Energy Band Diagram

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ELEC 3908, Physical Devices Lecture 3

Energy Band Diagramsand Doping


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Lecture Outline

Continue the study of semiconductor devices by looking atthe material used to make most devices

The energy band diagram is a representation of carrier

energy in a semiconducting material and will be related to

an orbital bonding representation

Devices require materials with tailored characteristics,

obtained through doping, the controlled introduction of

impurities

Will discuss electronsand holes, as well as intrinsic, n-type

andp-typematerials Later lectures will apply these concepts to diode, bipolar

junction transistor and FET


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Atomic Electron Energy Levels

A free electron can assume any

energy level (continuous)

Quantum mechanics predicts a

boundelectron can only assumediscrete energy levels

This is a result of the interaction

between the electron and the nuclearproton(s)


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Crystal Energy Bands

Crystal is composed of a large

number of atoms (!1022cm-3 for

silicon)

Interaction between the electrons of

each atom and the protons of other

atoms

Result is a perturbation of each

electrons discrete energy level to

form continua at the previous energylevels


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Covalent Bonding

Silicon crystal formed by covalent

bonds

Covalent bonds share electrons

between atoms in lattice so each

thinks its orbitals are full

Most important bands are therefore

band which would be filled at 0 K -

valenceband

next band above in energy -conductionband


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Simplified Energy Band Diagram

Movement within a band is notdifficult due to continuum of energy

levels

Movement between bands requires

acquisition of difference in energy

between bands (in pure crystal, cant

exist in between)

Main features of interest for first

order device analysis are

top of valence band (Ev) bottom of conduction band (Ec)

difference in energy betweenEcandEv,

energy gapEg


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Orbital Bonding Model

Represent valence and conduction bands by separate siliconlattice structures

The two diagrams coexist in space -the same set of silicon

atoms is represented in each diagram


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Electron Transitions -Energy Band Diagram

At room temperature, very

few electrons can gain energy

Egto move to the conduction

band ( !1010cm-3at 300K =

23C)

In pure silicon at 300K, most

valence band orbitals ( !1022

cm-3) are full, most

conduction band orbitals areempty


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Electron Transitions Orbital Bonding


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Electrons and Holes

Conduction of current occurs through electron movement

Two mechanisms of electron movement are possible:

movement within the nearly empty conduction band orbital

structure

movement within the nearly full valence band orbital structure Conduction in the valence band structure is more conveniently

modeled as the movement of an empty orbital

Model this empty valence band orbital as a positively charged

pseudo-particle called a hole

Density of electrons in conduction band is n(cm-3)

Density of holes in valence band isp(cm-3)


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Electron and Hole Conduction

Electron movement in

conduction band can be

modeled directly

Movement of electrons in

valence band modeled as

movement (in opposite

direction) of positively

charged hole

Electric Field


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Intrinsic Material

Semiconducting material which has not had any impuritiesadded is called intrinsic

In an intrinsic material, the number of electrons and holes must

be equal because they are generated in pairs

Call the density of electrons and holes in intrinsic material theintrinsic density ni(for Si@300K, ni!1.45x10

10cm-3)

Therefore, for intrinsic material


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Extrinsic Material

Intentional addition of impurities during manufacture or in

specialized fabrication steps is termed doping

Doped material is called extrinsic

Ability to change the electrical characteristics of the materialthrough selective introduction of impurities is the basic reason

why semiconductor devices are possible

Later lectures will outline the processes used to introduce

impurities in a controlled and repeatable way


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Mass-Action Law

For intrinsic material, n=p= ni, therefore

This turns out to be a general relationship called the

mass-action law, which can be used for doped material

in equilibrium


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Group V Impurity Atom

An atom from group V of the periodic table has one morenuclear proton and valence electron than silicon

If the atom replaces a silicon atom in the lattice, the extra

electron can move into the conduction band (ionization)

A group V atom is a donorsince it donates an electron to thesilicon lattice

Density of donor dopant atoms given symbolND(cm-3)


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Donor Ionization - Energy Band Diagram


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Donor Ionization Orbital Bonding Model


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Donor Doping -Electron and Hole Densities


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Example 3.1: Arsenic Doping


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Example 3.1: Solution


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Group III Impurity Atom

An atom from group III of the periodic table has one less nuclearproton and valence electron than silicon

If the atom replaces a silicon atom in the lattice, the empty

valence orbital can be filled by an electron (ionization)

A group III atom is an acceptorsince it accepts an electron fromthe silicon lattice

Density of acceptor dopant atoms given symbolNA(cm-3)


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Acceptor Ionization - Energy Band Diagram


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Acceptor Ionization Orbital Bonding Model


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Acceptor Doping - Electron and Hole Densities


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Example 3.2: Gallium Doping


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Compensated Doping


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Example 3.3: Compensated Doping


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Lecture Summary

Energy Band Diagram

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