Reverse bias behavior: Foundations — Hardware deep dive

Before you can read the parent note, you need to know what every letter means and, more importantly, what picture it points at. We build them in the order they depend on each other: charges → junction → depletion zone → the field/voltage across it → the current that leaks through → temperature → breakdown.

1. Charge carriers: electrons and holes

Look at the figure: the coral dots are electrons (charge $- q$ ), the lavender rings are holes (charge $+ q$ ). When electrons shuffle right, the empty hole appears to move left. Both count as current.

$q$ — the elementary charge, the size of one electron's charge, $q \approx 1.6 \times 1 0^{- 19} C$ (coulombs). It is the "unit of charge" that every carrier carries.

2. Doping: making an N-side and a P-side

The parent note uses these symbols for "how much doping":

$N_{D}$ — donor concentration: how many electron-donating atoms per cubic metre on the N-side.
$N_{A}$ — acceptor concentration: how many hole-creating atoms per cubic metre on the P-side.

$p_{n 0}$ — equilibrium hole concentration on the N-side (holes are minority there).
$n_{p 0}$ — equilibrium electron concentration on the P-side (electrons are minority there).

The subscript reads "which carrier, which side, at rest (0)". So $p_{n 0}$ = "holes, N-side, at equilibrium".

3. The junction and the depletion region

When P and N are joined, mobile carriers near the boundary meet and cancel: electrons fill holes. This leaves a thin strip empty of mobile charge — but full of the fixed ionised dopant atoms that can no longer be neutralised.

In the figure the middle band has no dots — only bare + ions on the N-side and − ions on the P-side. Those bare charges create an internal electric field pointing across the gap. Full detail lives in Depletion region & built-in potential.

$A$ — the cross-sectional area of the junction (metres²). Bigger area = more parallel paths = more current and more capacitance, so it multiplies things.
$ε$ — the permittivity of the semiconductor: how easily the material stores electric field/charge. It appears in both $W$ and the capacitance.

4. Current $I$ : what it is and which way it points

Before we build voltage hills, we need to be crystal-clear about the quantity the parent note keeps writing: $I$ .

5. Field, potential, and the built-in barrier

We need language for "how hard it is to push a charge across the gap".

$V_{bi}$ — the built-in potential: the height of the voltage hill that exists with no battery attached, purely from the P and N sides balancing. Measured in volts.
$V$ — the applied voltage from the battery, following the same P-to-N reference as $I$ .

6. The Shockley current: symbols in the exponential

The parent's master formula is $I = I_{S} (e^{V / (n V_{T})} - 1)$ from the Shockley diode equation. Decode each piece:

$k$ — Boltzmann's constant, converting temperature into energy.
$T$ — absolute temperature in kelvin (K). $300 K \approx 27 ° C$ .
$n$ — the ideality factor, a fudge number ( $\approx 1$ – $2$ ) describing how close the real diode is to the ideal theory.

$n_{i}$ — the intrinsic carrier concentration: how many electron–hole pairs heat alone creates in the pure material. Since $I_{S} \propto n_{i}^{2}$ , and $n_{i}$ climbs steeply with $T$ , this is why reverse leakage doubles roughly every $10 ° C$ .
$E_{g}$ — the band gap energy: the energy needed to free one electron and make a pair. It sits in $n_{i}^{2} \propto e^{- E_{g} / (k T)}$ .
$D_{p}, D_{n}$ — diffusion constants (how fast holes / electrons spread out); $L_{p}, L_{n}$ — diffusion lengths (how far a minority carrier travels before recombining). They set the size of $I_{S}$ .

7. Junction capacitance

This is the whole basis of Varactor diodes — a voltage-tunable capacitor. $C_{j 0}$ is simply $C_{j}$ at zero applied voltage.

8. Breakdown vocabulary

$V_{B R}$ — the breakdown voltage: the reverse voltage at which the current suddenly surges. Below it, current stays at $\approx I_{S}$ ; at it, the physics changes (tunneling or impact ionisation). This anchors Zener diodes.

Prerequisite map

Equipment checklist

What does a hole represent physically?

A missing electron that behaves like a mobile positive charge.

Which carriers are the majority on the N-side?

Electrons.

Which carriers cause the tiny reverse (saturation) current?

Thermally generated minority carriers.

What do

N_{A}

and

N_{D}

measure?

Acceptor (P-side) and donor (N-side) dopant concentrations per volume.

What is the depletion region?

The strip around the junction empty of mobile carriers, leaving fixed exposed ions.

What does the symbol

W

stand for?

The width (thickness) of the depletion region.

What is the sign convention for the diode current

I

I > 0

for conventional current flowing P→N (forward);

I < 0

for N→P (reverse), so

I \approx - I_{S}

is a backward trickle.

What is

V_{bi}

The built-in potential hill present with no battery attached.

Sign convention for

V

— forward vs reverse?

V > 0

forward (hill lowered, big

I > 0

);

V < 0

reverse (hill raised,

I < 0

locks at

- I_{S}

Why is the field

E (x)

a straight ramp across the depletion region?

Gauss's law

d E / d x = ρ / ε

with a roughly constant dopant charge density gives a constant slope, hence a linear field.

Why does

W \propto V_{bi} - V

Charge grows with

W

but the voltage it supports (area under the linear field) grows with

W^{2}

, so width scales with the square root of voltage.

What is

V_{T}

and its room-temperature value?

Thermal voltage

k T / q \approx 25.85

mV at 300 K.

Why is the diode current an exponential in

V

The count of carriers able to climb the voltage hill falls off exponentially (Boltzmann), so current changes exponentially with barrier height.

What sets

I_{S}

's steep temperature rise?

I_{S} \propto n_{i}^{2} \propto e^{- E_{g} / (k T)}

Formula for junction capacitance?

C_{j} = ε A / W

, so wider

W

gives smaller

C_{j}

What is

V_{B R}

The reverse breakdown voltage where current suddenly surges.