Semiconductor Electronics: Materials, Devices and Simple Circuits

Before 1948 electronics ran on vacuum tubes: electrons boiled off a heated cathode travelled through a vacuum to the anode, so a tube needed a heater, about a hundred volts and an evacuated envelope, and was bulky, fragile and short-lived. Its useful property was that current flowed only from cathode to anode.

In the late 1940s it was found that a suitably doped semiconductor does the same job with no heater, no vacuum and a small voltage. The carriers, electrons and holes, are already inside the solid, and their flow can be controlled by light, heat or an applied voltage. Semiconductor devices are small, cheap, rugged, low-power and fast.

The chapter follows its title: the material (Si, Ge, doping), the device (the p-n junction diode) and the circuit (the rectifier). Every board question is built from five blocks: energy bands, doping, junction formation, the biased diode with its characteristics, and the rectifiers with their waveforms.

By conductivity: metals have resistivity ρ of about 10⁻² to 10⁻⁸ Ω m, semiconductors 10⁻⁵ to 10⁶ Ω m, insulators 10¹¹ to 10¹⁹ Ω m. Semiconductors may be elemental (Si, Ge) or compound: inorganic (CdS, GaAs, CdSe, InP), organic (anthracene, doped phthalocyanines) and organic polymers (polypyrrole, polyaniline, polythiophene). The chapter deals with Si and Ge.

The physical classification uses energy bands. In an isolated atom the electron energies are sharp levels. In a crystal the outer levels of neighbouring atoms overlap and, by the Pauli principle, spread into bands of closely spaced allowed energies. The highest band filled at 0 K is the valence band; the next above it is the conduction band; their separation, from E_v to E_c, is the energy band gap E_g. Electrons in the conduction band move freely and conduct; those in a full valence band cannot.

Metals: the conduction band is partly filled or overlaps the valence band, E_g = 0. Insulators: full valence band, empty conduction band, large gap E_g > 3 eV that thermal energy cannot bridge. Semiconductors: the same picture with a small gap, E_g < 3 eV, so at room temperature some electrons cross. Diamond has E_g = 5.4 eV, Si 1.1 eV, Ge 0.7 eV; carbon with the same lattice is an insulator while Si and Ge are semiconductors.

Asked every year: heating a metal increases lattice vibrations and its resistance rises; heating a semiconductor creates more carriers and its resistance falls.

A pure semiconductor is called intrinsic. Si and Ge have four valence electrons and the diamond structure: each atom shares one electron with each of four neighbours, so all four valence electrons sit in covalent bonds. At 0 K every bond is intact, the valence band is full, the conduction band empty, and the crystal is an insulator.

At room temperature thermal energy breaks a few bonds. The freed electron goes to the conduction band. The vacancy left in the bond is short of one electron, so it carries a net positive charge, and is called a hole. A bound electron from a neighbouring bond can jump into it, which moves the hole to the neighbour's site; the hole therefore behaves as a free carrier of charge +e. In band language, a bond breaking lifts an electron to the conduction band and leaves a hole in the valence band.

Electrons and holes are generated in pairs, so n_e = n_h = n_i, the intrinsic carrier concentration. Generation is balanced by recombination, an electron falling into a hole so that both vanish; n_i is fixed at a given temperature but rises steeply with it.

Under a field electrons move against it and holes along it; both currents add, I = I_e + I_h, and σ = e(n_eμ_e + n_hμ_h). Intrinsic conductivity is small and strongly temperature dependent, so pure Si is of little use in devices; doping is the fix.

Adding a small, controlled amount of impurity, a few parts per million, is doping; the result is an extrinsic semiconductor. The dopant must be nearly the same size as Si or Ge so it replaces a host atom without distorting the lattice. Two kinds are used: pentavalent (As, Sb, P) and trivalent (In, B, Al).

n-type. A pentavalent atom uses four electrons in bonds with its four Si neighbours; the fifth is bound only weakly, with an ionisation energy of about 0.01 eV in Ge and 0.05 eV in Si, so thermal energy frees it into the conduction band. Each dopant donates one electron: a donor, with level E_D just below the conduction band. Electrons are majority carriers, thermally generated holes minority carriers, n_e >> n_h. The crystal stays neutral: the extra electron is balanced by the extra proton in the dopant nucleus.

p-type. A trivalent atom completes only three bonds; the fourth has a vacancy, a hole. An electron from a neighbouring bond can fill it, so the impurity accepts an electron: an acceptor, with level E_A just above the valence band. Holes are majority, electrons minority, n_h >> n_e.

Doping raises one carrier density and, by increasing recombination, lowers the other; in equilibrium n_en_h = n_i². Example: Si with 5 × 10²⁸ atoms m⁻³ doped with 1 ppm As, n_i = 1.5 × 10¹⁶ m⁻³: n_e = 5 × 10²² m⁻³, n_h = 2.25 × 10³²/5 × 10²² = 4.5 × 10⁹ m⁻³. Conductivity is then set by the doping, not by temperature.

A p-n junction is the boundary between p-type and n-type regions inside one crystal. It cannot be made by pressing two slabs together: any surface is rough on the atomic scale, far rougher than the interatomic spacing, so continuous atomic contact is impossible. Instead a pentavalent impurity is diffused into part of a p-type wafer, converting that part to n-type.

Diffusion. Holes are far more concentrated on the p-side and electrons on the n-side, so holes diffuse p → n and electrons n → p. A hole leaving the p-side (or an electron arriving and recombining) leaves a negative immobile acceptor ion; an electron leaving the n-side leaves a positive immobile donor ion. A layer of fixed charge, emptied of mobile carriers, forms on both sides: the depletion region (space-charge region), about a tenth of a micrometre thick.

Drift. The fixed charges set up an electric field across the depletion region, from n to p. It opposes further diffusion of majority carriers but sweeps minority carriers across: electrons p → n, holes n → p. This drift current is opposite to the diffusion current.

As ions accumulate the field grows, diffusion falls and drift rises until the two are equal and opposite; net current is zero and the depletion width is fixed. The potential difference across the depletion region, produced by the loss of electrons from the n-side and their gain by the p-side, is the barrier potential V₀, n-side higher: about 0.7 V for Si and 0.3 V for Ge. It is a barrier because it opposes the movement of majority carriers.

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

Forward bias. p-side to the positive terminal. The depletion region has almost no carriers and hence very high resistance, so nearly all the applied voltage V drops across it, opposing the built-in field. The barrier becomes V₀ − V and the width decreases. Majority carriers cross: electrons n → p, holes p → n. On the far side they are minority carriers (minority carrier injection) and diffuse away, keeping the current flowing. The current is of the order of milliamperes and rises sharply beyond the cut-in (threshold) voltage, about 0.2 V for Ge and 0.7 V for Si.

Reverse bias. n-side to the positive terminal. The applied voltage adds to the built-in field: the barrier becomes V₀ + V and the width increases. Majority carriers are blocked; only minority carriers are swept across. Their number is set by thermal generation, not by the voltage, so the reverse current is a few microamperes and nearly constant: the reverse saturation current. At the breakdown voltage V_br the current rises suddenly; an ordinary diode is not operated there.

V–I characteristics. Connect the diode to a battery through a potentiometer, with a milliammeter in series and a voltmeter across the diode; reverse the battery and use a microammeter for reverse bias. The forward curve stays near zero up to the cut-in voltage then rises steeply; the reverse curve is a small flat current up to V_br. The diode conducts one way only, which rectification uses. Because the curve is non-linear one defines the dynamic resistance r_d = ΔV/ΔI: for a Si diode at 0.7 V, 10 mA and 0.8 V, 20 mA, r_d = 0.1 V/10 mA = 10 Ω; with 1 μA at −10 V the reverse resistance is 10⁷ Ω.

Rectification is converting alternating voltage into unidirectional voltage. A diode conducts only when forward biased, so it passes one half of each cycle and blocks the other.

Half-wave rectifier. The AC input feeds a transformer primary; the secondary is in series with the diode and a load R_L. In the positive half-cycle the end joined to the p-side is positive, the diode conducts and the voltage across R_L follows the input. In the negative half-cycle the diode is reverse biased and the output is zero. One pulse per input cycle, so the output frequency equals the input: 50 Hz in, 50 Hz out.

Full-wave rectifier. Diodes D₁ and D₂ are connected to the two ends of a centre-tapped secondary, both pointing to a common point, and R_L runs from that point to the centre tap. The two ends are always at opposite polarity with respect to the tap. In the positive half-cycle the upper end is positive: D₁ conducts, D₂ is off. In the negative half-cycle the lower end is positive: D₂ conducts, D₁ is off. Current through R_L is in the same direction in both halves, one pulse per half-cycle, so the output frequency is twice the input: 100 Hz for 50 Hz mains. The diodes conduct alternately, never together.

Filter. A capacitor across R_L charges to the peak while the diode conducts and discharges slowly through R_L as the input falls, so the output stays near the peak; the larger R_LC compared with the period, the smaller the ripple. Series inductors also serve as filters. Transformer, rectifier and filter form the DC supply in almost every electronic device.