Diodes and bias voltage

January 10, 2013 3:34:31 PM CST

A quick review of the diode's internal electrical field:

Last time I talked about what happens when you put P-type silicon right next to N-type silicon: diffusion pulls electrons from the N-type material into the P-type material and holes from the P-type into the N-type. In both cases, the carriers recombine with dopants on the opposite side and leave a 'depletion zone' where there are no free carriers in the lattice and no free orbitals around the dopants.

Dopants in the depletion zone either have one more electron than they want (in the P-type material) or one less electron than they want (in the N-type material), but they're held in place by the silicon lattice, making them 'fixed charges'.

Whenever you have fixed charges with different values and space between them, you have an electrical field. As more carriers recombine across the PN junction, the depletion zone gets wider and the electrical field gets stronger.

Whenever you put charged particles in an electrical field, you get drift. For a diode, the electrical field tries to push carriers back into their native material, and the depletion zone stops growing when every particle's tendency to diffuse across the PN junction exactly equals its tendency to drift back into its native material. The short way of saying that is "when the drift current balances the diffusion current".

Eventually they do balance, and the diode reaches equilibrium.

Now let's mess with that:

Bias voltage:

Electrical fields obey a rule called 'superposition', which is a fancy way of saying you can add them together. If you stack two electrical fields on top of each other, the effect on a charged particle will just be "the effect of field A" plus "the effect of field B".

That's important here because every diode comes with its own little built-in electric field.

If you apply an external field to the diode, its effects get added to the effects of the internal field.. and since the internal field controls the width of the depletion zone, we can tune the depletion zone by changing the external field.

Now, technically the strength of an electrical field depends on the strength of the fixed charges and the distance between them, but the 'distance' part gets set when the diode is made. The only part we can change is the strength of the charge at each end.

We call that charge the 'bias voltage', and since diodes are built to have one contact at each end, there are two ways to bias a diode.

Reverse bias:

You could say that a diode's built-in electrical field sits backwards in relation to the silicon. The positive end of the field is in the N-type silicon, where the majority carriers are electrons (with negative charge). The negative end of the built-in field is in the P-type silicon where the majority carriers are holes (with positive charge).

When the external electrical field pushes the same way as the built-in field, we say the diode is 'reverse biased'. Adding the effects of the external field to those of the internal field makes the drift current inside the diode stronger, and that pulls the depletion zone open wider.

We already knew current couldn't cross the depletion zone (there are no free carriers), so an even wider depletion zone gives us even more nothing.

.. okay, there are some limits: you can raise the reverse bias voltage to a point where it shoots carriers straight through the depletion zone. It can happen through 'quantum tunneling', where you push the energy levels so hard that carriers from the valence (low) band on the P side can jump to the conduction (high) band on the N side.. known as the 'Zener effect'. It's also possible to do the 'grid of mousetraps with ping pong balls' thing, where one fast-moving electron knocks an electron free from a dopant ion, then both of those knock electrons free from additional ions, etc.. that's known as the 'avalanche effect'. The voltage where either of those effects happen is called the 'breakdown voltage', and can be tuned quite accurately. All 'Zener diodes' use one of those two effects.

.. there's also the whole phenomenon of 'junction capacitance': a capacitor is a layer of non-conductive material with charges on both sides, and that description fits the depletion zone to a tee. The capacitance of the depletion zone changes as it gets wider or narrower, so you can use a reverse-biassed diode as an adjustable capacitor. Devices tuned to do that well are called 'varicaps' or 'PIN diodes'.

Diodes reverse-biased below the breakdown voltage (and not being used as capacitors) just sit there being non-conductive though.

Forward bias:

If the external electrical field matches the polarity of the silicon (positive end of the field on the P-end of the diode, negative end of the field on the N-end of the diode), we call it 'forward bias'.

When a diode is forward biased, we subtract the effects of external electrical field from the effects of the built-in electrical field. That makes the drift current inside the diode weaker, so the depletion zone gets narrower.

The external electrical field doesn't change the diffusion current directly, but it does have an indirect effect.

The carrier concentration gradient:

Diffusion is proportional to the 'carrier concentration gradient', which is a fancy way of saying 'how fast the concentration changes'. We simplify the math by assuming the concentrations outside the depletion zone are constant, so all the interesting stuff happens inside the depletion zone.. which gets narrower when you apply forward bias.

I won't go into details with the actual math.. it involves differential equations, several constants that all require their own explanations, plus a couple of tricks that only make sense if you already know they'll give you the answer you want. Worse yet, it's all 'half-step' knowledge.. too specific to help build intuition, but too theoretical to let you design an actual diode. It's basic vocabulary for engineers who design semiconductor devices, but way too much information to be useful here.

That's okay though. There's a much easier way to build intuition: the mechanics of heat transfer follow exactly the same rules as electrons moving through a diode.

I'll talk about that next time.

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