Single Electron Transistor

Coulomb Blockade
and
Single Electron Transistor
29-05-2021 Arpan Deyasi, RCCIIT, Kolkata 1
Arpan Deyasi
RCCIIT, India

Coulomb Blockade

Effect of single electron transfer
Quantum system
lead

A single electron transferred from lead
to quantum system
Redistribution of charge in the lead
Change in electrostatic potential energy
Effect of Single charge transfer

Effect of Single charge transfer
For macroscopic system,
change of electrostatic energy is negligible (U ≃ kBT)
For microscopic system at low temperature,
change of electrostatic energy is very significant (U >> kBT)
For microscopic system,
change of electrostatic energy is significant (U > kBT)

Coulomb Blockade
Large change in electrostatic energy of a system due to
transfer of a single carrier results an energy gap in the
system, defined as Coulomb blockade
Material and geometry of the quantum structure controls
coulomb blockade
Blocking of electron tunneling through
a junction due to repulsion of electrons
by Coulomb field
Applied
bias
Energy gap
Coulomb
island

Criteria of Single charge transfer
consider a single tunnel under application of external bias ‘V’
energy stored in the tunnel junction
2
2
q
U
C
=
Under application of bias V, an electron at source electrode with K.E. ES(κ) will
tunnel into the drain electrode with K.E. ED(κ’)

energy conservation gives
2
2
1 ( )
( ) ( ')
2 2
S D
CV q
E CV E
C
 
−
+ = +
satisfying Pauli’s exclusion principle
( ) ( )
S F B
E E k T
  − ( ') ( )
D F B
E E k T
  −

Inequality conditions together gives
( ( ') ( )) 2
D S B
E E k T
 
− 
tunneling condition is given by
2
2
2
B
q
qV k T
C
 −

Inference: [i] no current can flow at a bias below a threshold voltage
which depends on the temperature
Inference: [ii] At T = 0, no current below
can flow
f
q
V
C

This region is called the Coulomb region

Inference: [iii] The prohibition of tunneling is called
Coulomb blockade
Inference: [iv] The energy
is called the Coulomb gap energy
2
2
C
q
qV E
C
= =

I-V
characteristics
indicating
Coulomb
gap
V
I
-(q/2C)
(q/2C)

Criteria for Coulomb Blockade
Applied bias should be less than q/C
System thermal energy should be less than q2/C
Tunneling resistance should be greater than h/q2
f
q
V
C

2
B
q
k T
C

2
T
h
R
q


Single Electron Transistor

Criteria for Single Electron Tunneling
Applied bias should be greater than q/C
System thermal energy should be greater than q2/C
Tunneling resistance should be less than h/q2
f
q
V
C

2
B
q
k T
C

2
T
h
R
q


Source Drain
Gate
Quantum
Dot
CS
CD
CG
Schematic Structure
RS RD

Definition
SET is switching type of transistor where
source and drain are quantum-mechanically connected
through quantum confined structure (Q. Wire or Q. Dot)
that works as channel;
and uses controlled electron tunneling for amplification of current

Operating Principle
Operation is based on quantum tunneling phenomena
By application of bias, electron transfers between source and drain via
tunneling mechanism
Gate potential effectively helps to raise eigenstates of the quantum
wire/dot

Operating Principle
In blocking state, no accessible energy levels are within the tunneling
range of electron on source contact
All energy levels of the quantum device with lower energies are
occupied

After application of positive bias, energy levels of the dot are lower.
Operating Principle
Then one electron can tunnel to the dot, occupying a previously vacant
energy levels.
From there it tunnels to drain.

MATHEMATICAL MODELING
total capacitance of the device is given by
S D G
C C C C
 = + +
change of free energies at drain and source ends due to nS and nD number of electrons flow
0
( , ) { ( ) ( ) }
2
S S D e G D G G
q q
F n n N Q C C V C V
C


 =  − + 
0
( , ) { ( ) }
2
D S D e S G G
q q
F n n N Q C V C V
C


 = −
N is the number of electrons in the single dot, and Q0 is the background charge

electron tunneling rates
2
1
( )
1 exp( / )
S
S
S S B
F
N
R q F k T



 
−
 =  
− 
 
2
1
( )
1 exp( / )
D
D
D D B
F
N
R q F k T



 
−
 =  
− 
 

time rate of probability density
( , )
( 1)[ ( 1) ( 1)] ( )[ ( ) ( )]
D S D S
N t
N N N N N N
t

 
+ − − +

= +  + +  + −  + 

Under steady state condition
( )[ ( ) ( )] ( 1) [ ( 1) ( 1)]
D S D S
N N N N N N
 
− + + −
 +  = +   + +  +

Boundary condition
N → 
( ) 0
N
 →
For normalization
( ) 1
N
N


=−
=


drain current is given by
( )
( ) [ ( ) ( )]
S S
N
I V q N
N N

 + −
=−
=  −

( )
( ) [ ( ) ( )]
D D
N
I V q N
N N

 + −
=−
=  −


Why SET is advantageous?
Consumes less power for operation --- reduces
circuit power dissipation
▪ Operation at Room Temp
▪ Fabrication
▪ Charge Offset
Drawbacks

Application
1. Detection of Infrared Radiation
Calculation of photo-response of single electron system subject to
electromagnetic radiation can be easily determined since
tunneling events are uncorrelated

Application
2. Spectroscopic application
If one electron in an otherwise single electron system is added;
then the additional energy can easily be distinguished.
This property is utilized to design ultra-sensitive photodetector.

Application
3. Programmable Logic
SET has nonvolatile memory function.
Its phase shift can be considered NMOS device for anticlock
direction & PMOS device for clockwise direction.
This helps to form CMOS switch which is the backbone of quantum-
mechanical VLSI circuits.

Single Electron Transistor

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