Semiconductor Electronics — NEET Notes

Classification of solids — metals, semiconductors, insulators

Solids are sorted into three electrical classes by the relative values of resistivity ρ (or its inverse, conductivity σ). Metals have very low resistivity, of the order of 10⁻² to 10⁻⁸ Ω m. Insulators have very high resistivity, of the order of 10¹¹ to 10¹⁹ Ω m. Semiconductors sit between them, at 10⁻⁵ to 10⁶ Ω m. But this is only a phenomenological label. The deeper explanation — the one NEET tests — comes from band theory.

In an isolated atom, an electron occupies a discrete energy level. When atoms crowd together to form a solid, their outer orbits overlap and what were once discrete levels broaden into energy bands, each containing a near-continuum of closely spaced states. The highest band still completely occupied by valence electrons at absolute zero is the valence band. The band above it, which holds the mobile electrons that carry current, is the conduction band. The gap between the top of the valence band (E_V) and the bottom of the conduction band (E_C) is the energy band gap, E_g. The size of this gap is what separates a copper wire from a sheet of diamond.

The band gap is destiny — its size alone decides whether a solid conducts, insulates, or sits in between.

The band-theory principle

Intrinsic semiconductors — pure Si and Ge

A pure crystal of silicon or germanium, free of any impurity, is an intrinsic semiconductor. Si and Ge both crystallise in the diamond-like structure, in which every atom shares one of its four valence electrons with each of four nearest neighbours through covalent bonds. At absolute zero, every bond is intact, the valence band is fully occupied, and the conduction band is empty — the crystal is an insulator.

At room temperature, thermal vibrations break a few covalent bonds. Each broken bond releases a free electron into the conduction band and leaves behind a vacancy in the valence band — a hole. The hole behaves as a mobile particle of effective positive charge, because an electron from a neighbouring bond can jump into the vacancy, shifting the hole one site over. In intrinsic semiconductors every broken bond produces exactly one electron and one hole, so the two populations are equal:

n_e = n_h = n_i

Intrinsic carrier concentration — pure Si or Ge

Under an applied electric field, both populations contribute to current. Electrons drift opposite to the field and holes drift along it; the total current I is the sum I_e + I_h. At every instant a simultaneous process of recombination destroys electron-hole pairs, and at equilibrium the rate of generation equals the rate of recombination. Because the population n_i at room temperature is small — about 1.5 × 10¹⁶ m⁻³ for silicon — intrinsic conductivity is too low for any useful device. NCERT's Example 14.1 makes the point: carbon, silicon and germanium share the same lattice, but C's gap (5.4 eV) is so large that thermal excitation yields essentially zero free electrons, while Si and Ge yield enough to qualify as semiconductors.

Extrinsic semiconductors — n-type and p-type

Intrinsic semiconductors are not useful by themselves. To raise the conductivity by orders of magnitude — and to make it controllable, not just temperature-dependent — we add a controlled trace of impurity. The deliberate addition is called doping; the impurity is the dopant. The dopant atom must have nearly the same size as Si or Ge so it occupies a lattice site without distorting the crystal. Two choices fit: an element from group 15 with five valence electrons, or one from group 13 with three.

n-type semiconductors — pentavalent dopants

When silicon is doped with a pentavalent atom — phosphorus (P), arsenic (As), or antimony (Sb) — the impurity contributes five valence electrons. Four of them bond covalently with the four Si neighbours. The fifth is left loose, weakly bound to its parent atom by a residual coulomb attraction. The ionisation energy needed to free this fifth electron is only about 0.05 eV in Si and 0.01 eV in Ge — well below the 1.1 eV needed to break a Si-Si bond. At room temperature essentially every dopant atom has ionised, donating its extra electron to the conduction band. For this reason a pentavalent dopant is called a donor. The resulting semiconductor is called n-type, because conduction is dominated by negative electrons.

p-type semiconductors — trivalent dopants

The opposite trick is to use a trivalent atom — boron (B), aluminium (Al), or indium (In) — with only three valence electrons. The impurity bonds with three Si neighbours but cannot supply the fourth electron. The fourth site is a vacancy — a hole. A neighbouring bond's electron jumps in to fill the vacancy, leaving a hole at its own former site. Each trivalent dopant therefore creates a mobile hole. The dopant is called an acceptor because it accepts an electron from the lattice. The crystal is called p-type, since conduction is dominated by positive holes.

Notice that the crystal as a whole remains electrically neutral. A pentavalent donor contributes one free electron and remains as a positively charged immobile ion fixed in the lattice. A trivalent acceptor contributes one mobile hole and becomes a fixed negative ion. Doping shifts the populations of mobile carriers; the immobile ion cores keep the bookkeeping balanced. NCERT also emphasises the mass-action law: at thermal equilibrium n_e n_h = n_i², so increasing one carrier by doping necessarily depresses the other.

Majority and minority carriers

The terms majority and minority carrier sound obvious but carry serious NEET weight. In an n-type semiconductor, electrons are the majority and holes are the minority. In a p-type semiconductor, holes are the majority and electrons are the minority. The minority carriers do not vanish — they are still generated thermally — but their concentration is suppressed by the mass-action law because doping has flooded the crystal with the opposite carrier type, raising the recombination rate. NEET 2021 directly compared currents in n-type and p-type samples with equal majority concentrations and tested the fact that electron mobility µ_e exceeds hole mobility µ_h, so the n-type sample carries more current.

The p-n junction — formation and depletion region

A p-n junction is the basic building block of nearly every semiconductor device — every diode, every transistor, every solar cell. You cannot make a junction by simply pressing a slab of p-Si against a slab of n-Si; the surface irregularities are vast on an atomic scale, so charge carriers cannot flow continuously across. Instead, a single wafer is processed so that part of it is doped p-type and the adjacent part n-type, with a metallurgical interface between them.

The instant a junction forms, two processes start simultaneously. First, diffusion: the steep concentration gradient drives holes from the p-side (where they are abundant) into the n-side, and electrons from the n-side into the p-side. Each migrating carrier leaves behind an immobile ionised dopant ion — a positive donor ion on the n-side, a negative acceptor ion on the p-side. A narrow region around the junction is thus stripped of mobile carriers and is called the depletion region, typically of the order of a tenth of a micrometre wide.

The exposed ions set up an electric field directed from the n-side to the p-side. This field gives rise to the second process — drift — which sweeps any electron straying onto the p-side back toward the n-side, and any hole straying onto the n-side back toward the p-side. Drift current flows opposite to diffusion current. Initially diffusion dominates, but as the depletion region thickens, the field strengthens until drift exactly cancels diffusion. At equilibrium there is no net current. The potential difference set up across the depletion region by this charge separation is the barrier potential V₀ — about 0.3 V for germanium and 0.7 V for silicon.

Biasing — forward vs reverse

The junction at equilibrium is interesting but not useful. The device becomes a diode the moment we apply an external voltage across it — a process called biasing. There are exactly two possibilities, and they produce wildly different behaviour.

Forward bias — low resistance, current flows

Connect the positive terminal of the battery to the p-side and the negative terminal to the n-side. The applied voltage opposes the built-in barrier, so the effective barrier height drops from V₀ to (V₀ − V), the depletion region narrows, and the field across it weakens. Holes are pushed across the junction from p to n, electrons are pushed from n to p — this is called minority carrier injection, because each carrier becomes a minority in the region it enters. Beyond a threshold of about 0.7 V (Si) or 0.3 V (Ge), the current rises sharply, almost exponentially, with applied voltage. The forward-biased diode has low resistance and conducts a current typically in the milliampere range.

Reverse bias — high resistance, almost no current

Reverse the battery — positive to the n-side, negative to the p-side. The applied voltage now adds to the built-in barrier, raising the effective barrier to (V₀ + V). The depletion region widens and the field across it strengthens. Diffusion of majority carriers is suppressed almost completely. A tiny drift current persists — it is carried by minority carriers swept across the junction by the strong field, and is of the order of a few microamperes. This reverse saturation current is nearly independent of the applied voltage because it is limited not by voltage but by the small thermally-generated minority population. The reverse-biased diode has very high resistance and is essentially off.

Semiconductor diode — I-V characteristics

The current-voltage (I-V) curve of a junction diode is the experimental signature of everything we have just described. In the forward direction, the current is negligibly small until the applied voltage crosses the cut-in voltage (also called the threshold or knee voltage) — about 0.7 V for silicon, about 0.3 V for germanium. Beyond cut-in, the current rises almost exponentially with small voltage increments. In the reverse direction, the current is a tiny, almost flat reverse saturation current in microamperes — until the applied voltage reaches the breakdown voltage V_br, beyond which the current rises sharply. Ordinary diodes are not designed to operate in this breakdown region; if external resistance does not limit the current, the diode is destroyed by heating. Special diodes — Zener diodes, NEET 2023 Q.12 — exploit the reverse breakdown region intentionally for voltage regulation.

The forward I-V relation is captured by the Shockley diode equation: I = I₀ (e^qV/kT − 1), which makes explicit the temperature sensitivity — NEET 2018 Q.7 tested that temperature changes the overall V-I characteristic. The dynamic resistance r_d = ΔV/ΔI is the slope of the I-V curve at the operating point and can range from ~10 Ω in forward bias to ~10⁷ Ω in reverse bias — a ratio of a million, which is exactly why the diode functions as a one-way valve.

Junction diode as a rectifier

The diode's most important application — and the one NEET tests every single year — is rectification: converting alternating current (AC) into direct current (DC). The idea is simple. A diode conducts only when forward biased. If we feed an alternating voltage to it, only the half-cycle that forward-biases the diode produces current at the load; the other half-cycle is blocked. The output is pulsating, but unidirectional. There are two standard variations.

Half-wave rectifier

One diode in series with the load. During the positive half-cycle of the AC input, the diode is forward biased and conducts current through the load. During the negative half-cycle, the diode is reverse biased and blocks current. Only one half-cycle reaches the load per input cycle, so the output frequency equals the input frequency (50 Hz in → 50 Hz out, or 60 Hz in → 60 Hz out — NEET 2022 Q.6 tested this exact identity). Half the input power is wasted; the rectified output is highly non-uniform.

Full-wave rectifier — centre-tap design

Two diodes and a centre-tapped transformer. The two ends of the transformer secondary feed the p-sides of two diodes whose n-sides are tied together at the output. The load is connected between this common cathode and the centre tap. During the positive half-cycle, the top end goes positive — diode D₁ is forward biased and conducts; D₂ is reverse biased. During the negative half-cycle, the bottom end goes positive — D₂ conducts; D₁ blocks. Each diode handles alternate half-cycles, so the load sees a pulse every half-cycle. Output frequency is twice the input (50 Hz in → 100 Hz out).

Full-wave rectifier — bridge design

Four diodes in a bridge — no centre tap required. The diodes are arranged so that during either half-cycle, two of them conduct in series and deliver current through the load in the same direction. The bridge design avoids the need for a special centre-tap transformer, uses the full secondary voltage rather than half, and is by far the most common rectifier in modern power supplies.

The smoothing capacitor

The rectified output is unidirectional but still pulsating — it would be useless for powering any device that needs a steady DC supply. To smooth it, we connect a large capacitor across the load resistor R_L. During each pulse, the capacitor charges nearly to the peak rectified voltage. Between pulses, the capacitor discharges through R_L, holding the load voltage up. The fall is governed by the time constant RC; large C means slow discharge and nearly constant load voltage. The combination is called a capacitor input filter, and it is the standard in every power supply. NEET 2023 Q.3 asked which component in a full-wave rectifier removes the AC ripple — neither the transformer nor the diodes nor the load: it is the capacitor.