Semiconductor Doping and P-N Junctions: Band Gaps, Diodes, Transistors

Silicon is a semiconductor because a small energy gap, about 1.1 electron volts, separates its bound electrons from the states where they can move. Doping adds a few phosphorus atoms (extra electrons, n-type) or boron atoms (missing electrons, p-type). Where n-type meets p-type, a p-n junction forms: the one way valve behind diodes, transistors, LEDs and solar cells.

This post goes one level below our explainers on how semiconductors are made from sand to chip and the Schrödinger equation, wave functions, tunnelling and transistors. It works through band gaps, carrier concentrations, the depletion region, the diode equation, bipolar transistors and MOSFETs, wide band gap power devices, and the LED and solar cell as mirror images of one another, each with numbers you can check. If you want to see where those junctions end up in a factory, our post on how solar panels are made from polysilicon to module and inverter follows a junction from wafer to rooftop, and Maxwell's equations explained covers the fields those devices switch.

A note on numbers: constants come from NIST's CODATA 2022 values, band gaps from the US Department of Energy (DOE) and HyperPhysics (citing Kittel), and carrier figures from MIT's 6.012 notes. Typical textbook values we did not confirm on a primary source, such as mobilities, are labelled illustrative. The arithmetic is ours; the walkthrough script reruns it.

Key takeaways

• A band gap is the forbidden energy range between the valence band (electrons tied up in bonds) and the conduction band (electrons free to move). HyperPhysics, citing Kittel, lists 1.11 eV for silicon at 300 K, 0.66 eV for germanium and 1.43 eV for gallium arsenide. DOE lists 3.3 eV for silicon carbide and 3.4 eV for gallium nitride.
• Pure silicon at room temperature has about 1 × 10¹⁰ free electrons per cubic centimetre, out of about 5 × 10²² atoms, according to MIT 6.012. That is why it is a poor conductor until doped.
• Phosphorus, arsenic and antimony have five valence electrons and donate one (n-type). Boron, aluminium and gallium have three and leave a hole (p-type). The product of electron and hole densities stays fixed at the intrinsic value squared, so doping one carrier up pushes the other down.
• At a p-n junction, electrons and holes diffuse across and annihilate, leaving fixed ions that form a depletion region and a built in voltage of roughly 0.6 to 0.9 V in silicon, depending on doping.
• The ideal diode equation says current grows exponentially with forward voltage: about tenfold for every 60 mV at room temperature. In reverse bias only a tiny saturation current flows until breakdown.
• A bipolar transistor is two junctions back to back with a thin middle layer; a MOSFET uses a gate voltage across an insulating oxide to create a conducting channel. Both are junction devices at heart.
• Wide band gap materials sustain about ten times the electric field before breakdown. DOE says that lets them handle voltages more than ten times higher, run above 300 °C and switch at least ten times faster than silicon devices, which shrinks EV inverters and chargers.
• An LED runs a junction forward and turns recombining carriers into light at a wavelength set by the band gap. A solar cell runs the same physics backwards: light makes carriers and the junction's field sorts them into a current.

A dated timeline from a cracked silicon slab to wide band gap inverters

Every date in this table was checked against the source in the right hand column.

What makes silicon a semiconductor, and what is a band gap?

Bands instead of levels

A single isolated atom has sharp energy levels. Pack about 5 × 10²² silicon atoms into each cubic centimetre, as a crystal does, and the outer levels of neighbouring atoms overlap and spread into continuous bands. HyperPhysics puts it simply: instead of discrete energies, the available states in a solid form bands, and what matters for conduction is whether any electrons sit in the conduction band.

Silicon has four valence electrons. In the crystal each atom shares one with each of four neighbours in a tetrahedral arrangement, so every valence electron is locked into a covalent bond. Those bonding states make up the valence band, which is completely full at absolute zero. A full band carries no current, because for every electron moving one way there is another moving the other way and no empty state to shift into. The next band up, the conduction band, is empty at absolute zero. Between the two is a range of energies with no allowed states at all: the band gap.

You can check the atom count from NIST. The CODATA 2022 lattice parameter of silicon is 5.431 020 511 × 10⁻¹⁰ m. The diamond cubic unit cell holds eight atoms, so the density is 8 divided by the cube of 5.431 × 10⁻⁸ cm, which comes to 4.99 × 10²² atoms per cubic centimetre. MIT 6.012 rounds this to 5 × 10²², and we use that figure below.

Conductor, insulator, semiconductor

HyperPhysics draws the three cases with one picture:

• In a metal, the valence and conduction bands overlap, so there are always empty states next to filled ones and electrons move freely.
• In an insulator, the gap is large. Glass is the example HyperPhysics uses: visible light photons do not carry enough energy to lift electrons across its gap, which is also why glass is transparent.
• In a semiconductor, the gap is small enough that heat, light or an applied field can lift some electrons across. Each electron that crosses leaves behind an empty bonding state, a hole, which behaves like a positive charge carrier.

Band gap values

Two cautions on that table. First, band gaps shrink as temperature rises: HyperPhysics lists silicon at 1.17 eV at 0 K and 1.11 eV at 300 K, and a second table it reproduces (citing Blatt) gives 1.14 eV at 273 K. Different textbooks quote 1.12 eV for silicon at room temperature; the spread is within the measurement and rounding differences of the sources. Second, silicon carbide comes in many crystal stackings called polytypes, and the gap differs between them. DOE's 3.3 eV is a rounded figure that fits the polytype used in power devices; do not treat the third digit as exact.

Direct and indirect gaps

The table's "gap type" column matters for light. In a direct gap material such as GaAs or GaN, the lowest conduction state and the highest valence state sit at the same crystal momentum, so an electron can drop across the gap and emit a photon without help. In an indirect gap material such as silicon, the electron also has to shed momentum, which needs a lattice vibration (a phonon) to take part. The Nobel Committee's 2014 background paper makes the point directly: LEDs need direct band gaps, and GaAs was attractive because recombination there happens "without involvement of phonons." That is why your phone's flash is a GaN LED and not a silicon one, even though silicon absorbs sunlight well enough to dominate solar.

Intrinsic carriers: why pure silicon barely conducts

At any temperature above absolute zero, thermal vibrations occasionally break a bond and lift an electron into the conduction band, leaving a hole. In pure (intrinsic) silicon, electrons and holes are created in pairs, so their densities are equal. MIT 6.012 calls this common value the intrinsic carrier concentration, written nᵢ, and gives nᵢ ≈ 1 × 10¹⁰ cm⁻³ for silicon at 300 K. Other references quote values near 9.7 × 10⁹ cm⁻³; the difference does not change any conclusion below.

Compare that with the atom density: 10¹⁰ free electrons among 5 × 10²² atoms is one carrier per five trillion atoms. Copper, by contrast, contributes about one free electron per atom. That ratio is why intrinsic silicon is a poor conductor, and it is also why tiny, controlled impurities change silicon so dramatically.

nᵢ depends very strongly on temperature, because the chance of an electron crossing the gap scales roughly with exp(-E_g / 2kT). MIT's notes stress the point: as T goes up, nᵢ goes up steeply. The thermal energy kT at 300 K is 0.02585 eV (NIST gives Boltzmann's constant as 8.617 333 262 × 10⁻⁵ eV per kelvin), about one forty third of silicon's gap. Germanium's smaller gap means a much higher nᵢ, which is one reason germanium transistors misbehaved when warm and silicon took over.

How does doping with phosphorus or boron create n-type and p-type material?

Donors and acceptors

HyperPhysics describes the two families of dopant:

• Pentavalent impurities with five valence electrons, such as phosphorus, arsenic and antimony, sit in silicon lattice sites, use four electrons for bonds and have one left over. That extra electron is so loosely bound that room temperature frees it into the conduction band. The atom becomes a fixed positive ion, a donor, and the material is n-type because its majority carriers are negative electrons.
• Trivalent impurities with three valence electrons, such as boron, aluminium and gallium, leave one bond short. A neighbouring electron easily hops into the gap, which moves the hole away and leaves the boron as a fixed negative ion, an acceptor. The material is p-type because its majority carriers are positive holes.

In the band picture, donors add energy levels just below the conduction band and acceptors add levels just above the valence band, so very little energy is needed to ionise them. HyperPhysics notes that phosphorus is commonly introduced by diffusing phosphine gas and boron by diffusing diborane. Modern fabs also use ion implantation, which our semiconductor manufacturing explainer covers step by step.

Ohl's 1940 discovery was exactly this, found by accident. The Computer History Museum's account says the slab had a seam where one side contained phosphorus, giving a slight excess of electrons, and the other contained boron, giving a slight deficiency. Ohl and Scaff named the regions n-type and p-type, and the boundary between them became the p-n junction.

The mass action law

The key equation is short. In thermal equilibrium, the product of the electron density n and the hole density p is constant:

n × p = nᵢ²

Shockley, in his 1956 Nobel lecture, compared this to the dissociation of water, where the product of hydrogen and hydroxide ion concentrations is fixed. Add an acid and the hydroxide concentration falls; add donors to silicon and the hole concentration falls. Generation of electron hole pairs by heat is balanced by recombination, and recombination is faster when there are more partners to recombine with.

MIT 6.012 gives the rule of thumb that follows: when the donor density N_d is much larger than nᵢ, doping controls the carrier concentrations and n ≈ N_d, p ≈ nᵢ² / N_d. Typical donor densities run from about 10¹⁵ to 10²⁰ cm⁻³.

Worked example 1: carrier concentrations in phosphorus doped silicon

Take silicon doped with phosphorus at N_d = 1 × 10¹⁶ cm⁻³, a common level for a lightly doped device region.

1. Fraction of atoms replaced. 10¹⁶ divided by 5 × 10²² is 2 × 10⁻⁷, or one phosphorus atom for every five million silicon atoms. That is purity far beyond anything in ordinary chemistry, which is why semiconductor grade silicon is refined to such extremes before it is doped.
2. Electron density. Every donor is ionised at room temperature, so n ≈ 1 × 10¹⁶ cm⁻³, a millionfold more than intrinsic silicon's 10¹⁰.
3. Hole density. p = nᵢ² / n = (10¹⁰)² / 10¹⁶ = 10⁴ cm⁻³. Doping did not merely add electrons; it suppressed holes by a factor of a million. MIT's notes give the same pattern for N_d = 10¹⁷: n = 10¹⁷ and p = 10³ cm⁻³.

Now do the same with boron at N_a = 1 × 10¹⁷ cm⁻³ for a p-type region: p ≈ 10¹⁷ cm⁻³ and n = 10²⁰ / 10¹⁷ = 10³ cm⁻³.

Worked example 2: how much does the conductivity change?

Conductivity is σ = q (n μ_n + p μ_p), where q is the elementary charge (exactly 1.602 176 634 × 10⁻¹⁹ coulombs, per NIST) and μ is the mobility, how fast carriers drift per unit field. Mobility depends on doping and temperature, and we did not confirm a value on a primary source, so the figures below use typical textbook values and are illustrative: about 1,400 cm²/V·s for electrons and 450 cm²/V·s for holes in pure silicon, and about 1,200 cm²/V·s for electrons at 10¹⁶ cm⁻³ doping.

• Intrinsic silicon. σ = 1.602 × 10⁻¹⁹ × 10¹⁰ × (1,400 + 450) ≈ 2.96 × 10⁻⁶ S/cm, so the resistivity is about 3.4 × 10⁵ Ω·cm.
• Phosphorus at 10¹⁶ cm⁻³. σ ≈ 1.602 × 10⁻¹⁹ × 10¹⁶ × 1,200 ≈ 1.92 S/cm, a resistivity of about 0.52 Ω·cm.

The ratio is about 650,000. One impurity atom in five million changes the resistivity by nearly six orders of magnitude. HyperPhysics makes the same qualitative point: with such a small gap, a small percentage of dopant "can increase conductivity dramatically."

Compensation and heavy doping

Two refinements matter in real devices.

Compensation. If a region contains both donors and acceptors, they cancel. Silicon with 10¹⁷ boron and 10¹⁶ phosphorus behaves like p-type with a net 9 × 10¹⁶ acceptors. This is how a fab builds an n-type well inside a p-type wafer: it adds enough donors to overwhelm the background acceptors locally. Shockley's lecture describes the same idea for crystals grown from a melt whose doping was changed partway through, which is how the first grown junctions were made.

Degenerate doping. At very high concentrations, around 10¹⁹ to 10²⁰ cm⁻³, the dopant levels merge into the bands, the simple n × p = nᵢ² rule starts to fail, and the silicon behaves almost like a metal. Device engineers mark such regions n⁺ or p⁺. They are used for contacts, because a metal touching heavily doped silicon makes a low resistance ohmic contact instead of a rectifying one.

What happens at a p-n junction?

The depletion region

Put p-type and n-type silicon in intimate contact, as a fab does by doping adjacent regions of one crystal. The n side has a huge excess of electrons and the p side a huge excess of holes, so both diffuse across the boundary. HyperPhysics describes what happens next: electrons that cross combine with holes, each filled hole leaves a negative acceptor ion on the p side, and each departed electron leaves a positive donor ion on the n side.

Those ions are bolted into the lattice and cannot move. Within a short distance of the boundary there are almost no free carriers left, only fixed charge: negative on the p side, positive on the n side. This zone is the depletion region, also called the space charge region. Its fixed charge creates an electric field pointing from n to p, and that field pushes back on further diffusion. Equilibrium arrives when the drift caused by the field exactly balances diffusion, for electrons and for holes separately.

HyperPhysics's energy band sketch shows the same thing another way: in equilibrium the Fermi level is flat across the junction, so the bands themselves bend. The conduction band on the p side sits higher than on the n side, so an electron on the n side sees a hill.

Built in voltage

The height of that hill is the built in potential, which MIT 6.012 writes as:

φ_B = (kT/q) × ln( N_a × N_d / nᵢ² )

N_a is the acceptor density on the p side and N_d the donor density on the n side. kT/q, the thermal voltage, is 25.85 mV at 300 K from NIST's values for k and q.

Worked example 3: built in voltage of a real junction

Take a one sided junction with boron at N_a = 10¹⁷ cm⁻³ and phosphorus at N_d = 10¹⁶ cm⁻³.

• N_a × N_d = 10³³; nᵢ² = 10²⁰; the ratio is 10¹³.
• ln(10¹³) = 29.93.
• φ_B = 0.02585 × 29.93 ≈ 0.774 V.

Double either doping and φ_B rises by only 0.02585 × ln 2, about 18 mV, because of the logarithm. That is why silicon junctions cluster between about 0.6 and 0.9 V of built in potential across a huge range of doping, and why the familiar "0.6 to 0.7 V diode drop" is so consistent from one part to the next.

A common confusion: you cannot measure φ_B with a voltmeter across an unbiased diode. The contact potentials at the metal leads cancel it exactly, which MIT's lecture 5 covers under "contact potentials." If they did not cancel, a diode on a shelf would be a perpetual battery.

Worked example 4: how wide is the depletion region, and how strong is the field?

For an abrupt junction under an applied voltage V (positive for forward bias), the standard depletion approximation in MIT's lecture 6 gives:

x_d = sqrt( 2 ε_s (φ_B - V) / q × (N_a + N_d) / (N_a × N_d) )

ε_s is the permittivity of silicon. We use a relative permittivity of 11.7 (HyperPhysics lists 12, rounded) times NIST's vacuum permittivity of 8.854 187 8188 × 10⁻¹² F/m, which gives ε_s ≈ 1.036 × 10⁻¹² F/cm.

With the same junction (N_a = 10¹⁷, N_d = 10¹⁶, φ_B = 0.774 V):

Three lessons sit in that table.

1. The depletion region lives on the lightly doped side. Charge neutrality means the ions uncovered on each side must balance, so the side with ten times fewer dopants needs ten times the width. In a one sided junction almost all the action is in the light side. Power devices exploit this: a thick, lightly doped "drift" layer holds the voltage.
2. Reverse bias widens the region. HyperPhysics describes it as both electrons and holes being pulled away from the junction until the potential across the widened layer matches the applied voltage. The width grows with the square root of the voltage.
3. The field gets large quickly. At 10 V the peak field is already about 0.17 MV/cm. Keep raising the reverse voltage and the field approaches silicon's breakdown field, a few hundred kilovolts per centimetre, at which point the junction stops blocking. That limit is the starting point for the wide band gap story below.

Because x_d changes with voltage, a junction also behaves like a voltage dependent capacitor, which MIT's lecture 6 derives as the depletion capacitance. Radio tuning diodes (varactors) are junctions designed to exploit exactly this.

Forward and reverse bias

HyperPhysics describes forward conduction in band terms: forward bias makes the path "downhill" for electrons, so electrons from the n side cross, find themselves at higher energy than the holes on the p side, and recombine, sustaining a continuous current. Under reverse bias the hill is steeper, the majority carriers are held back, and only the thermally generated minority carriers that wander into the field get swept across.

Breakdown: avalanche and tunnelling

Two mechanisms end reverse blocking. In avalanche breakdown, carriers accelerated by the field gain enough energy to knock new electron hole pairs loose, which are accelerated in turn. In Zener breakdown, found in very heavily doped junctions with very thin depletion regions, electrons tunnel straight through the band gap from the valence band on the p side to the conduction band on the n side. The tunnelling side of that story is the subject of our Schrödinger equation explainer. Voltage reference diodes use either mechanism on purpose; in a power switch, breakdown is the limit you design around.

How does the diode equation describe current?

The ideal diode equation

Shockley's 1949 Bell System Technical Journal paper derived the current through an ideal junction from the physics above: forward bias lowers the barrier by V, and the number of carriers able to climb the remaining barrier rises by the Boltzmann factor exp(qV/kT). The result is:

I = I_s × ( exp( q V / (n k T) ) - 1 )

• I_s is the saturation current, set by doping, area, the diffusion of minority carriers and above all nᵢ². For a small silicon signal diode it is extremely small, often around 10⁻¹⁴ A or less.
• n is the ideality factor, 1 for the ideal case and between 1 and 2 in real diodes, where recombination inside the depletion region adds current.
• kT/q is the thermal voltage, 25.85 mV at 300 K.

For large forward bias the -1 is negligible and the current is a pure exponential. For reverse bias the exponential vanishes and I ≈ -I_s.

Worked example 5: the current voltage table

Take an ideal diode (n = 1) with I_s = 1 × 10⁻¹⁴ A at 300 K. This I_s is an illustrative value typical of a small silicon diode.

Going from 0.60 V to 0.70 V raises the current about 48 times. This is why the diode seems to "turn on" at about 0.6 to 0.7 V: below that, the current is too small to notice; above it, the current climbs so steeply that the voltage barely moves.

The 60 millivolts per decade rule

Solve the forward equation for V and you get V = (kT/q) × ln(I / I_s). A tenfold increase in current adds (kT/q) × ln 10 = 0.02585 × 2.3026 = 59.5 mV at 300 K. Engineers round this to 60 mV per decade. It shows up everywhere: in temperature sensors, in logarithmic amplifiers, and as the theoretical floor on how sharply a MOSFET can switch off below threshold, which is about 60 mV of gate voltage per tenfold change in current at room temperature.

Real diodes depart from the ideal

• Series resistance. At high current the voltage drop across the bulk silicon and contacts adds to the junction voltage, so the curve bends away from the exponential.
• Ideality factor. Recombination in the depletion region gives n near 2 at low currents; diffusion current gives n near 1 at moderate currents.
• Temperature. At a fixed current, the forward voltage falls as temperature rises, because I_s grows very steeply with temperature through nᵢ². Differentiating the ideal equation with I_s proportional to T³ exp(-E_g / kT) gives a slope of about (V - E_g/q - 3kT/q) / T. For V = 0.7 V and E_g = 1.12 eV at 300 K, that is about -1.7 mV per kelvin. This derived figure is the physics behind the silicon diode thermometer in many chips.

How do bipolar transistors and MOSFETs use junctions and gates to switch?

The bipolar junction transistor

HyperPhysics describes a bipolar junction transistor (BJT) as three regions of doped semiconductor, emitter, base and collector, in either n-p-n or p-n-p order. The base is thin and lightly doped. In normal operation:

1. The base emitter junction is forward biased. Electrons pour from the heavily doped emitter into the base, exactly as in a forward biased diode. This is Shockley's "minority carrier injection," because electrons are minority carriers in the p-type base.
2. The base is so thin that most injected electrons diffuse across it before they can recombine with holes.
3. The base collector junction is reverse biased. Its field sweeps the arriving electrons straight into the collector.

A small base current, which mostly replaces the holes lost to recombination, controls a much larger collector current. HyperPhysics writes this as I_C = β I_B and adds the more precise statement that the collector current is set by the base emitter voltage. Because the base emitter junction is a diode, the collector current follows the same exponential law: about tenfold for every 60 mV of V_BE.

Illustrative numbers. A transistor with β = 100 and a base current of 50 µA carries about 5 mA in the collector. As a switch, the base is driven hard enough that the transistor saturates, both junctions become forward biased, and the collector emitter voltage falls to a few tenths of a volt.

The MOSFET

The MOSFET won the integrated circuit. The Computer History Museum's account of Atalla and Kahng's 1959 to 1960 work explains why it took so long: earlier field effect designs by Lilienfeld, Heil and Shockley failed because "surface states" blocked the gate's field from reaching the silicon. Atalla and Kahng found that a thermally grown silicon dioxide layer reduced those states enough to work, and the metal, oxide, semiconductor sandwich gave the device its name.

An n-channel MOSFET, as MIT 6.012 lecture 9 draws it, has:

• a p-type body,
• two heavily doped n⁺ regions, the source and the drain, each forming a p-n junction with the body,
• a thin oxide insulator over the gap between them, and
• a gate electrode on top of the oxide.

With no gate voltage, source and drain are two back to back diodes: whichever way you apply voltage, one junction is reverse biased and no current flows. Raise the gate voltage and the field through the oxide first pushes holes away from the surface (depletion) and then, beyond the threshold voltage V_T, pulls enough electrons to the surface to invert it into a thin n-type layer. That inversion layer connects source to drain, and current flows. MIT's lecture puts the switching rule in two lines: with V_GS and V_GD below V_T there is no inversion and I_D = 0; above V_T an inversion layer forms and current flows.

HyperPhysics notes that the oxide gives the MOSFET an input impedance of 10⁹ to 10¹⁴ ohms. Almost no current flows into the gate in steady state, which is why billions of MOSFETs can sit on one chip without the control signals melting it.

Worked example 6: how much current does a MOSFET carry?

The simplest long channel model for the saturation current is:

I_D = (1/2) × (W/L) × μ_n × C_ox × (V_GS - V_T)²

C_ox is the oxide capacitance per unit area, the oxide permittivity (3.9 times NIST's vacuum permittivity) divided by its thickness. All the device values below are illustrative.

• Oxide thickness 10 nm: C_ox = 3.9 × 8.854 × 10⁻¹⁴ F/cm ÷ 10⁻⁶ cm ≈ 3.45 × 10⁻⁷ F/cm².
• Channel width to length ratio W/L = 10.
• Inversion layer electron mobility 400 cm²/V·s, lower than in bulk silicon because the electrons scatter off the oxide interface.
• Overdrive V_GS - V_T = 1 V.

I_D = 0.5 × 10 × 400 × 3.45 × 10⁻⁷ × 1² ≈ 0.69 mA.

Halve the oxide thickness and C_ox doubles, and so does the current. That one relation explains decades of scaling, and it also explains the problem scaling hit: once oxides were only a few atoms thick, electrons began tunnelling through them, the effect our Schrödinger post works through with numbers. The industry's answer was gate insulators with higher permittivity, so the oxide could stay physically thicker while behaving electrically thinner.

Diodes, BJTs, MOSFETs and IGBTs compared

Why do wide band gap materials like SiC and GaN matter for EV inverters and chargers?

What a traction inverter and a charger do

An electric car's battery supplies direct current at several hundred volts. Its motor needs three phase alternating current at a variable frequency. The traction inverter makes that conversion with six power switches, chopping the DC thousands of times per second into pulses whose width traces out a sine wave. An on board charger does the reverse when you plug in at home, turning grid AC into DC for the battery, and a DC fast charger does the same at much higher power from a cabinet beside the parking space. Every one of those conversions loses some energy as heat in the switches, and every switch is a junction device.

What DOE says wide band gap devices change

DOE's Advanced Manufacturing Office fact sheet says wide band gap power devices can be smaller, faster, more reliable and more efficient than silicon, and lists the specific benefits:

• They eliminate up to 90 percent of the power losses in AC to DC and DC to AC conversion.
• They handle voltages more than 10 times higher than silicon devices.
• They operate at temperatures over 300 °C, twice the maximum for silicon devices.
• They switch at frequencies at least 10 times higher, which lets the inductors, capacitors and transformers around them shrink.

DOE's 2015 Quadrennial Technology Review chapter on wide bandgap power electronics adds the dividing line most engineers still use: SiC is expected to be the prevailing replacement for silicon above about 600 volts, GaN below about 600 volts. It names hybrid and electric vehicles as a significant SiC market and PV inverters and vehicle chargers among GaN uses, and it is candid that substrate and epitaxy cost and material maturity were the main barriers.

The physics behind "10 times the voltage"

The band gap sets how much energy a carrier must gain before it can knock a new electron hole pair loose, so a wider gap raises the critical electric field at which avalanche breakdown starts. Silicon's is a few hundred kilovolts per centimetre; SiC's is roughly ten times higher, consistent with DOE's "more than 10 times higher" voltage figure. That factor of ten compounds through the device design.

Worked example 7: the drift layer of a 1,200 V switch

A power MOSFET holds its blocking voltage across a lightly doped drift layer, the thick side of a one sided junction from worked example 4. For a simple triangular field profile that reaches the critical field E_c exactly at the rated voltage V:

drift layer thickness  W = 2V / E_c
maximum drift doping   N_d = ε_s × E_c² / (2 q V)

Using silicon's permittivity for both cases to keep the comparison simple, and illustrative critical fields of 0.3 MV/cm for silicon and 3 MV/cm for SiC, at V = 1,200 V:

The resistance of the drift layer scales with its thickness divided by its doping, so ten times thinner and a hundred times more heavily doped means about a thousand times lower resistance per unit area. SiC's lower electron mobility and slightly different permittivity take some of that back, but the advantage that remains is still large. It is the reason a SiC MOSFET can do at 1,200 V what in silicon needs an IGBT, with its slower switching and turn off tail.

DOE's EV power electronics targets

The October 2017 roadmap from the US DRIVE Electrical and Electronics Technical Team, a partnership of DOE, automakers and utilities, set 2025 targets for a single 100 kW power module:

The roadmap says the 2025 power electronics targets "are driven by the opportunity to replace silicon switches with WBG devices," which shrink the power modules and allow higher temperatures and frequencies, while acknowledging that wide band gap devices cost more than silicon equivalents individually. The roadmap set targets; it did not report whether they were met, and we have not seen a DOE source that grades them.

Silicon, SiC and GaN for power, side by side

How do LEDs and solar cells use the same junction physics in opposite directions?

A p-n junction converts between electrical and optical energy in both directions. Forward bias it in a direct gap material and recombining carriers emit light: an LED. Shine light on it and the photons create carriers that the built in field separates: a solar cell or photodiode. Ohl saw the second effect first, in 1940, when his silicon slab's current jumped under a lamp.

The LED: injection, recombination, light

In an LED the forward biased junction injects electrons into the p side and holes into the n side, exactly as in worked example 5. When an electron drops from the conduction band into a hole in a direct gap material, it gives up an energy close to the band gap as a photon. The wavelength follows from E = hc / λ. Using NIST's exact values for Planck's constant and the speed of light, hc = 1,239.84 eV·nm, so:

λ (nm) ≈ 1240 / E_g (eV)

Worked example 8: band gap to colour

Blue and green LEDs do not use pure GaN: alloying it with indium (InGaN) narrows the gap and pulls the emission into the visible. The Nobel Committee's background paper explains that heterojunctions and quantum wells of InGaN and AlGaN confine electrons and holes in a thin layer where they recombine efficiently, the structure behind Nakamura's 1994 result of 2.7 percent quantum efficiency. White LED lamps then use a blue chip to excite a phosphor.

The hard part of the blue LED was doping, not band gaps. GaN tends to be naturally n-type, and the Nobel paper explains that magnesium acceptors were passivated by hydrogen, which formed complexes with them. Amano and Akasaki found in 1989 that low energy electron irradiation improved p-type doping; Nakamura showed in 1992 that thermal annealing alone activates the magnesium. Without a working p-type layer there is no p-n junction, and without the junction there is no LED. The Nobel popular summary notes that the efficiency record for LED light had reached just over 300 lumens per watt, against 16 for regular incandescent bulbs and close to 70 for fluorescent lamps.

The solar cell: absorption, separation, current

A solar cell runs the junction backwards. DOE's PV basics page puts it plainly: when the semiconductor absorbs sunlight, the light's energy goes to electrons. In junction terms:

1. A photon with energy above the band gap lifts an electron into the conduction band, creating an electron hole pair. Photons below the gap pass through unabsorbed; energy above the gap is lost as heat almost at once.
2. If the pair is created in or near the depletion region, the built in field separates it before it recombines: electrons are swept to the n side, holes to the p side.
3. The separated charges build up as a voltage across the cell. Connect a load and they flow through it as current.

The cell is effectively a large diode with a light generated current I_L running in the reverse direction:

I = I_L - I_0 × ( exp( q V / (n k T) ) - 1 )

At open circuit I = 0, so the open circuit voltage is V_oc = (nkT/q) × ln(I_L / I_0 + 1).

Worked example 9: open circuit voltage of a silicon cell

With illustrative values per square centimetre of I_L = 40 mA (roughly full sunlight on a good silicon cell) and I_0 = 1 × 10⁻¹² A, and n = 1:

V_oc = 0.02585 × ln(4 × 10¹⁰) = 0.02585 × 24.41 ≈ 0.63 V.

Two things follow. First, a single silicon cell gives a little over half a volt, which is why modules wire dozens of cells in series. Second, cutting I_0 by ten, through better surface passivation and cleaner silicon, adds about 60 mV of voltage, the same 60 mV per decade rule as the diode. That is what most of the cell architectures in our solar panel manufacturing post are fighting for.

Why band gap sets a ceiling on solar efficiency

Shockley and Queisser's 1961 paper in the Journal of Applied Physics, "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells," made the trade off rigorous. A small gap absorbs more of the spectrum but wastes the excess energy of blue photons as heat and gives a low voltage. A large gap gives a high voltage per carrier but lets most of the spectrum pass straight through. Balancing absorption against unavoidable radiative recombination gives a maximum efficiency for a single junction that peaks for band gaps a little above silicon's, which is one reason silicon works so well. Multijunction cells beat that limit by stacking materials with different gaps, each taking a slice of the spectrum, and NLR (formerly NREL) maintains the Best Research Cell Efficiency Chart that records confirmed results by technology since 1976.

LED, photodiode and solar cell compared

Walkthrough: compute and simulate a p-n junction yourself

Everything above can be reproduced on a laptop in a few minutes. This walkthrough uses Python's standard library, so there is nothing to install for the calculations, and the open source circuit simulator ngspice for the diode curve. None of these commands touch hardware or delete anything.

Step 1: make a clean working folder and virtual environment

mkdir -p ~/pn-junction && cd ~/pn-junction
python3 -m venv .venv
source .venv/bin/activate
python3 --version

The script below needs no third party packages. If you later add plotting libraries, pin them in a requirements.txt with hashes and install with pip install --require-hashes -r requirements.txt, so a rebuild next month installs exactly what you tested.

Step 2: write the calculator

Save this as junction.py. The constants are the NIST CODATA 2022 values; the mobility and saturation current are illustrative and are labelled as such in the code.

import math

# NIST CODATA 2022 (exact or recommended values)
q = 1.602176634e-19          # elementary charge, C
k = 1.380649e-23             # Boltzmann constant, J/K
eps0 = 8.8541878188e-14      # vacuum permittivity, F/cm
h = 6.62607015e-34           # Planck constant, J s
c = 299792458.0              # speed of light, m/s

# Silicon at 300 K
T = 300.0
ni = 1.0e10                  # cm^-3, MIT 6.012 value
eps_si = 11.7 * eps0         # F/cm
VT = k * T / q               # thermal voltage, V

def carriers(Nd=0.0, Na=0.0):
    net = Nd - Na
    if net >= 0:
        n = net / 2 + math.sqrt((net / 2) ** 2 + ni ** 2)
        p = ni ** 2 / n
    else:
        p = -net / 2 + math.sqrt((net / 2) ** 2 + ni ** 2)
        n = ni ** 2 / p
    return n, p

def built_in(Na, Nd):
    return VT * math.log(Na * Nd / ni ** 2)

def depletion(Na, Nd, V=0.0):
    phi = built_in(Na, Nd)
    w = math.sqrt(2 * eps_si * (phi - V) / q * (Na + Nd) / (Na * Nd))
    return w, 2 * (phi - V) / w

def diode_current(V, Is=1e-14, n=1.0):   # Is is illustrative
    return Is * (math.exp(V / (n * VT)) - 1)

if __name__ == "__main__":
    print(f"thermal voltage {VT*1000:.2f} mV, {VT*math.log(10)*1000:.1f} mV/decade")
    n, p = carriers(Nd=1e16)
    print(f"Nd=1e16: n={n:.3g} cm^-3, p={p:.3g} cm^-3")
    Na, Nd = 1e17, 1e16
    print(f"built-in voltage {built_in(Na, Nd):.3f} V")
    for V in (0.5, 0.0, -5.0, -10.0):
        w, e = depletion(Na, Nd, V)
        print(f"V={V:+.1f} V: width {w*1e4:.3f} um, peak field {e/1e3:.0f} kV/cm")
    for V in (0.5, 0.6, 0.65, 0.7, 0.75):
        print(f"diode at {V:.2f} V: {diode_current(V):.3g} A")
    hc_eVnm = h * c / q * 1e9
    for name, eg in (("Si", 1.11), ("GaAs", 1.43), ("GaN", 3.4)):
        print(f"{name}: {hc_eVnm/eg:.0f} nm")

Step 3: run it and compare with this post

python3 junction.py

You should see a thermal voltage of 25.85 mV and 59.5 mV per decade, n of 1 × 10¹⁶ and p of 1 × 10⁴ for the doped sample, a built in voltage of 0.774 V, a zero bias depletion width of 0.332 µm, and currents from 2.5 µA at 0.5 V to about 40 mA at 0.75 V. If any number differs, check units first: the most common error is mixing metres and centimetres in the permittivity.

Step 4: simulate the diode curve with ngspice

Install ngspice from your operating system's package manager (for example sudo apt install ngspice on Debian or Ubuntu, or brew install ngspice on macOS), then save this netlist as diode.cir:

* Forward sweep of an ideal silicon diode
V1 a 0 DC 0
D1 a 0 DSI
.model DSI D(IS=1e-14 N=1 RS=0)
.temp 26.85
.control
dc V1 0.4 0.8 0.05
print v(a) i(V1)
.endc
.end

Run it in batch mode:

ngspice -b diode.cir

The .temp 26.85 line sets 300 K. The currents printed (as negative values, because SPICE reports current into the source) should match the table in worked example 5. Now set RS=1 to add a 1 ohm series resistance and rerun: above about 30 mA the curve bends away from the pure exponential, which is the real diode behaviour described earlier.

Step 5: sanity check against the physics

• The current should rise about tenfold per 60 mV at low current.
• The reverse current should be about -1 × 10⁻¹⁴ A, independent of voltage, because the model has no breakdown or leakage.
• Raise .temp to 76.85 (350 K) and the thermal voltage becomes 30.2 mV. Note that SPICE also raises IS with temperature through its own model parameters, so at a fixed current the forward voltage falls, consistent with the derived -1.7 mV per kelvin.

The software that runs power electronics: an honest bridge

A SiC traction inverter or a GaN charger is not only a stack of junctions. A microcontroller or digital signal processor runs control loops that decide when each gate switches, a battery management system reports cell voltages and temperatures, and the charger talks to the car and often to a network service. All of that is software, much of it built with vendor SDKs, real time operating systems and open source libraries, and the cloud services that manage charge points are ordinary web applications with ordinary dependency trees. Safeguard does not do physics or chemistry, does not design, test or analyse semiconductor devices, and does not scan firmware images or hardware; its models are single purpose security models for software. Where it can help is the software your team builds and ships around such devices, such as a charge point management backend, a lab test harness written in Python, or the container image for a fleet monitoring service: scanning those repositories, images and SBOM files for known vulnerable open source components and, when a fixed version exists, proposing the upgrade.

A rebuilt test bench or charger backend pulls its dependencies again on every build, and the gateways and control boards around power electronics ship TLS libraries, parsers and web servers from open source projects. The fit is indirect for the devices themselves, but for the open source code you build and ship around them, the same dependency hygiene applies.

Common mistakes

• Treating the "0.7 V drop" as a constant. It is a consequence of the exponential diode equation at milliamp currents. At microamps a silicon junction drops closer to 0.5 V, at amps it drops more because of series resistance, and it falls by roughly 1.7 mV per kelvin as the junction heats.
• Thinking holes are positrons or missing atoms. A hole is a missing electron in a bond, and its motion is the collective shuffle of many valence electrons. It behaves as a positive carrier with its own mobility and effective mass.
• Assuming doping adds charge to the crystal. A donor atom brings its own extra proton along with its extra electron, so doped silicon is electrically neutral. Net charge appears only where carriers have moved away from their ions, as in the depletion region.
• Forgetting that n × p stays constant. Raising one carrier type lowers the other. A designer who forgets this misjudges minority carrier currents, which are what actually set a diode's reverse current and a BJT's gain.
• Mixing up which side the depletion region occupies. It extends mostly into the lightly doped side, as worked example 4 shows. Power device voltage ratings come from that light side's thickness and doping.
• Expecting to measure the built in voltage with a meter. Contact potentials at the leads cancel it exactly.
• Calling every wide band gap device "better." SiC and GaN cost more per device, have different gate drive needs and reliability questions, and DOE's own documents describe silicon as the right answer for many lower voltage jobs. The benefit comes from the system: smaller passives, less cooling, higher efficiency.
• Quoting band gaps to more precision than the sources support. Values differ by temperature, polytype, alloy and source. Quote the temperature and the source.
• Assuming silicon makes efficient LEDs because it makes efficient solar cells. Silicon's indirect gap makes it a fine absorber when thick enough but a very poor light emitter.
• Pinning a calculation to unpinned software. If you run device models in Python, a silently upgraded library can change results. Pin versions and record them with the output.

FAQ

What is a p-n junction in simple terms?

It is the boundary inside one crystal where a region doped to have spare electrons (n-type) meets a region doped to have missing electrons, or holes (p-type). Carriers near the boundary cancel out and leave fixed charged atoms behind, which creates an electric field. That field lets current flow easily one way and blocks it the other way.

Why is silicon a semiconductor and not a conductor?

Its valence electrons are all tied up in bonds, and the next available energy states lie about 1.1 eV higher. At room temperature only about one electron in every five trillion atoms has enough thermal energy to cross that gap, according to MIT's figure for intrinsic carrier concentration, so pure silicon conducts poorly until it is doped.

What is the band gap of silicon, GaN and SiC?

DOE lists silicon at 1.1 eV, silicon carbide at 3.3 eV and gallium nitride at 3.4 eV. HyperPhysics, citing Kittel, gives silicon as 1.11 eV at 300 K and 1.17 eV at absolute zero. Germanium is about 0.66 to 0.7 eV and gallium arsenide about 1.4 eV.

What is the difference between n-type and p-type semiconductors?

n-type silicon is doped with atoms that have five valence electrons, such as phosphorus or arsenic, so it has extra free electrons. p-type silicon is doped with atoms that have three, such as boron, so it has holes. Both stay electrically neutral overall; they differ in which carrier dominates.

Why does a diode drop about 0.7 volts?

The ideal diode equation makes current grow by about ten times for every 60 mV of forward voltage at room temperature. For a typical small silicon diode, the current reaches milliamps at around 0.6 to 0.7 V, and beyond that it rises so steeply that the voltage barely changes. It is a consequence of the exponential, not a fixed threshold.

What is the difference between a BJT and a MOSFET?

A bipolar transistor uses a small base current through a forward biased junction to control a larger collector current. A MOSFET uses a voltage on an insulated gate to create or remove a conducting channel between two junctions, drawing almost no steady gate current. MOSFETs dominate integrated circuits because they are easy to shrink and integrate in huge numbers.

Why are electric cars switching to silicon carbide?

Silicon carbide's wider band gap gives it roughly ten times silicon's critical electric field. A SiC power switch can therefore block high voltages with a much thinner, more heavily doped layer, giving lower losses, higher temperature limits and faster switching. DOE's roadmap tied its 2025 target of 100 kW per litre for EV power electronics to replacing silicon switches with wide band gap devices.

How is an LED different from a solar cell?

They are the same junction used in opposite directions. An LED is forward biased so that injected electrons and holes recombine and emit light at a wavelength set by the band gap. A solar cell absorbs light, which creates electron hole pairs that the junction's built in field separates into a current.

Why are blue LEDs so hard to make?

They need a direct, wide band gap material such as gallium nitride, and GaN was very hard to dope p-type because hydrogen passivated the magnesium acceptors. The Nobel Committee credits Amano and Akasaki's 1989 discovery that electron irradiation improves p-doping and Nakamura's 1992 demonstration that thermal annealing activates the acceptors. Those advances made GaN p-n junctions, and blue LEDs, practical.

Fix it without waiting for upstream

Whatever the vulnerability, most of the risk sits in two gaps. The first is the time between a fix being published and that fix actually running in your production builds. The second, and worse, is the time before any fix exists at all, while a maintainer works out a patch and a release schedule. Waiting through both gaps is a habit, not a requirement. Safeguard gives teams three ways to close them.

1. Autonomous remediation: pull requests, not tickets

When a fixed version exists, Safeguard's Griffin models open a tested, policy gated pull request that moves the affected dependency to the safe version. You can run it on one repository or in bulk across every project that carries the vulnerable version. Remediation covers eight categories, including dependencies, licenses, security posture and findings. Reachability analysis ranks the vulnerable code paths your application actually calls first, so the first pull requests you merge are the ones that matter most. Autonomous remediation ships switched off, with every category set to Manual, so your team decides how much runs on its own and what still needs a human approval.

2. Gold Open Source: the safe version in seconds, free

gold.safeguard.sh is free and needs no login. Search any CVE or package to see affected and fixed versions, CVSS, EPSS, CISA KEV status and a recommended safe version, or use the "Am I affected?" checker. The same data is available through a free read API, README status badges and RSS threat feeds. The safeguard-sh/gold-scan-action GitHub Action can fail a build on a known exploited vulnerability, on any known vulnerability, or never, so a version you have just removed cannot quietly come back in next week's merge.

3. Gold Registry: start from components that are already fixed

registry.safeguard.sh provides hardened, drop in replacements for upstream packages and container images. Every Gold artifact is held continuously to zero exploitable critical or high CVEs, zero malware and a completed license check, with SLSA L3 or higher provenance, a Sigstore signature and a public evidence page you can hand to an auditor. An artifact loses its Gold badge if it regresses. Teams can point their own package directory at the registry so hardened equivalents resolve without changing how developers install anything.

When upstream has no fix yet, or will not ship one, Safeguard first works to get the fix accepted upstream. If the issue is severe or upstream will not move, Safeguard builds a fork, fixes the vulnerability there and publishes a hardened Gold build, so you are not stuck on a maintainer's release schedule. You can also request a hardened, compatibility tested build of a specific package. This fork and patch flow is in early access today, so ask which packages it covers before you plan around it.

One honest limit: when the vulnerable code lives in a vendor appliance, a hosted service or an operating system runtime you do not build yourself, the fix still has to come from that vendor or distribution. The steps above apply to the open source dependencies and container images you build and ship, which is where most teams carry the largest and least tracked share of their exposure.

See how Safeguard would help

None of these demos involve semiconductor physics; they show the software side described in the bridge above.

The first demo is a real Safeguard CLI session: it installs the CLI, opens the interactive terminal and asks it to fix a lodash CVE in a repository. It reads the finding and advisory, asks before each command, edits package.json to lodash 4.17.21, runs npm install and npm test with approval, prints a summary and pushes nothing. The same flow applies to a charge point management dashboard or a lab data portal your team maintains: scan the repository, then let the assistant propose the dependency upgrade under your approval.

Click through it at your own pace, or open it full screen.

The second demo sets up the Safeguard runner on your own machine, approves it with its device code and then scans from the terminal. That suits teams that keep test bench software, device simulation scripts or build tooling on their own hardware and want the scan to run where the build runs.

Click through it at your own pace, or open it full screen.

The third demo connects Claude to the Safeguard MCP server with OAuth and lets you choose which tools Claude can use. For an engineer who already uses Claude while working on a test harness or a backend service, it puts dependency findings in the same conversation, limited to the tools you allow.

Click through it at your own pace, or open it full screen.

To try it on your own repositories, download Safeguard and follow the CLI documentation.

Quick check

Sources

• NobelPrize.org, The Nobel Prize in Physics 1956 (summary)
• NobelPrize.org, Award ceremony speech, Nobel Prize in Physics 1956
• William Shockley, Nobel Lecture, 11 December 1956 (PDF)
• John Bardeen, Nobel Lecture, 11 December 1956 (PDF)
• NobelPrize.org, The Nobel Prize in Physics 2000 (summary)
• NobelPrize.org, The Nobel Prize in Physics 2014, press release (7 October 2014)
• Nobel Committee for Physics, Scientific Background on the Nobel Prize in Physics 2014: Efficient blue light-emitting diodes (PDF)
• NobelPrize.org, Popular information on the Nobel Prize in Physics 2014 (PDF)
• NIST CODATA 2022, Boltzmann constant
• NIST CODATA 2022, Boltzmann constant in eV/K
• NIST CODATA 2022, Elementary charge
• NIST CODATA 2022, Vacuum electric permittivity
• NIST CODATA 2022, Lattice parameter of silicon
• MIT OpenCourseWare, 6.012 Microelectronic Devices and Circuits, Fall 2005 (course page)
• MIT OCW 6.012, Lecture 2: Electrons and holes, generation and recombination, doping (PDF)
• MIT OCW 6.012, Lecture 5: pn junction in thermal equilibrium (PDF)
• MIT OCW 6.012, Lecture 6: pn junction under bias, depletion capacitance (PDF)
• MIT OCW 6.012, Lecture 9: MOSFET I-V characteristics (PDF)
• HyperPhysics (Georgia State University), Band Theory of Solids
• HyperPhysics, Semiconductor Band Gaps table
• HyperPhysics, Intrinsic Semiconductors
• HyperPhysics, Doped Semiconductors
• HyperPhysics, The P-N Junction
• HyperPhysics, Biasing of P-N Junctions
• HyperPhysics, Diodes
• HyperPhysics, Transistors
• HyperPhysics, MOSFETs
• HyperPhysics, Light Emitting Diodes
• Computer History Museum, The Silicon Engine: 1940, Discovery of the p-n Junction
• Computer History Museum, The Silicon Engine: 1947, Invention of the Point-Contact Transistor
• Computer History Museum, The Silicon Engine: 1948, Conception of the Junction Transistor
• Computer History Museum, The Silicon Engine: 1960, Metal Oxide Semiconductor (MOS) Transistor Demonstrated
• W. Shockley, The Theory of p-n Junctions in Semiconductors and p-n Junction Transistors, Bell System Technical Journal 28, 435 to 489 (July 1949)
• W. Shockley and H. J. Queisser, Detailed Balance Limit of Efficiency of p-n Junction Solar Cells, Journal of Applied Physics 32, 510 to 519 (March 1961)
• US DOE Advanced Manufacturing Office, Wide Bandgap Semiconductors: Pursuing the Promise (2013, PDF)
• US DOE, Quadrennial Technology Review 2015, Chapter 8 technology assessment: Wide Bandgap Power Electronics (PDF)
• US DRIVE, Electrical and Electronics Technical Team Roadmap (October 2017, PDF)
• US DOE, Solar Photovoltaic Cell Basics
• NLR (formerly NREL), Best Research-Cell Efficiency Chart

Last reviewed: 23 October 2026.