Electronic Devices Formula Sheet — JEE Main Physics

Every key Electronic Devices formula, definition and theorem for JEE Main Physics in one place — with common examiner traps and worked examples. Free to read; blurt from memory, then check your gaps.

Syllabus — topics coveredNTA · 7 sub-topics

Semiconductors
Semiconductor diode: I-V characteristics
Diode as a rectifier
I-V characteristics of LED, photodiode, solar cell
Zener diode
Zener diode as voltage regulator
Logic gates: OR, AND, NOT, NAND and NOR

Semiconductors — Bands & Intrinsic

Energy band gap

E_{g}

: Gap between valence-band top and conduction-band bottom.

Conductor

: bands overlap (

E_{g} \approx 0

);

Semiconductor

E_{g} < 3

eV (Si

1.1

, Ge 0.72);

Insulator

E_{g} > 3

eV (diamond

5.4

Comparative: by conductivity

Class	$E_{g}$	$σ$ as $T ↑$
Conductor	$\approx 0$ (overlap)	falls
Semiconductor	$< 3$ eV	rises
Insulator	$> 3$ eV	negligible

Energy band diagrams: conductor with overlapping bands, semiconductor with a small gap under 3 eV, insulator with a large gap over 3 eV — Conduction needs electrons to cross $E_{g}$ .

Intrinsic semiconductor: Pure Si/Ge. Thermal energy breaks a covalent bond

\to

a free electron

+

hole

(effective charge

+ e

). Both carry current.

Intrinsic carriers

n_{e} = n_{h} = n_{i}, I = I_{e} + I_{h}

n_{i} =

intrinsic concentration; conduction by electrons AND holes

🚫 Examiner Trap · Bands & intrinsic

(1) A semiconductor's conductivity

rises

with T (more e–h pairs) — OPPOSITE to a metal. (2) At

T = 0

K a pure semiconductor is an

insulator

. (3) Diamond, Si, Ge share a lattice but differ in

E_{g}

— C is an insulator. (4) A hole is a

moving vacancy

, not a real particle, but carries

+ e

Extrinsic Semiconductors (n & p)

Doping: Adding a few ppm of impurity to raise conductivity. The doped crystal is

extrinsic

and stays overall

charge-neutral

Comparative: n-type vs p-type

	n-type	p-type
Dopant	pentavalent (As, P, Sb)	trivalent (B, Al, In)
Adds	donor electron	acceptor hole
Majority	electrons	holes
Minority	holes	electrons

Law of mass action

n_{e} n_{h} = n_{i}^{2}

holds in thermal equilibrium for intrinsic AND extrinsic; raising majority lowers minority

n-type lattice with a pentavalent +5 donor contributing a free electron; p-type lattice with a trivalent +3 acceptor creating a hole — Donor $\to$ spare electron (n); acceptor $\to$ hole (p).

🚫 Examiner Trap · Extrinsic semiconductors

(1) Doped crystals are

neutral

— donor/acceptor ion cores balance the extra carriers; n-type is NOT negatively charged. (2) Law of mass action

n_{e} n_{h} = n_{i}^{2}

— adding donors raises

n_{e}

but

lowers

n_{h}

. (3) Majority carrier set by dopant valency (5

\to

n, 3

\to

p). (4) Doping concentration

≪

host atoms (ppm) yet hugely raises

σ

p–n Junction & Diode I–V

Junction formation

▸ $Diffusion$ of majority carriers leaves immobile ions $\to$ $depletion region$ .
▸Its field drives $drift$ (opposite to diffusion); at equilibrium they balance (no net current).
▸Built-in $barrier$ $V_{0}$ : Si $\approx 0.7$ V, Ge $\approx 0.3$ V.

p-n junction at equilibrium: depletion region of width W with negative ions on the p-side and positive ions on the n-side, and the barrier potential V0 across it — Depletion width W and barrier $V_{0}$ at equilibrium.

Bias

Forward: (V_{0} - V), W ↓, I \sim mA; Reverse: (V_{0} + V), W ↑, I \sim μ A

forward lowers the barrier; reverse widens depletion

Diode I-V curve: negligible current until the forward knee near 0.7 V then a steep rise in mA; tiny reverse saturation current in microamps until reverse breakdown at V_br — Conducts forward past the knee; blocks in reverse.

Key voltages

V_{kn ee} : Si \approx 0.7, Ge \approx 0.3 V; r_{d} = \frac{Δ V}{Δ I}

r_{d} =

dynamic resistance (slope of the I-V curve)

🚫 Examiner Trap · p–n junction & diode

(1) The diode conducts only

above

the knee (

\approx 0.7

V for Si) in forward bias — not at any small voltage. (2) Reverse current (

μ

A) is nearly constant until breakdown

V_{b r}

. (3) Depletion width: forward

↓

, reverse

↑

. (4) The one-way (low forward / high reverse R) asymmetry is what rectifies.

Rectifiers & Filters

Rectifier: A circuit that converts AC to DC using a diode's one-way conduction — current passes only when the diode is forward biased.

Comparative: half-wave vs full-wave

	Half-wave	Full-wave
Diodes	1	2 (centre-tap) / 4 (bridge)
Output	$+$ halves only	both halves
Ripple freq	$f_{in}$	$2 f_{in}$
Efficiency	lower	higher

Rectifier output waveforms: half-wave passes only the positive halves of the input sine; full-wave flips the negative halves up so both halves appear — Half-wave: $+$ halves only. Full-wave: both halves.

⚡ Shortcut · Capacitor filter

A capacitor C across the load charges to the peak and discharges slowly (

τ = R_{L} C

), smoothing the pulses toward steady DC. Larger C

\Rightarrow

smaller ripple.

🚫 Examiner Trap · Rectifiers

(1) Full-wave ripple frequency is

2 f_{in}

(both halves) — half-wave is

f_{in}

. (2) A

bridge

(4 diodes) needs no centre-tap and uses the full secondary voltage; two opposite diodes conduct each half-cycle. (3) Each diode's reverse-breakdown rating must exceed the peak. (4) A rectifier gives

pulsating

DC; the filter makes it steady.

Special-Purpose Diodes

Zener diode: Heavily-doped diode run in reverse

breakdown

, where

V_{z}

stays nearly constant over a wide current range

\Rightarrow

voltage regulator.

Voltage regulator

V_{i} = I R_{S} + V_{z}, I = I_{z} + I_{L}

Zener reverse-biased, parallel with load; pick

I_{z} ≫ I_{L}

for good regulation

Left: Zener I-V with a sharp reverse breakdown holding constant Vz. Right: voltage-regulator circuit with series resistor Rs, Zener in reverse across the load RL, giving a steady output Vz — Breakdown holds $V_{z}$ constant $\to$ steady output.

Comparative: optoelectronic diodes

Device	Bias	Action
Zener	reverse	constant $V_{z}$ (regulator)
LED	forward	emits light ( $h ν \approx E_{g}$ )
Photodiode	reverse	photocurrent $\propto$ intensity
Solar cell	none	photovoltaic emf

🚫 Examiner Trap · Special diodes

(1) Zener & photodiode work in

reverse

bias; LED in

forward

; solar cell with

no

bias — a classic match question. (2) LED needs

E_{g} \geq 1.8

eV for visible light. (3) Solar-cell I–V lies in the

4th quadrant

(

V_{oc}

I_{sc}

). (4) Photodiode current

\propto

light intensity (a detector).

Junction Transistor & Amplifier

Junction transistor: Two back-to-back junctions (

npn

pnp

): emitter (heavily doped), base (thin, lightly doped), collector (moderately doped).

Active region

▸Emitter–Base $forward$ biased; Collector–Base $reverse$ biased.
▸Most carriers cross the thin base to C; only a few recombine ( $I_{B}$ small).

Current relations

I_{E} = I_{B} + I_{C}, α = \frac{I _{C}}{I _{E}} (< 1), β = \frac{I _{C}}{I _{B}} = \frac{α}{1 - α}

β

typically 20–200

npn transistor in common-emitter mode: emitter current in, base current out at the thin base, collector current out; with the current relations and voltage gain — Common-emitter: small $I_{B}$ controls large $I_{C}$ .

CE amplifier

A_{v} = \frac{V _{o u t}}{V _{in}} = β \frac{R _{o u t}}{R _{in}}

large voltage & power gain; output

18 0^{\circ}

out of phase with input

🚫 Examiner Trap · Transistor

(1) For amplification: E–B

forward

, C–B

reverse

— both wrong

\Rightarrow

cut-off/saturation. (2)

α < 1

always;

β = α / (1 - α)

can be large. (3) The base must be

thin, lightly doped

so few carriers recombine. (4) CE output is

inverted

(

18 0^{\circ}

) — a favourite exam point.

Logic Gates

Y = A + B

AND

Y = A \cdot B

NOT

Y = \overset{ˉ}{A}

NAND

Y = \overline{A \cdot B}

NOR

Y = \overline{A + B}

A	B	OR	AND	NAND	NOR
0	0	0	0	1	1
1	0	1	0	1	0
0	1	1	0	1	0
1	1	1	1	0	0

De Morgan's theorems

\overline{A + B} = \overset{ˉ}{A} \cdot \overset{ˉ}{B}, \overline{A \cdot B} = \overset{ˉ}{A} + \overset{ˉ}{B}

🚫 Examiner Trap · Logic gates

(1)

NAND

and

NOR

are

universal

— any gate can be built from only NANDs (or only NORs). (2) A NAND/NOR with both inputs tied together acts as a

NOT

. (3) De Morgan: bar of a sum

=

product of bars (and vice-versa). (4) NAND

=

AND then NOT (output inverted) — don't read it as AND.

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Frequently Asked Questions

What are the most important Electronic Devices formulas for JEE Main?

This Electronic Devices formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Semiconductors, Semiconductor diode: I-V characteristics, Diode as a rectifier, I-V characteristics of LED, photodiode, solar cell, Zener diode — each shown with the key result and, where useful, a worked example.

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How should I revise Electronic Devices formulas?

Blurt the Electronic Devices formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

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