Semiconductor Electronics

Energy bands · doping · the p–n junction · diodes & rectifiers · Zener · transistors · logic gates · Class 12 Physics

1Why some solids conduct: energy bands

In a single atom electrons can only sit at sharply defined energy levels. Bring 10²³ atoms together into a crystal and every one of those levels splits, over and over, into a near-continuous smear of allowed energies called an energy band. Two bands decide everything about how a solid conducts: the valence band, the highest band that is filled with the atoms' outer electrons, and the conduction band just above it, where an electron is free to roam and carry current. Between them lies a stretch of forbidden energies — the band gap E_g — that an electron must leap to become mobile.

The size of that gap sorts every solid into one of three families:

• Conductors (metals): the valence and conduction bands overlap, so E_g ≈ 0. Electrons are free at any temperature — huge conductivity.
• Semiconductors (silicon E_g ≈ 1.1 eV, germanium E_g ≈ 0.7 eV): the gap is small enough that ordinary thermal energy kicks a few electrons across at room temperature. Cold, they behave like insulators; warm them and conductivity rises.
• Insulators (diamond E_g ≈ 6 eV): the gap is so wide that essentially no electron ever reaches the conduction band.

Note the giveaway: heating a metal lowers its conductivity (the jostling ions scatter the already-free electrons), but heating a semiconductor raises it, because the gain from freeing new carriers dwarfs the scattering. A semiconductor has a negative temperature coefficient of resistance — a fingerprint that separates it from a metal.

2Intrinsic semiconductors

A perfectly pure crystal of silicon or germanium is an intrinsic semiconductor. Each atom has four valence electrons and shares them in covalent bonds with four neighbours, so at absolute zero every electron is locked in a bond and the crystal is a perfect insulator. Warm it, and a bond occasionally breaks: the freed electron jumps to the conduction band and leaves behind an empty bond — a hole.

The hole is the clever idea. A neighbouring bonded electron can slip into the vacancy, which just moves the vacancy the other way. So the hole drifts through the crystal exactly as if it were a positive particle carrying charge +e. Current in a semiconductor is therefore carried by two kinds of carrier — negative electrons in the conduction band and positive holes in the valence band — flowing in opposite directions under a field.

Because every broken bond makes one electron and one hole, in a pure crystal the two populations are exactly equal:

where n_i is the intrinsic concentration, which climbs steeply with temperature. On its own an intrinsic semiconductor is a poor conductor — far too few carriers to be useful. The whole art of electronics comes from the next step: adding impurities on purpose.

3Doping: n-type and p-type

Deliberately adding a trace of a chosen impurity — perhaps one atom in 10⁶ — is called doping, and the result is an extrinsic semiconductor whose conductivity can be raised by a factor of thousands. There are exactly two choices, decided by whether the dopant brings one electron too many or one too few.

n-type — a pentavalent donor

Dope silicon with a pentavalent atom (five valence electrons — arsenic, phosphorus or antimony). Four of its electrons form the usual bonds; the fifth is left over, loosely held, and needs only a whisper of energy to break free into the conduction band. The impurity has thus donated a free electron and is called a donor. Electrons now vastly outnumber holes, so they are the majority carriers and holes the minority carriers. Since the mobile charge is negative, this is an n-type semiconductor. The crystal stays electrically neutral overall — the donor atom that lost an electron is a fixed positive ion.

p-type — a trivalent acceptor

Dope instead with a trivalent atom (three valence electrons — boron, aluminium, indium or gallium). It can complete only three of the four bonds; the fourth bond is left with a vacancy — a ready-made hole. The impurity accepts an electron from a nearby bond and is called an acceptor. Now holes are the majority carriers and electrons the minority, giving a p-type semiconductor. Again the crystal is neutral: the acceptor that grabbed an electron becomes a fixed negative ion.

4The p–n junction & the depletion region

Join a p-type block to an n-type block in a single crystal and something happens on its own, with no battery attached. Electrons on the crowded n-side diffuse across into the p-side, and holes diffuse the other way. Where an electron meets a hole they recombine, wiping out both mobile carriers near the boundary.

What is left behind is a thin zone swept clean of free carriers — the depletion region, typically a fraction of a micrometre wide. But the atoms there are not neutral any more: the n-side has lost electrons and is dotted with fixed positive donor ions; the p-side has lost holes and holds fixed negative acceptor ions. These uncovered charges set up an electric field pointing from n to p, and a potential barrier V₀ (about 0.7 V for silicon, 0.3 V for germanium) that opposes any further diffusion. Diffusion stops when the barrier just balances it, and the junction settles into equilibrium.

5Forward vs reverse bias

A junction becomes useful the moment we apply an external voltage — a bias — because the two directions behave utterly differently. That asymmetry is the whole point of a diode.

Forward bias — the gate opens

Connect the battery's + to the p-side and − to the n-side. The applied voltage opposes the built-in barrier, so the effective barrier drops and the depletion region narrows. Once the applied voltage exceeds the barrier (the knee or cut-in voltage, ≈ 0.7 V for silicon), majority carriers pour across and a large current flows. In forward bias the diode is a low-resistance path — practically a closed switch.

Reverse bias — the gate shuts

Reverse the battery: + to the n-side, − to the p-side. Now the applied voltage adds to the barrier, widening the depletion region and pushing majority carriers away from the junction. Almost no current flows — only a tiny reverse saturation current (microamps or less) driven by the few thermally generated minority carriers. The diode is now a high-resistance path — an open switch. Push the reverse voltage too far and the junction suffers breakdown; for an ordinary diode that is destructive, but the Zener turns it into a feature.

6The diode as a rectifier

Mains electricity is alternating current (AC) — it reverses 50 times a second — but electronics needs steady direct current (DC). A rectifier uses the diode's one-way behaviour to convert one to the other.

Half-wave rectifier

A single diode in series with the load conducts only when its anode is positive — during one half of each AC cycle. On the other half it blocks, so the output is a train of positive humps with gaps where the negative halves used to be. The output has the same frequency as the input (50 Hz), and half of every cycle is wasted. Crude, but it works.

Full-wave rectifier

Better to use both halves. A centre-tapped transformer with two diodes (or a four-diode bridge) arranges for one diode to conduct on the positive half-cycle and the other on the negative half — but always steering current through the load the same way. Every negative hump is flipped up to become a positive one, so no half is wasted. The output pulses twice per input cycle, so its ripple frequency is double the input (100 Hz for 50 Hz mains).

Ripple and smoothing

Even a full-wave output is bumpy, not flat — the leftover AC wobble is called ripple. Because a full-wave output has twice as many pulses and never drops to zero for a whole half-cycle, it carries much less ripple than the half-wave version, which is why it is nearly always preferred. A large capacitor across the load (a filter) then charges on each peak and discharges slowly through the load between peaks, smoothing the humps toward a steady DC level. The bigger the capacitor and load resistance, the smaller the ripple.

7The Zener diode as a voltage regulator

A Zener diode is a heavily doped junction designed to be run in reverse breakdown — the very region that destroys an ordinary diode. Because it is heavily doped its depletion region is thin, so breakdown happens at a low, sharply defined Zener voltage V_Z (a few volts). In that region a large change in reverse current produces almost no change in voltage: the reverse characteristic is a near-vertical line at V_Z.

That flatness is exactly what a voltage regulator needs. Put the Zener in reverse across the load, fed through a series resistor. If the input voltage rises, the Zener simply draws more current — but the voltage across it, and therefore across the load, stays pinned at V_Z. The series resistor absorbs the surplus. The load sees a rock-steady voltage even as the supply wanders, which is why the Zener is the textbook regulator.

8The transistor: α and β

A bipolar junction transistor is a sandwich of three doped regions — emitter, base and collector — making two junctions back to back. It comes as n-p-n or p-n-p. The base is made very thin and lightly doped; the emitter is heavily doped to inject plenty of carriers.

In normal operation the emitter–base junction is forward biased and the collector–base junction is reverse biased. The emitter injects a flood of carriers into the base; because the base is so thin, only a small fraction recombine there (this is the small base current), and the reverse-biased collector sweeps up almost all the rest. So the three currents obey the simple node rule:

Two current gains describe how faithfully the emitter current reaches the collector:

Because I_C is a little less than I_E, α is just under 1 (typically 0.95–0.99). But I_B is tiny, so β is large (typically 20–200) — that is the transistor's power to amplify: a small base current controls a much larger collector current. The two gains are not independent. Start from the definitions and the node rule:

Dividing top and bottom of I_C / (I_E − I_C) by I_E turns every current ratio into α, and out drops the relation. Rearranged the other way, α = β / (1 + β). Because α sits so close to 1, the denominator 1 − α is tiny, which is why a modest α = 0.99 already means β = 99.

9Logic gates

Digital electronics treats voltage as just two states — high = 1 and low = 0 — and builds every computation from a handful of logic gates, each a circuit that turns input bits into an output bit by a fixed rule. A truth table lists that rule for every combination of inputs.

• NOT (inverter): one input, output is its opposite. Y = A̅.
• AND: output 1 only when all inputs are 1. Y = A · B.
• OR: output 1 when any input is 1. Y = A + B.
• NAND = AND then NOT: output 0 only when both inputs are 1.
• NOR = OR then NOT: output 1 only when both inputs are 0.
• XOR (exclusive-OR): output 1 only when the inputs differ. Y = A ⊕ B.

10Common confusions to clear up

• A hole is not just "the absence of an electron sitting still" — it moves and carries current. Treat it as a real positive carrier of charge +e drifting through the valence band.
• Doped semiconductors are still electrically neutral. n-type is not negatively charged: the extra free electrons are exactly balanced by the fixed positive donor ions. "n" and "p" name the mobile majority carrier, not a net charge.
• Forward bias means + to the p-side, not + to the n-side. Forward bias shrinks the barrier and the depletion region; reverse bias widens both.
• A Zener is meant to work in reverse breakdown. The breakdown that wrecks an ordinary diode is the Zener's normal, useful operating region.
• α is always less than 1; β is much greater than 1. They are not two names for the same number — they are linked by β = α/(1−α).
• Semiconductor resistance falls with heating. Opposite to a metal — a negative temperature coefficient.

11Check yourself

Class 12 Physics · Semiconductor Electronics · aligned to NCERT Chapter 14 · SmartStudy.School