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Semiconductor Materials

A semiconductor is a material that has a conductivity somewhere between the extremes of an insulator and a conductor.

nergy Band Diagram

Eg = 1.1 eV(Si), Eg = 0.67 eV(Ge), Eg = 1.41 eV (Ga As)

Types of Semiconductor

Intrinsic Material : A perfect semiconductor crystal with no impurities or lattice defect is called an intrinsic semiconductor. The electron-hole pair is the only way of charge carrier in intrinsic materials.

For intrinsic material.


Where, ni = intrinsic carrier concentration.

Under steady state carrier concentration the rate of recombination (ri) of EHP (Electron-Hole Pair) is equal to rate of generation (gi) of EHP. so,


At any temperature, 472.png 

where, no and po are equilibrium concentration of electrons and holes.

Extrinsic Material: 
The characteristics of semiconductor materials can be altered significantly by the addition of certain impurity atoms into the relatively pure semiconductor material by doping process. A semiconductor material that has been subjected to the doping process is called an extrinsic material.

Pure semiconductor material without any impurity is known as an intrinsic semiconductor material.

-type Materials

The n-type is created by introducing impurity elements that are (penta valent) such as antimony, arsenic and phosphorous. These diffused impurities are called donor atoms.

With doping Eg of Si becomes 0.05 eV from 1.1 eV and Eg of Ge becomes 0.01 eV from 0.67 eV

-type Materials

The p-type material is formed by doping a pure germanium or Si crystal with elements that are trivalent like Boron, Gallium and Indium.

The diffused impurities are called acceptor atoms.

If a valence electron acquires sufficient KE to break its covalent bond and fills the void created by a hole, then a vacancy or hole will be created in the covalent bond that released the electron.

In n-type material, the electron is called the majority carrier and the hole the minority carrier.

In p-type material holes are majority carriers and electron are the minority carries.

Fermi - level

f(Ef) = 477.png = 482.png

Fermi-level in the energy level at which it has probability of 487.png of being occupied by electron.

Electron and Hole Concentration at equilibrium

The concentration of electron in conduction band is :


Where, NC = Effective density of states in conduction band


Nc = 2497.png


mn* = effective mass

h = planck constant

k = Boltzman constant

The concentration of holes in valence band is


Nv = effective density of states in valence band.

Nv = 2507.png


mp* = effective mass of hole.

Intrinsic electron and hole concentration are : —


Intrinsic concentration is also given by


Another convenient way of writing electron concentration and hole concentration at equilibrium is :

no = 527.png

po = 532.png

Temperature Dependence of Carrier Concentration

ni (T) = 2537.png542.png

From above equation it is clear that the intrinsic concentration depends on temperature. As temperature increases the intrinsic concentration increases as


Mobility of charge carrier is drift velocity per unit electric field. It defines how fast the charge travel from one place to another and is given by.

μ = 552.png

Vd = drift velocity

E = Electric field

The electron and hole mobility for Ge and Si is given as under :



Hall Effect

Hall effect states that if a specimen (metal or semiconductor) carrying current I each placed in a transverse magnetic field B, an electric field intensity E is induced in a direction perpendicular to both I and B.


Hall Voltage VH = Ed volts


ρ → Charge Density




  • By Hall Experiment


OR 593.png


σ = Conductivity Of Given Specimen.

Optical Absorption: 
The photon with energy hv > Eg is absorbed in the semi- conductor. A photon with energy less than Eg is unable to excite an electron from the valence band to the conduction band. If a beam hv > Eg fall on a semiconductor, there will be some predictable amount of absorption. The ratio of transmitted to incident light intensity depend on photon wavelength and thickness of sample.

603.png = 608.pngI(x)

I(x) = I0 e614.pngx

I(x) = intensity of photon remaining

I0 = Intensity of photon beam at x = 0

619.png = absorption coefficient (cm–1)

Diffusion of Carriers

When excess carriers are created non- uniformly in semi-conductor, the electron and hole concentration vary with position in the sample. Any such spacial variation in n and p calls for a net motion of carriers from a region of high carrier concentration to region of low carrier concentration. This type of motion is called diffusion.

The diffusion current crossing a unit area (the current density) is the particle flux density multiplied by charge of carrier.


Jn (deff) = q Dn624.png

Jp (deff) = –qDp629.png

Jn, Jp = electron and hole current density respectively.

Dn, Dp = electron and hole diffusion coefficient.

Diffusion and Drift of Carrier


and J(x) = Jn(x) + Jp(x)

Einstein Relation



D = Diffusion coefficient

μ = Mobility

k = Boltzman constant

Diffusion and Recombination


654.png = Rate of electron and hole build up.

 = Carrier lifetime for electron and hole respectively.

Ln & Lp are electron and hole diffusion length respectively.


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