Full-Band/Full-Wave Simulations of InGaAs-based Pseudomorphic HEMTs

Nanostructures Research Group
CENTER FOR SOLID STATE ELECTRONICS RESEARCH 1
ARIZONA INSTITUTE FOR NANOELECTRONICS

2007

F. Schwierz and J.J. Liou, Modern microwave
Nanostructures Research Group transistors: theory, design, and performance, John
CENTER FOR SOLID STATE ELECTRONICS RESEARCH Wiley & Sons, Inc., New Jersey, 2003. 2

6
4

energ y [eV]
•  Hybrid CMC/EMC approach
•  M. Saraniti and S.M. Goodnick, IEEE TED, 47, 2
1909 (2000)
0
•  Bandstructure: -2
•  empirical pseudopotential method. -4 EMC
•  local, nonlocal, and spinorbit interactions.
-6 CMC
L Γ X U,K Γ
•  Full phonon spectra:
•  valence shell model. wave vector

Hybrid/MC performance ratio

time per iter. [sec/5000 e ]
-
•  Scattering mechanisms:
•  Deformation potential (optical/acoustic)
•  Polar optical phonons.
•  Impurity scattering (Ridley model).

•  Poisson solver:
•  Multi-grid

CENTER FOR SOLID STATE ELECTRONICS RESEARCH
field [V/m] 3

Strained In0.75Ga0.25As

Eg = 0.57 eV


LSD = 0.30 µm
dg = gate-to-channel separation

Vd = 0.8 V


z
H
G
(
1800
y
c
n
e 1600
u
q L = 20 nm
G
e 1400
r
Small signal F

fT (GHz)
1200
analysis i (t)
f
f
o
L = 35 nm
G D t
u
1000 G

v (t) C

S 800 L = 70 nm
G

J. S. Ayubi-Moak, et al., IEEE TED,
v (t) 600
54(9), pp. 2327-38, Sept. 2007.
i (t)
ΔV 10
-1
10
0

Source-Drain Spacing (µm)

0 T 0 T

Lg=50 nm Lg=10 nm

fT=1.3 THz fT=2.2 THz


z K.S. Yee, IEEE Trans. Antennas Propagat., 14(302) 1966
“Yee cell”
Maxwell’s equations •  Most direct explicit solution of
Ey
Maxwell’s equations available (i.e.
 Ex Ex
no matrix inversion required).

Hz

∂H Ez

∇ × E = −µ
Ex
Ey
•  A complete “full-wave” method
∂t Hx without approximation (i.e. no
 Hy Hy
pre-selection of output modes or
 ∂E 
Ez Ex
solution form necessary.)
∇× H = ε +J Ex
Hx
Ey Ex
y
∂t Hz

Ey

x
PML Absorbing Boundary Conditions
•   “artificial” anisotropic electric/magnetic*
conductivities within domain boundaries allow
for absorption/attenuation waves.
•  Numerical “split-field” approach allowing
perfect transmission into absorbing layer
(regardless of frequency, polarization, or angle
of incidence).

J. P. Bérenger, IEEE Trans. Antennas Propagat., 44(110) 1996.

Task 0
Setup
Parallel Region

Initial Scatter

Task 1 Task N
BC's BC's BC's

calc H field calc H field calc H field

calc E field calc E field calc E field

Communication – plane exchange

Output & Finish

y

x
2D slice εr = 12.0
z
•  Photonic crystals/PBM shown great deal of
promise for true integrated optics.
•  Waveguides with small bends possible
making compact integrated photonic circuits
(IPCs) achievable.

εr = 1.0 a

3D MIT structure

Source plane 370 x 520 x 50 grid
Bipolar pulse ~107 grid points
Si slab (εr =12.0)
Nanostructures Research Group 44 cylinders (εr =6.0)

PML
d
Air Top View of Coupled Simulation Domain:
SiN GATE SiN DRAIN
SOURCE SOURCE
In 0.53 Ga 0.47 As In 0.53 Ga 0.47 As
(cap) (cap)
Excitation
Source
Plane
In 0.52 Al0.48 As (barrier) δ − doping
d
(spacer)
PML InAs
PML
GATE DRAIN
In 0.75 Ga 0.25 As (channel)

In 0.52 Al0.48 As (buffer)
15 µm
InP (substrate)
SOURCE
GROUND
PLANE

SiN SiN

S.I. Substrate S.I. Substrate

15 µm

PML

d Air Top View of Coupled Simulation Domain:
SiN GATE SiN DRAIN
SOURCE
In 0.53 Ga 0.47 As In 0.53 Ga 0.47 As SOURCE
(cap) (cap)

Excitation
In 0.52 Al0.48 As (barrier)
Source
δ − doping Plane
PML
(spacer)
PML d
InAs

In 0.75 Ga 0.25 As (channel)
GATE DRAIN
In 0.52 Al0.48 As (buffer)

InP (substrate)

15 µm

Nanostructures Research Group SOURCE

Steps full-wave simulation:
FDTD:
 Initialization
 ∂H
∇ × E = −µ
∂t 1. Obtain quasi-static dc solution for dc bias point
 (CMC/Poisson) and store E fields and J.
 ∂E 
∇× H = ε +J 2. Initialize H field in FDTD solver using:
∂t

∇× E = 0
CMC:  
∇ × H dc = J dc
1 ⎛ N (i , j ,k ) ⎞
J (i, j , k ) = ⎜ ∑ S n vn ⎟
ΔxΔyΔz ⎜ n =1 ⎟ 3.  Apply excitation source and begin updating
⎝ ⎠ fields:
 
J tot ∂E 1
∂t ε
[
 ac  tot  dc
= ∇× H − J − J ( )]
FDTD 
CMC ∂H 1 
  = − ∇× E
(Etot , H tot ) ∂t µ

Excitation method:

•   Voltage on gate (or drain) in
perturbed (Gaussian pulse, sinusoid,
step voltage).
•  Transverse E-fields (Ex, Ez )
computed via 2D Poisson solver
(SOR) and applied to source plane at
each timestep. 

z 
y 

x 


•  Simulations suggest fT well above 1 THz for 10-50 nm gate pHEMTs
with source-to-drain spacing of 300 nm.

• Analysis of average carrier velocity under the gate suggests an effective
gate length that becomes important for small gate length devices.

•  3D domain decomposition/parallel processing required for realistic
simulation times using coupled simulator.


•  3D decomposition works best for
more general geometries and
particularly for large problem
domains ( >108 grid cells)


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