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UK SiGe Research Programme
Review Meeting, 3rd April, 2003
Advanced Silicon/Silicon-Germanium
Device Simulations
John Barker
in collaboration with
Asen Asenov, Mirela Borici, Scott Roy,
Jeremy Watling, Richard Wilkins, Lianfeng Yang
Nanoelectronics Research Centre
Department of Electronics and Electrical Engineering
University of Glasgow
Outline
•
Is silicon near its end?
•
Physics, Modelling and Simulation
•
Interface Roughness
•
Silicon-Germanium studies
•
Advanced Simulation methodology
•
Advanced Devices
•
Fully quantum atomistic simulation
•
Summary
1. Is silicon near its end?
1978:red brick
wall 0.25µm
limit,alternatives
included
magnetic
bubble logic
conv. &
quantum
devices based
on GaAs and
InP!
House of Commons Select Committee
(2002)
Red brick wall between 2005-2007
Fundamental limit: 2015
Theory Limit: 10-20 nm
Suggests: single electronics,magnetic
and atomic devices
carbon nanotubes, quantum computing
and other radical alternatives to CMOS
be pursued
Concentrate on microprocessor design
and architecture
Atomic scale MOSFET in the near future ??
We still firmly believe the Si route is the best
Reality check:
Scaling of MOSFETs to decanano dimensions
House of Lords
International Technology Roadmap 2001 Edition
Year
2001 2004 2007 2010 2013 2016
130
100
65
45
32
22
Technology node (nm)
65
37
25
18
13
9
MPU Gate Length (nm)
1.3-1.6 0.9-1.4 0.6-1.1 0.5-0.8 0.4-0.6 0.4-0.5
Oxide thickness (nm)
Intel Roadmap June 2001 (Kyoto)
Year
2000/1 2003 2005 2007 2009
130
90
65
45
30
Technology node (nm)
70
50
30
20
15
Gate length (nm)
IEDM 2001 amendment
60
50
30
20
15
Gate length (nm)
Solution exis ts
Solution Being Pursued
No Known Solutions
The accelerating road map!
The accelerating road map!
Paradigm shift
MOSFET Technology
50 nm gates
Intel
30 nm gates
Raised Source Drain: power reduction
High k dielectric: leakage, avoid too thin
SOI : kill leakage; better materials:strained Si, SiGe
Beyond the House of Lords!
2001-2
Intel 20 nm transistor
Intel 10 nm transistor (2002)
The IBM 6 nm silicon transistor (IEDM 2002)
demonstrated
Silicon Nanoelectronics
Today’s transistors 130 nm to 90 nm
Tomorrows transistors: still silicon!
new programmes
US,
Projection:
a vision down to 4nm-2 nm exists
(width of a Carbon NT)
Japan
Europe,
corresponding to a timescale 2023-2025
UK??
Huge possibilities: versatile platform
for new and emerging technologies
Device issues (partial): routes forward exist
Leakage
Power
dissipation
Voltage
scaling
Frequency
Direct S-D
tunnelling
Off-On control
Fluctuation
phenomena
device architecture
engineered Si compatible materials
novel dielectrics
SOI
RSD
interface roughness
many-body “mobility” degradation
atomistic effects
quantum effects
System issues
Will need different kinds of transistors in system blocks:
•Datapaths (speed, leakage)
•Dedicated DSP (power, leakage)
•Memory (density is main concern)
•Analogue
Power and leakage determine the size ratios
between these blocks
Number of different transistors types is determined by
parameter spread
Less devices could solve the problem, but, need
control of the threshold (4th terminal), with strong
transfer function.
System solutions: adaptive control, coding, ...
Future of mainstream electronics
Silicon nanoelectronics
Lifetime: beyond 2025
Device design and System design required together
to solve issues of: power, leakage, fluctuations, stability
Silicon, strained silicon, silicon-germanium, germanium
III-V on silicon/germanium good versatile materials technology
ALL subscribed to by major industry players
THIS IS OUR MOTIVATION FOR BEING IN THE SiGe Project
2. Physics, modelling and simulation
Why is simulation useful?
•Part of the design-optimisation cycle
•Extraction of circuit parameters
•Calibration and extension of commercial tools
•Develop device physics and architecture
•Getting ahead of the game.
Summary of Progress (2002-2003) - see also posters
Simulation tools
Development of a fully bipolar (electrons and holes)
2-D Full-Band Monte Carlo device simulator for Si/strained Si/SiGe
that includes degeneracy, high doping effects, advanced screening
models,
quantum potential and interface roughness scattering. Down to
30 nm.
Device Physics and new Simulation tools
–
–
–
–
–
–
Investigation of carrier transport and scattering at interfaces
New non-perturbative models for interface roughness scattering
Effects of degeneracy, high doping, band-gap narrowing
Advanced screening models
Quantum transport extensions: density gradient, quantum potential, Wigner
function, Green function
Atomistic studies: classical , semi-classical and full quantum transport
Design - optimisation with partners
–
–
Layer and device design for consortium partners
Modelling and scaling study of high linearity MODFETs, based on
experimental data from Daimler Chrysler
Applications to partners and industry
SiGe MODFETs, RF devices, Si, strained Si and SiGe well tempered
devices, double gate devices, atomistic devices.
Course on Device Modelling
4. Interface Roughness: new non-perturbative model
• An extension of semi-classical Boltzmann-Fuchs theory,
that is suitable for efficient inclusion within the Monte Carlo
framework.
• Probability of specular or diffuse scattering is chosen
according to the carrier k-vector and incident scattering
angle. This overcomes one of the major failings of the
traditional semi-classical model.

Ps  exp
2
2
2
4rms k cos 

The scattering from a rough surface, has strong randomizing effects,
resulting in a broad distribution over the emergent angles, while scattering
from a smoother interface has a high probability at emergent angles
close to specular
Diffuse scattering, depends on the autocorrelation function considered.
Gaussian auto-covariance
RMS height: 
3nm
0.5nm
Exponential auto-covariance
Correlation Length: Lc =
Polar plot of probability of scattering through a given angle
surface
in
diffuse
P=1.0
specular
diffuse
Semi-classical model versus ab-initio quantum calculations
Ab initio interface scattering:Gaussian wavepacket scattering
off a smooth interface
Time
Real Space
0.0 ps
Initial Motion
of Wave Packet
0.02 ps
0.05 ps
Electron rest mass,
V(r) = 0; kx0 = ky0 = 109 m-1;
E = 76meV
k (Fourier) Space
Ab initio interface scattering:Gaussian wavepacket
scattering off a rough interface
Time
Real Space
k (Fourier) Space
0.0 ps
Initial Motion
of Wave Packet
0.02 ps
0.05 ps
Electron rest mass,
V(r) = 0; kx0 = ky0 = 109 m-1;
E = 76meV
back
scattering
&
diffuse
scattering
4. Silicon-Germanium Studies: 2 examples
• Simulation of 67nm IBM
Relaxed and Strained Si n-MOSFET.
Provides test for interface roughness simulations
• Optimizations of Si/SiGe 70 nm MODFET for RF
and high linearity applications:
using Daimler-Chrysler data
(part of support for experimental RF
and linear systems programme)
Other work: see posters
4.1 Simulation of 67nm IBM Relaxed and Strained Si n-MOSFET
Comparison between the n-type
Strained
Si
and
control
Si
MOSFETs:
• 67nm effective channel length
• Similar processing and the same
doping conditions
For the strained Si MOSFET:
• 20nm strained Si layer thickness
• Strained Si on relaxed SiGe
(Ge content: 15%)
K.Rim, et. al., Symposium on VLSI Technology 2001
http://www.research.ibm.com/resources/press/strainedsilicon/
Id-Vg Current Characteristics: Monte Carlo v Experiment
Id-Vg Current Characteristics (higher fields)
Channel Velocities: Monte Carlo
Electron Velocities along the channel of IBM 67nm Si n-MOSFET,
V =V =1V
Strained Si 67nm n-channel MOSFET Structure
Id-Vg Current Characteristics for strained Si n-MOSFET
Study 2: Optimizations of Si/SiGe MODFET
for RF and high linearity applications
•
Based on the understanding of a Daimler-Chrysler
70nm Si/SiGe MODFET
•
Aim for high RF performance and high linearity:
• RF: fT=f(gm,Cg, etc); fmax=f(fT, gm,Cgs,Cgd, gds,etc)
• Linearity: PIP3=4gm/(gm2 RL) High is Good
•
Trade-off designs between fT and linearity
• Gate-to-channel distance
• Gate position (Lgs/Lds)
• Doping in the channel (MODFETs vs. DCFETs)
•
Effects of scaling on RF performance and linearity
L. Yang, A. Asenov, M. Boriçi, J. R. Watling, J. R. Barker, S. Roy, K.
Elgaid1, I. Thayne, T. Hackbarth
Device Structure
• MODFET
• DaimlerChrysler structure
• double-side modulation
doping
• high mobility
• MODFET with doped channel
• sandwich-like doped channel
• reduced mobility
• high carrier density
• Doped Channel FET (DCFET)
• sandwich-like doped channel
• without modulation doping
• high carrier density
• lower mobility
Calibrations of drift-diffusion simulators
Calibrated Id-Vg characteristics of DaimlerChrysler
70nm Si/SiGe MODFET
One example: Effects of the gate-to-channel distance
small d
is worst
for linearity
but good
for RF
Effects of the gate-to-channel distance d on the linearity (PIP3);
the inset is the effect of d on the transconductance gm
Results
• Trade-off designs for RF performance and linearity
• Gate-to-channel distance d: decreasing d enhances
RF, but lowers linearity
• Gate position Lgs/Lds: increasing Lgs/Lds achieves
high linearity, but reduces gm and drive current ID
• Doped channel – leads to good linearity, although
gives a decrease for gm and drive current ID
•
Scaling
• improved RF performance
• slightly decreased linearity
5. Development of Advanced Simulation Methodologies
•SiGe heterostructure FET models
•Full Band Monte Carlo Device & bulk
simulation,Poisson-Schrödinger
•Drift Diffusion, Hydrodynamic,
Quantum corrected versions
Grants
NASA
IBM
•Density gradient & space-dependent mass
•Wigner equation (2002)
EPSRC
•Quasi-Classical atomistic simulator(2002)
Ind.
partners
(Platform)
unique to Glasgow
•Full Non-Equilibrium Green Function simulator (2003)
•Green function - T-matrix quantum hydrodynamic NEW
atomistic simulator (2003) unique to Glasgow
Possible quantum effects within a MOSFET
Quantum transport
Gate
Tunnelling
B-to-B
Tunnelling
Quantum
Confinement
S-to-D
Tunnelling
6. Advanced Devices
•
•
Intel have announced conventional MOSFETs scaled down to
10nm, and IBM have even announced a 6nm channel length.
The scaling of this design below 10nm is likely to require
intolerably thin gate oxides and unacceptably high channel
doping, therefore advocating a departure from the
conventional MOSFET concept.
4 nm Double gate MOSFET:
An Artist’s Impression
•
One of the most promising new device structures is the
double-gate MOSFET, with the possibility of scaling to 10nm
and below, where direct source-drain tunnelling will become a
real possibility.
6.1 Double-Gate MOSFET structure
density-gradient
Classical
Based on structure of Z. Ren, R. Venugopal, S. Datta, M. Lundstrom, D. Jovanovic, J.
Fossum IEDM Technical Digest pp. 715-718 (2000)
Quantum
Source-Drain Tunnelling
Classical and Density Gradient Simulations
ID-VG characteristics obtained from classical and calibrated DG
simulations for double gate MOSFETs with channel lengths of
20nm and 4nm. VD=1V, VG is applied to both gates. The quantum
mechanical threshold voltage shift,VT, is illustrated.
Non-equilibrium Green’s Function Method
• Equations of motion for Green’s functions:
• (E-H-Sr) Gr (r,r',E) = d(r-r')
• (E-H-Sr) G< (r,r',E) = S< Ga (r,r',E)
• (E-H-Sr) G> (r,r',E) = S> Ga (r,r',E)
Sr represents self-energy due to
open boundaries and scattering
Sr = U gr (surface) U
• Poisson’s equation
MOSFET Quantum Mechanical Effects: Sub-bands
Jovanovich et al (2001)
Quantum mechanical DOS (spectral function) data
taken at Si-SiO2 interface
Striations in DOS plots are sub-bands. Spectral shift evident near source
barrier. Multiple sub-bands are required for accurate scattering calculations
Non-equilibrium Green’s Function and low-cost
Density Gradient Simulations for double gate structure
ID-VG characteristics obtained from Non-equilibrium Green’s
function and calibrated DG simulations for double gate
MOSFETs with gate lengths ranging from 20nm to 4nm. VD=1V.
6.2 The transition to atomistic devices
need more advanced simulation tools
4 nm
Fig. 4 The current approach to
semiconductor device simulation
assumes continuous ionised dopant
charge and smooth boundaries and
interfaces.
Fig. 5 Sketch of a 22 nm M OSFET
expected in mass production in 2 008.
There are less than 50 Si atoms along
channel. Random discrete dopants,
atomic scale interface roughness and
line edge roughness introduce
significant parameter fluctuations.
Fig. 6 Sketch of a 4 nm MOSFET
expected in mass production in 2 023.
There are less than 10 Si atoms along
the channel. The size of the device
becomes smaller than the size of a
large molecule.
Atomistic effects: being studied in depth at Glasgow
Discrete nature of charge
Discrete nature of dopants
Line edge roughness
Interface roughness
Atomic segregation
Discrete
many-body
carrier
interactions
Fischetti
asenov et al
7. Fully quantum atomistic simulation
Barker, Physica (2003)
 Large systems: self-averaging
 Small systems: random micro-configurations
 Conventional perturbation methods
inadequate including NEGF
 Exact non-asymptotic T-matrix partial-wave
analysis of hard sphere model for impurities
and roughness
open 3D
slab confined
open box geometry
Results sensitive to configuration
No self-averaging
Treat impurity/roughness scattering non-perturbatively

Random impurity potential: the Kohn and Luttinger ansatz
NI
Vtotal(r)  V(r  rj )
Fourier
transform
j 1
structure
factor
Vtotal(q)  I (q)V(q)

NI
I (q )   e
iq.r j
j 1

ensemble
average
NI
 e
standard GF theory
iq 1 .r j
 N I dq 1 0
j1
NI
 e
j1
iq 1 .r j
NI
e
j'1
iq 2 .r j '
  N I dq 1 q 2 0  N I (N I 1)dq 1 0dq 2 0
d  N
1
N
 exp(iq.r )  d
I
q0
plotted for qmax  10 /boxside
I 1
N=3
N=10
N=100
N=1000

N
Re{d}  N 1 Re{ exp(iq.rI )}
I 1
N
Im{ d}  N 1 Im{  exp(iq.rI )}
I 1
strong interference
self-averaged
Impurity array: N short range scatterering centres
|  | in  

2m*
2
G0V |   | in  

2m*
2
G0T | in 
T matrix
1 e ik|r r ' |
G (r  r') 
4 | r  r'|

0
N
Vtotal(r)  V (r  rj )
j1
G=
+

+
+
X
G≠
+…
+
+
+
STANDARD NON-EQUILIBRIUM GREEN FUNCTION FAILS
T-matrix approximation: no self-averaging
NI
NI
T   tj  
tj  Vj VjG0tj
j 1
j 1
NI
t G t
j
0 j'
 ...
j '1
NI
T  V VG0T
T  t j
j1
NI

i(kk').r j
 k | T | k'   e
 k | t | k'
j1



 FI (k  k')  k | t | k'
2
| k | T | k'|  N I | k | t | k'| {1
(  cosq.(r j  r j' )}
N I j j'
interference term O(NI (NI 1)/2)
2
cross-section~
2
NI   NI 
2

open
slab
box
ka=0.25
k=0.1
a=2.5 nm
low energy
ka=1
a=2.5 nm
medium
energy
incoming current interferes with scattered current from impurity & boundary
classical trajectories
strong blocking by impurities or remote fluctuation pot
3 impurity system: box geometry z=0 plane
quantum flow meanders through despite classical blocking
Box geometry 25 X 25 X 25 nm :density & current
ka=2.5
Si
300K
S
DS
strong diffraction
meandering flow
between impurities & vortices effects; some
multiple scattering
D

Transmission coefficients and conductance
T

drain
j(r)d 2 r /

jin (r)d 2 r
Why do small devices work?
source
Compute conductance using Landauer formula
Thermal superposition: Lundstrom picture
Results for devices with < 25 nm geometries
•Conductance very sensitive to impurity cluster orientation
•Conductance not given by standard GF or Boltzmann
•Flow between vortices is reversible: quasi-ballistic
suggests flow between impurities and vortices is relaxive
Conjecture: actual flow is semi-classical fluid but within a
renormalised fluctuation potential landscape.
8. Summary
• A new interface roughness scattering model
developed:gives good agreement with 67 nm
n-channel Si and Strained Si MOSFETs.
• Design and scaling studies provide useful results for
RF and linear devices
• A state-of-the-art Monte Carlo simulator
• Practical and new ab initio quantum simulation tools
• Role of atomicity and fluctuations
• Advanced device studies down to 4 nm scale
• Silicon nanoelectronics has a great future
-lets not ignore it!
END