Tunnel diode
= Tunnel diode
{wiki}
= Esaki diode
{c}
{synonym}
A <tunnel diode> is a <p-n junction> with sufficiently heavy <semiconductor doping> on both sides to make a thin <depletion region> and permit substantial <interband tunnelling>. The neutral regions are <degenerate semiconductors>. Its distinctive forward <current-voltage characteristic> contains a peak followed by a valley: over part of the curve, increasing the applied <electric potential difference> decreases the <electric current>. The <Esaki tunnel-diode experiment> made this behavior experimentally concrete.
The useful quantity is the local slope, not the ratio of total voltage to total <electric current>. With conventional <electric current> $I$ entering the positive-voltage terminal, define
$$
g_d=\frac{dI}{dV},\qquad r_d=\frac{dV}{dI}=\frac1{g_d}\quad(g_d\ne0).
$$
<Negative differential resistance> means $g_d<0$, hence $r_d<0$ where defined. A forward <operating point> can still have $V>0$, $I>0$ and absorbed <power> $VI>0$. A small voltage increase then gives a negative current increment; this does not make the total <electric current> negative or turn the device into an unlimited source of <energy>. The external supply sets the <operating point> and supplies the <energy> available for an <electronic amplifier>.
An original idealized construction explains the shape. Put the <n-type semiconductor> on the left and the <p-type semiconductor> on the right. Take $q>0$ as the <elementary charge> and $V=V_p-V_n$. Increasing <forward bias> lowers the right-hand <Electron> <energy> levels relative to the left. Denote the two reservoir <electrochemical potentials> by $\mu_n,\mu_p$, so that $\mu_n-\mu_p=qV$. At zero <temperature>, occupied left-hand <conduction band> states extend up to $\mu_n$; empty right-hand <valence band> states start at $\mu_p$. For transfer conserving <Electron> <energy>, the available interval is
$$
\max(E_{c,n},\mu_p)<E<\min(\mu_n,E_{v,p}).
$$
It is nonempty only when its upper endpoint exceeds its lower endpoint. Both an occupied initial <quantum state> and an empty final <quantum state> must exist at the same <energy>. The <Pauli exclusion principle> prevents transfer into an already occupied final <quantum state>.
For the original diagram, choose arbitrary <energy> units with $E_{c,n}=-0.5$, $\mu_n=0$, $\mu_p=-u$ and $E_{v,p}=0.5-u$, where $u$ is $qV$ in those units. The available interval has width
$$
L(u)=\max\!\left(0,\min(0,0.5-u)-\max(-0.5,-u)\right),\qquad u\ge0.
$$
Thus $L(0.25)=0.25$, $L(0.50)=0.50$, $L(0.70)=0.30$, and $L(1.15)=0$. Initially <forward bias> opens a transfer window; further <forward bias> closes it by moving the right-hand <valence band> edge below the left-hand <conduction band> edge. This is a state-counting illustration, not a formula for a measured <electric current>.
\Image[/tunnel-diode-band-state-overlap.png]
{title=<Tunnel diode>: <energy band> alignment and occupied-to-empty state overlap}
{description=Original chosen <energy band> construction, with <n-type semiconductor> on the left and <p-type semiconductor> on the right. Blue shading denotes occupied reservoir states; orange hatching denotes empty reservoir states. Green arrows mark equal-<energy> transfer. The central barrier and <band bending> are schematic; all <energies> are arbitrary, and the drawing is not an experimental image or measured band profile.}
{source=tunnel-diode-band-state-overlap.py}
For <reverse bias>, the transfer direction changes: occupied right-hand <valence band> states can feed empty left-hand <conduction band> states. In the same construction, $u=-0.70$ opens the interval $0<E<0.70$ for this reverse transfer. A narrow <depletion region> allows a large reverse <quantum tunnelling> <electric current> at small <electric potential difference>, whereas the ordinary <Shockley diode equation> predicts only a small reverse saturation <electric current> before <diode reverse breakdown>. At zero <biasing>, equal reservoir occupations give zero net <electric current>; <quantum tunnelling> does not require a net equilibrium flow.
A finite-<temperature> refinement replaces sharp occupation cutoffs with the <Fermi-Dirac distribution>. An illustrative weak-transfer expression is
$$
I_{n\to p}(V)=K\int \mathcal W(E,V)\,[f_n(E)-f_p(E)]\,dE,\qquad K>0.
$$
Here $\mathcal W\ge0$ describes allowed initial/final <quantum states> and their coupling, and $f_n,f_p$ are <Fermi-Dirac distributions> with the respective <electrochemical potentials>. The occupation difference follows by subtracting the reverse transfer factor from the forward one: $f_n(1-f_p)-f_p(1-f_n)=f_n-f_p$. An overlap interval alone does not determine $\mathcal W$: <transmission probability>, <density of states>, <crystal momentum> selection and <phonons> can matter. A complete <germanium> calculation is more demanding than multiplying two constant <density of states> factors. At larger <forward bias>, ordinary <carrier injection> and <diffusion> supply a rising current branch even after direct band overlap is lost.