Semiconductor Physics Refresher

Lesson 1 named the goal: predict and control how a transistor behaves. Every later lesson in this path, the junction and MOS capacitor in lesson 3, the MOSFET in lesson 4, FinFETs and gate-all-around in lesson 5, rests on a small set of physics ideas: energy bands, doping, and the two mechanisms, drift and diffusion, that move charge through a semiconductor. This lesson is a refresher on those ideas, at the depth the rest of the path actually uses.

Reading time: about 8 minutes.

2.1 Energy bands

In a crystalline solid, the discrete energy levels electrons occupy in an isolated atom broaden, from the enormous number of atoms interacting in a crystal lattice, into continuous bands of allowed energy, separated by a band gap of forbidden energy. In a semiconductor, the valence band (the highest band that is essentially full of electrons at low temperature) and the conduction band (the next band up, essentially empty at low temperature) are separated by a band gap small enough (around 1.12 eV for silicon at room temperature) that thermal energy alone excites a meaningful number of electrons across it at normal operating temperatures. An electron excited into the conduction band leaves behind an empty state in the valence band, a hole, which behaves, for most purposes, like a mobile positive charge carrier in its own right. A semiconductor's defining property is exactly this: a band gap small enough that both electrons (in the conduction band) and holes (in the valence band) exist in meaningful numbers and can both conduct current, unlike an insulator (too large a gap) or a metal (no gap at all, bands already overlap).

2.2 Doping

Intrinsic (undoped) silicon has equal, and at room temperature quite small, concentrations of thermally generated electrons and holes. Doping, deliberately introducing a small, controlled concentration of impurity atoms into the silicon lattice, changes this balance enormously:

• n-type: doping with a group-V element (commonly phosphorus or arsenic), which has one more valence electron than silicon. That extra electron is only loosely bound and is readily donated to the conduction band at room temperature; the dopant is called a donor, and the doped material has a large excess of mobile electrons (majority carriers) over holes (minority carriers).
• p-type: doping with a group-III element (commonly boron), which has one fewer valence electron than silicon. The resulting missing bond readily accepts an electron from a nearby silicon-silicon bond, effectively creating a mobile hole; the dopant is called an acceptor, and the doped material has a large excess of holes over electrons.

Doping concentration, not an intrinsic material property, is what engineers actually control precisely during fabrication (through ion implantation, covered later in this site's physical design material, and diffusion/anneal, covered in process simulation, lesson 6); every device structure in lessons 3-5 is built from regions of silicon doped n-type and p-type in a specific, deliberately engineered spatial pattern.

A useful way to picture why doping works so effectively: silicon's intrinsic carrier concentration at room temperature is extremely small compared to the doping concentrations actually used in a transistor, commonly many orders of magnitude smaller. Adding even a comparatively modest concentration of donor or acceptor atoms therefore completely dominates the carrier population in that region; the material's electrical behavior is set almost entirely by the deliberately introduced dopant, not by the small intrinsic background. This is also why doping concentration has to be controlled so precisely during fabrication: because doped carrier concentration so thoroughly dominates intrinsic concentration, even a modest unintended variation in dopant dose or placement translates directly into a correspondingly large variation in the region's actual electrical behavior, exactly the mechanism behind random dopant fluctuation, covered in lesson 8.

2.3 Drift and diffusion

Charge carriers move through a semiconductor by two mechanisms, and the current equations used throughout the rest of this path, and in SPICE-level device models, are built from both added together:

• Drift: carriers accelerate in response to an applied electric field, producing a current proportional to the field, the carrier concentration, and the carrier's mobility (how readily that carrier type moves through the lattice, which is itself reduced by factors like impurity scattering from dopant atoms and phonon scattering from lattice vibrations, both increasing with temperature or doping concentration).
• Diffusion: carriers move from a region of higher concentration toward a region of lower concentration, exactly like a dye spreading through still water, driven by the concentration gradient itself rather than by an electric field.

Both mechanisms operate simultaneously almost everywhere in a real device; lesson 3's p-n junction is the clearest illustration, because at equilibrium, a diffusion current trying to even out the large majority-carrier concentration difference across the junction is exactly balanced by a drift current from the electric field that same concentration difference itself creates, with neither current winning out, which is precisely what "equilibrium" means for a junction with no external bias applied.

Mobility itself is not a fixed material constant independent of conditions; it depends measurably on temperature (generally decreasing at higher temperature, as lattice vibrations scatter carriers more frequently) and on local doping concentration (generally decreasing at higher doping, as ionized dopant atoms themselves scatter carriers more frequently too). This temperature and doping dependence is exactly why a device's electrical characteristics shift with operating temperature, and why a heavily doped region of a transistor (the source/drain, for example) does not simply conduct better the more it is doped without limit, mobility degradation works against the benefit of adding more carriers past a certain doping level.

2.4 Interview questions

What makes a material a semiconductor rather than an insulator or a metal? Its band gap, the forbidden energy range between the valence and conduction bands, is small enough that meaningful numbers of electrons and holes exist and can conduct at normal temperatures, unlike an insulator's much larger gap or a metal's overlapping bands.

What is a hole, physically? An empty state left in the valence band when an electron is excited into the conduction band; it behaves, for most transport purposes, like a mobile positive charge carrier.

Explain the difference between n-type and p-type doping. n-type doping uses donor atoms (one more valence electron than silicon, commonly phosphorus or arsenic) that readily supply electrons as majority carriers; p-type doping uses acceptor atoms (one fewer valence electron, commonly boron) that readily supply holes as majority carriers.

What is the difference between drift and diffusion current? Drift current is driven by an applied electric field accelerating carriers; diffusion current is driven by a concentration gradient, carriers moving from higher to lower concentration, independent of any field.

Why do drift and diffusion currents balance at a p-n junction with no applied bias? The concentration difference across the junction drives a diffusion current, but that same concentration difference also sets up a built-in electric field, which drives an equal and opposite drift current; at equilibrium, with zero external bias, the two exactly cancel.