Energy Bands in Semiconductors & Carrier Concentrations

Dr. Mohammad Aminul IslamAssistant Professor

Dept. of EEEInternational Islamic University Chittagong

Chapter 1

OutlinesoMetals, Semiconductor and Insulators

oAccording to the bonding energyoAccording to the energy bandgap

oEnergy bandgapsoDirect and indirect bandgap semiconductor

oColors in SemiconductoroAbsorption

oDirect and indirect absorption in semiconductoro Photoconductivity

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Bonding Forces & Energy Bands in Solids

• Isolated Atoms: conductor • Solid Materials: conduction depends on the bonding force

3rd Band2nd Band

1st Band

Core

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Bonding Forces in Solids

• Na (Z=11) [Ne]3s1

• Cl (Z=17) [Ne]3s1 3p5

Na+ Cl_

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Bonding Forces in Solids

e_

Na+

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3-1-1. Bonding Forces in Solids

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Bonding Forces in Solids

Si<100>

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Metals, Semiconductors & Insulators

• The difference bet-ween insulators and semiconductor mat-erials lies in the size of the band gap Eg, which is much small-er in semiconductors than in insulators.

Insulator Semiconductor

Filled

Filled

Empty

Empty

Eg

Eg

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Metals, Semiconductors & Insulators

Metal

Filled

Partially Filled

Overlap

In metals the bands either overlap or are only partially filled. Thus electrons and empty energy states

Metal

are intermixed with-in the bands so that electrons can move freely under the infl-uence of an electric field.M A Islam, EEE, IIUC

• energy gap or bandgap, is an energy range in a solid where no electron states can exist.

• A semiconductor is a material with a small but non-zero band gap that behaves as an insulator at absolute zero but allows thermal excitation of electrons into its conduction band at temperatures that are below its melting point.

• In contrast, a material with a large band gap is an insulator.

• In conductors, the valence and conduction bands may overlap, so they may not have a band gap.

Energy Band gap & Solid Materials

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Visual Appearance of Insulators, Metals, & Semiconductors

• A material’s appearance & color depend on the interaction between light with the electron configuration of the material.

NormallyHigh resistivity materials (Insulators) are Transparent

High conductivity materials (Metals) have a “Metallic

Luster” & are Opaque

Semiconductors can be opaque or transparentThis & their color depend on the material band gap

• For semiconductors the energy band diagram can explain the appearance of the material in terms of both luster & color.

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Group Material Symbol Band gap (eV) @ 302K

IV Diamond C 5.5IV Silicon Si 1.11IV Germanium Ge 0.67III–V Gallium(III) nitride GaN 3.4III–V Gallium(III) phosphide GaP 2.26III–V Gallium(III) arsenide GaAs 1.43

IV–V Silicon nitride Si3N4 5

IV–VI Lead(II) sulfide PbS 0.37

IV–VI Silicon dioxide SiO2 9

Copper(I) oxide Cu2O 2.1

List of band gaps of semiconductor materials.

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Semiconductor Materialso Element : Si, Geo IV compounds : SiC, SiGeo III-V compounds: AIP, AlAs, AlSb, GaN,GaP, GaAs,

GaSb, InP, InAs, InSbo II-VI: SnS, ZnSe, ZnTe, CdS, CdSe, CdTeo LED(GaN, GaP, GaAs), Three-elements(GaAsP,

InGaAsP), Fluorescent(II-VI, ZnS), Light detector(InSb, CdSe), PbTe, HgCdTe, Si, Ge)

II III IV V VI

BBoron

CCarbon

NNitrogen

OOxygen

AlAluminum

SiSilicon

PPhosphorus

SSulfur

ZnZinc

GaGalium

GeGermanium

AsArsenic

SeSelenium

CdCadmium

InIndium

SnTin

SbAntimony

TeTellurium M A Islam, EEE, IIUC

Direct & Indirect Semiconductors

In a direct band gap semiconductor, the top of the valence band and the bottom of the conduction band occur at the same value of momentum, as in the schematic below.

Direct Band Gap

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3-1-4. Direct & Indirect Semiconductors

Indirect Band GapIn an indirect band gap semiconductor, the maximum energy of the valence band occurs at a different value of momentum when comparing with the minimum in the conduction band.

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3-1-4. Direct & Indirect Semiconductors

Eg=hνEg Et

k k

EE

Direct IndirectExample 3-1

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Direct & Indirect SemiconductorsFor an indirect-band gap material; the minimum of the CB and maximum of the VB lie at different k-values.

When an e- and hole recombine in an indirect-band gap s/c, phonons must be involved to conserve momentum.

In indirect band gap semiconductors may have iso electronic impurity states or Defect state which are direct, and therefore the recombination from these states may also be radiative.

Direct band gap semiconductors are capable of photon emission, by radiative recombination,but indirect semiconductors have a low probability of radiative recombination.

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• Recall: Semiconductor Bandgaps Eg are usually

in the range: 0 < Eg < 3 eV(up to 6 eV if diamond is included)

• Also, at equilibrium, at temperature T = 0, the valence band is full & the

conduction band is empty.• Now, consider what happens if electromagnetic

radiation (“light”) is shined on the material.

• In the photon representation of this radiationIf hν Eg, some electrons can be promoted to the conduction band leaving some holes in the

valence band. M A Islam, EEE, IIUC

Colors of Semiconductors

I B G Y O R

EEvisvis= 1.8eV = 1.8eV 3.1eV 3.1eV

If the Photon Energy is Evis > Egap Photons will be absorbed

If the Photon Energy is Evis < Egap Photons will transmitted

If the Photon Energy is in the range of Egap those with higher energy than Egap will be absorbed.

We see the color of the light being transmitted.If all colors are transmitted the light is White

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Question Why is Silicon Black & Shiny?

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To Answer This:• We need to know that the energy gap of Si is:

Egap = 1.2eV • We also need to know that, for visible light, the

photon energy is in the range:

Evis ~ 1.8 – 3.1eVSo, for Silicon, Evis is larger than Egap

• So, all visible light will be absorbed & Silicon appears black

So, why is Si shiny?• The answer is somewhat subtle: Significant photon

absorption occurs in silicon, because there are a significant

number of electrons in the conduction band. These electrons are delocalized. They scatter photons. M A Islam, EEE, IIUC

Why is GaP Yellow?

• We need to know that the energy gap of GaP is:

Egap = 2.26 eV This is equivalent to a

Photon of Wavelength = 549 nm. • So photons with E = h > 2.26 eV (i.e. green, blue,

violet) are absorbed.• Also photons with E = h < 2.26eV (i.e. yellow,

orange, red) are transmitted.• Also, the sensitivity of the human eye is greater for yellow

than for red, so

GaP Appears Yellow/Orange.

To Answer This:

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Why is Glass Transparent?• Glass is an insulator (with a huge band gap). Its is difficult

for electrons to jump across a big energy gap: Egap >> 5eV

Egap >> E(visible light) ~ 2.7- 1.6eV• All colored photons are transmitted, with no absorption, hence the

light is transmitted & the material is transparent.• Define transmission & absorption by

Lambert’s Law: I = Ioexp(-x)Io = incident beam intensity, I = transmitted beam intensityx = distance of light penetration into material from a surface

total linear absorption coefficient (m-1) takes into account the loss of intensity from scattering centers & absorption centers. approaches zero for a pure insulator. M A Islam, EEE, IIUC

What happens during the photon absorption process?

Photons interact with the lattice

Photons interact with defects

Photons interact with

valence electrons

Photons interact with …..

AbsorptionAn Important Phenomena in the Description of

the Optical Properties of Semiconductors• Light (electromagnetic radiation) interacts with

the electronic structure of the material.

The Initial Interaction is Absorption• This occurs because valence electrons on the

surface of a material absorb the photon energy & move to higher-energy states.

• The degree of absorption depends, among many other things, on the number of valence electrons capable of receiving the photon energy. M A Islam, EEE, IIUC

• The photon-electron interaction process obviously depends strongly on the photon energy.

• Lower Energy Photons interact principally by ionization or excitation of the solid’s valence electrons.

• Low Energy Photons (< 10 eV) are in the infrared (IR), visible & ultraviolet (UV) in the EM spectrum.

• High Energy Photons (> 104 eV) are in the X-Ray & Gamma Ray region of the EM spectrum.

• The minimum photon energy to excite and/or ionize a solid’s valence electrons is called the

Absorption Edge orAbsorption Threshold.

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Valence Band – Conduction Band Absorption(Band to Band Absorption)

Conduction Band, EC

Valence Band, EV

Egaph = Ephoton

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Conduction Band, EC

Valence Band, EV

Egaph = Ephoton

This process obviously requires that the minimum energy of a photon to initiate an electron transition must satisfy

EC - EV = h = Egap

Valence Band – Conduction Band Absorption(Band to Band Absorption)

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Valence Band – Conduction Band Absorption(Band to Band Absorption)

Conduction Band, EC

Valence Band, EV

Egaph = Ephoton

This process obviously requires that the minimum energy of a photon to initiate an electron transition must satisfy

EC - EV = h = Egap

If h > Egap then obviously a transition can happen. Electrons are then excited to the

conduction band.

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After the Absorption Then What? 2 Primary Absorption Types

Direct Absorption & Indirect Absorption• All absorption processes must satisfy:

Conservation of Total EnergyConservation of Momentum or Wavevector

• The production of electron-hole pairs is very important for electronics devices especially photovoltaic & photodetector devices.

• The conduction electrons produced by the absorbed light can be converted into a current in these devices.

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Direct Band Gap Absorption

K (wave number)h

Conservation of Energyh = EC(min) - Ev (max) = Egap

Conservation of Momentum

Kvmax + qphoton = kc

EA Direct Vertical

Transition!

The Photon Momentum is Negligible

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Indirect Band Gap Absorption

E

K (wave number) h

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• If a semiconductor or insulator does not have many impurity levels in the band gap, photons with energies smaller than the band gap energy can’t be absorbed– There are no quantum states with energies in the band gap

• This explains why many insulators or wide band gap semiconductors are transparent to visible light, whereas narrow band semiconductors (Si, GaAs) are not

Another Viewpoint

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Some of the many applications– Emission:

light emitting diodes (LED) & Laser Diodes (LD)– Absorption: – Filtering: Sunglasses, ..

Si filters (transmission of infra red light with simultaneous blocking of visible light)

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• If there are many impurity levels the photons with energies smaller than the band gap energy can be absorbed, by exciting electrons or holes from these energy levels into the conduction or valence band, respectively– Example: Colored Diamonds

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Photoconductivity• Charge carriers (electrons or

holes or both) created in the corresponding bands by absorbed light can also participate in current flow, and thus should increase the current for a given applied voltage, i.e., the conductivity increases

• This effect is called Photoconductivity

• Want conductivity to be controlled by light. So want few carriers in dark → A semiconductor

• But want light to be absorbed, creating photoelectrons

• → Band gap of intrinsic photoconductors should be smaller than the energy of the photons that are absorbed

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