Semiconductors

Focus: Intrinsic and extrinsic semiconductors, P–N junction diode, rectifiers, transistors, amplifiers and oscillators (JEE Main).

1) Semiconductors

• Electrical properties lie between conductors and insulators.
• Energy gap ≈ 1 eV.
• At absolute zero (0 K), semiconductors behave like insulators.

Intrinsic Semiconductor

• Pure semiconductor without impurities.
• Number of electrons = number of holes.

Relations:

n_e = n_h

n_e × n_h = n_i²

where n_i = intrinsic charge carrier density

2) Extrinsic (Doped) Semiconductors

N-Type

• Electrons are majority carriers.
• Holes are minority carriers.

P-Type

• Holes are majority carriers.
• Electrons are minority carriers.

3) P–N Junction Diode

• P-side → holes are majority carriers.
• N-side → electrons are majority carriers.
• Diffusion of charge carriers creates a depletion region.
• Potential barrier prevents further diffusion.

Dynamic Resistance

R = ΔV / Δi

Equal to the reciprocal of the slope of the V–I characteristic.

4) Special Purpose Diodes

Photodiode

• Operated in reverse bias.
• Incident light generates electron–hole pairs.
• Current is proportional to light intensity.

Light Emitting Diode (LED)

• Electron-hole recombination emits photons.
• Visible light is emitted if wavelength lies in visible range.

Zener Diode

• Operates in Zener breakdown region.
• Voltage remains nearly constant.
• Used for voltage regulation.

5) P–N Junction as a Rectifier

(a) Half-Wave Rectifier

Average output current:

I_avg = I₀ / π

RMS value of output current:

I_rms = I₀ / 2

(b) Full-Wave Rectifier

Average output current:

I_avg = 2I₀ / π

RMS value of output current:

I_rms = I₀ / √2

6) Junction Transistor

• Three terminals: Emitter, Base, Collector.
• Emitter: heavily doped.
• Base: thin and lightly doped.
• Collector: moderately doped.

Modes of operation:

• Common Base
• Common Emitter
• Common Collector

7) Transistor as an Amplifier

Common Base Configuration

Current gain:

α = ΔI_c / ΔI_e

Voltage gain:

A_v = α × (R_o / R_i)

Power gain:

α² × resistance gain

Common Emitter Configuration

Current gain:

β = ΔI_c / ΔI_b

Voltage gain:

A_v = β × (R_o / R_i)

Power gain:

β² × resistance gain

8) Transistor as an Oscillator

• Converts DC into AC.
• Uses positive feedback.

Frequency of oscillation (LC circuit):

f₀ = 1 / (2π√LC)