Semiconductor Electronics: Materials, Devices and Simple Circuits notes: CBSE Class 12 Physics

1. Energy bands

In a crystal, atomic energy levels spread into bands: the valence band (valence electrons) and the conduction band (free electrons), separated by the band gap $E_g$ .
Conductor: bands overlap; many free electrons; resistivity about $10^{-8}$ – $10^{-6}$ Ω m.
Semiconductor: small gap, about 1 eV (Si 1.1 eV, Ge 0.7 eV); a few electrons cross it at room temperature; resistivity about $10^{-5}$ – $10^{6}$ Ω m; resistance falls on heating.
Insulator: large gap, over 3 eV (diamond 5.4 eV); resistivity about $10^{11}$ – $10^{19}$ Ω m.
A photon can create an electron–hole pair only if $h\nu \ge E_g$ , i.e. $\lambda \le hc/E_g$ .

Gaps drawn to scale: Si 1.1 eV, diamond 5.4 eV.

Formulas

Longest wavelength that can excite across the gap
$\lambda_\text{max} = \dfrac{hc}{E_g}$

Key terms

Band gap: The forbidden energy range between the top of the valence band and the bottom of the conduction band.

2. Intrinsic and extrinsic semiconductors

Intrinsic (pure Si, Ge): thermal energy breaks bonds, creating equal numbers of free electrons and holes: $n_e = n_h = n_i$ . A hole is a missing electron in a bond and behaves as a positive carrier. Current $I = I_e + I_h$ .
n-type: doped with a pentavalent impurity (P, As, Sb), a donor; majority carriers electrons, minority holes.
p-type: doped with a trivalent impurity (B, Al, In), an acceptor; majority carriers holes, minority electrons.
Doping level is tiny (≈ 1 in 10⁶) but raises conductivity enormously. Doped crystals remain electrically neutral (fixed ions balance the carriers).
In equilibrium $n_e n_h = n_i^2$ .

Formulas

Mass-action law
$n_e n_h = n_i^2$

Key terms

Hole: A vacancy left by an electron in a covalent bond; it acts as a positive charge carrier.
Donor: A pentavalent impurity atom that gives a free electron.
Acceptor: A trivalent impurity atom that creates a hole.

3. The p-n junction and its characteristics

Formation: electrons diffuse from n to p and holes from p to n and recombine, leaving a depletion layer of fixed ions (negative on the p side, positive on the n side). The field points n → p, creating a barrier potential (≈ 0.7 V Si, ≈ 0.3 V Ge). In equilibrium, diffusion current = drift current.
Forward bias (p to +): barrier lowered, depletion layer narrows; current rises sharply above the knee voltage; current in mA.
Reverse bias (p to −): barrier raised, depletion layer widens; tiny, nearly constant reverse saturation current of minority carriers (μA); sharp rise at the breakdown voltage.
The diode is non-ohmic; dynamic resistance $r_d = \Delta V/\Delta I$ .

silicon diode (model I = 10 mA × e⁽(V − 0.70)/0.05))

Below the knee the barrier blocks most carriers; above it the current rises exponentially.

reverse saturation current, then breakdown (schematic)

Note the different scale: microamperes in reverse, milliamperes forward.

Formulas

Dynamic resistance
$r_d = \dfrac{\Delta V}{\Delta I}$

Key terms

Depletion layer: Region around a p-n junction emptied of mobile carriers, containing fixed ions.
Barrier potential: Potential difference across the depletion layer that opposes further diffusion.
Knee voltage: Forward voltage beyond which the diode current rises sharply.

4. The diode as a rectifier

Rectification: converting AC into unidirectional (DC) current, using the diode’s one-way conduction.
Half-wave: one diode in series with the load; conducts only in half-cycles when it is forward biased; output frequency = input frequency $f$ .
Full-wave (centre tap): two diodes; D₁ conducts when one end of the secondary is positive, D₂ in the other half-cycle; current through the load is always in the same direction; output pulse frequency $2f$ .
Peak output ≈ peak input − diode drop (≈ 0.7 V for Si); $V_0 = \sqrt{2}V_\text{rms}$ .
A capacitor filter across the load smooths the pulsating output.

input (AC)
output across the load (half-wave)

Output pulses at the input frequency; half the input is wasted.

input (AC)
output across the load (full-wave)

Output pulse frequency = 2 × input frequency.

Formulas

Peak voltage of the AC input
$V_0 = \sqrt{2}\,V_\text{rms}$

Key terms

Rectifier: A circuit that converts alternating current into direct (unidirectional) current.

Exam tips

Band diagrams: label valence band, conduction band and $E_g$ for all three types.
Donors P, As, Sb → n-type; acceptors B, Al, In → p-type; both neutral.
Depletion layer narrows in forward bias, widens in reverse bias.
Rectifiers: draw circuit and aligned input/output waveforms; full-wave output frequency $2f$ .

1. Energy bands

Formulas

Key terms

2. Intrinsic and extrinsic semiconductors

Formulas

Key terms

3. The p-n junction and its characteristics

Formulas

Key terms

4. The diode as a rectifier

Formulas

Key terms

Exam tips

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