Formula sheet: Semiconductor Electronics

1.1 How to use this sheet

The chapter has few formulas but many working numbers. Learn the carrier relations and the diode numbers first, because they carry both the numericals and the one-mark questions.

1.2 Resistivity and conductivity

Conductivity is the reciprocal of resistivity: σ = 1/ρ. For classifying solids, the orders of magnitude matter. Metals have ρ between about 10 to the -2 and 10 to the -8 ohm metre. Semiconductors sit between about 10 to the -5 and 10 to the 6 ohm metre. Insulators are above about 10 to the 11 ohm metre. The ranges are indicative, not sharp boundaries.

1.3 Charge carriers

In an intrinsic semiconductor the number of free electrons equals the number of holes:

n e = n h = n i

In any semiconductor in thermal equilibrium the product of the two concentrations is fixed by the material and the temperature:

n e n h = n i squared

For an extrinsic semiconductor, n-type has n e much greater than n h, and p-type has n h much greater than n e. The material stays electrically neutral because the ionised dopant cores balance the added carriers.

1.4 The p-n junction

The barrier potential is the built-in potential difference across the depletion region, written V0. Forward bias lowers the effective barrier to V0 - V, reverse bias raises it to V0 + V. The depletion layer is roughly 0.1 micrometre thick and grows wider under reverse bias.

1.5 Diode numbers and dynamic resistance

The dynamic resistance of a diode is the ratio of a small change in voltage to the small change in current: r d = ΔV/ΔI. Typical values are about 10 ohm in forward bias and about 10 to the 7 ohm in reverse bias.

Threshold or cut-in voltage: about 0.7 V for a silicon diode and about 0.2 V for a germanium diode. Reverse saturation current is of the order of microamperes, and it stays nearly constant with voltage until breakdown, where it rises sharply.

1.6 Energy gaps

Energy gap values to remember: carbon about 5.4 eV, silicon about 1.1 eV, germanium about 0.72 eV, and tin about 0 eV, which is why tin is a metal. For the classification used in the chapter, insulators have a gap above about 3 eV, semiconductors between about 0.2 and 3 eV, and metals essentially zero. The donor level in n-type material sits just below the conduction band, and the acceptor level in p-type material just above the valence band, which is why these impurities ionise at room temperature.

1.7 Rectification

The output frequency of a half-wave rectifier equals the input frequency, while a full-wave rectifier gives twice the input frequency. The capacitor filter smooths the pulsating output, with the time constant set by the product C times the load resistance R L.