Prof.P. Ravindran, - folk.uio.nofolk.uio.no/ravi/cutn/cmp/semiconductor_intro.pdf · P.Ravindran,...

P.Ravindran, PHY075- Condensed Matter Physics, Spring 2013 16 July: Introduction to Semiconductor Physics

http://folk.uio.no/ravi/CMP2013

Prof.P. Ravindran, Department of Physics, Central University of Tamil

Nadu, India

Introduction to Semiconductor Physics

1


Review of Semiconductor Physics

Semiconductor fundamentals

Doping

PN junction

P.Ravindran, PHY075- Condensed Matter Physics, Spring 2013 16 July: Introduction to Semiconductor Physics3

The electric resistance of all substances is found to change more or less with a change

in temperature. Three types of changes are observed:

1) The resistance may increase with increasing temperature, which is true for all

pure metals and most alloys.

2) The resistance may decrease with increase of temperature, which is true for

semiconductors.

3) The resistance may be independent of temperature, which is approximately true for

some special alloys, such as manganese (Cu 0.84; Ni 0.12; Mn 0.04)

Temperature dependence of Resistivity

P.Ravindran, PHY075- Condensed Matter Physics, Spring 2013 16 July: Introduction to Semiconductor Physics 4

Specific Resistivity of Metals as a Function of Temperature

P.Ravindran, PHY075- Condensed Matter Physics, Spring 2013 16 July: Introduction to Semiconductor Physics 5

Residual Resistivity and Defects

Shown here are measured curves of the low temperature

resistivity of Na with different defect concentrations

The resistivity is constant for very small temperatures.

In the "bend" it shows T 5 characteristics.

For most of the temperature range it is proportional to T.

Defects clearly do increase the residual resistance (the upper two curves are for Na with defects, the lower one for rather

perfect Na); the effect can be much large in other metals or for larger defect densities.


What Is a Semiconductor?

•Many materials, such as most metals, allow electrical current to flow

through them

•These are known as conductors

•Materials that do not allow electrical current to flow through them are

called insulators

•Pure silicon, the base material of most transistors, is considered a

semiconductor because its conductivity can be modulated by the

introduction of impurities


Semiconductors

A material whose properties are such that it is not quite a conductor, not quite an insulator

Some common semiconductors– elemental

Si - Silicon (most common)

Ge - Germanium

– compound GaAs - Gallium arsenide

GaP - Gallium phosphide

AlAs - Aluminum arsenide

AlP - Aluminum phosphide

InP - Indium Phosphide


Crystalline Solids

In a crystalline solid, the periodic arrangement of atoms is repeated over the entire crystal

Silicon crystal has a diamond lattice


Crystalline Nature of Silicon

Silicon as utilized in integrated circuits is crystalline in nature

As with all crystalline material, silicon consists of a repeating basic unit structure called a unit cell

For silicon, the unit cell consists of an atom surrounded by four equidistant nearest neighbors which lie at the corners of the tetrahedron


What’s so special about Silicon?

Cheap and abundant

Amazing mechanical, chemical and electronic properties

The material is very well-known to mankind

SiO2: sand, glass

Si is column IV of

the periodic table

Similar to the

carbon (C) and the

germanium (Ge)

Has 3s² and 3p²

valence electrons


Nature of Intrinsic Silicon

Silicon that is free of doping impurities is called intrinsic

Silicon has a valence of 4 and forms covalent bonds with four other neighboring silicon atoms


Semiconductor Crystalline Structure

Semiconductors have a regular crystalline structure

– for monocrystal, extends through entire structure

– for polycrystal, structure is interrupted at irregular boundaries

Monocrystal has uniform 3-dimensional structure

Atoms occupy fixed positions relative to one another, butare in constant vibration about equilibrium


Semiconductor Crystalline Structure

Silicon atoms have 4 electrons (valence) in outer shell

– inner electrons (core) are very closely bound to atom

These electrons are shared with neighbor atoms on both sides to “fill” the shell

– resulting structure is very stable

– electrons are fairly tightly bound no “loose” electrons

– at room temperature, if battery applied, very little electric current flows


Conduction in Crystal Lattices

Semiconductors (Si and Ge) have 4 electrons in their outer shell– 2 in the s subshell

– 2 in the p subshell

As the distance between atoms decreases the discrete subshells spread out into bands

As the distance decreases further, the bands overlap and then separate– the subshell model doesn’t hold anymore, and the electrons can be

thought of as being part of the crystal, not part of the atom

– 4 possible electrons in the lower band (valence band)

– 4 possible electrons in the upper band (conduction band)


Energy Bands in Semiconductors

The space

between the

bands is the

energy gap, or

forbidden band


Insulators, Semiconductors, and Metals

This separation of the valence and conduction bands determines the electrical properties of the material

Insulators have a large energy gap– electrons can’t jump from valence to conduction bands– no current flows

Conductors (metals) have a very small (or nonexistent) energy gap (overlapping CB and VB)– electrons easily jump to conduction bands due to thermal

excitation– current flows easily

Semiconductors have a moderate energy gap– only a few electrons can jump to the conduction band

leaving “holes”– only a little current can flow


Insulators, Semiconductors, and Metals

(continued)

Conduction Band

Valence Band

Conductor Semiconductor Insulator


Hole - Electron Pairs

Sometimes thermal energy is enough to cause an electron to jump from the valence band to the conduction band

– produces a hole - electron pair

Electrons also “fall” back out of the conduction band into the valence band, combining with a hole

pair elimination

hole electron

pair creation


Improving Conduction by Doping

To make semiconductors better conductors, add impurities (dopants) to contribute extra electrons or extra holes– elements with 5 outer electrons contribute an extra electron to

the lattice (donor dopant)

– elements with 3 outer electrons accept an electron from the

silicon (acceptor dopant)


Improving Conduction by Doping (cont.)

Phosphorus and arsenic are donor dopants– if phosphorus is

introduced into the silicon lattice, there is an extra electron “free” to move around and contribute to electric current very loosely bound to

atom and can easily jump to conduction band

– produces n type silicon sometimes use +

symbol to indicate heavier doping, so n+ silicon

– phosphorus becomes positive ion after giving up electron


Improving Conduction by Doping (cont.)

Boron has 3 electrons in its outer shell, so it contributes a hole if it displaces a silicon atom

– boron is an acceptor dopant

– yields p type silicon

– boron becomes negative ion after accepting an electron


Epitaxial Growth of

Silicon

Epitaxy grows silicon on top of existing silicon

– uses chemical vapor deposition

– new silicon has same crystal structure as original

Silicon is placed in chamber at high temperature

– 1200 o C (2150 o F) Appropriate gases are fed into

the chamber

– other gases add impurities to the mix

Can grow n type, then switch to p type very quickly


Diffusion of Dopants

It is also possible to introduce dopants into silicon by heating them so they diffuse into the silicon

– no new silicon is added

– high heat causes diffusion

Can be done with constant concentration in atmosphere

– close to straight line concentration gradient

Or with constant number of atoms per unit area

– predeposition– bell-shaped gradient

Diffusion causes spreading of doped areas

top

side


Diffusion of Dopants (continued)

Concentration of dopant in

surrounding atmosphere kept

constant per unit volume

Dopant deposited on

surface - constant

amount per unit area


Ion Implantation of Dopants

One way to reduce the spreading found with diffusion is to use ion implantation– also gives better uniformity of dopant– yields faster devices– lower temperature process

Ions are accelerated from 5 KeV to 10 MeV and directed at silicon– higher energy gives greater depth penetration– total dose is measured by flux

number of ions per cm2

typically 1012 per cm2 - 1016 per cm2

Flux is over entire surface of silicon– use masks to cover areas where implantation is not wanted

Heat afterward to work into crystal lattice


Hole and Electron Concentrations

To produce reasonable levels of conduction doesn’t require much doping

– silicon has about 5 x 1022 atoms/cm3

– typical dopant levels are about 1015 atoms/cm3

In undoped (intrinsic) silicon, the number of holes and number of free electrons is equal, and their product equals a constant

– actually, ni increases with increasing temperature

This equation holds true for doped silicon as well, so increasing the number of free electrons decreases the number of holes

np = ni2


INTRINSIC (PURE) SILICON

At 0 Kelvin Silicon density is

5*10²³ particles/cm³

Silicon has 4 valence electrons,

it covalently bonds with four

adjacent atoms in the crystal

lattice

Higher temperatures create free

charge carriers.

A “hole” is created in the

absence of an electron.

At 23C there are 10¹º

particles/cm³ of free carriers


DOPING

The N in N-type stands for negative.

A column V ion is inserted.

The extra valence electron is free to move about the

lattice

There are two types of doping

N-type and P-type.

The P in P-type stands for positive.

A column III ion is inserted.

Electrons from the surrounding Silicon move to fill the

“hole.”


Energy-band Diagram

A very important concept in the study of semiconductors is the energy-

band diagram

It is used to represent the range of energy a valence electron can have

For semiconductors the electrons can have any one value of a continuous

range of energy levels while they occupy the valence shell of the atom

– That band of energy levels is called the valence band

Within the same valence shell, but at a slightly higher energy level, is yet

another band of continuously variable, allowed energy levels

– This is the conduction band


Band Gap

Between the valence and the conduction band is a range of energy levels where there are no allowed states for an electron

This is the band gap

In silicon at room temperature [in electron volts]:

Electron volt is an atomic measurement unit, 1 eV energy is necessary to decrease of the potential of the electron with 1 V.

EGE eVG 11.

joule101.6021eV 19


Impurities

Silicon crystal in pure form is

good insulator - all electrons are

bonded to silicon atom

Replacement of Si atoms can

alter electrical properties of

semiconductor

Group number - indicates

number of electrons in valence

level (Si - Group IV)


Impurities

Replace Si atom in crystal with Group V atom– substitution of 5 electrons for 4 electrons in outer shell– extra electron not needed for crystal bonding structure

can move to other areas of semiconductor current flows more easily - resistivity decreases many extra electrons --> “donor” or n-type material

Replace Si atom with Group III atom– substitution of 3 electrons for 4 electrons – extra electron now needed for crystal bonding structure

“hole” created (missing electron) hole can move to other areas of semiconductor if

electrons continually fill holes again, current flows more easily - resistivity

decreases electrons needed --> “acceptor” or p-type material


Counter Doping

Insert more than one

type of Ion

The extra electron and

the extra hole cancel out


A Little Math

n= number of free electrons

p=number of holes

ni=number of electrons in intrinsic silicon=10¹º/cm³

pi-number of holes in intrinsic silicon= 10¹º/cm³

Mobile negative charge = -1.6*10-19 Coulombs

Mobile positive charge = 1.6*10-19 Coulombs

At thermal equilibrium (no applied voltage) n*p=(ni)2 (room temperature

approximation)

The substrate is called n-type when it has more than 10¹º free electrons

(similar for p-type)


P-N Junction

Also known as a diode

One of the basics of semiconductor technology -

Created by placing n-type and p-type material in close contact

Diffusion - mobile charges (holes) in p-type combine with mobile charges (electrons) in n-type


P-N Junction

Region of charges left behind (dopants fixed in crystal lattice)– Group III in p-type (one less proton than Si-

negative charge)– Group IV in n-type (one more proton than Si -

positive charge)

Region is totally depleted of mobile charges - “depletion region”– Electric field forms due to fixed charges in the

depletion region– Depletion region has high resistance due to

lack of mobile charges


THE P-N JUNCTION


The Junction

The “potential” or voltage across

the silicon changes in the depletion

region and goes from + in the n

region to – in the p region


Biasing the P-N Diode

Forward Bias

Applies - voltage

to the n region

and + voltage to

the p region

CURRENT!

Reverse Bias

Applies + voltage to

n region and –

voltage to p region

NO CURRENT

THINK OF THE DIODE AS A SWITCH


P-N Junction – Reverse Bias

positive voltage placed on n-type material electrons in n-type move closer to positive terminal, holes

in p-type move closer to negative terminal width of depletion region increases allowed current is essentially zero (small “drift” current)


P-N Junction – Forward Bias

positive voltage placed on p-type material holes in p-type move away from positive terminal,

electrons in n-type move further from negative terminal depletion region becomes smaller - resistance of device

decreases voltage increased until critical voltage is reached, depletion

region disappears, current can flow freely


P-N Junction - V-I characteristics

Voltage-Current relationship for a p-n junction (diode)


Current-Voltage Characteristics

THE IDEAL DIODE

Positive voltage yields

finite current

Negative voltage yields zero

currentREAL DIODE


The Ideal Diode Equation

I IqV

kT

where

I diode current with reverse bias

q coulomb the electronic ch e

keV

KBoltzmann s cons t

0

0

19

5

1

1602 10

8 62 10

exp ,

. , arg

. , ' tan

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