PHS 468: SEMICONDUCTOR
DEVICES
DR. O. D. AKINYEMI
DEPARTMENT OF PHYSICS,
UNIVERSITY OF AGRICULTURE,
ABEOKUTA, NIGERIA.
This lecture note was prepared using materials from lecture notes
prepared by Professor Ali Javey (Integrated Circuit Devices) and that of
Dr. K. Fobelets (An introduction to semiconductor devices)
Why study semiconductor devices?
Present day devices are no longer just diodes or transistors,
but are either large scale integrated circuits or special
purpose components whose design and performance are
intimately connected with their physics and processing.
For the future engineer it is no longer enough to study the
terminal electrical characteristics of the semiconductor
device while treating the device itself as a “black box”.
Most of the sophistication of modern electronics is hidden
in that box, and more and more engineering and scientific
effort will be required in device development, design,
simulation, production and testing in the future.
Why study semiconductor devices?
The devices in fact become subsystems, ready for use for
the system engineer. Even he, the user of the devices, will
not be able to get the most out of them or contribute
towards design of more advanced devices and systems
without a good knowledge of the principles underlying
their operation and the technology used in
manufacturing them. This course therefore aims to give
you the basic knowledge to understand simple
semiconductor devices and to give you a background that
will enable you to understand more complicated structures.
The course aims
• To give insight into the structure of
semiconductors
• To give insight into the physics of semiconductor
diodes and transistors.
• To give models of device behaviour that can be
used as a basis for understanding the functioning
of other/new semiconductor devices.
• To give insight into the fabrication methods of
diodes and transistors.
Objectives
•
•
•
•
At the end of the course students should be able to:
Discuss the characteristics of semiconductors, in particular
Si, that make the material suitable for electronic devices
Explain qualitatively the mechanisms of electronic
conduction in semiconductors, and calculate relevant
quantities from given data.
Calculate and explain the DC current-voltage behaviour of
diodes and transistors, given their geometry and material
properties.
Explain the fabrication of simple diodes and transistors.
Course synopsis
1. Introduction into semiconductor materials
A semiconductor is a material with a conductivity level between metals and
insulators. Unlike metals, the charges in the semiconductor are more tightly
bound to the atoms and although some of these charges travel around
in the semiconductor, they are only quasi-free as they feel the
continuous influence of the surrounding lattice (atoms). Semiconductors’
strength is based on the existence of 2 types of moving charges: negatively
charged electrons and positively charged holes. The energetic state of the
charges is described using an “energy band model” which is based on sound
quantum-mechanical calculations but which will be introduced in a more
informal way in this course. The energy band diagram with its associated
bandgap and position of the Fermi level will form the basis of understanding
the operation of semiconductor devices.
Two different types of currents, drift and diffusion, can occur in a
semiconductor. Although these currents normally occur at the same time in
“real” devices, in this course we take the liberty to make approximations such
that only one of them will occur at any one time. The reasoning behind the
approximations is based on the concept of majority and minority carriers.
2. The MOS capacitor and MOSFET
Semiconductors become devices the moment they are combined with
other types of semiconductors or metals. A semiconductor with two
metal contacts becomes a resistor or a Schottky diode depending on the
material characteristics of both the semiconductor and the metal. We
will look into this kind of metal-semiconductor junctions.
Although in traditional textbooks it is common to start with discussing
the functioning of a pn-diode, in this course we will first focus on what
is called majority carrier devices - devices where only one type of
carriers play an important role in its operation. A metal-oxidesemiconductor (MOS) contact can be used as a capacitor in integrated
circuits but is also used in MOS Field Effect Transistors (MOSFETs)
to control the conduction in the channel without injecting carriers. We
will study the functioning of this device using energy band diagrams
and investigate the parameters that influence the operation of this
device.
3. The p-n junction and BJT
Diodes can be made from pn junctions - thus the same material but
different doping types at each side. This is a device where both
majority and minority carriers play an important role. The current is
governed by diffusion of minority carriers rather than by drift of
majority carriers as was the case in the MOSFET. We will explore the
reason for the rectifying behaviour of these pn-diodes.
A more complicated npn or pnp junction is the basis for the bipolar
junction transistor (BJT). Based on our knowledge of pn junctions, the
functioning of a BJT will be described. We will find out how current
gain exist in this device and we will find out why BJTs are used in
high-speed analogue applications whilst MOSFETs govern the digital
world.
SEMICONDUCTORS
* Intrinsic (i.e. pure, undoped) semiconductors have
a small amount of free carriers at room
temperature and therefore have a very low
conductivity (e.g. diamond). The number of holes
and electrons are equal in an intrinsic
semiconductor as the free carriers are generated by
thermal energy and thus whilst and electron is
created a holes occurs simultaneously (electronhole pairs).
ni =
pi
ni is the intrinsic number of electrons
pi is the intrinsic number of holes
* Extrinsic (i.e. doped) semiconductors have
better conductivity.
dopants +
intrinsic =
extrinsic
semiconductor semiconductor
• Impurities, donors or acceptors, are introduced in
the pure intrinsic semiconductor. Thermal energy
frees electrons from donor atoms, and holes from
acceptor atoms.
• Donor doping (donors donate an extra electron)
creates an n-type material. The donor density
notation is ND Acceptor doping creates a p-type
material. The acceptor density notation is NA
• The density of dopants is normally higher than the
intrinsic density of free carriers in the
semiconductor. (e.g. for Si ni=1.45x 1010cm-3
whilst doping density introduced in the lattice is
>1015cm-3)
In semiconductors two types of current can
exist: drift and diffusion currents. It is the
aim of this section to generate an
understanding into the physical principles
behind the existence of the currents.
Drift currents
If an electric (or magnetic) field is applied
then the motion of the carriers is still under
the influence of scattering processes, and
each individual carrier might not take
necessarily the same path, but the average
direction of movement (velocity) of all the
carriers is determined by the applied electric
field. This motion of carriers under an
applied electric field is called drift.
Diffusion Currents
As seen before generation of carriers via temperature is always in pairs
of electrons and holes and thus the number of
electrons and holes caused by generation is equal (the intrinsic carrier
concentration at a certain temperature). Assume
that a process exists that can create locally an excess of one type of
carriers compared to the other. This would generate
a local gradient of carriers. The carriers are going to react as what you
would expect from gas molecules. If at a corner
of the room a chemical (e.g. gas molecules different than nitrogen and
oxygen that normally occur in air) the after a
while the observer can smell the gas at the other side of the room
because the molecules have diffuse throughout the
room to cancel the gradient in its density. The same happens with
excess carriers in a semiconductor, they will diffuse in
order to eliminate the excess. This diffusion is indeed not completely
random any more as it moves the carriers on
average in the direction determined by the gradient. This process will
cause diffusion currents.
PN Junctions
Donors
N-type
P-type
– V +
I
I
N
P
V
Reverse bias
Forward bias
diode
symbol
A PN junction is present in every semiconductor device.
Energy Band Diagram and Depletion Layer of a PN Junction
N-region
P-region
Ef
(a)
Ec
(b)
Ec
Ef
Ev
Ev
Ec
Ef
Ev
(c)
Neutral
N-region
Depletion
layer
Neutral
P-region
Ec
(d)
Ef
Ev
A depletion layer
exists at the PN
junction. n  0 and
p  0 in the
depletion layer.
Doping Profile of “Idealized Junctions”
p
n
p
n
Qualitative Electrostatics
Band diagram
Built in-potential
From e=-dV/dx
Formation of pn junctions
When the junction is formed, electrons from the n-side and holes
from the p-side will diffuse leaving behind charged dopant atoms.
Remember that the dopant atoms cannot move! Electrons will
leave behind positively charged donor atoms and holes will leave
behind negatively charged acceptor atoms.
The net result is the build up of an electric field from the positively
charged atoms to the negatively charged atoms, i.e., from the nside to p-side. When steady state condition is reached after the
formation of junction (how long this takes?) the net electric field
(or the built in potential) will prevent further diffusion of electrons
and holes. In other words, there will be drift and diffusion currents
such that net electron and hole currents will be zero.
Equilibrium Conditions
Under equilibrium conditions, the net electron current and hole current will
be zero.
E-field
N-type
P-type
NA = 1017 cm3
ND = 1016 cm3
hole diffusion current
net current = 0
hole drift current
Built-in Potential
N-region
n  N d  Nce
 q A kT
kT N c
 A
ln
q
Nd
2
ni
kT N c N a
 q B kT
P-region n 
 Nce
B
ln
2
Na
q
ni
Nc 
kT  N c N a
 ln

Vbi  B  A 

ln
2
q 
N d 
ni
Ec
qVbi
Ef
(b)
kT N d N a
Vbi 
ln
2
q
ni
qB
qA
Ev
The Depletion Approximation
We assume that the free carrier
concentration inside the depletion
region is zero.
We assume that the charge density
outside the depletion region is zero
and q(Nd-Na) inside the depletion.
a)
b)
Field in the Depletion Layer
N
Nd
N eut ra l Re gion
N
P
Na
D eple tion L a yer
–xn
N e utral R egi on
P
xp
0
d E   qN a
es
dx

qNd
xp
c)
–xn
E( x) 
x

 bi
es
( x p  x)
On the N-side,  = qNd
E
E( x) 
–xn
qN a
–qN a
)
)
On the P-side of the
depletion layer,  = –qNa
xp
0
V
x
qN d
es
( x + xn )
(a)
(b)
Field in the Depletion Layer
N
Nd
N eut ra l Re gion
N
P
Na
D eple tion L a yer
–xn
N e utral R egi on
P
xp
0

The electric field is continuous at x = 0.
qNd
(c)
–xn
Naxp = Ndxn
xp
x
–qN a
A one-sided junction is called
a N+P junction or P+N junction

(d)
Depletion Width
EXAMPLE: A P+N junction has Na=1020 cm-3 and Nd
=1017cm-3. What is a) its built in potential, b)Wdep , c)xn ?
Solution:
a)
b)
kT N d N a
10 20  1017 cm 6
bi 
ln
 0.026V ln
1V
2
20
6
q
10 cm
ni
Wdep
c)
1/ 2
2e sbi  2 12  8.85 10 1 


 
19
17
qN d
 1.6 10 10

14
xn  Wdep  0.12 μm
 0.12 μm
Reverse-Biased PN Junction
Forward Biased PN Junction
Junction Breakdown
I
Forward Current
V B, breakdown
voltage
V
Small leakage
Current
A Zener diode is designed to operate in the breakdown mode.
Quantum Mechanical Tunneling
Potential energy barrier
E
d
x
Tunneling Breakdown
(a)
Ec
Ef
Ev
(b)
Filled States -
Empty States
Ec
Ev
I
(c)
V
Breakdown
Dominant breakdown
cause when both sides of a
junction are very heavily
doped.
Avalanche Breakdown
Ec
original
electron
impact ionization
Efp
Ev
avalanche breakdown
electron-hole
pair generation
Ec
Efn
The PN Junction as a Temperature Sensor
I  I 0 (e qV
kT
 1)
 Dp
Dn 

I 0  Aqni
+
L N

 p d Ln N a 
2
What causes the IV curves to shift to lower V at higher T ?
Other PN Junction Devices–From Solar Cells to
Laser Diodes
Solar Cells
Also known as
photovoltaic cells,
solar cells can
convert sunlight
to electricity with
15-30% energy
efficiency
Solar Cells
short circuit
light
N
I
P
-
Dark IV
Eq.(4.9.4)
Isc
Ec
Ev
+
–Isc
(a)
0.7 V
0
V
Solar Cell
IV
Eq.(4.12.1)Maximum
power-output
(b)
p-i-n Photodiodes
•Only electron-hole pairs generated
in depletion region (or near
depletion region) contribute to
current
•Only light absorbed in depletion
region contributes to generation
–Stretch depletion region
–Can also operate near avalanche
to amplify signal
Light Emitting Diodes (LEDs)
•LEDs are typically made of
compound semiconductors
–Why not Si