Table 2 Dominant noise mechanisms of 2D photodetectors

From: How to characterize figures of merit of two-dimensional photodetectors

Noise mechanism

Thermal noise

Shot noise

g-r noise

1/f noise

\(\left\langle {i}_{{th}}^{2}\right\rangle=\frac{4{K}_{B}T}{{R}_{d}}\triangle f\)

\(\left\langle {i}_{{sh}}^{2}\right\rangle=2{qI}\triangle f\)

\(\left\langle {i}_{{gr}}^{2}\right\rangle=\frac{4{\overline{{\varDelta {N}^{2}}}}\tau }{1+{4\pi }^{2}{{f}^{2}\tau }^{2}}\)

\(\left\langle {i}_{1/f}^{2}\right\rangle=\frac{{{{\alpha }_{H}I}_{S}}^{2}}{{fN}}\triangle f\)

Noise

characteristics

White noise characteristic dominated at high frequency

For 2D photodetectors of photoconductive gain with a prolonged carrier lifetime \(\tau\) from photogenerated carriers trapped by impurities and defects, g-r noise is proportional to photoconductive gain \(\langle {i}_{{gr}}^{2}\rangle=4qI_{ph}G\triangle f\) when \({4\pi }^{2}{{f}^{2}\tau }^{2}\ll 1\)

For 2D photodetectors with complex defect state, 1/f noise related to random fluctuation of carrier concentration and mobility should not be neglected

It should not be neglected in 2D photodetectors operating at room temperature

It has usually been considered as the only noise component by the early published work on 2D photodetectors

  1. kB is the Boltzmann constant, T is the measurement temperature, \({R}_{d}\) is the resistance, and \(\,\triangle f\) is the operating bandwidth of the photodetector. \(q\) is the electron charge, \({I}\) is the mean current intensity. \(\bar{\triangle {N}^{2}}\) represents the mean square fluctuation of the number of carriers occupying the generation-recombination energy level. \(\tau={\left(1/{\tau }_{1}+1/{\tau }_{0}\right)}^{-1}\) is the characteristic time constant related to the temperature, where the lifetime \(\,{\tau }_{1}\) and \({\tau }_{0}\) is the average duration of the electron in the conduction band and trap level, respectively. \({\alpha }_{H}\) is the Hooge experiential parameter, N is the number of carriers, and \({I}_{s}\) is the net photocurrent. \(I_{ph}\) is the average photocurrent, \(G={\tau }/{{\tau }_{t}}\) is the photoconductive gain.