Monte Carlo Calculations of Amplification Spectrum for GaN THz Transit-time Resonance Maser

VLSI Design, Jul 2018

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 1 ∼ 2%.

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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)


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E. Starikov, P. Shiktorov, V. Gruinskis, L. Reggiani, L. Varani, J. C. Vaissière, Jian H. Zhao. Monte Carlo Calculations of Amplification Spectrum for GaN THz Transit-time Resonance Maser, VLSI Design, 13, DOI: 10.1155/2001/65961