The cut-off frequency of a Schottky diode is the ordinary RC corner formed by its forward resistance and its junction capacitance :

\(f_{co}=\dfrac{1}{2\pi R_{F}C_{F}}\)

— option 3.

A dimensional check settles it without any physics. A frequency must have units of s⁻¹. Since \(RC\) has units of seconds, \(1/2\pi RC\) is a frequency — but \(R^{2}C^{2}\) has units of s², so options 1 and 2 would give s⁻², and option 4's \(R^{2}C\) gives yet another wrong combination. Only option 3 is dimensionally a frequency at all.

What the two elements are. \(R_{F}\) is the diode's forward series resistance — the sum of the barrier's dynamic resistance and the ohmic resistance of the epitaxial layer and contacts. \(C_{F}\) is the junction capacitance of the metal-semiconductor barrier, which sits in parallel with it. The parallel capacitance shunts the signal, and above \(f_{co}\) it dominates, so the diode stops behaving as the non-linear element a mixer or detector needs.

Why this figure of merit matters for Schottky diodes in particular. A Schottky barrier is a majority-carrier device: conduction is by electrons flowing over the barrier, with essentially no minority-carrier injection and therefore no stored charge to be removed. That removes the reverse-recovery delay that limits p-n junction diodes, so the only remaining limit is the RC product — and it can be pushed very high:

\(R_{F}\approx5\ \Omega,\qquad C_{F}\approx0.1\ \text{pF}\quad\Rightarrow\quad f_{co}\approx320\ \text{GHz}\)

How the design is optimised. Both quantities are reduced by shrinking the anode: a smaller contact area lowers \(C_{F}\) directly, though it raises \(R_{F}\), so there is an optimum diameter for a given frequency — typically a few micrometres for millimetre-wave mixer diodes. This is exactly why the Schottky diode, and not the PIN or ordinary junction diode, is the standard microwave mixer and detector element.

Hence, f_co = 1/(2πR_FC_F).