Semiconductor Electronics

What the chapter is about

• Semiconductor devices replaced vacuum tubes because the supply and flow of charge carriers happens inside the solid itself: no heated cathode, no evacuated space. They are small, consume low power, work at low voltage and have long life and high reliability.
• The chapter runs in a straight line: classify solids by band gap, understand the pure (intrinsic) semiconductor, improve it by doping (extrinsic), join a p-type piece to an n-type piece (p-n junction), put contacts on it (diode), and use the diode to rectify ac.
• Semiconductors studied: elemental (Si, Ge) and compound inorganic (CdS, GaAs, CdSe, InP), plus organic ones (anthracene, doped phthalocyanines) and organic polymers (polypyrrole, polyaniline, polythiophene) mentioned only by name.

Classification by conductivity

• Resistivity alone is not the only criterion — the band picture and the way conductivity changes with temperature separate them far more sharply.

The band picture

• In an isolated atom the electron energies are discrete levels. In a solid the atoms are so close that the outer orbits overlap, every electron sees a slightly different pattern of surrounding charge, and the levels spread into continuous energy bands.
• Valence band: the band containing the energy levels of the valence electrons. Conduction band: the band above it. Energy band gap (forbidden gap) $E_g = E_C - E_V$: the range between the top of the valence band and the bottom of the conduction band in which no allowed electron energy state exists.
• For a Si or Ge crystal of $N$ atoms: $4N$ valence electrons and $8N$ available states, splitting into a valence band of $4N$ states (full at $0$ K) and a conduction band of $4N$ states (empty at $0$ K).
• Electrons in the conduction band are free to move and carry current; a vacancy left in the valence band (a hole) also conducts.

• Band diagrams in words. Metal: two shaded blocks touching or overlapping, no gap drawn. Insulator: two shaded blocks far apart with a wide blank strip labelled $E_g > 3$ eV. Semiconductor: the same two blocks with only a narrow blank strip labelled $E_g < 3$ eV; at $T > 0$ K put a few dots at the bottom of the conduction band and the same number of empty circles at the top of the valence band.
• Standard gaps: C (diamond) $5.4$ eV, Si $1.1$ eV, Ge $0.72$ eV, Sn $0$ eV. C, Si and Ge have the same diamond lattice and four valence electrons each; the difference is that carbon's bonding electrons are in the second orbit (tightly bound), silicon's in the third and germanium's in the fourth (progressively less tightly bound). Hence $(E_g)_C > (E_g)_{Si} > (E_g)_{Ge}$, and hence carbon is an insulator while Si and Ge are semiconductors.

Intrinsic semiconductor

• A pure semiconductor with no added impurity. Si and Ge form a diamond-like structure in which every atom shares one of its four valence electrons with each of its four nearest neighbours: four covalent (valence) bonds per atom.
• At $T = 0$ K all bonds are intact, the valence band is full and the conduction band empty, so the crystal is a perfect insulator.
• At $T > 0$ K thermal energy breaks a few bonds. Each broken bond releases a free electron (charge $-q$) into the conduction band and leaves behind a vacancy of effective charge $+q$, called a hole. The hole behaves like a free particle of positive charge.
• Hole conduction: an electron in a neighbouring bond jumps into the vacancy, so the vacancy — the hole — appears to move the other way. The originally freed electron takes no part in this; hole motion is a convenient description of the motion of bound valence electrons.
• $n_e = n_h = n_i$, and the total current $I = I_e + I_h$. Under a field, electrons drift one way and holes the other, and the two currents add.
• Generation and recombination go on together; at equilibrium their rates are equal.
• Temperature: raising $T$ generates more pairs, so $\sigma$ increases and $\rho$ (and resistance) decreases. This negative temperature coefficient of resistance is the sharpest single distinction between a semiconductor and a metal.
• Resistivity-temperature graphs. Conductor: $\rho$ rises with $T$ — steeply at the lowest temperatures, then almost linearly. Semiconductor: $\rho$ starts very large at low $T$ and falls steeply, like a decaying exponential, as $T$ rises to about $300$ K.

Extrinsic semiconductor and doping

• At room temperature an intrinsic semiconductor conducts far too little, and its conductivity is entirely at the mercy of temperature, so no reliable device can be built from it. Doping fixes this.
• Doping: the deliberate, controlled addition of a small quantity of a suitable impurity (typically about 1 part per million) to a pure semiconductor, to increase its conductivity manifold. The impurity is the dopant; the doped material is an extrinsic (impurity) semiconductor.
• The dopant must not distort the lattice, so its atoms must be about the same size as Si or Ge atoms — which is why the dopants come from the neighbouring third and fifth groups.
• Pentavalent dopants (donors): As, Sb, P. Trivalent dopants (acceptors): In, B, Al.

• Why the impurity level matters: the ionisation energy of a donor is only about $0.01$ eV in Ge and $0.05$ eV in Si, against band gaps of $0.72$ eV and $1.1$ eV. Practically every dopant atom is therefore ionised at room temperature, while only a negligible fraction of the host atoms is — so the carriers of an extrinsic semiconductor come almost entirely from the dopant.
• Mass-action law: $n_e n_h = n_i^2$ in every case, in thermal equilibrium. Adding donors increases $n_e$ and therefore decreases $n_h$, because the increased electron population raises the recombination rate for holes.
• Charge neutrality holds throughout: the mobile carriers added are exactly balanced by the immobile ionised dopant cores.
• Doping level does not change with temperature; the intrinsic contribution does. So raising $T$ adds electron-hole pairs in equal numbers to both counts, though in an n-type sample the electrons still vastly outnumber the holes.

p-n junction

• Made from a single crystal: part of a p-type wafer is converted to n-type by diffusing in a pentavalent impurity. Two separate slabs pressed together will not do — surface roughness is far larger than the interatomic spacing ($2$ to $3$ Å), so there is no continuous contact and the junction behaves as a discontinuity for the carriers.
• Two processes act. Diffusion: holes diffuse p to n and electrons diffuse n to p, down their concentration gradients, giving a diffusion current. Drift: the field that this leaves behind sweeps minority carriers the other way, giving a drift current.
• Depletion region: as electrons leave the n-side they uncover immobile positive donor ions there, and as holes leave the p-side they uncover immobile negative acceptor ions there. This narrow double layer of immobile charge, stripped of mobile carriers, is the depletion region — about $10^{-7}$ m thick.
• The double layer sets up an electric field from the n-side to the p-side and hence a potential difference $V_0$ across the junction (about $0.1$ V to $0.3$ V), with the n-side at the higher potential. This is the barrier potential; it opposes further diffusion.
• Equilibrium: diffusion current grows the depletion layer, which grows the field, which grows the drift current, until the two currents are equal and opposite. The net current through an unbiased junction is then zero — not because carriers stop crossing, but because the two crossings cancel.
• Diagram in words: a rectangle split into a left p-region (small circles for holes) and a right n-region (dots for electrons); at the boundary a narrow strip carrying $-$ signs on the p-side and $+$ signs on the n-side; an arrow across the strip marked $V_0$, pointing from the n-side to the p-side.

Semiconductor diode

• A p-n junction with metallic contacts at both ends for applying an external voltage — a two-terminal device.
• Circuit symbol in words: a solid triangle (the arrowhead) whose apex touches a short bar perpendicular to the line. The triangle is the p-side (anode), the bar is the n-side (cathode), and the arrow points in the direction of conventional current under forward bias.

• Minority carrier injection: under forward bias electrons from the n-side cross into the p-side (where they are minority carriers) and holes from the p-side cross into the n-side, so the minority concentration near the junction rises well above its equilibrium value. The resulting diffusion of these injected carriers away from the junction is the forward current.
• V-I characteristic in words. Forward branch (first quadrant, volts in tenths of a volt, current in mA): almost flat and negligible until the threshold voltage, then rising almost vertically. Threshold (cut-in, knee) voltage about $0.2$ to $0.3$ V for Ge, about $0.7$ V for Si. Reverse branch (third quadrant, volts in units of volts, current in $\mu$A): a small, almost constant reverse saturation current over a wide range, then a sudden near-vertical increase at the breakdown voltage $V_{br}$.
• Why the reverse current is voltage-independent: it is carried by the few thermally generated minority carriers, and even a small reverse voltage sweeps essentially all of them across. The current is limited by the minority-carrier concentration, not by the applied voltage.
• Why the reverse current shoots up at breakdown: the junction field becomes strong enough to break covalent bonds directly, or existing carriers gain enough energy to knock more loose by collision (avalanche), so a very large number of carriers appears at once.
• Resistances: dynamic resistance $r_d = \Delta V/\Delta I$ from the steep forward part; static resistance $V/I$ from a point on the flat reverse part. The forward resistance is a few ohms to a few tens of ohms; the reverse resistance is of the order of $10^{6}$ to $10^{7}\,\Omega$.
• Increasing the doping concentration narrows the depletion layer.

Junction diode as a rectifier

• Rectifier: a circuit that converts an alternating voltage into a unidirectional (pulsating dc) one. It works because the diode conducts in forward bias and blocks in reverse bias — one-way conduction.
• Half-wave rectifier, circuit in words: the ac mains feeds the primary of a step-down transformer; one end A of the secondary goes through the diode $D$ to the top of the load $R_L$; the other end B goes straight to the bottom of $R_L$; the output $V_o$ is taken across $R_L$.
• Half-wave working: in the positive half cycle A is positive, $D$ is forward biased and conducts, so current flows through $R_L$. In the negative half cycle A is negative, $D$ is reverse biased and blocks, so no current flows. Output = positive humps separated by flat zero gaps, one hump per input cycle.
• Full-wave rectifier, circuit in words: a centre-tapped step-down transformer; the two ends A and B of the secondary go to the p-sides of diodes $D_1$ and $D_2$; the n-sides of both diodes are joined at a common point X; the load $R_L$ is connected between X and the centre tap Y.
• Full-wave working: in the positive half cycle A is positive and B negative with respect to the centre tap, so $D_1$ conducts and $D_2$ does not. In the negative half cycle A is negative and B positive, so $D_2$ conducts and $D_1$ does not. In both halves the current through $R_L$ flows in the same direction (X to Y). Output = positive humps back to back, two per input cycle.

• There is also a bridge full-wave rectifier that uses four diodes and needs no centre tap; NCERT mentions it in a bracket only.
• Filter: the rectified output is unidirectional but not steady. A capacitor connected across the load (or an inductor in series with it) filters out the ac ripple. The capacitor charges to the peak of the rectified wave and discharges through $R_L$ between peaks; the fall depends inversely on the time constant $CR_L$, so a large $C$ gives a nearly steady dc close to the peak value. This capacitor-input filter is the one used in power supplies.

Traps that cost marks

• A hole is not a positron and not a "positive electron". It is a vacancy in a covalent bond that behaves as a free particle with an effective positive charge; its motion is really the motion of bound valence electrons.
• "Doping increases conductivity" is true, but "doping always increases the number of electrons" is false — p-type doping increases holes and reduces the electron count. CBSE has set exactly this as an assertion-reason question.
• A doped crystal is still electrically neutral. Extra electrons in n-type material are balanced by the positive ionised donors they came from.
• At $0$ K both n-type and p-type semiconductors are perfect insulators. Doping does not change that; the dopant levels are not ionised either.
• $E_g$ for a semiconductor is less than $3$ eV, for an insulator greater than $3$ eV; do not put a numerical band gap on a metal beyond $E_g \approx 0$.
• Metal resistivity rises with temperature; semiconductor resistivity falls. Reversing this loses the graph mark outright.
• Do not confuse the donor ionisation energy ($0.01$ eV in Ge, $0.05$ eV in Si) with the band gap ($0.72$ eV in Ge, $1.1$ eV in Si). A 1-mark MCQ has been set on exactly this pair of numbers.
• The mass-action law is $n_e n_h = n_i^2$, not $n_e + n_h = n_i$. And $n_i$ in it is the intrinsic value at that same temperature.
• Two slabs pressed together do not make a p-n junction. Say why: atomic-scale roughness prevents continuous contact.
• Net current across an unbiased junction is zero because the diffusion and drift currents cancel, not because no carriers cross.
• The n-side of an unbiased junction is at the higher potential (NCERT: "the n material is thus positive relative to the p material"). One CBSE 1-mark answer key states the opposite for the p-side; if a fill-in-the-blank of that type appears, write that the n-side is positive with respect to the p-side and say why, rather than quoting the blank alone.
• Forward bias narrows the depletion layer and lowers the barrier; reverse bias widens it and raises it. Increasing the doping also narrows it. Do not mix up the two causes.
• Reverse current is in $\mu$A and forward current in mA — use a microammeter in the reverse circuit and a milliammeter in the forward one, and say so when you draw the circuits.
• Threshold voltage and breakdown voltage are different things: threshold is a small forward voltage (about $0.7$ V for Si) past which the diode starts to conduct; breakdown is a large reverse voltage past which the reverse current suddenly becomes large.
• Dynamic resistance is $\Delta V/\Delta I$, not $V/I$. Convert mA to A before dividing, and quote the answer in $\Omega$.
• A half-wave rectifier output has the same frequency as the input, not half of it. Only a full-wave rectifier doubles it.
• A full-wave rectifier of the NCERT type needs a centre-tapped transformer and two diodes; if you draw two diodes on a plain secondary the circuit does not work.
• Rectified output is pulsating dc, not steady dc. The capacitor filter is what makes it nearly steady, and a larger capacitance gives a smaller ripple.
• Do not describe rectification as "the diode changes the direction of the negative half cycle". A half-wave rectifier blocks it; a full-wave rectifier routes the other half through a second diode so that the load current keeps the same direction.