lecture 5 energy bands and charge carriers

Energy bands and charge carriersin semiconductors

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Bonding Forces & Energy Bands in Solids In Isolated Atoms In Solid Materials

3rd Band2nd Band

1st Band

Core

3

Bonding Forces in Solids

Na (Z=11) [Ne]3s1

Cl (Z=17) [Ne]3s1 3p5

Na+ Cl_

4


e_

Na+

5


6


Si<100>

7

Energy Bands

Pauli Exclusion Principle

C (Z=6) 1s2 2s2 2p2

2 states for 1s level

2 states for 2s level

6 states for 2p level

For N atoms, there will be 2N, 2N, and 6N states of type 1s, 2s, and 2p, respectively.

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3-1-2. Energy Bands

Atomic separation

Diamond lattice

spacing

En

erg

y

1s

2s

2p

Valence band

Conduction band

2p

2s

2s-2p

4N States

4N States

Eg

1s

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Metals, Semiconductors & Insulators

For electrons to experience acceleration in an applied electric field, they must be able to move into new energy states. This implies there must be empty states (allowed energy states which are not already occupied by electrons) available to the electrons.

The diamond structure is such that the valence band is completely filled with electrons at 0ºK and the conduction band is empty. There can be no charge transport within the valence band, since no empty states are available into which electrons can move.

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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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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.

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3-2-3. Intrinsic Material

A perfect semiconductor crystal with

no impurities or lattice defects is

called an Intrinsic semiconductor.

In such material there are no charge

carriers at 0ºK, since the valence

band is filled with electrons and the

conduction band is empty.

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3-2-3. Intrinsic Material

SiEgh+

e-

n=p=ni

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3-2-3. Intrinsic Material If we denote the generation rate of EHPs

as and the recombination rate

as equilibrium requires that:

)(Tgi

)( 3scmEHPri

ii gr Each of these rates is temperature

depe-ndent. For example,

increases when the temperature is

raised.

)( 3scmEHPgi

iirri gnpnr 200

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3-2-4. Extrinsic Material

In addition to the intrinsic carriers generated thermally, it is possible to create carriers in semiconductors by purposely introducing impurities into the crystal. This process, called doping, is the most common technique for varying the conductivity of semiconductors.

When a crystal is doped such that the equilibrium carrier concentrations n0 and p0

are different from the intrinsic carrier concentration ni , the material is said to be

extrinsic.

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0ºK3ºK2ºK4ºK5ºK1ºK6ºK7ºK8ºK9ºK10ºK11ºK12ºK13ºK14ºK50ºK15ºK16ºK17ºK18ºK19ºK20ºK

Ec

Ev

Ed

Donor

V

P

As

Sb

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0ºK3ºK2ºK4ºK5ºK1ºK6ºK7ºK8ºK9ºK10ºK11ºK12ºK13ºK14ºK50ºK15ºK16ºK17ºK18ºK19ºK20ºK

Ec

Ev

Ea

Acceptor

ш

B

Al

Ga

In

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h+

Al

e- Sb

Si

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We can calculate the binding energy by using the Bohr model results, consider-ing the loosely bound electron as ranging about the tightly bound “core” electrons in a hydrogen-like orbit.

rKnhK

mqE 022

4

4, 1;2

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Example 3-3: Calculate the approximate donor binding energy for Ge(εr=16, mn

*=0.12m0).

21


eVJ

h

qmE

r

n

0064.01002.1

)1063.6()161085.8(8

)106.1)(1011.9(12.0

)(8

21

234212

41931

220

4*

Answer:

Thus the energy to excite the donor electron from n=1 state to the free state (n=∞) is ≈6meV.

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When a ш-V material is doped with Si or Ge, from column IV, these impurities are called amphoteric.

In Si, the intrinsic carrier concentration ni is about 1010cm-3 at

room tempera-ture. If we dope Si with 1015 Sb Atoms/cm3, the conduction electron concentration changes by five order of magnitude.

lecture 5 energy bands and charge carriers

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