Monte Carlo Calculations of Amplification Spectrum for GaN THz Transit-time Resonance Maser
International Journal of
Monte Carlo Calculations of Amplification Spectrum for GaN THz Transit-time Resonance Maser
E. STARIKOVa'c 0
P. SHIKTOROV 0
V. GRUINSKIS 0
L. REGGIANIb' 0
L. VARANI 0
J. C. VAISSIIRE 0
JIAN H. ZHAO'i 0
0 aSemiconductor Physics Institute , A. Go3tauto 11, 2600 Vilnius , Lithuania
We report Monte Carlo calculations of the amplification spectrum of microwave generation in bulk GaN and its dependence on applied electric fields, doping level, lattice temperature, etc. The amplification is shown to occur in a wide frequency range of 0.05 to 3 THz with an optimal generation efficiency of about 2%. *Corresponding author. Tel.: (3702) 614920, Fax: (3702) 627123, e-mail:
THz generation; GaN; Monte Carlo simulation
INTRODUCTION
During the last decades significant efforts have
been devoted to realize a tunable THz
semiconductor radiation source in view of its broad range
of applications. In bulk semiconductors, a physical
mechanism appropriate to this purpose is the
so called optical phonon transit-time resonance
(OPTTR) [
1
]. It consists of the periodic motion of
carriers inside the optical phonon sphere of
momentum space, resulting from the combined
action of carrier quasi-ballistic acceleration by an
applied electric field up to the optical phonon
energy and the subsequent emission of an optical
phonon, which pushes the carrier back near the
sphere center. As a consequence, the motion takes
an oscillatory character and a dynamic negative
differential mobility (DNDM) can appear at
frequencies near the inverse of the transit-time
and its harmonics [
1
]. In standard III-V
semiconductors, such as GaAs and InP, the maximum
generation frequency was found to be limited in
the range 300 to 400 GHz [
2
]. By contrast, for the
wide-gap materials, such as GaN, InN, SiC, etc.,
one can expect a considerable increase of the
maximum generation frequency and a general
improvement of the conditions for the DNDM
to occur, as a result of a higher value of the optical
phonon energy and a stronger interaction of
electrons with optical phonons. The aim of this
work is to confirm the above expectation by
calculating the amplification band and the
maximum gain for an OPTTR maser based on bulk
zincblende and wurtzite GaN.
COMPUTATIONAL PROCEDURES
In general, the amplification spectrum (or the gain,
a(f)) of microwaves (MW) which can propagate
in some active medium is described by the
frequency dependence of the real part of the
carrier MW mobility, Re[#(f)], as:
a(f)
-Re[#(f)]n
C0
(1)
where n is the carrier concentration, c the light
velocity in vacum, e0 the permittivity of vacuum,
and e the static dielectric constant of the material.
Under linear conditions, a(f) determines the
frequency region of amplification, gives a
threshold value of the net losses for generation to
appear, allows one to choose the optimal doping
level No of a sample, etc. Under nonlinear
conditions, when a(f) depends on the MW field
amplitude, it allows one to determine the energy
and power characteristics of generation. Under
multi-signal operation it allows one to determine
the characteristics of each radiation mode, the
spectral behavior of the amplification band under
single-mode generation, etc.
Small-signal Response
Under linear conditions the MW mobility is
independent of the MW field amplitude and is
determined by the Fourier transform of the linear
response function Kxx(S) as [
2, 3
]:
#xx(CO)
e
Kxx(S) exp(-ias)ds
(2)
where = 27rf is the circular frequency, and only
the longitudinal velocity response in the direction
of the constant applied electric field E0 (E0, 0, 0)
is taken to be of interest. In turn, when the
singleparticle history is simulated by the Monte Carlo
(MC) method, the longitudinal linear response
function can be expressed in terms of velocity
averaging over before- and after-scattering
ensembles as [
2
]:
Kxx(S)
eEo(7-------- [(Vx(S)),
<Vx(S))a]
where
(3)
(4)
(5)
(Vx(S))a
u[p(t- s)]vx[p(t)]dt
N
i Vx(t q- S)
are the probable velocities of a carrier at time s
under the condition that at time s--0 it was just
before or just after a scattering event, respectively.
Here N is the total number of scattering events in
the time interval [0, T] simulated by the MC
procedure, (r) TIN the mean time of free flight,
u(p) the scattering rate for momentum p, ti the
time moments of scattering events. Then,
substitution of Re[#] into Eq. (1) gives the static gain,
c0(f), defined in the absence of the MW field. The
advantage of this procedure is that, for a given
E0 and Nz, it allows one to obtain the whole
amplification/absorption spectrum during a single
MC simulation.
Large-signal Response
Under nonlinear conditions, the carrier mobility
depends on the MW field amplitude and the MW
mobility is directly calculated from the velocity
response. For this sake the MW electric field
of the amplified mode Emw(t)= Re[Eexp(it)] is
directly introduced into the equation of motion
fix(t) eEo + eE cos (t), which descri (...truncated)