Tunnel or Esaki Diode

1. Theory

• Definition: A tunnel (Esaki) diode is a PN junction with both sides degenerately doped, showing negative differential resistance in forward bias because of band-to-band tunnelling.
• Degenerate doping: Doping of about $10^{19}$ to $10^{20}\mathrm{c}{\mathrm{m}}^{-3}$ pushes the Fermi level into the conduction band on the N-side and into the valence band on the P-side.
• Ultra-thin junction: The depletion region is only a few nanometres wide, so electrons can tunnel directly through the bandgap.
• Band overlap: At small forward bias, filled N-side conduction states line up with empty P-side valence states, opening a tunnelling window.
• Three current components: Band-to-band tunnelling current, excess current through defect states, and ordinary thermal diffusion current.

2. Working Principle

• Reverse bias: Filled P-side valence states face empty N-side conduction states, so the diode conducts heavily in reverse (no blocking ability).
• Rising tunnelling ($0$ to $V_p$): Forward bias increases the overlap of filled and empty states, and current climbs to the peak current $I_p$.
• Negative resistance ($V_p$ to $V_v$): Further bias shrinks the overlap, so current falls as voltage rises.
• Valley and diffusion region (beyond $V_v$): Tunnelling stops; only excess current flows until normal diffusion current takes over like a regular diode.
• PVCR: The peak-to-valley current ratio measures how sharp the negative resistance is; it is limited by defect-assisted excess current.
• Fast switching: Tunnelling involves no minority-carrier storage, so switching is limited only by charging the junction capacitance (picosecond range).

3. Applications

• Current status: Mostly superseded by transistor oscillators and amplifiers, and by resonant tunnelling diodes (RTDs) for THz oscillators.
• Radiation-hard and cryogenic circuits: Tunnelling is barely affected by radiation or low temperature, so tunnel diode oscillators and amplifiers suit space and cryogenic electronics.
• Low-power microwave oscillators: Simple, low-voltage negative-resistance oscillators.

Name	Formula	Related Formulae	Variables/Constants
Degenerate doping condition	$N_D>N_C(n-side)$ $N_A>N_V(p-side)$	$\begin{array}{r}\text{(}{E}_F\text{lies}\text{inside}\text{the}\text{conduction}\text{or}\\ \text{valence}\text{band}\text{itself)}\end{array}$	$\begin{array}{r}{N}_C,N_V:effectivedensityofstates\\ (seeBasicSemiconductorEquationspage)\end{array}$
Depletion width (extremely thin)	$W=\sqrt{\frac{2{\epsilon }_s{V}_{bi}}{q}\left(\frac{1}{N_A}+\frac{1}{N_D}\right)}$	$\begin{array}{r}\text{(see}\text{PN}\text{Junction}\text{Diode}\text{page;}\text{here}\\ N_A,N_D\sim 10^{19}\text{–}10^{20}\mathrm{c}{\mathrm{m}}^{-3},\\ \text{giving}W\sim \text{a}\text{few}\text{nm)}\end{array}$	$\begin{array}{r}W:junctionwidth,thinenoughfor\\ directband-to-bandtunneling\end{array}$
Interband tunneling probability	$T\approx \exp \left(-\frac{4\sqrt{2m^{\ast }}{E}_g^{3/2}}{3q\hslash E}\right)$	$\text{(see Zener Diode page)}$	$T:WKBtunnelingprobability$
Total diode current (three components)	$I=I_T(V)+I_{exc}(V)+I_{th}(V)$	$I_{th}(V)=I_0\left[\exp \left(\frac{V}{V_T}\right)-1\right]\text{(see PN Junction Diode page)}$	$\begin{array}{r}{I}_T:band-to-bandtunneling\\ current(dominantatlowforwardbias)\end{array}$ $\begin{array}{r}{I}_{exc}:excesscurrent(tunnelingvia\\ defect/trapstates)\end{array}$ $\begin{array}{r}{I}_{th}:ordinarythermaldiffusioncurrent\\ (dominantbeyondthevalley)\end{array}$
Simplified empirical tunnel current model	$I_T(V)\approx I_p\frac{V}{V_p}\exp \left(1-\frac{V}{V_p}\right)$	${\left(\frac{d{I}_T}{dV}\right)}_{V=V_p}=0$	$I_p:peakcurrent$ $V_p:peakvoltage$
Peak-to-valley current ratio (PVCR)	$PVCR=\frac{I_p}{I_v}$		$\begin{array}{r}{I}_v:valleycurrent(minimumcurrent\\ followingthepeak)\end{array}$ $\begin{array}{r}PVCR:keyfigureofmerit;highervalues\\ giveasharper,moreusable\\ negative-resistanceregion\end{array}$
Negative differential resistance (magnitude)	$-R_n=\frac{dV}{dI}(V_p<V<V_v)$		$\begin{array}{r}{R}_n:magnitudeofthenegativeresistance\\ intheNDRregion\end{array}$
Resistive cutoff frequency	$f_{ro}=\frac{1}{2\pi R_n{C}_j}\sqrt{\frac{R_n}{R_s}-1}$		$\begin{array}{r}{f}_{ro}:frequencyabovewhichseries\\ resistancemasksthenegativeresistance,\\ limitingoscillatorusefulness\end{array}$ $R_s:parasiticseriesresistance$ $C_j:junctioncapacitance$
Switching time (charge-limited, not storage-limited)	$t_s\approx \frac{C_j(V_{fp}-V_p)}{I_p-I_v}$	$t_{rr}^{PN/PIN}\approx \tau \ln \left(1+\frac{I_F}{I_R}\right)\text{(see PN Junction Diode / PIN Diode pages)}$	$\begin{array}{r}{t}_s:timetoswitchbetweenthepeak\\ andvalleystates,limitedbyhowfast\\ C_{j}canbechargedthroughtheavailable\\ current,notbyminority-carrier\\ storage\end{array}$ $\begin{array}{r}{V}_{fp}:forwardvoltageatwhichthediffusion\\ currentequals{I}_p\end{array}$ $\text{(order-of-magnitude estimate)}$

Important Questions

Ques: What is physically happening between $V_p$ and $V_v$ that produces negative differential resistance?

At zero bias, degenerate doping places filled conduction-band states on the n-side directly across the thin junction from filled valence-band states on the p-side, so there are no empty states on the opposite side at matching energy for carriers to tunnel into, and no net current flows. As a small forward bias is applied, the bands shift so that filled n-side conduction-band states become aligned with empty p-side valence-band states, opening a window for net tunneling current, which grows as this energy overlap increases — reaching a maximum (the peak current $I_p$) when the overlap between filled and empty degenerate states is largest. As forward bias increases further, continued band shifting reduces this overlap again (the filled n-side states run out of aligned empty p-side states to tunnel into), so the tunneling current actually decreases even as voltage increases — this is the negative differential resistance region. Beyond the valley voltage $V_v$, the bands no longer overlap usefully for tunneling at all, and conduction switches over entirely to ordinary thermal diffusion current, which rises normally with voltage like a conventional forward-biased PN diode. Reference: L. Esaki, “New Phenomenon in Narrow Germanium p-n Junctions,” Phys. Rev. 109, 603 (1958); S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Why does PVCR matter so much as a figure of merit, and what limits it in practice?

A high peak-to-valley current ratio means the negative-resistance region is sharply defined against a low valley “floor,” giving a stronger, more usable negative resistance for oscillator and switching circuits; a low PVCR washes the NDR region out against background current and makes the device far less useful. PVCR is fundamentally limited by the excess current $I_{exc}$, which flows through defect and trap-assisted tunneling paths that don’t shut off the way the ideal band-to-band tunneling current does — so material quality (defect density) directly sets the achievable valley current and therefore the achievable PVCR, which is why germanium and GaAs tunnel diodes (which can be grown with very low defect densities) historically achieved higher PVCR than silicon tunnel diodes. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Does a tunnel diode have a reverse recovery time the way a PN or PIN diode does?

No, not in the same sense. Reverse recovery in a PN or PIN diode comes from discharging minority carriers that were stored by diffusion-based forward conduction; a tunnel diode operating in its peak-to-valley region conducts via band-to-band tunneling, which involves no meaningful minority-carrier storage to discharge. Its switching speed is instead set by how quickly the junction capacitance $C_j$ can be charged or discharged through the available current while moving between the peak and valley states — a charge-limited rather than storage-limited process — which is why tunnel diodes achieve switching times in the picosecond range and were historically used in some of the fastest digital logic circuits available before faster transistor technologies overtook them. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Why is resistive cutoff frequency $f_{ro}$ the relevant frequency limit, rather than just the junction’s $RC$ time constant?

A tunnel diode can only function as an active (oscillating or amplifying) element as long as its intrinsic negative resistance $R_n$ dominates over its parasitic series resistance $R_s$; $f_{ro}$ is specifically the frequency at which this condition stops holding, beyond which the device’s negative resistance is effectively swamped by ordinary resistive loss and it can no longer sustain oscillation or provide gain. This differs from a simple $1/(2\pi RC)$ cutoff because it explicitly incorporates the ratio $R_n/R_s$ — a device with very low $R_s$ relative to $R_n$ can usefully oscillate well above what a naive $RC$ estimate would suggest, which is why minimizing series resistance (heavily doped, low-resistivity contact regions) is as central to tunnel diode design as maximizing PVCR. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Related pages in this vault: Backward Diode, Zener Diode, PN Junction, PIN Diode, Gunn Diode, Diodes (PN, PIN, Schottky, Zener), Steep Slope FETs (Tunnel FET, Impact Ionization MOS, Negative Capacitance FET), Microwave Diodes (IMPATT, Gunn, Limiter, Mixer, Tunnel, Varactor), Quantum Mechanics Fundamentals.