Response times of two-dimensional photodetectors limited by intrinsic resistance and capacitance

TL;DR

This work addresses the RC-limited response of 2D material photodetectors with global gates and local light-sensitive junctions, clarifying how distributed channel resistance and gate-to-channel capacitance govern the modulation bandwidth. A circuit-level framework combines the continuity equation, local capacitance approximation, and Shockley-Ramo theorem to derive a frequency-dependent photocurrent $I_{ph}(\omega)$, governed by the parameter $q_p = \sqrt{ i\omega C_A / \sigma_{dc} }$, and a compact expression that relates $I_{ph}(\omega)$ to the spatial distribution of $j_{ph}(x)$. The key finding is that the maximum modulation frequency $f_{mod}^{max}$ scales with $1/(\pi R C)$ and with the inverse of the distance from the light-sensitive junction to the nearest contact, $f_{mod}^{max} = \frac{L}{\pi R C \min\{ x_{ph}, L - x_{ph} \}}$, implying that junctions near contacts yield the fastest RC-limited responses. This provides design guidance for high-speed detectors and extends RC-delay concepts to distributed 2D photodetectors, while noting limits of the local-capacitance and harmonic approximations.

Abstract

Most contemporary architectures of photodetectors based on two-dimensional materials include global gates for carrier density control and local p-n junctions in the channel. We study the dependence of photocurrent in such detectors on the light modulation frequency, fully taking into account the effects of distributed resistance and gate-channel capacitance. The decay of photocurrent with modulation frequency governs the response time. We find that the maximum modulation frequency is largely determined by the position of light-sensitive junction with respect to the middle of the channel. Largest modulation frequency is achieved for junctions in immediate vicinity of either source or drain contacts, while fast roll-off of the modulation characteristic is observed for junction in the middle of the channel.

Figures (2)

• Figure 1: (A) Schematic of the gated photodetector with 2d channel and its equivalent distributed RC circuit with localized photocurrent source (B-D) Possible physical realizations of 2d photodetectors fitting the scheme of panel (A): detector with p-n junction induced by split gate (B), detector with p-i-n junction due to dissimilar metal contacts (C), detector based on photon drag effect (D)
• Figure 2: Dependence of photocurrent on modulation frequency ${{f}_{\bmod }}=\omega /2\pi$ computed with Eq. (9) for different positions of the light-sensitive junction ${{x}_{ph}}$. Detector parameters are channel length L=10 µm, gate-channel separation $d=100$ nm, gate dielectric constant $\varepsilon =4$, channel resistivity $\sigma -1=100$ Ohm