Microwave and RF Semiconductor Devices Global Modeling ...quantities inside the semiconductor, for...

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