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CLASS 12 • PHYSICS
Semiconductors
1. Charge Carriers
Intrinsic Semiconductor
$n_e = n_h = n_i$
Mass Action Law
$n_e \times n_h = n_i^2$
Valid for both Intrinsic & Extrinsic
Energy Gap ($E_g$)
Silicon: $E_g \approx 1.1 \text{ eV}$
Germanium: $E_g \approx 0.7 \text{ eV}$
2. Conductivity
Total Current ($I$)
$I = I_e + I_h$
Conductivity ($\sigma$)
$\sigma = e(n_e \mu_e + n_h \mu_h)$
$\mu$ = Mobility ($v_d/E$)
Resistivity ($\rho$)
$\rho = \frac{1}{\sigma}$
3. PN Junction Diode
Forward Bias
$V > V_{barrier}$
Depletion width decreases. Current flows.
Reverse Bias
$V < 0$
Depletion width increases. No Current.
Dynamic Resistance
$r_d = \frac{\Delta V}{\Delta I}$
4. Rectifiers
Half Wave Rectifier
$f_{out} = f_{in}$
Uses 1 Diode. Efficiency $\approx 40.6\%$
Full Wave Rectifier
$f_{out} = 2f_{in}$
Uses 2 Diodes. Efficiency $\approx 81.2\%$
5. Logic Gates (Boolean Algebra)
| Gate | Boolean | Logic Trick |
|---|---|---|
| OR | $Y = A + B$ | Output is 1 if ANY input is 1. |
| AND | $Y = A \cdot B$ | Output is 1 ONLY if ALL inputs are 1. |
| NOT | $Y = \bar{A}$ | Inverter (1 becomes 0, 0 becomes 1). |
| NAND | $Y = \overline{A \cdot B}$ | AND followed by NOT. |
| NOR | $Y = \overline{A + B}$ | OR followed by NOT. |
De Morgan's Theorem: $\overline{A+B} = \bar{A} \cdot \bar{B}$ and $\overline{A \cdot B} = \bar{A} + \bar{B}$
6. Common Exam Traps
- ⚠️ Neutrality: N-type and P-type materials are ELECTRICALLY NEUTRAL. They have mobile carriers, but the total charge is zero (ions balance carriers).
- ⚠️ Solar Cell: It operates in the FOURTH QUADRANT of the I-V characteristics (Current is negative/generated).
- ⚠️ Temperature: Resistance of Semiconductor DECREASES with temp increase (Opposite to metals).
7. Golden Theory Rules
- Doping: Pentavalent impurity (P, As, Sb) $\to$ N-Type (Electrons). Trivalent impurity (B, Al, In) $\to$ P-Type (Holes).
- Zener Diode: Used as a Voltage Regulator. Always connected in REVERSE BIAS.
- Photodiode: Always operated in REVERSE BIAS because change in fractional current is easier to detect.
