基于<111>，<100>和<110>取向GaAs的IMPATT二极管：探索毫米波大气窗最佳方向的比较研究

1. Introduction

Impact avalanche transit time (IMPATT) diodes are well recognized two terminal solid-state devices to deliver sufficiently high power at both microwave and mm-wave frequency bands [1]. Silicon is the most popular base material for IMPATT diodes from the point of view of its advanced process technology [2–6]. However, GaAs is another vital base semiconductor for IMPATT diodes at the both microwave and mm-wave frequencies. Since early seventies, several researchers have fabricated IMPATT diodes based on GaAs and obtained higher DC to RF conversion efficiency and better avalanche noise performance of those as compared to their conventional Si counterparts [7–11].

The carrier ionization rates in a semiconductor material are key parameters which govern the RF performance of IMPATT sources. The inequality in ionization rates of electrons and holes (i.e., α n ≠ α p) in GaAs was first reported in late seventies [12]. Pearsall et al. [13] experimentally measured the carrier ionization rates in GaAs under the electric field along the normal to 〈111〉, 〈100〉, and 〈110〉 oriented crystal substances. They reported different values of α n and α p for different orientations. Thus, it is evident from the above-mentioned report [13] that the carrier ionization rates in GaAs depend significantly on the crystal orientation of the substrate. Since the RF performance of IMPATT diode is strongly dependent on the carrier ionization rates of the base material, the same must be significantly influenced by the crystal orientation of the substrate (here GaAs). This fact encouraged the authors to carry out a comparative study on the L-S performance of DDR IMPATT diodes based on 〈111〉, 〈100〉, and 〈110〉 oriented GaAs. Earlier in 1993, Pati et al. [14] investigated the high frequency properties of 〈111〉, 〈100〉, and 〈110〉 oriented p +-n-n +, n +-p-p + (single-drift region (SDR)), and n +-n-p-p + (DDR) GaAs IMPATT diodes at both 35 and 60 GHz frequencies by using a small-signal (S-S) simulation technique based on drift-diffusion model. Though the S-S simulation provides substantial insight into the IMPATT operation, it has some intrinsic restrictions due to a number of unrealistic assumptions. Several important properties of IMPATT source admittance characteristics, RF power output, DC to RF conversion efficiency, and so forth, cannot be precisely determined from the S-S simulation. Thus L-S simulation is essential to acquire the above-mentioned properties accurately. Therefore in the present paper authors have used a nonsinusoidal voltage excited (NSVE) L-S simulation method developed by them [15–20] to investigate both the static (DC) and L-S characteristics of DDR IMPATTs based on 〈111〉, 〈100〉, and 〈110〉 oriented GaAs at different mm-wave atmospheric window frequencies, such as 35, 94, 140, and 220 GHz.

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2. Large-Signal Modeling and Simulation Technique

Schematic of the one-dimensional (1-D) model of DDR IMPATT structure is shown in Figure 1. This 1-D model is used for the L-S simulation of the device. It is well known that the physical phenomena take place in the semiconductor bulk along the symmetry axis of the IMPATT devices. Thus the 1-D modeling and simulation of the device are absolutely justified. The fundamental time and space dependent device equations, that is, Poisson's equation, current continuity equations, and current density equations, are simultaneously solved under L-S condition subject to appropriate time varying boundary conditions by using a double-iterative simulation method [15–20] based on 1-D finite difference method (FDM). The fundamental device equations are given by

Dx[ξ(x,t)]=qεs(ND−NA+p(x,t)−n(x,t)),Dt[p,n(x,t)] =∓(1q)Dx⌊Jp,n(x,t)⌋+GAp,An(x,t)+GTp,Tn(x,t),Jp,n(x,t)=q[p,n(x,t)]vp,n(x,t)∓qDp,nDx[p,n(x,t)],

(1)

where D x and D t are the partial derivatives with respect to x and t, respectively (D x ≡ ∂/∂x and D t ≡ ∂/∂t); all other symbols are carrying their usual significance. A list of symbols is given in appendix at the end of this paper where the usual meaning of each symbol is provided. The avalanche generation rates of both types of charge carriers at the space point x and at the time instant t are given by

GAn(x,t)=GAp(x,t)=n(x,t)αn(x,t)vn(x,t) +p(x,t)αp(x,t)vp(x,t).

(2)

Figure 1

1-D model of DDR IMPATT diode.

The tunneling generation rate for electrons at the space point x at the instant t is a strong function of electric field at the same space point at the same instant. It can be derived from detailed quantum mechanical considerations [21–24]. In the present model, the authors have adopted Kane's model [22–24] of direct band to band tunneling assuming parabolic band approximation. It is given by

GTn(x,t)=aTξ2(x,t)exp(−bTξ(x,t)).

(3)

For parabolic band approximation the coefficients a T and b T can be expressed as [22]

aT=(q28π3ħ2)(2m∗dEg)−−−−−√,bT=(12qħ)(m∗dE3g2)−−−−−−−√.

(4)

The energy-band diagram of reverse biased n +-n-p-p + structure shown in Figure 2 is used to obtain the tunneling generation rate for holes. It is well known that the tunneling is an instantaneous phenomenon. The tunnel generation rate for holes at x at instant t is equal to that for electrons at some other space point x′ within the space charge layer at the same instant t. Thus

GTp(x, t) = GTn(x′, t), 

(5)

where the tunnel generation of an electron at x′ is simultaneously associated with the generation of a hole at x, where (x − x′) is the spatial separation between the edge of conduction band and valence band at the same energy. The relationship between x and x′ can be written as [23, 24]

x=x′(1−Eg/E)√ for  0≤x≤xj,x=W−{(W−x′)[1+(Eg/EB−E)]√} for  xj≤x≤W.

(6)

Figure 2

Energy-band diagram of reverse biased DDR IMPATT diode [24].