Scattering rates To show the advantages of nitrides in comparison with other materials for the realization of the optical phonon resonance, Fig. 1 presents the scattering rates for optical phonon emission as a function of the electron energy in wurtzite nitrides (InN, GaN and AlN) and zinc blende InP which have been introduced in the Monte Carlo simulation. As can be seen from the figure, the conditions for the streaming motion and the coherence of successive free flights are definitively superior in nitrides than in InP due to the high value of the optical phonon energy and the steep increase of the optical phonon emission rate. This constitutes the basis of our investigation of the amplification and generation characteristics of these materials. The main results are presented in the next section.
3. Linear and nonlinear analysis
2 -1 -1
0
1 2 3 4 5 6
ν (10
Reµ (10
13 -1
s )
-1
12
1
2
m V s )
The linear analysis of the conditions for amplification of microwave and THz radiation is based on the determination of the differential mobility spectrum mðf Þ obtained here from a single-particle Monte Carlo procedure based on
transient velocity averaging over the before- and after-scattering ensembles [3]. As an example, Fig. 2 reports the results of this calculation for the case of InN at T ¼ 10 K. The transit time resonance manifests itself in a sequence of minima of Refmðf Þg corresponding to the first and higher harmonics of the resonant frequency (we recall that in the frequency region where Refmðf Þg is negative, a bulk material can amplify and eventually generate electromagnetic waves). The broadening of the minima increases significantly for higher harmonics so that a DNDC is achieved usually in the first minimum only. At high electric fields (about 4 kV/cm in this case), the maximum value of Refmðf Þg decreases and finally goes to zero due to a significant penetration of carriers outside of the optical phonon sphere, which destroys the coherence of successive free flights. From the results of the differential mobility, we have evaluated the optimum generation frequency as a function of the applied electric field reported in Fig. 3, where the symbols show the field dependence of the generation frequency recently obtained experimentally in InP [5]. As expected, the generation frequency can be easily tuned by the static electric field magnitude, and the total band of amplification using different nitride materials covers practically the whole submillimeter region starting at f ¼ 0:1 THz and ending at about
InN GaN AlN InP
9 6
-1 -2 -3 0
3 0 0
0.05
0.1
0.15
energy (eV) Fig. 1. Scattering rates due to polar optical phonon emission in wurtzite nitrides and zinc blende InP as function of electron energy at lattice temperature T ¼ 10 K.
1 frequency (THz)
2
Fig. 2. General behavior of the differential mobility spectrum (curve 3) and variation of the resonance region with electric field (curves 1 to 5 for E0 ¼ 0:8; 1:6; 2:25; 3 and 4 kV/cm). Curve 6 refers to the maximum value of the DNDC negative differential mobility as a function of frequency in InN at a temperature T ¼ 10 K and for a carrier concentration n ¼ 1016 cm3 :
1
173
400
1 2 3 4 5 6
300 α (cm-1)
fopt (THz)
E. Starikov et al. / Physica B 314 (2002) 171–175
1 2 3 4
InN
200 100
0.1
0 10
f ¼ 5 THz. The good agreement with experimental results confirms the possibility of exploiting the optical-phonon resonance to obtain microwave generation. As a further step, we have calculated the amplification coefficient (static gain) aðf ; nÞ; with n the carrier concentration, for electromagnetic waves propagating inside the active medium. In the region where the differential mobility is negative, aðf ; nÞ is directly proportional to pthe ffiffi real part of m as aðf ; nÞ ¼ en Refmðf Þg=ðce0 eÞ; with e the unit charge, c the light velocity in vacuum, e0 the vacuum permittivity, and e the static dielectric constant of the material. Fig. 4 reports the amplification coefficient in three different nitrides: InN (a), GaN (b) and AlN (c). In accordance with the expression of aðf ; nÞ; the gain increases with the carrier concentration and, hence, the doping level. From another side, the increase of the doping level decreases the value of the DNDC, and finally leads to its disappearance due to the increase of the scattering with ionized impurities. The competition of these two opposite tendencies implies that there exists a certain optimum range of doping level and frequency associated with a maximum gain; for this reason, Fig. 4 reports the gain as a function of the optimum frequency for different carrier concentrations. As a general trend, maximum values of the gain are obtained for InN (300–400 cm1 ) with respect to GaN (100–
0.5
1
1.5
fopt (THz) 150
α (cm -1 )
Fig. 3. Optimum generation frequency as function of the applied electric field E0 calculated by the Monte Carlo method at T ¼ 10 K for InP with n ¼ 1015 cm3 (curve 1), InN (3), zinc blende and wurtzite GaN (4 and 5) and AlN (6) with n ¼ 1016 cm3 : Symbols show the field dependence of the generation frequency obtained experimentally in InP [5].
0 (a)
GaN
100
1 2 3 4
50
0 0
0.5
(b)
1
1.5 2 fopt (THz)
2.5
3
60 AlN -1
1 E 0 (kV/cm)
α (cm )
0.1
40
1 2 3 4
20
0 0 (c)
1
2 3 fopt (THz)
4
5
Fig. 4. Amplification coefficient as function of the optimum frequency calculated by the Monte Carlo method at T ¼ 10 K for: (a) InN (curves 1–4 correspond to n ¼ 1; 3; 10; 30 1015 cm3 ), (b) GaN (curves 1–4 correspond to n ¼ 3; 10; 20; 30 1015 cm3 ), (c) AlN (curves 1–4 correspond to n ¼ 10; 30; 60; 100 1015 cm3 ).
150 cm1 ) and AlN (50–60 cm1 ). However, as follows from Fig. 4, the optimum doping level strongly depends on the desired frequency and differs for about one order of magnitude in going from the left to the right wings of the amplification band. To achieve an actual generation of microwaves, it is necessary to put the active medium (here
E. Starikov et al. / Physica B 314 (2002) 171–175
Pgen (MW/cm-3)
1 1 2 3 4
InN
0.5
0
100
200
300
400
-1
αL (cm )
(a)
3
1 GaN 2 3 4 5
-3
Pgen (MWcm )
constituted by the bulk material) into a resonator system thus, constituting a hot-carrier THz maser. The amplification of the propagating electromagnetic waves is guaranteed by the presence of a DNDC under large-signal response. To look for the best conditions to obtain the maximum generated power a Monte Carlo simulation is performed introducing the microwave electric field of the amplified mode directly into the motion equation describing the free flight of a trial particle in momentum space. In the presence of DNDC, an external resonant system will lead to the onset and growth of microwave oscillations accompanied with a growth in the amplitude of the microwave field inside the sample. At the initial stage, these growths will be accompanied with the growth of the microwave power. However, a considerable growth of the microwave field will result in decrease of the differential mobility and dynamical gain. Finally, when both the gain and the generated power will go down to zero, the amplification effect will disappear completely. Therefore, it is necessary to choose the characteristics of the resonator and the output of the generated power from the sample in such a manner to provide the maximum generated power inside the sample. Correspondingly, the dynamical gain ad starts from its small-signal value and monotonously goes to zero. Under the stable generation ad must be equal to the coefficient of the total loss aL of the resonant system, which includes both the power extraction and parasitic losses. Fig. 5 summarizes the results for generation in bulk nitrides where the amplitude of the microwave field has been eliminated by expressing the generated power as a function of the dynamical gain. With the decrease of the dynamical gain (ad ¼ aL ), the generated power increases, reaches the maximum at ad E0:5a and finally goes to zero as the dynamical gain decreases to zero. It means that, to obtain the maximum generated power at the output of a resonator, aL must be approximately half the value of the static gain. Moreover, the maximum values of the generated power are obtained for AlN (6–8 MW cm3 ) with respect to GaN (2:5–3 MW cm3 ) and InN (0:8– 1 MW cm3 ).
2
1
0 0
50
100
150
αL (cm-1)
(b)
8 1 2 3 4
AlN Pgen (MWcm-3)
174
6 4 2 0 0
(c)
20
40
60
-1
αL (cm )
Fig. 5. Generated power calculated as a function of the coefficient of the total losses inside the resonator for: (a) InN at the fundamental frequencies of f ¼ 0:25; 0:5; 0:75; 1 THz (curves 1–4 obtained at optimum values of n and E0 given, respectively, by n ¼ 1; 3; 3; 3 1016 cm3 and E0 ¼ 0:85; 1:65; 2:4; 3:14 kV=cm); (b) GaN at f ¼ 0:25; 0:5; 1; 1:5; 2 THz (curves 1 to 5 obtained, respectively, at n ¼ 0:6; 1; 2; 3; 4 1016 cm3 and E0 ¼ 1:2; 2:25; 4:3; 6:35; :35 kV=cm); (c) AlN at f ¼ 1; 2; 3; 4 THz (curves 1–4 obtained, respectively, at n ¼ 0:4; 1; 1; 1 1017 cm3 and E0 ¼ 7; 14; 20; 27 kV=cm).
E. Starikov et al. / Physica B 314 (2002) 171–175
4. Conclusions The results of both linear and nonlinear studies of the optical phonon transit-time resonance performed by Monte Carlo simulations show that wide-gap nitrides are promising materials for power generation in the THz frequency range. By comparison with InP, the high values of both the polar optical phonon energy and the electron– phonon interaction strength allow to expand the generation frequency up to the THz range with sufficiently high values for the amplification coefficient and generated power. Additional calculations have shown that the generation phenomenon is present up to the liquid nitrogen temperature at least, thus simplifying considerably an experimental implementation of the effect. By comparing the characteristics of the power amplification and generation, one can conclude
175
that going from InN to GaN to AlN, the gain decreases while the generated power increases.
Acknowledgements This work has been supported by the CNRS PECO CEI Cooperation franco lituanienne no. 5380, by the GALILEO project no. 02874RA and by the NATO collaborative linkage Grant PST.CLG.976340.
References [1] [2] [3] [4] [5]
A. Andronov, V. Kozlov, Pis’ma ZhETF 17 (1973) 124. Yu. Pozhela, et al., Sem. Sci. Tech. 7 (1992) B386. E. Starikov, et al., J. Appl. Phys. 89 (2001) 1161. E. Starikov, et al., IEEE Trans. Electron Dev. 48 (2001) 438. L.E. Vorob’ev, et al., Pis’ma ZhETF 73 (2001) 253.
Monte Carlo calculations of THz generation in wide gap semiconductors E. Starikova, P. Shiktorova, V. Gru$zinskisa, L. Reggianib, L. Varanic,*, J.C. Vaissie" rec, Jian H. Zhaod a Semiconductor Physics Institute, A. Go$stauto 11, 2600 Vilnius, Lithuania INFM – National Nanotechnology Laboratory, Dipartimento di Ingegneria dell’Innovazione, Universita" di Lecce, Via Arnesano s/n, 73100 Lecce, Italy c Centre d’Electronique et de Micro-optoelectronique de Montpellier, cc 084, (CNRS UMR 5507) Universit!e Montpellier II, Place E. Bataillon, 34095 Montpellier Cedex 5, France d SiCLAB, Department of Electrical and Computer Engineering, Rutgers University, Piscataway, NJ 08855, USA b
Abstract The high-frequency generation associated with the optical-phonon transit-time resonance in a constant electric field is analyzed by Monte Carlo simulations of different nitrides such as InN, GaN and AlN. Calculations show that the microwave power generation occurs in a wide frequency range covering practically the whole submillimeter range and persisting in the THz frequency range up to the liquid nitrogen temperature. r 2002 Elsevier Science B.V. All rights reserved. PACS: 72.20.Ht; 72.30.+q; 72.80.Ey Keywords: Terahertz generation; Monte Carlo calculations; Nitrides
1. Introduction An interesting possibility to obtain microwave generation is associated with the mechanism of optical-phonon transit-time resonance where a dynamic negative differential conductivity (DNDC) is connected only with the quasi-periodic dynamics of carriers inside the optical phonon sphere in momentum space [1]. Indeed, when accelerated by an applied electric field at low temperatures (lower than that equivalent to the optical-phonon one), a carrier moves quasiballis*Tel.: +33-467143822; fax: +33-467547134. E-mail address: [email protected] (L. Varani).
tically up to the optical phonon energy, then quickly emits an optical phonon and returns to the sphere centrum. Accordingly, the carrier dynamics takes an oscillating character and regions of DNDC can appear near the transit-time frequency and its harmonics. In conventional compound semiconductors, the maximum generation frequency is limited to the GHz region [2] while a relevant increase in the maximum value of generation frequency can be expected in nitrides as a consequence of a higher energy of the optical phonon and a stronger interaction between electrons and optical phonons [3,4]. In the present paper, the above expectations are investigated through a Monte Carlo calculations
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 3 7 4 - 6
E. Starikov et al. / Physica B 314 (2002) 171–175
172
of the amplification band and gain (linear analysis) and the maximum generated power (nonlinear anaysis) in InN, GaN and AlN.
2. Scattering rates To show the advantages of nitrides in comparison with other materials for the realization of the optical phonon resonance, Fig. 1 presents the scattering rates for optical phonon emission as a function of the electron energy in wurtzite nitrides (InN, GaN and AlN) and zinc blende InP which have been introduced in the Monte Carlo simulation. As can be seen from the figure, the conditions for the streaming motion and the coherence of successive free flights are definitively superior in nitrides than in InP due to the high value of the optical phonon energy and the steep increase of the optical phonon emission rate. This constitutes the basis of our investigation of the amplification and generation characteristics of these materials. The main results are presented in the next section.
3. Linear and nonlinear analysis
2 -1 -1
0
1 2 3 4 5 6
ν (10
Reµ (10
13 -1
s )
-1
12
1
2
m V s )
The linear analysis of the conditions for amplification of microwave and THz radiation is based on the determination of the differential mobility spectrum mðf Þ obtained here from a single-particle Monte Carlo procedure based on
transient velocity averaging over the before- and after-scattering ensembles [3]. As an example, Fig. 2 reports the results of this calculation for the case of InN at T ¼ 10 K. The transit time resonance manifests itself in a sequence of minima of Refmðf Þg corresponding to the first and higher harmonics of the resonant frequency (we recall that in the frequency region where Refmðf Þg is negative, a bulk material can amplify and eventually generate electromagnetic waves). The broadening of the minima increases significantly for higher harmonics so that a DNDC is achieved usually in the first minimum only. At high electric fields (about 4 kV/cm in this case), the maximum value of Refmðf Þg decreases and finally goes to zero due to a significant penetration of carriers outside of the optical phonon sphere, which destroys the coherence of successive free flights. From the results of the differential mobility, we have evaluated the optimum generation frequency as a function of the applied electric field reported in Fig. 3, where the symbols show the field dependence of the generation frequency recently obtained experimentally in InP [5]. As expected, the generation frequency can be easily tuned by the static electric field magnitude, and the total band of amplification using different nitride materials covers practically the whole submillimeter region starting at f ¼ 0:1 THz and ending at about
InN GaN AlN InP
9 6
-1 -2 -3 0
3 0 0
0.05
0.1
0.15
energy (eV) Fig. 1. Scattering rates due to polar optical phonon emission in wurtzite nitrides and zinc blende InP as function of electron energy at lattice temperature T ¼ 10 K.
1 frequency (THz)
2
Fig. 2. General behavior of the differential mobility spectrum (curve 3) and variation of the resonance region with electric field (curves 1 to 5 for E0 ¼ 0:8; 1:6; 2:25; 3 and 4 kV/cm). Curve 6 refers to the maximum value of the DNDC negative differential mobility as a function of frequency in InN at a temperature T ¼ 10 K and for a carrier concentration n ¼ 1016 cm3 :
1
173
400
1 2 3 4 5 6
300 α (cm-1)
fopt (THz)
E. Starikov et al. / Physica B 314 (2002) 171–175
1 2 3 4
InN
200 100
0.1
0 10
f ¼ 5 THz. The good agreement with experimental results confirms the possibility of exploiting the optical-phonon resonance to obtain microwave generation. As a further step, we have calculated the amplification coefficient (static gain) aðf ; nÞ; with n the carrier concentration, for electromagnetic waves propagating inside the active medium. In the region where the differential mobility is negative, aðf ; nÞ is directly proportional to pthe ffiffi real part of m as aðf ; nÞ ¼ en Refmðf Þg=ðce0 eÞ; with e the unit charge, c the light velocity in vacuum, e0 the vacuum permittivity, and e the static dielectric constant of the material. Fig. 4 reports the amplification coefficient in three different nitrides: InN (a), GaN (b) and AlN (c). In accordance with the expression of aðf ; nÞ; the gain increases with the carrier concentration and, hence, the doping level. From another side, the increase of the doping level decreases the value of the DNDC, and finally leads to its disappearance due to the increase of the scattering with ionized impurities. The competition of these two opposite tendencies implies that there exists a certain optimum range of doping level and frequency associated with a maximum gain; for this reason, Fig. 4 reports the gain as a function of the optimum frequency for different carrier concentrations. As a general trend, maximum values of the gain are obtained for InN (300–400 cm1 ) with respect to GaN (100–
0.5
1
1.5
fopt (THz) 150
α (cm -1 )
Fig. 3. Optimum generation frequency as function of the applied electric field E0 calculated by the Monte Carlo method at T ¼ 10 K for InP with n ¼ 1015 cm3 (curve 1), InN (3), zinc blende and wurtzite GaN (4 and 5) and AlN (6) with n ¼ 1016 cm3 : Symbols show the field dependence of the generation frequency obtained experimentally in InP [5].
0 (a)
GaN
100
1 2 3 4
50
0 0
0.5
(b)
1
1.5 2 fopt (THz)
2.5
3
60 AlN -1
1 E 0 (kV/cm)
α (cm )
0.1
40
1 2 3 4
20
0 0 (c)
1
2 3 fopt (THz)
4
5
Fig. 4. Amplification coefficient as function of the optimum frequency calculated by the Monte Carlo method at T ¼ 10 K for: (a) InN (curves 1–4 correspond to n ¼ 1; 3; 10; 30 1015 cm3 ), (b) GaN (curves 1–4 correspond to n ¼ 3; 10; 20; 30 1015 cm3 ), (c) AlN (curves 1–4 correspond to n ¼ 10; 30; 60; 100 1015 cm3 ).
150 cm1 ) and AlN (50–60 cm1 ). However, as follows from Fig. 4, the optimum doping level strongly depends on the desired frequency and differs for about one order of magnitude in going from the left to the right wings of the amplification band. To achieve an actual generation of microwaves, it is necessary to put the active medium (here
E. Starikov et al. / Physica B 314 (2002) 171–175
Pgen (MW/cm-3)
1 1 2 3 4
InN
0.5
0
100
200
300
400
-1
αL (cm )
(a)
3
1 GaN 2 3 4 5
-3
Pgen (MWcm )
constituted by the bulk material) into a resonator system thus, constituting a hot-carrier THz maser. The amplification of the propagating electromagnetic waves is guaranteed by the presence of a DNDC under large-signal response. To look for the best conditions to obtain the maximum generated power a Monte Carlo simulation is performed introducing the microwave electric field of the amplified mode directly into the motion equation describing the free flight of a trial particle in momentum space. In the presence of DNDC, an external resonant system will lead to the onset and growth of microwave oscillations accompanied with a growth in the amplitude of the microwave field inside the sample. At the initial stage, these growths will be accompanied with the growth of the microwave power. However, a considerable growth of the microwave field will result in decrease of the differential mobility and dynamical gain. Finally, when both the gain and the generated power will go down to zero, the amplification effect will disappear completely. Therefore, it is necessary to choose the characteristics of the resonator and the output of the generated power from the sample in such a manner to provide the maximum generated power inside the sample. Correspondingly, the dynamical gain ad starts from its small-signal value and monotonously goes to zero. Under the stable generation ad must be equal to the coefficient of the total loss aL of the resonant system, which includes both the power extraction and parasitic losses. Fig. 5 summarizes the results for generation in bulk nitrides where the amplitude of the microwave field has been eliminated by expressing the generated power as a function of the dynamical gain. With the decrease of the dynamical gain (ad ¼ aL ), the generated power increases, reaches the maximum at ad E0:5a and finally goes to zero as the dynamical gain decreases to zero. It means that, to obtain the maximum generated power at the output of a resonator, aL must be approximately half the value of the static gain. Moreover, the maximum values of the generated power are obtained for AlN (6–8 MW cm3 ) with respect to GaN (2:5–3 MW cm3 ) and InN (0:8– 1 MW cm3 ).
2
1
0 0
50
100
150
αL (cm-1)
(b)
8 1 2 3 4
AlN Pgen (MWcm-3)
174
6 4 2 0 0
(c)
20
40
60
-1
αL (cm )
Fig. 5. Generated power calculated as a function of the coefficient of the total losses inside the resonator for: (a) InN at the fundamental frequencies of f ¼ 0:25; 0:5; 0:75; 1 THz (curves 1–4 obtained at optimum values of n and E0 given, respectively, by n ¼ 1; 3; 3; 3 1016 cm3 and E0 ¼ 0:85; 1:65; 2:4; 3:14 kV=cm); (b) GaN at f ¼ 0:25; 0:5; 1; 1:5; 2 THz (curves 1 to 5 obtained, respectively, at n ¼ 0:6; 1; 2; 3; 4 1016 cm3 and E0 ¼ 1:2; 2:25; 4:3; 6:35; :35 kV=cm); (c) AlN at f ¼ 1; 2; 3; 4 THz (curves 1–4 obtained, respectively, at n ¼ 0:4; 1; 1; 1 1017 cm3 and E0 ¼ 7; 14; 20; 27 kV=cm).
E. Starikov et al. / Physica B 314 (2002) 171–175
4. Conclusions The results of both linear and nonlinear studies of the optical phonon transit-time resonance performed by Monte Carlo simulations show that wide-gap nitrides are promising materials for power generation in the THz frequency range. By comparison with InP, the high values of both the polar optical phonon energy and the electron– phonon interaction strength allow to expand the generation frequency up to the THz range with sufficiently high values for the amplification coefficient and generated power. Additional calculations have shown that the generation phenomenon is present up to the liquid nitrogen temperature at least, thus simplifying considerably an experimental implementation of the effect. By comparing the characteristics of the power amplification and generation, one can conclude
175
that going from InN to GaN to AlN, the gain decreases while the generated power increases.
Acknowledgements This work has been supported by the CNRS PECO CEI Cooperation franco lituanienne no. 5380, by the GALILEO project no. 02874RA and by the NATO collaborative linkage Grant PST.CLG.976340.
References [1] [2] [3] [4] [5]
A. Andronov, V. Kozlov, Pis’ma ZhETF 17 (1973) 124. Yu. Pozhela, et al., Sem. Sci. Tech. 7 (1992) B386. E. Starikov, et al., J. Appl. Phys. 89 (2001) 1161. E. Starikov, et al., IEEE Trans. Electron Dev. 48 (2001) 438. L.E. Vorob’ev, et al., Pis’ma ZhETF 73 (2001) 253.