Discrete semiconductor devices

A gate that takes no current

A MOSFET has three terminals. The load current flows between the drain and the source, and the gate controls whether it flows at all. The gate sits on a thin insulating layer of oxide, out of contact with the silicon beneath, so it behaves as a very small capacitor rather than as a way in. Put a voltage on it and its field reaches through the oxide and draws carriers into a conducting channel underneath.

Nothing useful happens until the gate-source voltage passes the threshold voltage V_T$V_{T}$V_T. Below it no proper channel forms, so the drain current is negligible, a leakage far smaller than the current the device carries when it is on, for any drain voltage within the maker's rating. Driven past that rating any MOSFET breaks down and conducts, which is a failure rather than a mode of operation.

Past the threshold the channel opens and widens, and provided the drain voltage is large enough to keep the channel saturated, the drain current is approximately proportional to the square of the excess above threshold. Take that pair of statements as the model for the rest of this lesson: an idealised switch, off below threshold and square-law above it, working inside its ratings.

Switching a load

That shape of characteristic makes a superb switch. Wire the load in series with the drain and drive the gate from a logic output. At 0 V the channel is shut, the drain-source resistance is megohms, and the load sees microvolts. At a gate voltage comfortably past the threshold, 5 V on a logic-level device whose data sheet specifies its low on-resistance there, the channel is fully enhanced, its resistance falls to a fraction of an ohm, and almost the whole supply lands on the load. Reaching the threshold alone is not enough: the threshold is where conduction begins, and the guaranteed low resistance arrives at the higher gate voltage the data sheet names.

Work the on state as a potential divider, modelling the lamp as a constant 24 Ω at its working temperature. Lamp and channel carry 12/24.05 = 0.499 A between them, the lamp keeps 11.98 V, and the MOSFET dissipates I²R$I^{2}R$I^2R = 0.012 W against nearly 6.0 W in the lamp. A component wasting a hundredth of a watt to control six of them needs no heat sink.

The gate is insulated, so only a negligible leakage current enters it once it is charged. A logic output has only to charge a gate capacitance of a nanofarad or two, which it does in microseconds, and in between it supplies almost nothing.

Holding a rail steady

Run an ordinary diode backwards and it blocks until the reverse voltage grows large enough to destroy it. A zener diode is built to break down gently at a chosen voltage V_Z$V_{Z}$V_Z and to survive the experience indefinitely, so long as its rated current and power are respected. Past breakdown its characteristic is nearly vertical, so the current through it can swing by tens of milliamps while its pd barely moves.

A component whose voltage stays almost constant is what a supply rail needs. So the zener goes across the load, reverse biased, with a series resistor between it and the raw supply. The load gets V_Z$V_{Z}$V_Z, everything left over is dropped across the resistor, and when the supply wanders it is the resistor's share that changes.

The resistor sets the current, and the current is what the design turns on:

Too small a current and the diode never properly reaches breakdown. Too large and it overheats. In the figure the resistor carries 10.0 mA at 9 V in and 25.4 mA at 15 V in, and the zener carries whatever the load leaves.

Light into current

A photodiode is a diode with a window, used reverse biased so that almost nothing flows in the dark. A photon absorbed in the depletion layer frees an electron-hole pair, and the strong field there sweeps the two apart before they can recombine. Every absorbed photon therefore adds to a small reverse current, the photocurrent, and doubling the illumination doubles the pairs freed each second.

Those flat lines carry two messages. Photocurrent is proportional to illumination, so a single constant, the responsivity, describes the device where a curved characteristic would have needed a whole calibration graph. That is not the same as needing no calibration at all. The constant itself still has to be found against a known source, and it depends on the wavelength of the light, differs from one device to the next and drifts with temperature, while the small dark current that flows with no light on the window has to be subtracted as well. Linearity makes the calibration short, not unnecessary.

The second message is that the current hardly depends on the applied pd, so the diode behaves as a current source. Read it by dropping its current across a resistor: 40 μA through 50 kΩ gives 2.0 V, and 60 μA gives 3.0 V.

Against a light-dependent resistor the photodiode wins on speed and on linearity. Carriers in an LDR take milliseconds to build up and longer to disperse, so it cannot follow anything flickering faster than a few hundred hertz, and its resistance is nowhere near proportional to the light. A photodiode responds in nanoseconds, which puts one at the end of every optical fibre. Where the light changes slowly, the cheaper LDR is fine.

Measuring a field, and noticing a magnet

Send a current along a thin slab of semiconductor and put a magnetic field through its face. Each moving carrier feels a force BQv$BQv$BQv at right angles to both, so carriers pile up along one edge and leave the opposite edge short of them. The separated charge builds a field that opposes further pile-up, and matters settle once the two forces balance. What remains is a steady Hall voltage across the faces.

Hold the current constant and that voltage is proportional to the flux density, so the slab is a direct-reading field meter. A Hall probe is exactly that, calibrated. Its reading is largest when the field runs perpendicular to the slab's face, so a probe is rotated for a maximum before the number is taken. The sensor above gives 2.4 mV in 0.20 T and 4.8 mV in 0.40 T, a sensitivity of 12 mV per tesla.