Electrical Spectroscopy of Intervalley Relaxation in WSe${}_2$ Transistors

Abstract

We show that the transconductance of multilayer WSe${}_2$ field-effect transistors serves as a direct electrical spectrometer of the intervalley relaxation time ${\tau }_{\mathrm{iv}}$, previously accessible only by ultrafast optical techniques. Extending an equilibrium valley-thermodynamics framework with a single relaxation equation for the $\Gamma$-valley carrier fraction $f_{\Gamma }(t)$, we predict three signatures: (i)~a Lorentzian transconductance $g_m(\omega )=g_{m,0}+g_{m,v}^0/(1+i\omega {\tau }_{\mathrm{iv}})$, whose imaginary part peaks at ${\omega }_c={\tau }_{\mathrm{iv}}^{-1}$ with opposite signs for bilayer and trilayer; (ii)~a two-stage current transient after a gate step, exhibiting bilayer overshoot or trilayer undershoot; and (iii)~sweep-rate-proportional hysteresis whose gate-voltage profile and the layer-dependent transconductance sign reversal distinguish valley from trap-induced dynamics. All three signatures provide quantitative electrical access to ${\tau }_{\mathrm{iv}}$ with standard radio-frequency (rf) and direct-current (dc) instrumentation.

8 pages; 5 figures