Semiconductors are a special class of elements having a conductivity between that of a good conductor and that of an insulator.

They are fall into two classes : single crystal and compound

Single crystal e.g Ge and Si Compound e.g GaAs , CdS, GaN and

GaAsPGe-germanium; Si-silicon; Ga-gallium ;As –arsenide; Cd-cadmium; S-sulfide; N-nitride; P-phosphide

Semiconductor Material

Group → 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

↓ Period

11H

2He

23Li

4Be

5B

6C

7N

8O

9F

10Ne

311Na

12Mg

13Al

14Si

15P

16S

17Cl

18Ar

419K

20Ca

21Sc

22Ti

23V

24Cr

25Mn

26Fe

27Co

28Ni

29Cu

30Zn

31Ga

32Ge

33As

34Se

35Br

36Kr

537Rb

38Sr

39Y

40Zr

41Nb

42Mo

43Tc

44Ru

45Rh

46Pd

47Ag

48Cd

49In

50Sn

51Sb

52Te

53I

54Xe

655Cs

56Ba

* 72Hf

73Ta

74W

75Re

76Os

77Ir

78Pt

79Au

80Hg

81Tl

82Pb

83Bi

84Po

85At

86Rn

787Fr

88Ra

** 104Rf

105Db

106Sg

107Bh

108Hs

109Mt

110Ds

111Rg

112Uub

113Uut

114Uuq

115Uup

116Uuh

117Uus

118Uuo

* Lanthanides57La

58Ce

59Pr

60Nd

61Pm

62Sm

63Eu

64Gd

65Tb

66Dy

67Ho

68Er

69Tm

70Yb

71Lu

** Actinides89Ac

90Th

91Pa

92U

93Np

94Pu

95Am

96Cm

97Bk

98Cf

99Es

100Fm

101Md

102No

103Lr

Historical Diode , in 1939 was using Ge Transistor, in 1947 was using Ge In1954 Si was used in Transistor because Si is

less temperature sensitive and abundantly available.

High speed transistor was using GaAs in 1970 (which is 5 times faster compared to Si)

Si, Ge and GaAs are the semiconductor of choice

Atomic structure

+

Valence shell (4 valence electrons)

Valenceelectron

Nucleus

orbitingelectrons

Silicon

shells

+

Valence shell (4 valence electrons)

Valenceelectron

orbitingelectrons

Germanium

14 orbiting electrons (Tetravalent)

32 orbiting electrons (tetravalent)

Atomic structure

Nucleus

shells

+

Valence shell (3 valence electrons)

Valenceelectron

orbitingelectrons

Gallium

Nucleus

shells

+

Valence shell (5 valence electrons)

Valenceelectron

orbitingelectrons

Arsenic

31 orbiting electrons (trivalent)

33 orbiting electrons (pentavalent)

ENERGY LEVELS Each and every isolated electron has

a specific energy level associated with shell and orbiting electron.

The farther an electron from the nucleus, the higher is the energy state.

Electron left its parent atom has a higher energy state than any electron in the atomic structure.

Band Theory

Analogy to atoms–From chemistry, we are familiar with the idea of “electron clouds” orbiting the nucleus. –The energy of the different clouds, or levels, is discrete. Adding energy can cause an electron to “jump” into a higher level. In the same way, an electron can lose energy and emit a specific wavelength of light when falling to a lower energy level. (Atomic spectra)–Pauli Exclusion Principle: no two electrons can occupy the same exact state at the same time. This is why electrons fill the energy levels in the way they do.–Valence electrons are the electrons bound farthest from the nucleus

Covalent bonding

This bonding of atoms, strengthened by the sharing of electrons, is called covalent bonding

Covalent bonding of Si crystalCovalent bonding of GaAs crystal

Exercise 1

Name the materials that suitable for electronic devices

What are the advantages and disadvantages of each materials?

What is a covalent bonding? Describe it.

Free state Energy from external natural cause the

valence electrons to absorb sufficient kinetic energy and break the covalent bond. This is assume to be free state.

Electron that has separated from the fixed lattice structure is called free carriers.

At room temperature, approximately 1.5X 1010 free carriers in 1 cm3 of intrinsic silicon material

*intrinsic means material has been refined to a very low level of impurities.

Table: Intrinsic carriers

Semiconductor Intrinsic carriers/cm3

GaAs 1.7 X 106

Si 1.5 X 1010

Ge 2.5 X 1013

Relative mobility n

Relative mobility is the ability of free carriers to move throughout the material.

Semiconductor n (cm2/V-s)

Si 1500

Ge 3900

GaAs 8500

Effect on temperature

Conductor – increase resistance with increase in heat ( number of carrier do not increase)- is said to have a positive temperature coefficient.

Semiconductor- increase conductivity with increase in heat ( number of carrier increase)- is said to have a negative temperature coefficient.

Band Theory

What is a crystalline solid? –A volume of atoms covalently bonded in a periodic structure with well defined symmetries. –Example: Silicon•Face-Centered Cubic (FCC) structure•Group-IV elements (4 valence electrons)

Where are the electrons?–Covalent bonds share electrons. The e-are delocalized, they can move around the crystal, orbit any atom, as long as there is an open state (cannot violate Pauli Exclusion)–This forms discrete energy bands. Solving Schroedinger’s Equation in the specific periodic structure reveals these bands.

In an atom, electrons orbit in their shell, at a given energy.

•In a crystal, many electrons occupy a small energy band. There is a width to the energy band, which is why Pauli Exclusion is not violated.

•Within the band, electrons can move easily if there are available states, because the difference in energy is tiny.

•Between bands, electrons must get energy from another source, because the band gap can be significant.

Specifics of Crystals

Fermi Energy

The highest energy an electron reached if you were to fill the solid with the intrinsic number of electrons at absolute zero. (No added thermal energy)•Meaningful! There is a sea of electrons sitting beneath this energy.–If you bring two solids together with different Fermi energies, the electrons will move around to reach an equilibrium. (Foreshadowing: PN junction)–If you try to put a lower energy electron into a solid (at absolute zero) with a higher Fermi energy, it won’t fit. It cannot be done due to Pauli Exclusion.•If the highest energy electron exactly fills a band, the Fermi Energy is near the center of the bands.

The level of a single quantum number n and the energies are given as

22

22

2n

mL

hEn

Fermi Energy

22

22

2/2

NmL

hE f

Fermi energy for N particles and the spin is half , thus

h=plank’s constant; n =quantum no. , m mass ;L =side length

Fermi level in three dimension

3/13

N

n f

3/222 3

2

V

N

m

hE f

3/2

2

222

2

22 3

22

N

mL

hn

mL

hE ff

3

3

4

8

12 fnN

2

2

22

2n

mL

hEn

Where is a vector quantum staten

Number of fermions is given by

Therefore

Then the Fermi energy is given by

By replacing L2 with V2/3

V=volume

Typical Fermi Energy of Nucleus

3/1151025.1 AmR

MeV30eV1030

1

1063

26

3/2

3

4322

mm

hE

pf

344

3102.1

3

4 m

R

An

A is a nucleons (proton and neutron)

Number density of nucleons in nucleus is

Fermi Energy of a Nucleus

Beyond 0 K: Fermi-Dirac Statistics

•Fermi Energy: The energy state whose probability of being occupied is exactly 1/2 .•Electrons obey Fermi-Dirac-statistics, which describe the probability of an electron being present in an allowed energy state.•Note that if there are no states at a given energy (i.e., in the band gap) there will be no electrons, even if there is finite probability.

kT

EEF

e

Ef

1

1Fermi function

k=Boltzmann’s constant, T=temp, E =energy , Ef=Fermi energy

Different Types of Solids

Fermi level falls between bands, with a large band gap. SiO2: 9 eV.

>5eV

Fermi level falls between bands, with a small band gap.Si: 1.11 eV, Ge:0.67 eV, GaAs: 1.43

Fermi level falls inside the energy band. Easy for electrons to move around

Fermi level

Transport in Semiconductors

Electrons that get excited into the conduction band carry current.•The space left behind in the valence band is called a hole.•Holes also conduct current. In reality, it’s the movement of all the other electrons. The hole allows this motion. (Bubbles)•Holes can easily travel “up” in energy.•Holes have positive charge.•Current flows in the same direction as the holes move.•Holes have different mass (effective mass) and mobility compared to electrons.

Intrinsic Semiconductor

Fermi Level: All solids are characterized by an energy that describes the highest energy electron at 0K, the level which has1/2 probability of being occupied at finite temperature.•Semiconductors: A solid with its Fermi level exactly between bands, with a band gap small enough to be overcome at room temperature.•Both electrons and holes carry current.

Silicon bond model: electrons and holes

Si is in Column IV of periodic table:

Electronic structure of Si atom:• 10 core electrons (tightly bound)• 4 valence electrons (loosely bound, responsible for mostchemical properties)Other semiconductors:• Ge, C (diamond form), SiGe• GaAs, InP, InGaAs, InGaAsP, ZnSe, CdTe(on average, 4 valence electrons per atom)

Silicon crystal structure

• Silicon is a crystalline material:– long range atomic arrangement• Diamond lattice:– atoms tetrahedrally bonded by sharing valence electrons(covalent bonding)• Each atom shares 8 electrons:– low energy and stable situation• Si atomic density: 5 × 1022 cm−3

Controlling the properties of aSemiconductor

Silicon: 4 valence electrons. Each Si atom bonds to four

others. Doping

•Replace some Si atoms with atoms that do not have four valence electrons. •These atoms will have an extra electron (group IV), or an extra hole (group III).•Doping increases the number of carriers and changes the Fermi level.

Extrinsic materials

A semiconductor material that has been subjected to the doping process is called an extrinsic material.

Type of materials n-type p-type

Phosphorus Doping (n-type)

Phosphorus has 5 valence electrons. •P atoms will sit in the location of a Si atom in the lattice, to avoid breaking symmetry, but each will have an extra electron that does not bond in the same way.•These electrons form their own band. Exactly where depends on the amounts of the two materials.•This new band is located closer to the conduction band, because these extra electrons are easier to excite (and can move around more easily)

Eg. Of n-type material doping

Doping with Sb

Sb - antimony

One electron loosely bound and freely to move in the crystal structure. The atoms (in this case is antimony (Sb)) with five valence electrons are called the donor atoms. Similarly with Phosphorus (P) which also a donor.

Boron Doping (p-type)

Boron has 3 valence electrons.•B will sit at a lattice site, but the adjacent Si atoms lack an electron to fill its shell. This creates a hole.•These holes form their own energy band.•This band is located closer to the valence band, because these extra holes are easy to “excite down” into the valence band.

Eg of p-type material

Boron (B)

•In this case, an insufficient number of electrons to complete the covalent bonds.•The impurities with three valence electrons are called acceptor atoms. E.g of materials are Gallium (Ga), Indium (In)•Void is called hole

Doping

• Doping involves in adding dopant atoms to an intrinsic semiconductor.

• n-type materials: Doping Si with a Group V element, providing extra electrons (n for negative) and moving the Fermi level up.

• p-type materials: Doping Si with a Group III element, providing extra holes (p for positive) and moving the Fermi level down.

Dopant

Group V (n-type) –usually antimony(Sb), arsenic(A), phosphorus(P)

Group III (p-type)-usually Boron(B) , Gallium (Ga) and Indium (In)

Electron versus hole flow

•The valence electron acquires sufficient kinetic energy to break its covalent bond and fills the void created by hole•When the electron move to fill the hole therefore a transfer of holes to the left and electrons to the right •This flow is known as conventional flow.

Majority and Minority Carriers

•N-type material, the electron is called majority carrier and hole the minority carrier•P-type material, the hole is called majority carrier and electron the minority carrier.

Equilibrium Concentrations: electrons

statesofdensityeffective*2

22/3

2

h

kTmN nC

no=equilibrium electron carrier concentration

N(E)=density of states

kTEE

CkTEEC

CCE

oFC

FCeN

e

NEfNdEENEfn

C

/

/1

f(E) =fermi function k=Boltzmann’s const.

Equilibrium Concentrations: holes

statesofdensityeffective*2

2

2/3

2

h

kTmN p

po=equilibrium hole carrier concentration

N(E)=density of states

kTEE

kTEEC

E

oF

FeN

e

NEfNdEENEfp /

/111

f(E) =fermi function k=Boltzmann’s const.

Intrinsic Semiconductors

• In intrinsic semiconductors (no doping) the electron and hole concentrations are equal because carriers are created in pairs

kTEEi

kTEE

CiiFC eNpeNn

//

kTEEkTEE

CooFFC eNeNpn

//

kTEEio

Fienp/

kTEE

ioiFenn/

2//

iiikTE

C

kTEE

C npneNNeNN gC

•This allows us to write

–As the Fermi level moves closer to the conduction [valence] band, the n0[p0] increases exponentially

ni=no. of electrons (intrinsic) pi= no. of holes (intrinsic)

Temperature Dependence of Carrier Concentrations

310 /105.1 cmni

•The intrinsic concentration depends exponentially on temperature. The T3dependence is negligible.•Ionization: only a few donors [acceptors] are ionized. •Extrinsic: All donors [acceptors] are ionized•Intrinsic: As the temperature increases past the point where it is high enough to excite carriers across the full band gap, intrinsic carriers eventually contribute more.•At room temp (300K), the intrinsic carrier concentration of silicon is:

kTEEkTEpno

iFg eemmh

kTn

/2/4/32/3

2**

22

Moving Carriers (i.e., current)

There are two mechanisms by which mobile carriers move in semiconductors –resulting in current flow–Drift•Carrier movement is induced by a force of some type–Diffusion•Carriers move (diffuse) from a place of higher concentration to a place of lower concentration

Drude Model of Conductivity

The current is the charge*number of electrons*area*velocity in a unit of time. For j = current density, divide by the area. The drift velocity (vd) is a function of charge mobility (μn) and electric field (E).•At equilibrium, there is no net motion of charge, vavg= 0.•With an applied electric field, there is a net drift of electrons [holes] against [with] the electric field resulting in an average velocity.•This model allows us to apply Newton’s equations, but with an effective mass. The effective mass takes the interactions with the rest of the solid into account.

•Electrons are assumed to move in a direct path, free of interactions with the lattice or other electrons, until it collides.•This collision abruptly alters its velocity and momentum.•The probability of a collision occurring in time dtis simply dt/, whereis the mean free time is the average amount of time it takes for an electron to collide. nga qnqnJ

DrudeModel

ato maqEF m

qEa

Em

qt ga

*

EpnqJ pn

Em

nqEJ

*

2

qn

*m

qEga

*

2

m

nq

•Consider an electron just after a collision. The velocity it acquires before the next collision will be acceleration*time

•We want the average velocity of all the electrons, which can be obtained by simply averaging the time, which we already know is •We can also write this in terms of mobility:

•Taking both holes and electrons into account, we end up with the following formula for current density due to drift.

Hall Effect

BqF

qn

BJE zxy

Moving electrons experience a force due to a perpendicular B field

yresistivit

qn

1

An electric field develops in response to this force.•The sign of this field perpendicular to the flow of current determines the carrier type. •Density and mobility can also be calculated.

Diffusion

•Diffusion results in a net flux of particles from the region of higher concentration to the region of lower concentration–This flux leads to current (movement of charged particles)–Magnitude of current depends on the gradient of concentration

dx

xdnqDxJ nn

)()(diffusion,

q

kTDD

p

p

n

n

–Dnis the diffusivity coefficient

•Diffusivity is related to mobility by Einstein’s relationship

–Typical values for Si at room temp•Dn= 34 cm2/s and Dp= 13 cm2/s