Tunnel Diode: Negative Resistance Region

A tunnel diode is one of the few two-terminal devices whose I–V curve bends backward — current falls as voltage rises over part of its range. That negative differential resistance (NDR) makes it usable directly as a microwave oscillator, a fast switch, or an amplifier without any active three-terminal device. It's a niche part today, but understanding why the NDR appears is a compact lesson in degenerate semiconductor physics and quantum tunneling that also explains related effects in resonant-tunneling diodes and Esaki-type structures still used in mm-wave sources.

Structure and the Key Difference from a Normal Diode

A tunnel diode is a p-n junction like any other, but with both sides doped extremely heavily — degenerately, at levels around 10¹⁹–10²⁰ cm⁻³, roughly 1000× higher than a standard signal diode. Two consequences follow directly:

• Extremely thin depletion region. Built-in field E ≈ V_bi/W scales inversely with width, and heavy doping shrinks W to ~10 nm or less — thin enough for electrons to tunnel through the barrier rather than go over it.
• Degenerate doping. Doping is so heavy that the Fermi level moves into the conduction band on the n-side and into the valence band on the p-side. This means at equilibrium there are filled electron states in the n-side conduction band that sit at the same energy as empty allowed states (the valence band) on the p-side — the precondition for tunneling.

Because the barrier is thin (≈nm-scale, not the ~100 nm–1 µm of a regular junction), quantum-mechanical tunneling current is significant even at zero or very low forward bias, well before the normal diffusion current defined by the Shockley equation turns on.

Where the Negative Resistance Comes From

The total forward current is the sum of two components that dominate in different bias ranges:

1. Band-to-band tunneling current — electrons tunnel directly from filled conduction-band states on the n-side to empty valence-band states on the p-side (or vice versa), without needing to be thermally excited over the barrier.
2. Normal injection (diffusion) current — the same exponential diode current from the Shockley equation, I = I₀·(exp(V/nVT) − 1), which dominates at higher forward bias once tunneling has died out.

The interplay of these two mechanisms across bias produces four distinct regions:

At V = 0, filled n-side conduction states directly face empty p-side valence states, so tunneling current is near zero (no bias to align energies favorably) but rises quickly with small forward bias as the overlap of filled/empty aligned states increases — this produces the initial rising edge up to the peak current I_P at peak voltage V_P (typically 50–100 mV).

Beyond V_P, increasing forward bias starts pushing the n-side conduction band edge past the p-side valence band edge in energy — the bands "de-align," fewer filled states face empty allowed states at the same energy, and tunneling current decreases even though voltage is increasing. This is the negative differential resistance region, running from V_P to the valley voltage V_V, where tunnel current bottoms out at the valley current I_V, at the valley voltage V_V (typically a few hundred mV).

Above V_V, band overlap for tunneling is gone, but the junction now has enough forward bias to drive normal minority-carrier diffusion current, which takes over and the curve resumes the familiar exponential diode rise.

Characteristic I-V Curve

 I
 │        Ip ●
 │         /│\
 │        / │ \___
 │       /  │     \___          ___●  (normal diode rise)
 │      /   │         \___  ___/
 │     /    │             \/  
 │    /     │            Iv●  (valley)
 │   /      │
 │  /       │
 └─────────────────────────────────── V
 0         Vp            Vv
     (tunneling rise) (NDR)  (diffusion takeover)

The region between V_P and V_V has negative slope on the I–V curve — that is the negative resistance region, characterized by a differential resistance r_d = dV/dI < 0.

Key Figures of Merit

• Peak-to-valley current ratio (PVCR) = I_P/I_V — the primary figure of merit; higher PVCR means a more pronounced, more useful NDR region. Classic germanium tunnel diodes achieve PVCR ~8–10; GaAs devices are generally lower, typically ~4–6, while materials like GaSb can reach ~10–20.
• Peak voltage V_P — typically 50–100 mV, set by doping and material bandgap.
• Valley voltage V_V — typically 300–500 mV.
• Negative resistance magnitude — typically tens of ohms in the NDR region, important for impedance-matching an oscillator or amplifier circuit built around the device.

Why Negative Resistance Enables Oscillation and Switching

A two-terminal device with a region of dI/dV < 0 can cancel the positive resistance (loss) of an LC tank. Model the diode's NDR region locally as a resistor of value −R_d in parallel with a tank of inductance L, capacitance C, and parasitic loss R_p:

Net parallel conductance: G_net = 1/R_p − 1/R_d

If 1/R_d > 1/R_p (i.e., |R_d| < R_p), G_net is negative, meaning the circuit supplies more energy per cycle than it dissipates — oscillation builds up (limited eventually by the diode's own nonlinearity clamping the swing to stay within the NDR bias range). This is the same principle behind Gunn diodes and IMPATT diodes, and it's why tunnel diodes were historically used as simple microwave oscillators (up into the tens of GHz) and as high-speed switching elements — because tunneling is a majority-carrier quantum process with no minority-carrier storage delay, switching speeds in the picosecond range are achievable, far faster than a conventional p-n diode limited by minority-carrier recombination.

Worked Example: Biasing in the NDR Region

Suppose a germanium tunnel diode has I_P = 5 mA at V_P = 65 mV, and I_V = 0.6 mA at V_V = 400 mV (PVCR ≈ 8.3, typical for Ge).

Approximate the NDR region as roughly linear between these two points:

r_d ≈ ΔV / ΔI = (400 mV − 65 mV) / (0.6 mA − 5 mA)
             = 335 mV / (−4.4 mA)
             ≈ −76 Ω

Check: at the midpoint bias (≈230 mV), current should sit between I_V and I_P, decreasing as V increases — consistent with a negative slope of about −76 Ω. If this diode is placed in parallel with a tank whose parasitic loss resistance R_p is, say, 200 Ω, then |r_d| = 76 Ω < R_p = 200 Ω, so 1/r_d in magnitude exceeds 1/R_p and net conductance is negative — the combination will oscillate rather than settle, consistent with the intended use as an oscillator core. If R_p were instead 50 Ω (more heavily loaded tank), |r_d| = 76 Ω > R_p, net conductance stays positive, and the circuit would just damp — a useful design check before assuming a tunnel diode oscillator will start up.

Practical Notes and Limitations

• Bias point stability: because the I–V curve is triple-valued in current for a given voltage set by an external load line, tunnel diode oscillator/switch circuits must be carefully load-line-designed so the operating point sits where intended (often exploited deliberately as a bistable switch between the two positive-slope regions).
• Low output power: peak currents are in the mA range and voltage swing is limited to a few hundred mV, so tunnel diode oscillators produce only modest RF power (µW–mW), unlike Gunn or IMPATT diodes used for higher-power microwave generation.
• Sensitivity to doping/temperature: PVCR degrades with temperature because valley current (dominated by excess/defect tunneling and thermal diffusion) rises faster than peak current — this limits high-temperature use.
• Largely superseded: modern designs favor Gunn diodes, varactor-tuned oscillators, or active transistor oscillators for most applications; tunnel diodes remain of interest mainly in fast trigger circuits, some specialized microwave sources, and as a teaching example of quantum tunneling in a practical device.

Key Takeaways

• Tunnel diodes use degenerate (very heavy) doping and an ultra-thin depletion region to enable direct band-to-band quantum tunneling current at low forward bias.
• The I–V curve has four regions: rising tunneling current (0→V_P), negative differential resistance (V_P→V_V), a valley/transition, and normal exponential diffusion current above V_V.
• Negative resistance arises because increasing forward bias past V_P misaligns the filled/empty band states needed for tunneling, collapsing tunnel current even as voltage rises.
• Peak-to-valley current ratio (PVCR) is the key figure of merit; higher PVCR gives a stronger, more useful NDR region for oscillator or switch design.
• Placing the NDR region (|r_d|) in parallel with a resonant tank whose loss resistance exceeds |r_d| cancels net loss and sustains oscillation — the basis of tunnel diode microwave oscillators and picosecond-speed switches.