Semiconductors Formulae for NEET

Semiconductors are materials which have a conductivity between conductors and insulators. Most examples of semiconductors are SIlicon and Germanium.

Conductivity and Resistivity

Conductivity (σ) S/m Resistivity (ρ) Ω m
Metals 102 – 108 10-2 – 10-8
Semiconductors 105 – 10-6 10-5 – 106
Insulators 10-11 – 1019 1011 – 1019

Charge Concentration and Current

Intrinsic Semiconductors

ne = nn =ni

Here,

ne = the free electron density in the conduction band

nn = the hole density in the valence band

ni = the intrinsic carrier concentration

Extrinsic Semiconductors

ne ≃ Nd >nn (n-type)

nn ≃ Nd >ne (p-type)

Nd is the number density

Number of electrons reaching from the valence band to conduction band

ղ = AT3/2e-Eg/2kT

A is the material constant

Eg is the bandwidth

T is the temperature

Mobility

μ = Vd/E

Vis the drift velocity

E is the electric field

Electrical conductivity of a semiconductor

The conductivity of an intrinsic semiconductor increases exponentially with temperature as

\(\sigma =\sigma _{0}exp\left ( -\frac{E_{g}}{2K_{B}T} \right )\)

Action of Transistor

IE=IC+IB

Here

IE is the emitter current

IC is the collector current

IB is the base current

Transistor Parameters

Common base current application factor or ac current,

\(\alpha =\left [ \frac{\delta I_{c}}{\delta I_{E}} \right ]_{V_{CB}=constant}\)

Here

IE is the small change in emitter current

IC is the small change in collector current

Common emitter current application factor or ac current,

\(\beta =\left [ \frac{\delta I_{c}}{\delta I_{B}} \right ]_{V_{CE}=constant}\)

IC is the small change in collector current

IB is the small change in base current

Relations between α and β

α = β/(1+β)

β = α/(1-α)

Expression for Voltage gain

Voltage gain of an amplifier is given by

Av= V0/Vi = A small in output voltage/A small change in input voltage

Av = β (Routput/Rinput)

here,

Routput is the load resistance

Rinput is the input resistance