Semiconductors Formulae for NEET

On the basis of conductivity, materials can be categorized. If a material conducts electricity, it is a metal and if it does not conduct, it is an insulator. When a material shows properties from both categories, they are termed semiconductors. Semiconductors are materials that have a conductivity between conductors and insulators. Most examples of semiconductors are Silicon and Germanium.

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The very attribute of semiconductors to exhibit conductivity based on their ambience makes it possible to regulate the flow of electrons in a circuit.

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

n_e = n_n =n_i

Here,

n_e = the free electron density in the conduction band

n_n = the hole density in the valence band

ni = the intrinsic carrier concentration

Extrinsic Semiconductors

n_e ≃ N_d ＞n_n(n-type)

n_n ≃ N_d ＞n_e(p-type)

N_dis the number density

Number of electrons reaching from the valence band to conduction band

ղ = AT^3/2e^-Eg/2kT

A is the material constant

Eg is the bandwidth

T is the temperature

Mobility

μ = V_d/E

V_dis the drift velocity

E is the electric field

Electrical conductivity of a semiconductor

The conductivity of an intrinsic semiconductor increases exponentially with temperature as

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

Action of Transistor

I_E=I_C+I_B

Here

I_E is the emitter current

I_Cis the collector current

I_Bis the base current

Transistor Parameters

Common base current application factor or ac current,

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

Here

I_E is the small change in emitter current

I_Cis the small change in collector current

Common emitter current application factor or ac current,

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

I_Cis the small change in collector current

I_Bis 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

A_v= V₀/V_i= A small in output voltage/A small change in input voltage

A_v = β (R_output/R_input)

here,

R_output is the load resistance

R_inputis the input resistance

Recommended Video:

Top 10 Questions from Semiconductors Class 12 Physics (Concepts + Questions)

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