The P-N Diode

Hook: Why Only One Way?

In 1939 at Bell Labs, Russell Ohl was testing an impure silicon crystal when he noticed something odd: shining light on it produced a voltage in one direction only, not the other. The crystal converted light to electricity one way and blocked the reverse. On closer inspection the two halves of the crystal carried different impurities — one had extra electrons, the other had extra holes. The first p-n diode, discovered by accident.

Today a diode on a chip isn’t just for “turning light into voltage”. It underpins all modern electronics: AC to DC rectification, LEDs, reverse-polarity protection, complex logic. A transistor is essentially a “three-terminal diode”.

Even the SIDRA 1S1R (1-Selector + 1-Resistor) memristor cell has a diode-like part: the OTS selector, a valve that blocks reverse current and suppresses leakage. This chapter shows how a diode works; in Module 5 you’ll see how the selector gets yoked to the memristor.

Intuition: Holes + Electrons Side by Side

From Module 1.2:

p-type silicon (e.g. Boron-doped) → free holes, positive carriers.
n-type silicon (e.g. Phosphorus-doped) → free electrons, negative carriers.

Now put the two sides together (not physically glued — two regions of the same crystal). At the boundary:

Electrons from the n-side see the abundant holes on the p-side. They diffuse across and recombine.
Holes from the p-side likewise diffuse into the n-side and recombine with electrons.
Near the junction, no free carriers remain. What’s left are the ionic charges of the dopant atoms themselves: on the p-side, negative ions (B⁻), on the n-side, positive ions (P⁺).
These fixed ionic charges create an electric field across the junction. The field eventually stops the diffusion — equilibrium.

This thin boundary is the depletion region. Only ionic charge, no free carriers. The potential difference across it is the built-in voltage ( $V_{bi}$ ): ~0.7 V for silicon, ~0.3 V for germanium.

Apply an external bias:

Forward bias (+ on P, − on N): the external field weakens the built-in field; depletion narrows. Above $V_{bi}$ the barrier effectively collapses and carriers flood across → current flows.
Reverse bias (− on P, + on N): external field adds to the built-in field; depletion widens, carriers pull away → current is tiny (leakage only).

That’s why the diode is “one-way”. The p-n junction itself is a valve.

Formalism: The Shockley Diode Equation

L1 · Intro

The I-V characteristic has three regions:

$V < 0$ (reverse): nearly zero current (tiny leakage $I_s$ , picoampere range)
$0 < V < V_{bi}$ (forward but small): still very little current — barrier not yet overcome
$V > V_{bi}$ (forward, strong): current rises exponentially — near-wall-like sharp turn-on

“Turn-on voltage” ≈ $V_{bi}$ (Si 0.7 V, Ge 0.3 V, LED typically 2-3 V). No practical current flows below this.

L2 · Full

Shockley diode equation:

I = I_s \left( e^{V / (n V_T)} - 1 \right)

$I_s$ : reverse saturation current (~ $10^{-12}$ A for Si — essentially zero)
$V_T = k_B T / q \approx 0.026$ V at room temperature — thermal voltage
$n$ : ideality factor (ideal 1, real Si 1.0-1.5, LED ~2)

Two regimes:

Forward: $V \gg V_T$ → $I \approx I_s e^{V/V_T}$ — exponential. Every 26 mV increase in $V$ multiplies $I$ by $e$ .
Reverse: $V \ll -V_T$ → $I \approx -I_s$ — constant, tiny.

Depletion width (abridged derivation):

W = \sqrt{\frac{2 \varepsilon_s (V_{bi} - V)}{q} \left( \frac{N_A + N_D}{N_A N_D} \right)}

$\varepsilon_s$ : silicon permittivity (~ $1.04 \times 10^{-12}$ F/cm)
$N_A$ , $N_D$ : acceptor and donor concentrations
Forward $V \to V_{bi}$ → $W \to 0$ (depletion collapses)
Reverse $V \to -\infty$ → $W$ grows (until breakdown)

Reverse breakdown: when reverse voltage is large enough (~−5 V to −100 V for Si depending on design), Zener or avalanche mechanisms turn on current abruptly. Zener diodes use this region on purpose for voltage regulation.

L3 · Deep

From a quantum viewpoint a p-n junction is a potential step. The probability of an electron crossing the barrier follows a Boltzmann distribution, giving a current exponential in $qV/kT$ . That’s where the Boltzmann factor in the equation comes from.

Small-signal model under forward bias:

r_d = \frac{dV}{dI} = \frac{V_T}{I_D}

So at $I_D = 1$ mA the dynamic resistance is ~26 Ω. At transistor bias, this resistance is the basis of the amplifier gain formula.

p-i-n diode: insert an intrinsic (undoped) layer between P and N. Depletion widens into this layer, capacitance drops, breakdown voltage rises. Useful in RF, fast switching, photodiodes. SIDRA’s 1S1R cell has a similar-shaped structure for a different reason — the OTS selector’s “off” state is amorphous-semiconductor-like, behaving high-resistance at low bias.

Ovonic Threshold Switch (OTS): in SIDRA, NbOx-based amorphous semiconductor. It is not a diode but shows diode-like threshold behavior: high resistance at low voltage (off), sudden drop to low resistance above $V_{th}$ (on). When bias is removed, it resets. It fixes the “sneak path” problem in memristor crossbars — detailed in later chapters.

Experiment: Slide the Bias, Watch the Diode

Slide the bias slider from −1 V to +1 V. Compare the three regimes:

Observation points:

V = 0 (equilibrium): depletion region sits in the middle. Potential profile (below) shows high on P side, low on N — the built-in barrier. No carrier motion.
V = +0.3 V (forward, low): depletion narrowed slightly, barrier lowered, still no current. This is the “pre-turn-on” region.
V = +0.7 V (forward, turn-on): barrier nearly flat — electrons from N to P, holes reverse, current meter rises.
V = +1.0 V (forward, saturated): pedagogical clip at ~1 mA (real chips can handle mA to A).
V = −0.5 V (reverse): depletion widened. Barrier grew. Carriers retreated. No current.
V = −1.0 V (reverse, deep): stronger of the same. A real diode would hit breakdown eventually — we don’t model it here.

The potential profile under the diode updates live with bias.

Quiz

1/5What sits in the depletion region?

Lab Task: Diode Current Calculation

Use Shockley’s equation to compute Si diode currents at several biases.

Data: $I_s = 10^{-12}$ A, $V_T = 0.026$ V, $n = 1$ .

1. Forward $V = 0.6$ V:

I = I_s (e^{V/V_T} - 1) = 10^{-12} (e^{0.6/0.026} - 1)

Exponent: $0.6 / 0.026 = 23.08$ . $e^{23.08} \approx 1.06 \times 10^{10}$ . So $I \approx 10^{-12} \times 1.06 \times 10^{10} = 10.6$ mA.

2. Forward $V = 0.7$ V:

$0.7 / 0.026 = 26.92$ , $e^{26.92} \approx 4.9 \times 10^{11}$ . $I \approx 0.49$ A (nearly half an amp).

Your turn:

(a) Current at $V = 0.5$ V? (Hint: less than 1 mA) (b) Current at $V = -0.5$ V? (Hint: $e^{-0.5/0.026}$ is essentially zero, so $I \approx -I_s$ ) (c) Dynamic resistance $r_d = V_T / I_D$ at $I_D = 10$ mA?

Answers

(a) $0.5/0.026 = 19.23$ , $e^{19.23} \approx 2.25 \times 10^8$ , $I \approx 225$ µA ≈ 0.2 mA. One more 0.1 V (0.5 → 0.6) multiplies current by 50 — that’s the diode’s “sharpness”.

(b) $I \approx -I_s = -10^{-12}$ A. Reverse current is practically nothing.

(c) $r_d = 0.026 / 0.01 = 2.6$ Ω. At higher currents, dynamic resistance shrinks — the basis of transistor amplifier gain.

Next step: imagine this equation with different $n$ and $I_s$ for LEDs and photodiodes. Same formula, different material. In the next chapter (MOSFET) we’ll apply the p-n junction backwards — making the junction itself a controlled gate.

Cheat Sheet

P-N junction: p-type (holes) + n-type (electrons) side by side → carriers diffuse across, recombine, leave behind ionic charge.
Depletion region: thin boundary zone with only ionic charge. Creates an electric field.
Built-in potential $V_{bi}$ : Si 0.7 V, Ge 0.3 V, GaAs 1.4 V.
Forward bias: $V > V_{bi}$ — current rises exponentially ( $I = I_s e^{V/V_T}$ ).
Reverse bias: current near-constant $-I_s$ (~pA); breakdown occurs at high reverse.
Thermal voltage: $V_T = k_B T / q \approx 26$ mV (room T).
Shockley equation: $I = I_s (e^{V/nV_T} - 1)$ .
Dynamic resistance: $r_d = V_T / I_D$ (~26 Ω / mA).
SIDRA: OTS selector is not a p-n diode but diode-like in threshold; solves the crossbar sneak-path problem.

Vision: Beyond P-N

The silicon p-n diode has been standard for 80 years; alternatives dominate specific niches. Advanced options:

GaN / SiC diodes: wide-bandgap, high-voltage (600-1700 V), high-T (200°C+). EV inverters, datacenter power distribution.
2D p-n heterojunctions: MoS₂/WSe₂ atomic p-n; flexible electronics.
Perovskite / organic diodes: LED and solar cell; cheap, printable.
Tunnel FET (TFET): band-to-band tunneling; sub-60 mV/decade (the MOSFET physical floor). High gain at low power, not yet commercial.
Next SIDRA selector: beyond OTS (NbOx) — Mott transition (VO₂, NbO₂) gives sharper threshold, 100× less leakage.
Esaki tunnel diode: negative differential resistance (NDR) — single-device oscillators, neuromorphic spiking-neuron models.
Schottky barrier FET: metal-semiconductor instead of p-n — low contact resistance in 2D materials.
Photonic diode (one-way light): resonator-based nonreciprocity; required for optical-interconnect isolation.

Biggest lever for post-Y10 SIDRA: a Mott-selector + memristor 3D stack — one 1S1R per layer, 16 layers deep → 16× density in the same footprint, with OTS suppressing leakage by 10⁴× per cell. 2028 horizon.

The P-N Diode

Prerequisites

What you'll learn here

Hook: Why Only One Way?

Intuition: Holes + Electrons Side by Side

Formalism: The Shockley Diode Equation

Experiment: Slide the Bias, Watch the Diode

Quiz

Lab Task: Diode Current Calculation

Cheat Sheet

Vision: Beyond P-N

Further Reading

Prerequisites

What you'll learn here

🪝 Hook: Why Only One Way?

🧭 Intuition: Holes + Electrons Side by Side

📐 Formalism: The Shockley Diode Equation

🧪 Experiment: Slide the Bias, Watch the Diode

📝 Quiz

🛠️ Lab Task: Diode Current Calculation

🗂️ Cheat Sheet

🔮 Vision: Beyond P-N

📚 Further Reading

Hook: Why Only One Way?

Intuition: Holes + Electrons Side by Side

Formalism: The Shockley Diode Equation

Experiment: Slide the Bias, Watch the Diode

Quiz

Lab Task: Diode Current Calculation

Cheat Sheet

Vision: Beyond P-N

Further Reading