Gunn Diode

1. Theory

• Definition: A Gunn diode is a two-terminal transferred-electron device made from a uniformly doped bulk N-type semiconductor (usually GaAs or InP) that generates microwave oscillations.
• No junction: It has no PN or metal-semiconductor junction, so no depletion region, built-in potential or rectifying barrier; it sits in the Diodes folder only by convention as a two-terminal RF device.
• Two-valley conduction band: Electrons sit in a low-mass, high-mobility central ($\Gamma$) valley; higher-energy satellite ($L$) valleys have heavy mass and low mobility.
• Transferred-electron effect: Above a threshold field ($\approx 3.2$ kV/cm in GaAs), hot electrons scatter into the satellite valleys, so the average drift velocity falls as the field rises.
• Negative differential mobility: This falling velocity-field curve gives bulk negative differential resistance (Ridley-Watkins-Hilsum mechanism), unrelated to tunnelling.

2. Working Principle

• Below threshold: The device behaves as an ordinary ohmic resistor.
• Domain formation: Above threshold, a small charge fluctuation near the cathode grows into a high-field dipole domain, provided the doping-length product $n_{0}L$ exceeds about $10^{12}\mathrm{c}{\mathrm{m}}^{-2}$ (GaAs).
• Domain transit: The domain drifts to the anode at roughly the saturation velocity; when it is absorbed, current rises and a new domain forms at the cathode.
• Oscillation frequency: One current pulse per transit, so frequency is set mainly by the active-region length ($f_0\approx v_{sat}/L$), not by bias.
• Sub-critical operation: If $n_{0}L$ is too small, no domain forms and the device acts as a stable negative-conductance reflection amplifier.
• LSA mode: In a high-Q resonant circuit, the field swings through the negative-mobility region faster than a domain can form, allowing frequency set by the circuit rather than the length.

3. Applications

• Microwave and mm-wave oscillators: Compact, low-phase-noise signal sources from about 10 GHz into the 100+ GHz range.
• Doppler radar sensors: Traffic radar guns, intruder alarms and automatic door motion sensors.
• Radiometry and test sources: Low-noise local oscillators for receivers and laboratory sources.

Name	Formula	Related Formulae	Variables/Constants
Intervalley electron population ratio (two-valley model)	$\frac{n_2}{n_1}=\frac{M_2}{M_1}{\left(\frac{m_2^{\ast }}{m_1^{\ast }}\right)}^{3/2}\exp \left(-\frac{\Delta E}{k_B{T}_e}\right)$	$n_1+n_2=n$	$\begin{array}{r}{n}_1,n_2:electronpopulationinthe\\ lower(central,\Gamma )andupper\\ (satellite,L)valleys\end{array}$ $\begin{array}{r}{m}_1^{\ast },m_2^{\ast }:effectivemassesin\\ eachvalley(m_2^{\ast }\gg m_1^{\ast })\end{array}$ $\Delta E:intervalleyenergyseparation$ $\begin{array}{r}{M}_2/M_1:ratioofthenumberofequivalentupper\\ andlowervalleys(4Lvalleysagainstone\Gamma \\ valleyinGaAs)\end{array}$ $\begin{array}{r}{T}_e:effectiveelectrontemperature,set\\ bytheappliedfieldratherthanthe\\ latticetemperature\end{array}$ $k_B:Boltzmannconstant$
Average drift velocity (two-valley conduction)	$\bar{v}=\frac{n_1{\mu }_1+n_2{\mu }_2}{n_1+n_2}E$	$J=qn\bar{v}$	$\bar{v}:averageelectrondriftvelocity$ $\begin{array}{r}{\mu }_1,{\mu }_2:mobilityinthelowerand\\ uppervalleys({\mu }_1\gg {\mu }_2)\end{array}$ $J:currentdensity$
Negative differential mobility condition	${\mu }_n=\frac{dv}{dE}<0(E>E_{th})$	$v_p(\text{peak velocity at}E=E_{th})$ $v_{sat}(\text{high-field saturation velocity})$	$\begin{array}{r}{\mu }_n:differentialmobility,negativein\\ theNDRregime\end{array}$ $\begin{array}{r}{E}_{th}:thresholdfieldforonsetof\\ intervalleytransfer(\approx 3.2\\ kV/cmforGaAs)\end{array}$
Domain (space-charge) formation criterion	$n_{0}L\gtrsim (n_{0}L{)}_{crit}\approx 10^{12}\mathrm{c}{\mathrm{m}}^{-2}\text{(GaAs)}$		$n_0:dopingconcentrationoftheactiveregion$ $L:activeregionlength$ $\begin{array}{r}(n_{0}L{)}_{crit}:criticalproductfora\\ stabletravelingdomaintoform\end{array}$
Domain transit time	${\tau }_t=\frac{L}{v_{dom}}$	$v_{dom}\approx v_{sat}$	$\begin{array}{r}{\tau }_t:timeforthehigh-field\\ domaintotraversetheactiveregion\end{array}$ $v_{dom}:domainpropagationvelocity$
Transit-time-mode oscillation frequency	$f_0=\frac{1}{{\tau }_t}=\frac{v_{dom}}{L}$	$f_{0}L=v_{dom}\text{(frequency–length product)}$	$f_0:fundamentalGunnoscillationfrequency$

Important Questions

Ques: What physically causes negative differential mobility in a Gunn diode, and how does this differ from the negative differential resistance mechanism in a tunnel diode?

In materials like GaAs and InP, the conduction band has a low-energy central ($\Gamma$) valley with very low effective mass and high mobility, and higher-energy satellite ($L$) valleys with much larger effective mass and lower mobility. At low applied field, nearly all electrons sit in the favorable central valley and drift velocity rises normally with field. Once the field exceeds a threshold $E_{th}$, electrons gain enough kinetic energy to scatter into the satellite valleys, where their much lower mobility causes the average drift velocity to actually decrease even as the field keeps increasing — this is the Ridley-Watkins-Hilsum (transferred-electron) mechanism, and it is a purely bulk, momentum-space (intervalley) transfer effect with no junction, depletion region, or quantum tunneling involved at all. This is fundamentally different from a tunnel diode’s negative resistance, which arises from a shrinking band-to-band tunneling overlap across a degenerately doped junction as forward bias increases. Reference: J.B. Gunn, “Microwave oscillations of current in III-V semiconductors,” Solid State Communications 1, 88 (1963); B.K. Ridley and T.B. Watkins, Proc. Phys. Soc. 78, 293 (1961); C. Hilsum, Proc. IRE 50, 185 (1962).

Ques: Why is device length the primary design parameter for setting Gunn oscillator frequency, rather than doping or bias voltage?

In the standard transit-time mode of operation, oscillation arises from a single high-field domain nucleating near the cathode and traveling the length of the active region at roughly the saturation velocity $v_{sat}$, with oscillation occurring once per domain transit. Since $v_{sat}$ is set by the material itself and varies relatively little with bias once the domain has formed, the oscillation frequency $f_0=v_{dom}/L$ is overwhelmingly determined by the physical length $L$ of the active region — which is why Gunn diode frequency is primarily a fabrication (device length) choice rather than something tuned electrically the way a varactor-loaded oscillator’s frequency is, and why Gunn diodes for different microwave bands are essentially different physical device lengths of the same material and doping. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: What does the $n_{0}L$ criterion physically represent, and what happens if it isn’t satisfied?

A negative differential mobility region is necessary but not sufficient for stable traveling domains to form — small charge fluctuations in the device need enough total charge (set by the product of doping and length) to grow via the negative-mobility instability faster than they diffuse away or get swept out of the device before a domain can fully form. When $n_{0}L$ is comfortably above the critical value, stable, well-formed dipole domains nucleate and propagate reliably, giving clean transit-time-mode oscillation. When $n_{0}L$ falls below this threshold, domains do not form: the device stays stable with a negative differential conductance and can be used as a reflection amplifier rather than an oscillator. The Limited Space-charge Accumulation (LSA) mode is a separate regime, reached at high field and drive with $2\times 10^4<n_0/f<2\times 10^5\mathrm{s}\mathrm{c}{\mathrm{m}}^{-3}$, in which the field swings through the negative-mobility region too quickly for a domain to form. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Related pages in this vault: Impact Ionization Avalanche Transit Time (IMPATT) Diode, Tunnel or Esaki Diode, Backward Diode, Zener Diode, Trapped Plasma Avalanche Triggered Transit (TRAPATT) Diode, Microwave Diodes (IMPATT, Gunn, Limiter, Mixer, Tunnel, Varactor), Metal Semiconductor Field Effect Transistor (MESFET).