Microwave and RF Semiconductor Devices Global Modeling Analysis

Giorgio Leuzzi, Vincenzo Stornelli

Dept. Of Electrical and Information Engineering giorgio.leuzzi@univaq.it; vincenzo.stornelli@univaq.itgiorgio.leuzzi@univaq.it; vincenzo.stornelli@univaq.it

INTRODUCTION

We here present a method that combines frequency-domain Fourier series expansion and space-domain polynomial expansion of the physical

quantities inside the semiconductor, for an efficient numerical modeling of high-frequency active devices, based on the solution of the physical transport equations in the semiconductor. The frequency- and space-domain expansions drastically reduce the number of time and space

sampling points where the equations are computed, greatly reducing the computational burden with respect to classical finite-differences computational burden with respect to classical finite-differences

approaches. Also the coupling with a EM program, for a global modeling simulator, becomes straightforward, due to the reduced interconnection

nodes with the physical simulator.

2i

i i i*0 z

d ( z )d 1 qV ( z ) ( z ) E ( z )2m dz m dz

D gd dV ( z )( z ) q N ( z ) n ( z )dz dz

2

g in ( z ) n ( z ) ( z )

Vertical Schrödinger and Poisson’s equations

Q2D MODEL

Time-Domain horizontal Transport equations

Poisson

Energy conservation

Momentum conservation

Charge conservation

i ii

i i i

i

i i i

i

i i

i i i

i i i

L LL

L L LL

L L L

L v

L LL L L

L L L

n ( x,t ) v ( x,t )n ( x,t )0

t xv ( x,t ) v ( x,t ) q ( x,t )

v ( x,t )t x m

n ( x,t )w ( x,t ) v ( x,t )23n ( x,t )m x

w ( x,t ) w ( x,t )v ( x,t ) qv ( x,t ) ( x,t )

t xn ( x,t )v ( x,t ) w ( x2

3n

iL 0,t ) w ( x,t ) w

x

i ii L c LL

o

n ( x ,t ) N ( x ,t )( x ,t )x ( )

g ii

3n wx

Microwave and RF Semiconductor Devices Global Modeling Analysis

Giorgio Leuzzi, Vincenzo Stornelli

Dept. Of Electrical and Information Engineering – Univ. of L’Aquila – Italygiorgio.leuzzi@univaq.it; vincenzo.stornelli@univaq.it

The proposed technique, combined with a commercial electromagneticsimulator, has been used to analyse a multifinger pHEMT devicemanufactured by Selex. The device has two gate fingers with a gate lengthof 0.3µm and gate width of 25µm each.

giorgio.leuzzi@univaq.it; vincenzo.stornelli@univaq.it

Discretisation and Fourier Series Expansion of all time and space-dependent quantities(e.g. electron density)

Kk jk t

m mk K

Kk jk t

m mk K

a t A e

b t B e

k jk t mn x,t A e x

Mm

mm 0M

mm

m 0

n x,t a t x

v x,t b t x

k jk t mmm k

k jk t mmm k

n x,t A e x

v x,t B e x

Electron velocity as a function of space (from source to drain) and time, computed with the proposed method and with a standard finite-

difference algorithm.

Relative error for the computed channel current and relative computation time of the proposed method with respect to the

standard FDTD approach as a function of the order of the polynomial M and of the

number of harmonics K