Fundamentals of Nanoelectronics
Prof. Supriyo Datta
ECE 453
Purdue University
08.23.2004
Lecture 1: Energy Level Diagram
Ref. Chapter 1.1
Network for Computational Nanotechnology
00:00
Transistors
Field Effect Transistor
ID
S
O
U
R
C
E
VD
VG
Gate
INSULATOR
D
R
A
I
N
L
CHANNEL
z
INSULATOR
x
• Denote the channel length
as ‘L’
• Since the source and drain regions are very
good conductors it is the resistance of the
channel region that limits the current and
determines how much current will flow through
the device when voltage is applied. Please do
note that as the devices are getting smaller the
parasitic resistances in the contacts become
important compared to the channel resistance
but that’s something we can ignore to start with.
• We are interested in the current that flows from
Source to Drain,I D (perpendicular to the cross
section of the channel). In the absence of good
fabrication, leakage current (in the z direction)
can exist in the insulator due to VG. This current
increases as the insulator thickness is reduced
and is problematic for nano-scale FET’s.
• There are two types of current-voltage characteristics: One is I D as a function of drain
voltage when a constant gate voltage is applied. The other is I D as a function of gate voltage
when a constant drain voltage is applied. We are mostly interested in the first one.
05:06
Transistor: I vs. V curves
Drain Current
I in Amperes
8 x 10
Drain Current
I in Amperes
-4
6
7
-4
VG =0.5V
5
VD = 0.5V
6
x 10
4
5
3
4
3
VT
2
2
VG = 0.025V
VD = 0.025V
1
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Gate Voltage, Vg in volts Æ
0
0
0.2
0.4
0.6
Drain Voltage, Vd in volts Æ
What is the physics behind these curves?
09:00
Transistor Scaling: 19602003
1 μm = 103 nm
100 μm
10 μm
Microelectronics
1 μm
100 nm
10 nm
Nanoelectronics
1 nm
1960
2003
How far will transistor scaling go?
19:02
Energy Level Diagram
How do we understand the I-V
characteristics?
• Begin by understanding the band
diagram which describes the energy
levels in the device e.g. in silicon. (See
right)
• But how do we know that these energy
levels form bands and where they are?
• Experimentally, filled levels are
determined from Photoemission
Spectroscopy (PES)
S + hν Æ S+ + e- (hv should be big
enough to knock out an electron;
typically hν > 5eV for semiconductors)
• Empty levels determined from Inverse
Photoemission Spectroscopy (IPE)
S + e-Æ S-+ hν
0eV
Vacuum Level
-3eV
-5eV
-9eV
29:00
Fermi Energy
0eV
E
Filled
Conduction
Band (CB)
EF
EF
Empty
0
½
1
Valence Band
(VB)
f0(E - EF)
Fermi Function: f0(E) = 1/ (e E / kBT + 1)
33:54
Gate Bias
Fermi energy (or electrochemical potential) is held fixed by source and
drain reservoirs
Channel energy levels with
Channel energy levels with
VG = 0
Empty
States
VG > 0
Vacuum
Level
Empty
States
μ
Filled
States
VG = 0
VG < 0
μ
Filled
States
• Apply a positive gate voltage and
• Apply a negative gate voltage and
band energy levels move down.
band energy levels move up.
39:20
Gate Bias & Conduction
ID
V-
Small Fixed VD
V+
VG
• V-, the negative bias
activation voltage, depends
on how far the Fermi energy
is from the valence band
• V+, the positive bias
activation voltage, depends
on how far the Fermi energy
is from the conduction band
46:50
A Simple Energy Level
Scenario
0eV
Peaks occur where EF crosses
an energy level due to an
applied VG bias
Small Fixed VD
E1
E2
E3
E5
E4
ID
E4
EF
E5
VG
E3
E2
E1
What if we had a carbon nano-tube or a hydrogen molecule? Answer:
Different energy levels but same basic story.