Summary & Master Memory Capsule

Master Classification & Carrier Sheet

By resistivity (ohm m): metals $10^{-2}$-$10^{-8}$; semiconductors $10^{-5}$-$10^{6}$; insulators $10^{11}$-$10^{19}$.

By bands: metals — overlap/partial filling ($E_g$ ≈ 0); semiconductors — $E_g$ < 3 eV; insulators — $E_g$ > 3 eV. Ladder: C 5.4 / Si 1.1 / Ge 0.7 / Sn 0 eV. Photon bridge: $E_g$(eV) = 1240/$\lambda$(nm).

	Intrinsic	n-type	p-type
Dopant	none	pentavalent (As, Sb, P) — donor	trivalent (In, B, Al) — acceptor
Carriers	$n_e = n_h = n_i$	$n_e \gg n_h$	$n_h \gg n_e$
New level	—	$E_D$ just below $E_C$	$E_A$ just above $E_V$
Ionisation cost	full gap	~0.01 eV Ge / 0.05 eV Si	similar (small)

Always: $n_en_h = n_i^2$ (mass action); crystal neutral overall; I = $I_e + I_h$; conductivity $\sigma = e(n_e\mu_e + n_h\mu_h)$; semiconductor resistance FALLS on heating (metals rise).

NCERT Example 14.2 anchor: $5 \times 10^{28}$ atoms/m³ + 1 ppm As → $n_e = 5 \times 10^{22}$, $n_h = 4.5 \times 10^{9}$ m⁻³.

Junction, Bias & Rectifier Tables

Formation (4 steps): majority diffusion (holes p→n, electrons n→p) → immobile ion layers = depletion region (~0.1 $\mu$m) → field (n→p) drives minority drift → equilibrium: drift = diffusion, barrier $V_0$, n-side positive.

Bias table:

	Forward (p to +)	Reverse (n to +)
Barrier	$V_0 - V$	$V_0 + V$
Depletion width	narrows	widens
Current	mA (injection + diffusion)	$\mu$A saturation (minority drift)
Meter	milliammeter	microammeter

V-I landmarks: cut-in 0.2 V (Ge) / 0.7 V (Si); exponential beyond; reverse flat until breakdown $V_{br}$ (destruction by overheating if unlimited — forward over-current too). Dynamic resistance $r_d = \Delta V/\Delta I$ (Example 14.4: 10 ohm fwd, $10^7$ ohm rev).

Rectifiers:

	Half-wave	Full-wave (centre-tap)	Bridge
Diodes	1	2 (+ centre tap)	4
Ripple (50 Hz in)	50 Hz	100 Hz	100 Hz
Per-diode voltage	full secondary	half secondary	full secondary

Filter: capacitor across $R_L$; droop rate ∝ $1/(R_LC)$; large C → output ≈ peak voltage. Diode $V_{br}$ must exceed peak secondary voltage.

Extras Quick Tables & Trap List — [JEE/NEET]

Special diodes:

Device	Bias	Job	Key fact
Zener	reverse (breakdown)	voltage regulator	heavy doping → thin depletion → sharp $V_Z$; $I_Z = \dfrac{V_{in}-V_Z}{R_s} - I_L$
LED	forward	light source	$h\nu \approx E_g$; visible needs 1.8-3 eV; turn-on ≈ $E_g$/e volts
Photodiode	reverse	light detector	photocurrent ∝ intensity; $\mu$A signal atop $\mu$A dark current
Solar cell	none	power generator	built-in field separates pairs; $V_{oc}$, $I_{sc}$; gap 1.0-1.8 eV ideal

Gates (signature rows): OR — 0 only at (0,0); AND — 1 only at (1,1); NOR — 1 only at (0,0); NAND — 0 only at (1,1); NOT inverts. NAND & NOR are universal. Tie NAND inputs → NOT; NAND+NOT → AND; invert-inputs-then-NAND → OR.

Trap list:

• n-type is NOT negatively charged (neutral overall — fixed ions balance carriers).
• Minority carriers are suppressed BELOW $n_i$ by doping ($n_i^2/n_{maj}$).
• Diffusion = majority carriers; drift = minority carriers. Field points n → p; n-side of barrier is positive.
• Reverse current: temperature-sensitive, voltage-flat.
• Rectifier ripple: half = f, full = 2f — never amplitude doubling.
• Ideal vs real diode: check for the word before subtracting 0.7 V.
• Centre-tap: each diode rectifies HALF the voltage but blocks the FULL peak (PIV).

One-Glance Revision Flow

The chapter in eight steps:

1. Classify: resistivity ranges + band picture; the 5.4/1.1/0.7/0 eV ladder.
2. Intrinsic: covalent bonds break thermally → electron-hole pairs; $n_e = n_h = n_i$; I = $I_e + I_h$; insulator at 0 K; resistance falls on heating.
3. Dope: ppm of pentavalent (donor → n-type) or trivalent (acceptor → p-type); $E_D$/$E_A$ in the gap; $n_en_h = n_i^2$ rules the populations.
4. Junction: diffusion vs drift → 0.1 $\mu$m depletion region → barrier $V_0$, n positive, zero net current.
5. Bias: forward — barrier down, injection, mA past 0.2/0.7 V; reverse — barrier up, $\mu$A saturation, breakdown at $V_{br}$; $r_d = \Delta V/\Delta I$.
6. Rectify: one-way conduction → half-wave (f) and centre-tap full-wave (2f); capacitor filter → near-peak dc.
7. Extras: Zener clamps at $V_Z$ (regulator); LED emits ≈ $E_g$; photodiode detects ∝ intensity; solar cell generates unbiased.
8. Gates: five truth tables, corner-row signatures, NAND/NOR universality.

Morning-of-exam checklist: 1240/λ ↔ $E_g$ … mass action $n_i^2$ division … donors below $E_C$, acceptors above $E_V$ … crystal always neutral … diffusion-majority, drift-minority … barrier n-positive … forward $V_0 - V$ mA, reverse $V_0 + V$ $\mu$A … cut-ins 0.2/0.7 V … ripple f vs 2f … capacitor filter ≈ peak … Zener: series drop ÷ $R_s$, minus load … LED colour = gap; bias table LED-fwd/photo-rev/solar-none … NAND (1,1)→0, NOR (0,0)→1. Go score — and that completes Class 12 Physics.