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Gerousis
Toward Nano-Networks and Architectures
C. Gerousis and D. BallDepartment of Physics, Computer Science and Engineering
Christopher Newport UniversityNewport News, VA 23606
2 1015/MAPLD 2005Gerousis
Nanoelectronic
Architectures• Limits of Conventional CMOS technology - Device physics scaling, power dissipation - Interconnects
• Nanoelectronic Integrated Circuits
• Present Work-Simulation of nano networks synthesized from single-electron tunneling transistors (SETs)-Demonstration of SET-CNN and SET neural applications
- Hybrid circuits of ultrascale CMOS coupled to locally connected cellular nonlinear networks (CNNs) of nanodevices for special purpose processing
3 1015/MAPLD 2005Gerousis
Nanoelectronic Integrated Circuit
CMOS drivers for fan-out
Single-electron transistors as processing elements
Photo-detector
CMOS and SETs are rather complementary: SET is the winner of low-power consumption and of new functionality while the advantages of CMOS such as high-speed, driving, voltage gain and input impedance can makeup for exactly for the SET's intrinsic shortcomings.
4 1015/MAPLD 2005Gerousis
R ,Cd d R ,Cs s
island
V a _+
V g _+
C g
__
n 1 n 2
sourcedrain
gate
Single-Electron Transistor
A single-electron tunneling (SET) transistor composed of a conducting island (or quantum dot) between two tunnel junctions characterized by junction capacitances, Cs and Cd,
and tunneling resistances, Rs and Rd.
5 1015/MAPLD 2005Gerousis
Electron tunneling is suppressed due to the Coulomb charging energy, e2/2C. A separate gate voltage changes the charge state of the dot (island), and periodically lifts the Coulomb blockade allowing tunneling.
EFl
EFr
e
0 1 2 30
1
G/Gmax
Vg (e/Cg)
Single-Electron Transistor
Si SOI Single Electron Transistor:D. H. Kim et al., IEEE Trans. ED 49, 2002
6 1015/MAPLD 2005Gerousis
Monte Carlo simulation of SET circuits
The Master Equation for a set of N dots (islands) in terms of the multi-island distribution function is given by
tnnfnnnntnnfnn
tnnfnndt
tnnndf
iiiii
iNi
iN
,,..,...,...,1,..1,...
,1,..1,...,,...,,
11111
1,1
121
kTE
n
tjne
eE
eRn
/1
/1
where the tunneling rate depends on change of total free energy of systems after tunneling
7 1015/MAPLD 2005Gerousis
)]()([)()]()([)( )( 1122 nnnfnnnfeVInn
Average quantities such as current in a two junction system are given as averages
Single electron tunnel events modeled as instantaneous events which are generated stochastically using the calculated tunneling rates for all possible events across all junctions, and using the computer random number generator
j
jr
rt .....
)(ln-
where r is random number 0,1 and tr is the random time between tunneling events. After tunneling, the new tunnel rates are computed, and the next tunneling event generated. The time evolution according to the master equation is modeled as random walk.
Monte Carlo simulation of SET circuits
8 1015/MAPLD 2005Gerousis
‘SIMON’ (SIMulation Of Nano structures)
C. Wassshuber and H. Kosina, "SIMON: A Single-Electron Device and Circuit Simulator", Superlattices and Microstructures 21, 37 (1997).
9 1015/MAPLD 2005Gerousis
SET Cellular Nonlinear Networks
Feedforward synapses Feedback synapses
xij
a ykl klb ukl kl
xij
A non-linear architecture suitable for SET devices is a locally interconnected CNN type array structure for use in array processing such as image processing applications. The center cell, Cij, receives a weighted
feedforward signal bklukl and a weighted feedback signal aklykl from each
neighboring cell Ckl.
10 1015/MAPLD 2005Gerousis
ijij
ijijijij
ijijij zubyax
dt
dx Cell state equation:
x
y
1
-1
1 1,-
1
1 ,1
112
1)(
ij
ijij
ij
ijijijij
x
xx
x
xxxfyCell output equation:
Transfer function:
Cellular Nonlinear Networks
11 1015/MAPLD 2005Gerousis
V in 1
C 11
V in 2
C 1 2
V b o u n d a ry -L
V b o u n d a ry -R
V in 3V o u t2
C 2 3
V o u t3
V o u t1
C 2 1
C 2 2
C 3 2
C 3 3
C12=C23=0.55aF
C11=C22= C22=0.1aF
Template:
Single-Electron Cellular Network - Shadowing
12 1015/MAPLD 2005Gerousis
Threshold Gate in SET Networks
Model of a TLG with SET technology (Lageweg et al.)
A threshold gate can be described by the following equations:
where ω are the weights, x represents the inputs, and ψ is the threshold
n
1i
iixXG
0xGif1
0xGif0XGxF
)(
)(
)()}(sgn{)(
13 1015/MAPLD 2005Gerousis
Threshold Gate - SET inverter
Model of a TLG with SET technology (Lageweg et al.)
14 1015/MAPLD 2005Gerousis
Network for Recognition of Bit Pattern
V1
V2
V3
V4
Vout
1111 1001
15 1015/MAPLD 2005Gerousis
Network for Recognition of Bit Pattern
V1
V2
V3
V4
Vout
1000 0001
16 1015/MAPLD 2005Gerousis
Number Recognition Sub-Networks
17 1015/MAPLD 2005Gerousis
Number Recognition Test Circuit
The network contains several levels/layers of hidden operations between input and output. These layers include row detection, number recognition, and encoding.
18 1015/MAPLD 2005Gerousis
M S1 S0
0 0 0
1 0 1
2 1 0
≥3 1 1
M2
M1 M2
M3 M4
Number Recognition Test Circuit
Input Matrices for V0-V19:
19 1015/MAPLD 2005Gerousis
0.00E+00
4.00E-03
8.00E-03
1.20E-02
1.60E-02
2.00E-02
0.00E+00
4.00E-03
8.00E-03
1.20E-02
1.60E-02
0.00E+00
4.00E-03
8.00E-03
1.20E-02
1.60E-02
2.00E-02
0.00E+00
4.00E-03
8.00E-03
1.20E-02
1.60E-02
2.00E-02
00 01
10 11
Number Recognition Network – Results
20 1015/MAPLD 2005Gerousis
• A neural nanoelectronics architecture with a low interconnection density, such as cellular neural networks (CNNs) are implemented in analog circuit techniques so that low power applications, such as intelligent sensor pre-processing are preferred applications.
• Limitations: - Small capacitance values required for room- temperature operation. - SET weights are hard wired by the use of capacitive connections, which limits the range of applications. - The charge sensitivity of the devices also imposes strong limitations on the allowable electrostatic interaction between different devices in a ULSI circuit.
Conclusions