Semiconductors, junctions and electronic device models

Start with the material picture

A semiconductor has electronic energy bands separated by a gap. Doping changes available carrier populations: donor doping commonly produces n-type material with electrons as majority carriers; acceptor doping produces p-type material with holes as majority carriers. A hole describes an unoccupied electronic state whose motion can be treated as positive charge transport. It is not a proton travelling through the crystal.

Joining p and n regions allows carriers to redistribute. A depletion region and associated electric field develop; at thermal equilibrium the opposing transport contributions balance, giving zero net terminal current. A built-in field is therefore compatible with equilibrium. It is not a free source that indefinitely supplies an external load.

Follow the carriers and the fixed charges

An energy band is a range of allowed electron energies in the material; a band gap separates ranges without ordinary allowed bulk states. It is not an empty physical trench between atoms. In the simple semiconductor picture, the valence band is nearly full and the conduction band has relatively few electrons. An electron excited into the conduction band can carry charge through the crystal, while its missing valence-band electron leaves a hole. When nearby electrons fill successive vacancies, the hole appears to move in the opposite direction. Both descriptions track electronic motion, not migrating protons.

A donor can release an electron that becomes mobile while the positively charged ionized donor remains attached to its lattice site. An acceptor can take an electron from the valence band, leaving a mobile hole and a negatively charged ionized acceptor at a fixed site. These are the simple donor/acceptor mechanisms behind the preceding majority-carrier names. Ionization and carrier numbers depend on material and temperature; the labels do not mean every dopant always contributes a mobile carrier. In a nearly neutral bulk region, mobile carrier charge is largely balanced by the fixed ion and other electronic charges.

Put p material on the left and n material on the right. The mobile electron concentration is initially higher on the n side, and the hole concentration higher on the p side. Random thermal motion produces net diffusion from a higher concentration toward a lower one: electrons tend to diffuse left and holes right across the junction. Carriers meeting across it can recombine, meaning that a conduction electron fills a valence-band hole. This redistribution exposes uncompensated fixed negative acceptor ions on the p side and fixed positive donor ions on the n side near the junction.

The resulting electric field points from the positive n-side charge toward the negative p-side charge: right to left in this drawing. A field drives positive holes along it and negative electrons against it. This drift therefore opposes each carrier type’s diffusion tendency. At thermal equilibrium with no illumination or applied bias, drift and diffusion currents balance for each carrier type, so terminal current is zero even though carriers still move and a built-in field exists. The field does not stop every crossing or all microscopic motion.

The depletion region is depleted of many mobile carriers relative to the nearby bulk, not emptied of all charge. Its fixed ion charge is precisely why it has an electric field. The sketch separates the signs and directions without predicting a depletion width, field strength or carrier count. Those quantities need doping, geometry, temperature and a more detailed model.

Specify the p-to-n voltage before naming the bias

Define vD=Vp−Vn, where Vp and Vn are the p-side and n-side terminal potentials. Forward bias means the p side is made more positive relative to the n side, vD>0. In the ordinary junction picture this reduces the internal barrier and usually narrows depletion, making majority-carrier injection across the junction easier. In reverse bias, vD<0, the p side is more negative; the barrier increases and depletion ordinarily widens. Below breakdown, the majority-carrier injection is strongly suppressed, while smaller leakage and minority-carrier contributions can remain.

These statements explain the direction of the effect, not an exact current or a magic turn-on voltage. Illumination, temperature, strong injection, breakdown and changing stored charge need their own treatment. Terminal voltages in an external circuit include its contacts and complete device; the built-in junction field is not an available battery that can power a load indefinitely at thermal equilibrium. The following circuit models deliberately replace this detailed physics with stated approximations.

Describe a relationship rather than a magic threshold

Forward bias changes the junction barrier and can increase current strongly; reverse bias usually gives a much smaller current until effects such as breakdown become relevant. Current depends on voltage, temperature and device construction. A real junction does not suddenly become a perfect wire at one universal silicon voltage.

Choose a model by purpose. An ideal diode permits one current direction with zero forward drop and blocks the opposite direction. A fixed-drop forward model inserts an assumed drop when conducting. A more detailed current–voltage or charge-storage model may be needed for precision, temperature variation or switching. Each added feature needs parameters and evidence; more complicated equations do not automatically make an answer trustworthy.

Make the external circuit and device agree

A device relation cannot determine operating current alone. The source and surrounding network impose another relation. Plotting both exposes the compatible operating point and prevents the mistaken idea that a diode simply takes any requested current without affecting voltage.

Our figure compares two deliberately invented fixed-drop models, not measured diode curves. It shows how uncertainty about the device description can change the current even when the source and resistor are exact mathematical values. This difference is a model comparison, not a statistical uncertainty interval or a manufacturer tolerance.

Compare assumptions on the same load line

An original mathematical loop contains an ideal 3 V source, 1000 Ω resistor and a forward-oriented diode. The resistor relation is I=(3−vD)/1000 amperes. With assumed forward drop 0.6 V, I=2.4 mA. With assumed drop 0.8 V, I=2.2 mA. Both assumed conducting solutions have positive current, so their forward-state assumption is consistent here.

The ideal zero-drop model instead predicts 3 mA. Relative to the 0.6 V model, that is 25% higher: (3−2.4)/2.4=0.25. This does not establish which model matches a real part. That requires the relevant device data or measurements at comparable current and temperature.

At 0.6 V and 2.4 mA, model diode power is 1.44 mW and resistor power is 5.76 mW; together they equal the source’s 7.2 mW. Keeping a power account checks that the assumed drop has not been ignored elsewhere.

A separate polarity check keeps p on the left and n on the right. In case A, Vp=0.15 V and Vn=0.45 V relative to the same reference, so vD=−0.30 V: reverse bias. The external bias increases the ordinary junction barrier below breakdown. In case B, interchange the two potentials: vD=+0.30 V, giving forward bias and a reduced barrier. The absolute reference values matter only through their difference here.

This comparison establishes which injection tendency is encouraged. It does not establish the numerical current in either case or assert zero forward current below an assumed 0.6 V drop. A fixed-drop approximation and the physical junction answer different levels of question; the load-line and power accounts above must still be checked with whichever device model is chosen.

Try the reasoning

1. Does p-type mean the whole specimen must carry a net positive charge?

   Show the answer and reasoning

   No. The label describes its majority mobile carrier type; carrier motion and bulk net charge are different questions.

2. Can a fixed 0.6 V drop be used as a universal measured silicon-junction fact?

   Show the answer and reasoning

   No. It is an explicit approximation here; actual behaviour depends on device, current, temperature and other conditions.

3. Why plot a load line as well as a device model?

   Show the answer and reasoning

   The operating point must satisfy both the external circuit and the device relation, not either one alone.

4. A redraw puts n material on the left and p material on the right. The left terminal is made more positive than the right. Is this forward bias?

   Show the answer and reasoning

   No. Identify the material labels, not left versus right. The n terminal is more positive, so Vp−Vn is negative: reverse bias in the defined convention, increasing the ordinary barrier below breakdown.

5. A learner says the depletion region contains no charge because its mobile carriers were depleted. What creates its field?

   Show the answer and reasoning

   Redistribution leaves uncompensated fixed negative acceptor ions on the p side and positive donor ions on the n side. Mobile-carrier depletion does not mean absence of charge; the fixed space charge produces the built-in field.

6. At equilibrium the diode has zero net current. Does that prove that diffusion has stopped or that donor ions are drifting through the crystal?

   Show the answer and reasoning

   Neither. Mobile-carrier drift and diffusion currents balance, while thermal motion continues. Ionized dopants are fixed at lattice sites in this model; they are not the mobile carriers that cancel diffusion.

What to carry forward

A device model is a conditional relationship. Check its operating point and energy account before interpreting its accuracy.