April 21, 2023 Conduction in Semiconductors 1

Conduction in Semiconductors

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Electrical Conduction in Electrical Conduction in Good ConductorsGood Conductors

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In addition to the random motion, the electrons drift towards the positive terminal.

This drift of the charge carriers results in an electric current, called drift current.

Drift CurrentDrift Current

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Drift Velocity It is the average velocity of charge carriers

in a definite direction under the influence of electric field.

Its value depends upon 1. The nature of charge carriers.

2. The applied electric field.

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Mobility

The constant μ is called mobility. It can be defined as the drift velocity (in

m/s) per unit applied field (in V/m). Thus,

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Conductivity

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Let n be the concentration of charge carriers.The time to cross the length is

t = L / vd

The drift current is given as

The current Density is

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• Putting σ = qnμ, we get

J = σE

• This is simply Ohm’s Law, put in another form. The constant σ is called Conductivity.

• Conductivity is the inverse of resistivity,

σ = 1 / ρ (S/m)

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Conduction in Intrinsic Semiconductors

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Drift of electrons and holes in an external field

The electrons in the conduction band and the holes in the valence band move in a random fashion within a crystal due to their thermal energy.

When an external voltage is applied to the semiconductor, a drift velocity is superimposed on the random thermal motion of the electrons and holes.

The drift of the electrons in the conduction band and that of the holes in the valence band produce an electric current.

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The electrons move towards the positive electrode and the holes towards the negative electrode.

Conventional current flows in semiconductors from the positive electrode to the negative electrode.

When the charge on an electron is same as the charge on a hole, why is the electron-drift current In is greater than the hole-drift current Ip ?

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Conductivity of Intrinsic Semiconductors

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Charge density = qn

Qn = (qn)(Avn)

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Total Current,

But

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Applying Ohm’s Law,

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Since in an intrinsic semiconductor, n = p = ni,

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Intrinsic Concentration• With increasing temperature, the density of electron-

hole pairs increases and correspondingly conductivity increases.

• It is found that intrinsic concentration ni varies with T as,

• EG0 = Energy gap at 0 K in electron volts

• k = Boltzman constant in eV/K

• A0 = a constant independent of T.

kT

ETAn G

i03

02 exp

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In case Germanium, 1 atom in about 109 contributes a free electron (and also a hole).

In case Silicon, 1 atom in about 1012 contributes a free electron (and also a hole).

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Energy Gap or Band GapThe forbidden energy gap in

semiconductors depends upon temperature.Experimentally it has been found that,

• For Germanium,

Eg = 0.785 – 2.23 X 10-4T

At 300 K, Eg = 0.72 eV.

• For Silicon,

Eg = 1.21 - 3.60 X 10-4T

At 300 K, Eg = 1.12 eV.

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Review• Electrical Conduction in Good ConductorsElectrical Conduction in Good Conductors

• Drift Current.Drift Current.

• Drift Velocity.

• Mobility.

• Conductivity.

• Conductivity of Intrinsic Semiconductors .

• Intrinsic Concentration.