Semiconductor Electronics: Materials, Devices and Simple Circuits: NEET notes

1. From valves to semiconductors

NCERT §14.1

• Every electronic circuit is built from devices that control a flow of electrons. Until the transistor arrived in 1948, those devices were mostly vacuum tubes.
• Vacuum tubes are named by their electrode count: the diode has two (anode, also called plate, and cathode), the triode three (cathode, plate, grid), the tetrode four and the pentode five.
• A heated cathode supplies the electrons, and the voltages on the electrodes steer them. The space between electrodes must be evacuated, or the electrons would lose energy colliding with air molecules.
• Electrons can travel only from cathode to anode, one way, which is why these tubes were also called valves.
• Valves are bulky, draw a lot of power, usually run at high voltages (around 100 V), and have short lives and poor reliability.
• From the 1930s it became clear that some solid semiconductors and their junctions let us control both how many charge carriers there are and which way they move. Light, heat or a small voltage can change the number of mobile charges.
• In a semiconductor device the carriers are produced and flow inside the solid itself, so there is no heated filament and no vacuum. The devices are small, use little power, work at low voltages and last long.
• Even cathode ray tube screens, which work like vacuum tubes, have given way to LCD monitors run by solid-state circuits. Long before the theory was understood, a galena crystal (lead sulphide, PbS) touched by a metal point served as a radio-wave detector.
• This chapter covers the p-n junction diode, a two-electrode device, and its use in rectifier circuits.

2. Classifying solids by conductivity

NCERT §14.2

• Solids can be sorted by conductivity σ, or by its reciprocal, resistivity ρ = 1/σ.
• Metals: ρ ~ 10⁻² to 10⁻⁸ Ω m, so σ ~ 10² to 10⁸ S m⁻¹.
• Semiconductors: ρ ~ 10⁻⁵ to 10⁶ Ω m, so σ ~ 10⁵ to 10⁻⁶ S m⁻¹, in between metals and insulators.
• Insulators: ρ ~ 10¹¹ to 10¹⁹ Ω m, so σ ~ 10⁻¹¹ to 10⁻¹⁹ S m⁻¹.
• These ranges only indicate orders of magnitude; real materials can fall outside them. Resistivity alone does not settle the class, and the band picture gives the deeper difference.
• Elemental semiconductors: silicon (Si) and germanium (Ge).
• Compound semiconductors can be inorganic (CdS, GaAs, CdSe, InP), organic (anthracene, doped phthalocyanines) or organic polymers (polypyrrole, polyaniline, polythiophene).
• Most devices today use Si, Ge or inorganic compounds. Since 1990 a few devices built on organic and polymer semiconductors have appeared, the beginnings of polymer and molecular electronics.
• The chapter sticks to inorganic, mainly elemental, semiconductors; the same ideas largely carry over to compound ones.

3. Energy bands

NCERT §14.2

• In an isolated atom an electron's energy is fixed by its orbit. In a solid the atoms are so close that outer orbits of neighbours come near or overlap, which changes how electrons move.
• No two electrons in a crystal see exactly the same surrounding charges, so each has a slightly different energy. These closely spaced levels merge into energy bands that vary almost continuously.
• The band holding the valence electrons' levels is the valence band; the band above it is the conduction band. With no outside energy, the valence electrons all stay in the valence band.
• Si's outermost electrons are in the n = 3 orbit and Ge's in n = 4. Each atom has 4 outer electrons but room for 8, so a crystal of N atoms has 4N valence electrons and 8N available states.
• At the atomic spacing of Si and Ge, the 8N states split into two bands of 4N each, separated by an energy gap Eg. At absolute zero the lower band (valence band) is completely full and the upper band (conduction band) is completely empty.
• EC is the bottom of the conduction band and EV the top of the valence band. The band gap is Eg = EC − EV; it can be large, small or zero depending on the material.
• Metals: the conduction band is partly filled, or the two bands overlap, so many electrons are free to move. Resistance is low.
• Insulators: Eg > 3 eV. The conduction band is empty and heat cannot lift electrons across so wide a gap, so no conduction occurs.
• Semiconductors: Eg < 3 eV. At room temperature a few electrons gain enough thermal energy to cross into the conduction band, so the resistance is far below an insulator's.
• When an electron is lifted across the gap it also leaves an empty level in the valence band, so conduction can happen both in the conduction band and through the vacancies in the valence band.

4. Intrinsic semiconductors

NCERT §14.3

• Pure Si and Ge form a diamond-like lattice: every atom has four nearest neighbours. The lattice spacing a is 3.56 Å for carbon, 5.43 Å for silicon and 5.66 Å for germanium.
• Each atom shares one of its four valence electrons with each neighbour and takes a share of one from each. Such a shared pair is a covalent (valence) bond.
• At low temperature every bond is intact. As temperature rises, thermal energy frees a few electrons, which become conduction electrons and leave behind a vacancy in the bond.
• The freed electron carries charge −q; the vacancy it leaves behaves like a particle of charge +q, called a hole.
• In an intrinsic (pure) semiconductor the numbers are equal: nₑ = nₕ = nᵢ (Eq. 14.1), where nᵢ is the intrinsic carrier concentration.
• Holes move: an electron from a neighbouring bond jumps into the vacancy, so the hole appears to shift to the site the electron left. This is really bound electrons moving, described as a hole moving; the originally freed electron plays no part.
• In an electric field, free electrons give an electron current Iₑ and holes drift towards the negative potential giving a hole current Iₕ. The total current is I = Iₑ + Iₕ (Eq. 14.2).
• Electron-hole pairs are also destroyed when an electron meets a hole (recombination). At equilibrium, generation and recombination go on at equal rates.
• At T = 0 K an intrinsic semiconductor behaves as an insulator; above 0 K thermal energy puts some electrons in the conduction band and an equal number of holes in the valence band.
• Example 14.1: C, Si and Ge share one lattice structure, but their four bonding electrons sit in the 2nd, 3rd and 4th orbits. The energy to free one is highest for C and least for Ge, so C has negligible free electrons (an insulator) while Si and Ge have significant numbers.

5. n-type and p-type semiconductors

NCERT §14.4

• At room temperature a pure semiconductor conducts too poorly to build useful devices. Adding a tiny amount of a suitable impurity, a few parts per million, raises its conductivity many times over.
• Deliberately adding impurity is doping, the impurity atoms are dopants, and the product is an extrinsic (impurity, doped) semiconductor. The dopant must not distort the lattice, so its atoms should be about the same size as Si or Ge.
• Pentavalent dopants (valency 5): arsenic (As), antimony (Sb), phosphorus (P). Trivalent dopants (valency 3): indium (In), boron (B), aluminium (Al).
• n-type: a pentavalent atom bonds four of its electrons with its Si neighbours. The fifth is barely held, needing only about 0.01 eV (Ge) or 0.05 eV (Si) to free it, against a gap of about 0.72 eV (Ge) or 1.1 eV (Si), so it is free at room temperature.
• Because it gives away an electron, a pentavalent dopant is a donor. The electrons it supplies depend on the doping level, not on temperature, while the intrinsic pairs from Si atoms grow only weakly with temperature.
• Extra electrons raise the recombination rate, so the holes fall even below the intrinsic number. Electrons are the majority carriers and holes the minority: nₑ ≫ nₕ (Eq. 14.3).
• p-type: a trivalent atom bonds with three neighbours, leaving the fourth bond one electron short, a hole. An electron from a nearby bond can fill it, moving the hole along. Each acceptor atom gives one hole.
• Once it takes that fourth electron, the acceptor becomes a fixed negative core. Holes are the majority carriers and electrons the minority: nₕ ≫ nₑ (Eq. 14.4).
• The crystal stays electrically neutral overall: the charge of the extra mobile carriers exactly balances the opposite charge on the fixed ionised dopant cores.
• Plentiful majority carriers mop up thermally made minority carriers, so doping indirectly lowers the minority concentration below nᵢ.

6. Carrier concentration and band levels

NCERT §14.4

• Doping adds energy levels inside the gap: a donor level ED just below EC in n-type material, and an acceptor level EA just above EV in p-type material.
• n-type: very little energy lifts electrons from ED into the conduction band. At room temperature most donors are ionised while only about 10¹² Si atoms are, so almost all conduction electrons come from donors.
• p-type: a small energy lets a valence electron jump up to EA and ionise the acceptor negatively; equivalently, a hole drops from EA into the valence band. Electrons rise and holes sink when they gain energy.
• At room temperature most acceptors are ionised, so the holes in the valence band come mainly from the impurity.
• In thermal equilibrium, nₑnₕ = nᵢ² (Eq. 14.5), whatever the doping.
• Band gaps: C (diamond) 5.4 eV, Si 1.1 eV, Ge 0.7 eV. Tin (Sn) is also in group IV but is a metal, because its gap is 0 eV.
• Example 14.2: pure Si with 5 × 10²⁸ atoms m⁻³ is doped with 1 ppm arsenic, so ND = 5 × 10²⁸ × 10⁻⁶ = 5 × 10²² m⁻³. Since nᵢ = 1.5 × 10¹⁶ m⁻³ is negligible beside this, nₑ ≈ ND = 5 × 10²² m⁻³.
• Then nₕ = nᵢ²/nₑ = (2.25 × 10³²)/(5 × 10²²) ≈ 4.5 × 10⁹ m⁻³: over ten trillion times fewer holes than electrons.
• In compound semiconductors, shifting the ratio of elements can also change the type. Ideal GaAs has Ga : As = 1 : 1, but Ga-rich or As-rich crystals such as Ga₁.₁As₀.₉ or Ga₀.₉As₁.₁ act as defects that alter its properties.
• EC and EV are not located at any particular place in the solid; drawn as straight lines, they just mark the bottom of the conduction band and the top of the valence band.

7. Formation of a p-n junction

NCERT §14.5.1

• A p-n junction underlies the diode, the transistor and many other devices. It is made by adding a precise small amount of pentavalent impurity to part of a thin p-type Si wafer, turning that part n-type.
• Two processes shape the junction: diffusion and drift.
• Diffusion: holes are concentrated on the p-side and electrons on the n-side, so holes spread p → n and electrons spread n → p. This gives the diffusion current.
• Each electron leaving the n-side leaves an immobile ionised donor (positive) behind; each hole leaving the p-side leaves an immobile ionised acceptor (negative). A positive space-charge layer builds on the n-side and a negative one on the p-side.
• Together these layers form the depletion region, emptied of free carriers. It is about one-tenth of a micrometre thick.
• The space charges set up an electric field from the n-side (positive) to the p-side (negative). It pushes electrons from p to n and holes from n to p; this field-driven motion is drift, and the drift current runs opposite to the diffusion current.
• At first diffusion dominates. As the space charge grows, so do the field and the drift current, until drift equals diffusion. In equilibrium there is no net current across the junction.
• The n-side has lost electrons and the p-side gained them, so the n-side is positive relative to the p-side. This barrier potential opposes further flow of electrons from n to p.
• Example 14.3: two separate slabs pressed together cannot make a junction. Even the flattest surface is far rougher than the interatomic spacing (about 2 to 3 Å), so there is no continuous atomic contact and carriers meet a break.

8. Diode under forward and reverse bias

NCERT §14.6

• A semiconductor diode is a p-n junction with metal contacts at its ends, a two-terminal device. In its symbol, the arrow points in the conventional direction of current under forward bias.
• Forward bias: p-side to the battery's positive terminal, n-side to the negative. The applied voltage drops almost entirely across the depletion region, whose resistance far exceeds that of the p and n regions.
• Forward bias opposes the built-in potential V₀, so the depletion layer narrows and the barrier falls to (V₀ − V).
• A small V lowers the barrier a little and only the most energetic carriers cross, so current is small. A larger V lowers it further, many more carriers cross, and the current rises.
• Electrons cross into the p-side and holes into the n-side, where each is a minority carrier: this is minority carrier injection. Their concentration peaks at the junction edges and they diffuse away from it, and these diffusion currents make up the forward current, typically in mA.
• Reverse bias: n-side positive, p-side negative. The applied voltage adds to the barrier, raising it to (V₀ + V) and widening the depletion region.
• This all but stops diffusion (electrons n → p, holes p → n), so the diffusion current falls enormously compared with forward bias.
• Minority carriers that wander near the junction are swept across by its field to their majority side. This drift current is only a few µA, because minority carriers are scarce; under forward bias it is still there but negligible beside the mA injected current.
• The reverse current hardly depends on voltage: even a small reverse bias sweeps across every minority carrier that arrives, so the current is limited by the supply of minority carriers, not by V.

9. Diode V-I characteristics

NCERT §14.6.2

• To trace the V-I curve, a battery feeds the diode through a potentiometer (or rheostat) so the voltage can be varied. A milliammeter reads the large forward current and a microammeter the tiny reverse current.
• Forward bias: the current stays almost zero until the voltage passes a threshold, then rises steeply (exponentially) for small further increases.
• This threshold or cut-in voltage is about 0.2 V for a germanium diode and about 0.7 V for a silicon diode.
• Reverse bias: the current is very small (µA) and almost constant as the voltage changes. This is the reverse saturation current.
• At a critical reverse voltage, the breakdown voltage Vbr, the reverse current suddenly shoots up. Unless an external circuit limits it below the rated value, overheating destroys the junction; the same happens in forward bias if the current exceeds its rating.
• General-purpose diodes are used only below breakdown, in the reverse saturation region.
• So a diode passes current essentially one way: its forward resistance is low and its reverse resistance is high. Rectifiers exploit this.
• Dynamic resistance: rd = ΔV/ΔI (Eq. 14.6), the ratio of a small change in voltage to the resulting small change in current.
• Example 14.4 (silicon diode): between 10 mA at 0.7 V and 20 mA at 0.8 V, the forward resistance is rfb = 0.1 V / 10 mA = 10 Ω.
• At V = −10 V the curve gives I = −1 µA, so the reverse resistance is rrb = 10 V / 1 µA = 1.0 × 10⁷ Ω, a million times the forward value.

10. Half-wave and full-wave rectifiers

NCERT §14.7

• Because a diode conducts only when forward biased, an alternating voltage across it drives current only in that part of the cycle. Turning ac into one-way voltage like this is rectification, and the circuit is a rectifier.
• Half-wave rectifier: one diode in series with a load resistor RL across a transformer secondary (terminals A and B). When A is positive the diode conducts; when A is negative it is reverse biased and blocks.
• The reverse saturation current is so small it counts as zero, so the output is a train of positive half-cycles with gaps: still varying, but in one direction only.
• The diode's reverse breakdown voltage must be well above the peak ac voltage of the secondary, or the negative half-cycle would break it down.
• Full-wave rectifier: two diodes whose p-sides go to the two ends of a centre-tapped secondary. Their n-sides are joined, and the output is taken between that common point and the centre tap.
• Each diode sees only half of the total secondary voltage. When A is positive with respect to the centre tap, B is negative (out of phase): D1 conducts and D2 blocks.
• In the other half-cycle A is negative and B positive, so D2 conducts and D1 blocks. Current flows through RL in the same direction both times, giving output in both halves of the cycle.
• Full-wave rectification uses both halves, so it is more efficient than half-wave. A second full-wave circuit, the bridge, uses four diodes and needs no centre tap.
• Output pulses: half-wave gives one per input cycle and full-wave two. For 50 Hz input, the output frequency is 50 Hz for half-wave and 100 Hz for full-wave (Exercise 14.6).

11. Filtering with a capacitor

NCERT §14.7

• Rectified output is a string of half-sine pulses: one-way, but not steady. Circuits that smooth it into nearly pure dc are called filters, because they seem to filter out the ac ripple.
• The usual filter is a capacitor across the output terminals, in parallel with RL. An inductor in series with RL can do the same job.
• While the rectified voltage rises the capacitor charges. With no load it would stay charged at the peak voltage.
• With a load, the capacitor discharges through RL between pulses and its voltage sags, then the next pulse recharges it to the peak.
• How fast the voltage sags depends inversely on the time constant, the product C × RL. A large time constant means a small sag.
• To make the time constant large, C must be large, so capacitor input filters use large capacitors.
• The filtered output stays near the peak of the rectified voltage. This capacitor input filter is the type most widely used in power supplies.

Must-know facts

1. Resistivity: metals 10⁻² to 10⁻⁸ Ω m, semiconductors 10⁻⁵ to 10⁶ Ω m, insulators 10¹¹ to 10¹⁹ Ω m.
2. Band gap: insulators Eg > 3 eV, semiconductors Eg < 3 eV, metals Eg ≈ 0 or overlapping bands.
3. Eg: C (diamond) 5.4 eV, Si 1.1 eV, Ge 0.7 eV, Sn 0 eV (a metal).
4. Si and Ge crystal: 4N valence electrons, 8N states split into a full valence band (4N) and an empty conduction band (4N) at 0 K.
5. Intrinsic: nₑ = nₕ = nᵢ; current I = Iₑ + Iₕ.
6. Lattice spacing: C 3.56 Å, Si 5.43 Å, Ge 5.66 Å.
7. Donors (n-type): As, Sb, P (pentavalent). Acceptors (p-type): In, B, Al (trivalent).
8. Energy to free a donor electron: about 0.01 eV in Ge and 0.05 eV in Si.
9. n-type: nₑ ≫ nₕ; p-type: nₕ ≫ nₑ; always nₑnₕ = nᵢ².
10. Example 14.2: 1 ppm As in Si gives nₑ ≈ 5 × 10²² m⁻³ and nₕ ≈ 4.5 × 10⁹ m⁻³.
11. Depletion region thickness: about one-tenth of a micrometre.
12. Barrier height: (V₀ − V) in forward bias, (V₀ + V) in reverse bias.
13. Cut-in voltage: about 0.7 V for Si and 0.2 V for Ge.
14. Forward current in mA; reverse saturation current in µA.
15. Dynamic resistance rd = ΔV/ΔI; Example 14.4 gives 10 Ω forward and 1.0 × 10⁷ Ω reverse.
16. Rectifier output frequency for 50 Hz input: 50 Hz half-wave, 100 Hz full-wave.
17. Full-wave with a centre tap: two diodes, each rectifying half the secondary voltage; the bridge circuit uses four diodes.
18. A capacitor filter goes in parallel with RL; a large C × RL gives a steadier dc near the peak voltage.

Common traps

Formulas

Key terms

Valence band

The band of energy levels holding the valence electrons; completely full at 0 K in Si and Ge.

Conduction band

The band above the valence band; electrons in it are free to move and carry current.

Band gap (Eg)

The energy between the top of the valence band and the bottom of the conduction band.

Hole

A vacancy in a covalent bond that acts as a mobile charge of +q.

Intrinsic semiconductor

A pure semiconductor, with equal numbers of free electrons and holes.

Doping

Adding a small, controlled amount of a suitable impurity to raise conductivity.

Donor

A pentavalent dopant that gives one free electron and becomes a fixed positive ion.

Acceptor

A trivalent dopant that takes an electron, creating a hole and becoming a fixed negative ion.

Majority carriers

The more numerous carriers: electrons in n-type, holes in p-type.

Depletion region

The layer at a p-n junction emptied of free carriers, holding only fixed ions.

Barrier potential

The potential difference across the junction that opposes further diffusion.

Drift current

Current from carriers pushed by the junction's electric field.

Cut-in voltage

The forward voltage beyond which diode current rises sharply: about 0.7 V (Si), 0.2 V (Ge).

Breakdown voltage

The reverse voltage at which the reverse current suddenly increases.

Rectifier

A circuit that turns alternating voltage into one-way (pulsating) voltage.

Filter

A capacitor or inductor that smooths the rectified pulses towards steady dc.