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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.


E
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.

462.png 

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,

467.png 

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.


n
-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


p
-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 :

492.png 


Where, NC = Effective density of states in conduction band

 

Nc = 2497.png
 

Where,

mn* = effective mass

h = planck constant

k = Boltzman constant


The concentration of holes in valence band is

502.png 


Nv = effective density of states in valence band.

Nv = 2507.png

where

mp* = effective mass of hole.


Intrinsic electron and hole concentration are : —

512.png517.png 


Intrinsic concentration is also given by

522.png 


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
547.png.


Mobility

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
 

where,
Vd = drift velocity

E = Electric field


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

 

557.png 

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.
 

563.png 

Hall Voltage VH = Ed volts
 

568.png 

ρ → Charge Density

573.png 

578.png 

583.png

  • By Hall Experiment

588.png

OR 593.png

598.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
 

where,
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

634.png 

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


Einstein Relation

639.png 


where,

D = Diffusion coefficient

μ = Mobility

k = Boltzman constant


Diffusion and Recombination

644.png 


649.png
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.
 

659.png 





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