Lecture 1 Semiconductor Theory

8/11/2019 Lecture 1 Semiconductor Theory

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Introduction to

Semiconductor Theory


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Introduction to Semiconductor Theory

Semiconductor Materials

Semiconductors, as the name implies, are a group of materials whose electrical

conductivity is greater than that of insulators but less than that of metals.

Semiconductor materials are found in Group IV and neighbouring columns of theperiodic table. The ones in group IV (C, Si, Ge) are called elemental semiconductors

because they are composed of the pure element.

InsulatorsMetals

Semiconductors

Increasing conductance

II III IV V VI

B C N

Al Si P S

Zn Ga Ge As Se

Cd In Sb Te


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Elemental IV compunds

Binary III-V

compounds

Binary II-VI

compunds

Ternary

compounds

Quaternary

compounds

Si SiC AlP ZnS GaAsP InGaAsP

Ge SiGe AlAs ZnSe AlGaAs

AlSb ZnTe

GaN CdS

GaP CdSe

GaAs CdTe

GaSb

InP

InAs

InSb

These compounds are widely used in various electronic and optical applications.


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Covalent Bond Structure of Semiconductors


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Charge Carriers and Energy Levels

Two types of charge carriers exist in semiconductors, namely: electrons and holes

A hole is the term used to describe an atom with a missing electron. An electron may be

shaken loose from a bond structure by lattice vibration caused from thermal heating. The

remaining atom (ion) now has a positive charge. The loose electron is usually called a free

electron.

The mechanism of conduction in semiconductors is best explained via energy level

diagrams

Specific energy levels are always associated with each shell of orbiting electrons in atomic

structures. While the energy of each shell is different, the further away an electron is from the

parent nucleus, the higher its energy state.

In order to break the covalent bond, a valence electron must gain a minimum energy, Eg,

called the bandgap energy.


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Energy level diagrams

Notice that : Eg (Ge) < Eg (Si) < Eg (GaAs)


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Types of Semiconductors

Intrinsic

Extrinsic

Intrinsic Semiconductors This is the term given to near perfect semiconductors crystals with no impurities or

lattice defects.

At 0 Kelvin there are no free charge carriers, but as temp increases a few electron-

hole pairs (EHP) are generated due to valence electrons getting thermally excited tohave enough energy to jump over the bandgap into the conduction band.

Since electron-holes are always created in pairs, then

n = p = n i

where n and p are the electrons and holes concentration (per cm3), respectively

Recombination occurs when an electron in the conduction band makes a transition to

the valence band to recreate a complete covalent bond structure with the hole

At steady state, EHPs recombine at the same rate as they are generated

Generation and recombination of EHP are dependent on temperature


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Extrinsic Semiconductors

It is usually desirable to have greater number of available charge carriers thatwill not be subjected to recombination. The bond structures of pure

semiconductors may be manipulated in such a way that an excess of free

electrons or Holes may be generated in predetermined and controllable

manner. The process used to generate these excess charge carriers is calledDOPING. Any semiconductor that has been subjected to the doping process is

called an extrinsic semiconductor.

Doping is the process of adding specific impurit ies to a pure semiconductor

in such a way that the newly formed covalent bonding creates excess chargecarriers within the crystal lattice

Semiconductors with predominantly excess Electrons are called n-Type

semiconductors

Semiconductors with predominantly excess Holes are called p-Type

semiconductors

When impurities or lattice defects are introduced into an otherwise perfect crystal additional energy

levels are created, usually within the bandgap


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n-Type Semiconductor

An n-type material is created by introducing impurity element thathave 5 valence electrons (e.g. arsenic, antimony and phosphorus)into pure Si or Ge.

Diffused impurities with 5 valence electrons are called donor atoms


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p-Type Semiconductor

The p-type semiconductor is formed by doping pure Si or Ge with impurity atomshaving 3 valence electrons. Typically Boron, gallium, or indium is use as the dopant.

Diffused impurity with 3 valence electrons are called acceptor atoms

In n-type material, the electron is the majority charge carrier and holes are minority.

In p-type material, the holes are the majority charge carrier and electrons are minority


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A fundamental relationship between the electron and hole concentration in a semiconductor in

thermal equilibrium is given by:

where,

no is the thermal equilibrium concentration of free electrons,

po is the thermal equilibrium concentration of holes, and

ni is the intrinsic carrier concentration.

At room temperature (T = 300 K), each donor atom donates a free electron to the semiconductor.If the donor concentration Nd is much larger than the intrinsic concentration, we can approximate

therefore

Similarly, at room temperature, if each acceptor atom accepts a valence electron, creating a hole.If the acceptor concentration, N

a, is much larger than the intrinsic concentration, we can

approximate

making

2

ioo npn =

do Nn d

io

Nnp

2

=

ao Np

a

i

oN

nn

2

=


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Drift and Diffusion Currents

The two basic processes which cause electrons

and holes to move in a semiconductor are:

(a) drift, which is the movement caused by electric

fields; and

(b) diffusion, which is the flow caused by variations

in the concentration, that is, concentration gradients.Such gradients can be caused by a non-

homogeneous doping distribution, or by the injection

of a quantity of electrons or holes into a region.


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When a stedy electric field E is applied to asemiconductor sample, each electrons willexperience a forceqE from the field and will beaccelerated in the opposite direction of the field.This is called the drift velocity and willsuperimpose upon the usual random thermalmotion of the electrons.

Each Hole will also be similarly affected by thefield, but drift will occur along the direction of thefield.


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Drift velocities for electrons and holes are:

Ev nn = Ev pp =

where n is called the electron mobil ity and p is the

hole mobility, both with units of cm2

/ V-s.


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Drift Currents

When an electric field E is applied across a length of uniformly doped semiconductor,of cross sectional area, A, the electron current density Jn flowing in the sample can

be found by summing the product of the charge (-q) on each electron times the

electron velocity over all electrons per unit volume (n):

where In is the electron current.

A similar argument applies to holes:

The total drift current may now be written as the sum

=

====n

i

nnin

n EqnqnvqvAIJ

0

)(

EqpqpvJ ppp ==

EqpqnJ pn )( +=


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Conductivity and Resistivity

The quantity in parenthesis from the previous equation is known as the conductivity:

The electron and hole contribution to conduction is simply additive. Thecorresponding resistivity of the semiconductor is:

Because of the many orders of magnitude difference between the majority carriers in

extrinsic semiconductor, the resistivity reduces to

and

)( pn qpqn +=

)(

11

pn qpqn

+

==

)(

1

nqn=

)(

1

pqp=

for n-type for p-type

I t d ti t S i d t Th


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Diffusion Currents

As stated earlier, if there is a spatial variation of carrier concentration in thesemiconductor material, carriers will move from a region of high concentration to a

region of low concentration. This current component is called diffusion current. The

electron and hole diffusion current may be expressed as

where Jn and Jp are the electron and hole diffusion density in units of cm2/s, and Dn

and Dp are the electron and hole diffusivity.

The Current Density Equation:

When E is present in addition to carrier concentration gradients, both drift and

diffusion currents will flow

dxdnqDJ nn =

dxdpqDJ pp =

pncond

ppp

nnn

JJJ

dx

dpqDpEqJ

dxdnqDnEqJ

+=

=

+=

For large E field

The E terms must

Be replaced by field

Dependent carrier

velocity


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At room temperature (3000K), EG = 1.1 eV


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For Si, m = 2.5 for electrons

= 2.7 for holes

For Ge, m = 1.66 for electrons= 2.33 for holes


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dx

dpqDpEqJ

dx

dn

qDnEqJ

ppp

nnn

=

+=



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The Fermi-Dirac Distribution Function

A very important property of the density of electrons in a crystal lattice is theirdistribution among the allowed states at thermal equilibrium. Electrons have integer

spin that obey Paulis exclusion principle. The occupational probability of an energy

level E by an electron is given by the Fermi-Dirac distribution function

where Ef is the reference energy called the Fermi Level.

Note that when E = Ef , f(E) =

Throughout any semiconductor structure at thermal equilibrium, the Fermi

Level is always constant. This may be expressed as:

The Fermi Level is one of the principal quantities which is used to describe the

behavior of semiconductor materials and devices

kT

EE f

e

Ef )(1

1)( +

= T is temp in Kelvink is Boltzman constant

0=dx

dEf

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Lecture 1 Semiconductor Theory