2636 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 6, JUNE 2006 Efficient Numerical Methods for Simulation of High-Frequency Active Devices Masoud Movahhedi, Student Member, IEEE, and Abdolali Abdipour, Member, IEEE Abstract—We present two new numerical approaches for phys- ical modeling of high-frequency semiconductor devices using filter- bank transforms and the alternating-direction implicit finite-dif- ference time-domain method. In the first proposed approach, a preconditioner based on the filter-bank and wavelet transforms is used to facilitate the iterative solution of Poisson’s equation and the other semiconductor equations discretized using implicit schemes. The second approach solves Maxwell’s equations which, in con- junction with the semiconductor equations, describe the complete behavior of high-frequency active devices, with larger time-step size. These approaches lead to the significant reduction of the full- wave simulation time. For the first time, we can reach over 95% re- duction in the simulation time by using these two techniques while maintaining the same degree of accuracy achieved using the con- ventional approach. Index Terms—Alternating-direction implicit finite-difference time-domain (ADI-FDTD) method, filter-bank transforms, full-wave analysis, global modeling, high-frequency devices, pre- conditioning. I. INTRODUCTION M ODERN high-frequency electronics are based on tech- nologies such as monolithic microwave integrated cir- cuits (MMICs) with a large number of closely packed passive and active structures, several levels of transmission lines, and discontinuities operating at high speeds and frequencies and sometimes over very broad bandwidths. It is thus anticipated that the design of MMICs should involve robust design tools that would simulate all of the circuit elements simultaneously. The possibility of achieving this type of modeling is addressed by full-wave device analysis and global circuit modeling pre- sented in [1]–[5]. The main issue in the global modeling all elements of the high-frequency circuits is the full-wave analysis of their active devices, which has been considered in this study. In the full- wave analysis, the equations that describe the transport physics in conjunction with Maxwell’s equations must be solved to pre- dict the interactions between the carriers and the propagating wave inside the devices [1], [2]. We must note that some phe- nomena such as imperfection in the crystal structure of the semi- conductor cannot be exactly considered in the equations. Imper- fections that perturb the periodicity of the crystal [6] can con- tribute significantly to the overall device behavior and are still very difficult to model. Manuscript received October 10, 2005; revised January 20, 2006. This work was supported in part by the Iran Telecommunication Research Center. The authors are with the Department of Electrical Engineering, AmirKabir University of Technology (Tehran Polytechnic), Tehran, Iran (e-mail: movah- hedi@aut.ac.ir; abdipour@aut.ac.ir). Digital Object Identifier 10.1109/TMTT.2006.872937 The full-wave analysis involves a fair amount of advanced numerical techniques and different algorithms that results in a very expensive computational cost [5]. Therefore, there is an imperative need to present a new approach to reduce the simu- lation time, while maintaining the same degree of accuracy pre- sented by the global modeling techniques. Due to the high com- plexity of the equations, usually the finite-difference time-do- main (FDTD) technique is used to solve them. In this numer- ical technique, a possible approach for reducing the simulation time is to use multiresolution nonuniform grids that can be im- plemented using interpolating wavelets [7], [8]. Wavelets were applied to the drift-diffusion model [7]. A new approach has been developed for applying wavelets to the full hydrodynamic model [8]. The interpolating wavelets can adaptively refine the mesh in domains where the unknowns quantities vary rapidly. This also leads to considerable reduction in the number of un- knowns and the simulation time. The best situation shows about a 75% reduction in CPU time [8]. In this paper, we propose to use two approaches for reducing the simulation time of the full-wave analysis. The first approach improves the simulation time and facilitates the steady-state dc solutions which are used as the initialization values in the full- wave analysis. The second one accelerates the transient simula- tion to obtain the time-domain ac solutions of the modeling. In the conventional approach for full-wave analysis using the FDTD method, all of the equations that include the time deriva- tive (e.g., hydrodynamic and Maxwell’s equations) are repre- sented by explicit FD schemes [1]. However, solving Poisson’s equation (as an elliptic equation) leads to a large system of linear equations, . Therefore, one of the key factors for simu- lation time reduction of active microwave devices is to decrease the solution time of the equation system, . Here, a new filter-bank-based preconditioning method [9] is used to facili- tate the iterative solution of Poisson’s equation. Another proposed approach accelerates the time-domain ac solution. Recently, a new method, called the alternating-direc- tion implicit FDTD (ADI-FDTD) method, to solve Maxwell’s curl equations has been introduced [10], [11]. This method is an attractive alternative to the standard FDTD due to its unconditional stability with moderate computational over- head. The unconditional stability means that the ADI-FDTD method is free of the Courant–Friedrich–Levy (CFL) stability restraint, allowing any choice of for a stable solution. The ADI-FDTD can be particularly useful for problems involving devices with fine geometric features that are much smaller than the wavelengths of interest. Here, the unconditionally stable FDTD method has been proposed for solving Maxwell’s equations, which together with the semiconductor equations perform the full-wave modeling. This allows using a larger 0018-9480/$20.00 © 2006 IEEE