A Frequency- and Space-Domain Series-Expansion Approach for Efficient Numerical Modeling of Semiconductor Devices

Global modeling of multifinger MOSFETs with SB-SP combined analysis

“…Any extension to embedded regions such as, substrate, passivation dielectric, etc., are included in the analysis by mean of an electromagnetic solver as demonstrated in [5,6]. The device Global Modeling of Multifinger MOSFETs with SB-SP combined analysis T 978-1-4244-3732-0/09/$25.00 ©2009 IEEE channel horizontal electron transport is modelled by the first three moments of the Boltzmann's Transport Equation in a simplified one dimensional form [8] and coupled with a self consistent Schrodinger-Poisson for the channel charge control model achieving a Quasi-2D simulator [5,6,7,9,10]: N ( x,t ) is the equilibrium carrier density in the channel as computed by the by the a priori self-consistent solution of Schrödinger's and Poisson's equations in the vertical direction for all gatechannel voltages; then, the results are fitted by a polynomial or by a rational function of the gate-channel voltage, and coupled to the transport equations. This arrangement accounts for the device layer structure and material composition, and allows extension of this model also to different types of FET's [5,6,7,9].…”

“…The choice of polynomials is justified by the actual behaviour of the physical quantities in the active region; however, it could be replaced by other basis functions [6]. The coefficients of the polynomials are dependent on time, because the space distributions of the physical quantities are driven by the timedependent input signal; if the latter is time periodic, the time dependence of the coefficients is periodic as well, and can be written as a Fourier series:…”

“…HE nonlinear analysis of microwave circuits using a completely frequency-domain approach has been tried with several approaches that include, among others, Volterra series [1], algebraic functional expansions and arithmetic operator technique (Spectral Balance, SB) [2,3,4,5,6]. For practical applicability, these schemes require that all the nonlinearities be in the form of power series.…”

“…Finally, multitone excitations are easily accounted for without the need for complex time-frequency transform schemes [4]. In this work also the space-domain finite-difference discretisation scheme is removed by expanding the physical quantities in polynomials in the space variable as demonstrated in [6] and applied to the physical analysis of multifinger MOSFET devices in linear and nonlinear regime. Moreover the analysis is coupled to a commercial electromagnetic solver [5,6], showing its viability for global modeling simulations [7], and its advantages in terms of CAD time consumption and easy coupling with EM simulators with respect to classical Time Domain, Harmonic Balance and Spectral Balance methods.…”

“…In this work also the space-domain finite-difference discretisation scheme is removed by expanding the physical quantities in polynomials in the space variable as demonstrated in [6] and applied to the physical analysis of multifinger MOSFET devices in linear and nonlinear regime. Moreover the analysis is coupled to a commercial electromagnetic solver [5,6], showing its viability for global modeling simulations [7], and its advantages in terms of CAD time consumption and easy coupling with EM simulators with respect to classical Time Domain, Harmonic Balance and Spectral Balance methods. In this combined spectral-balance and spatial polynomial (SB-SP) method, the unknowns are the coefficients of the polynomials transformed in the frequency domain; this greatly reduce the Jacobian factorization in the solution systems and reduces the algorithm computational time being the physical equations written in a number of space points equal to the degree of the polynomials (plus one), i.e.…”