Microwave and RF Semiconductor Devices Global Modeling ...quantities inside the semiconductor, for...
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Microwave and RF S Mode Giorgio Le Dept. Of Electrical and Inform giorgio.leuzzi@univ giorgio.leuzzi@univ 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. 2 i i i i * 0 z d (z) d 1 qV ( z ) (z) E (z) 2m dz m dz D g d dV ( z ) (z) q N (z) n (z) dz dz 2 g i n (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 i i i i i i i i i i i i i i i i i i L L L L L L L L L L L v L L L L L L L L n (x,t) v (x,t) n (x,t) 0 t x v (x,t) v (x,t) q ( x,t ) v (x,t) t x m n ( x,t )w ( x,t ) v (x,t) 2 3n ( x,t )m x w ( x,t ) w ( x,t ) v (x,t) qv ( x,t ) ( x,t ) t x n (x,t)v (x,t) w (x 2 3n i L 0 ,t ) w (x,t) w x i i i L cL L o n ( x,t ) N ( x,t ) ( x,t ) x ( ) g i i 3n w x Semiconductor Devices Global eling Analysis euzzi, Vincenzo Stornelli mation Engineering – Univ. of L’Aquila – Italy vaq.it; [email protected] The proposed technique, combined with a commercial electromagnetic simulator, has been used to analyse a multifinger pHEMT device manufactured by Selex. The device has two gate fingers with a gate length of 0.3µm and gate width of 25µm each. vaq.it; [email protected] Discretisation and Fourier Series Expansion of all time and space-dependent quantities (e.g. electron density) K k jk t m m k K K k jk t m m k K a t A e b t B e k jk t m n x,t A e x M m m m0 M m m m0 n x,t a t x v x,t b t x m m k k jk t m m m 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
Transcript of 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 [email protected]; [email protected]@univaq.it; [email protected]
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 – [email protected]; [email protected]
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.
[email protected]; [email protected]
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
