Semiconductor Electronics: Materials, Devices and Simple Circuits

In this chapter: classification of solids by conductivity and by energy bands, intrinsic semiconductors, electrons and holes, n-type and p-type semiconductors, the relation n_en_h = n_i², formation of a p-n junction, depletion region and barrier potential, the diode in forward and reverse bias, V-I characteristics, half-wave and full-wave rectifiers.

Classification of solids

On the basis of conductivity (NCERT values):

Elemental semiconductors are silicon and germanium. Compound semiconductors include inorganic ones such as CdS, GaAs, CdSe and InP, and organic ones such as anthracene and polymers like polypyrrole.

Energy bands

In a crystal, the energy levels of the atoms spread into bands. The valence band holds the valence electrons; above it lies the conduction band, and the gap between them is the energy gap E_g.

• Metals: the conduction band is partly filled or overlaps the valence band, so many electrons are free to move.
• Insulators: the gap is large (E_g > 3 eV); diamond, for example, has about 5.4 eV. Thermal energy cannot lift electrons across.
• Semiconductors: the gap is small (E_g < 3 eV): about 1.1 eV for silicon and 0.7 eV for germanium. At room temperature a few electrons cross the gap and conduct; at 0 K a semiconductor behaves as an insulator.

Intrinsic semiconductors

In pure Si or Ge, each atom forms four covalent bonds with its neighbours. When thermal energy breaks a bond, a free electron is released and leaves behind a vacancy with an effective charge +e, called a hole. A neighbouring bound electron can jump into the hole, so the hole effectively moves and carries current. In a pure semiconductor

Electrons and holes also recombine continuously, and at equilibrium the rate of generation equals the rate of recombination. Because n_i rises with temperature, the resistivity of a semiconductor falls as it gets hotter, the opposite of a metal.

Extrinsic semiconductors

Adding a tiny amount of a suitable impurity (doping, a few parts per million) increases conductivity enormously. The dopant atoms should be about the same size as the host atoms so they fit into the lattice without distorting it.

An n-type or p-type semiconductor is still electrically neutral: the extra electrons of an n-type crystal are balanced by the positive donor ions. In thermal equilibrium the product of the carrier concentrations is fixed:

Doping one type of carrier therefore suppresses the other, since extra electrons recombine with holes.

Worked example: A silicon crystal (5 × 10²⁸ atoms m⁻³, n_i = 1.5 × 10¹⁶ m⁻³) is doped with 1 ppm of arsenic. Find the electron and hole concentrations.
Solution: Donor atoms = 5 × 10²⁸ × 10⁻⁶ = 5 × 10²² m⁻³, so n_e ≈ 5 × 10²² m⁻³ (thermally generated electrons are negligible in comparison). n_h = n_i²/n_e = (2.25 × 10³²)/(5 × 10²²) = 4.5 × 10⁹ m⁻³.

The p-n junction

When p-type and n-type regions are formed in one crystal, electrons diffuse from the n side (where they are many) to the p side, and holes diffuse from p to n. This diffusion current flows from p to n. Each electron that leaves the n side uncovers a fixed positive donor ion, and each hole that leaves the p side uncovers a fixed negative acceptor ion. A thin layer on both sides of the junction is thus emptied of free carriers; it is called the depletion region.

The fixed ions set up an electric field from the n side to the p side. This field sweeps minority carriers across the junction, giving a drift current opposite to the diffusion current. At equilibrium the two currents are equal and there is no net current. The potential difference across the depletion region is the barrier potential V₀, with the n side at the higher potential.

Semiconductor diode

A p-n junction with metal contacts at its ends is a diode. Its symbol is an arrow (the p side) pointing to a bar (the n side); the arrow shows the direction of conventional current in forward bias.

Forward bias

The p side is connected to the positive terminal. The applied voltage opposes the built-in potential, so the effective barrier becomes V₀ − V and the depletion region becomes narrower. Majority carriers cross in large numbers and the current rises sharply once the applied voltage exceeds the threshold (cut-in) voltage, about 0.7 V for silicon and 0.2 V for germanium. Forward current is of the order of milliamperes.

Reverse bias

The n side is connected to the positive terminal. The barrier becomes V₀ + V and the depletion region widens. Diffusion of majority carriers almost stops; only minority carriers drift across, giving a small reverse current of a few microamperes that hardly changes with voltage (the reverse saturation current). At a large enough reverse voltage, the breakdown voltage V_br, the reverse current rises suddenly; an ordinary diode can be damaged if operated beyond it.

The dynamic resistance of a diode is r_d = ΔV/ΔI at a given point on the characteristic. It is low in forward bias and very high in reverse bias, which is the one-way behaviour that makes rectification possible.

Worked example: On the forward characteristic of a silicon diode, the current rises from 10 mA to 30 mA when the voltage rises from 0.7 V to 0.8 V. Find the dynamic resistance in this range.
Solution: r_d = ΔV/ΔI = 0.1 V/(20 × 10⁻³ A) = 5 Ω.

The diode as a rectifier

A rectifier converts AC into DC (in one direction, though not steady).

• Half-wave rectifier: a single diode in series with the load. It conducts only during the half cycle in which it is forward biased, so the output has one hump per cycle and the other half cycle is lost. The output frequency equals the input frequency (50 Hz for mains).
• Full-wave rectifier: two diodes and a centre-tap transformer. The two ends of the secondary are always in opposite phase with respect to the centre tap, so D₁ conducts in one half cycle and D₂ in the other. Current through the load is in the same direction in both halves, and the output has two humps per input cycle, so the ripple frequency is 100 Hz for a 50 Hz input.

The pulsating output is smoothed by a filter, usually a capacitor connected across the load. It charges to the peak voltage while a diode conducts and discharges slowly through the load in between, so the output stays close to the peak. A larger capacitor (larger CR_L) gives a smoother output.

Zener diodes, optoelectronic devices (photodiode, LED, solar cell), transistors and logic gates were removed from the rationalised NCERT book. Some of them still appear in the JEE Main syllabus, so check the current syllabus of your exam.

Common mistakes: (1) Saying an n-type semiconductor is negatively charged; it is neutral. (2) Mixing up donors and acceptors: pentavalent atoms give n-type, trivalent atoms give p-type. (3) Saying the depletion region widens in forward bias; it narrows in forward bias and widens in reverse bias. (4) Thinking reverse current is due to majority carriers; it is due to minority carriers. (5) Giving 50 Hz as the output frequency of a full-wave rectifier on 50 Hz mains; it is 100 Hz.

JEE and NEET focus

• Energy band pictures of metals, semiconductors and insulators, with typical band gaps.
• n-type and p-type doping, majority and minority carriers, and n_en_h = n_i² numericals.
• Formation of the depletion layer, barrier potential, diffusion and drift currents.
• Forward and reverse bias behaviour, the V-I characteristic and dynamic resistance.
• Half-wave and full-wave rectifier circuits, output waveforms and ripple frequency; circuits with ideal diodes.

Practice questions