 Photoconductor rise and fall asymmetry

Photoconductor rise and fall asymmetry means that a photoconductor's normalized turn-on and turn-off transients have different shapes or threshold-crossing durations under stated illumination and electrical conditions. Define the levels first: a ten-to-ninety-percent rise and a ninety-to-ten-percent fall exclude different portions of a long tail than a zero-to-ninety-percent measurement. Detector temperature is an essential condition because the primary PbS description reports changes in response speed, dark resistance and spectral sensitivity with temperature.^[ref]

The simplest linear carrier model predicts symmetry. For excess carrier density $n$ satisfying $\dot{n}=g-n/\tau$, a step to $g_0$ gives $n/n_{\infty }=1-e^{-t/\tau }$; switching off after equilibration gives $n/n_{\infty }=e^{-t/\tau }$. Both threshold durations equal $\tau \ln 9$. Thus different measured durations are evidence against that complete one-pole measurement model, rather than a result it already predicts.

A photoconductor transient with quadratic recombination supplies an illuminating alternative model. Stipulate constant mobility, fixed detector bias, zero dark excess density andUnder constant $g_0$, let $n_{\infty }=\sqrt{g_0/\beta }$ and ${\tau }_{\ast }=1/(\beta n_{\infty })$. Starting at zero gives $n/n_{\infty }=\tanh (t/{\tau }_{\ast })$. Starting at $n_{\infty }$ and setting $g=0$ gives $n/n_{\infty }=(1+t/{\tau }_{\ast }{)}^{-1}$. Direct substitution verifies both solutions.

For an output proportional to $n$, the resulting durations areWith stipulated ${\tau }_{\ast }=1\mathrm{ms}$, the rise takes $1.372\mathrm{ms}$ and the fall $8.889\mathrm{ms}$, despite having no separate fitted rise and fall constants. This is a derived nonlinear electron-hole recombination model, not measured behavior or a specification of the cited PbS or CdS detector. Its long algebraic tail also shows why a single exponential fit may depend strongly on the fitted interval.

The readout can itself introduce asymmetry. A resistance divider has output $V_s{R}_{L}G/(1+R_{L}G)$ as a function of detector electrical conductance $G$. Equal exponential rise and fall in $G$ need not give equal normalized threshold durations after this nonlinear conversion. Carrier dynamics, the electrical transfer curve and an amplifier's response must therefore be separated before assigning a material lifetime.

A proposed experiment switches a monitored optical source between two reproducible levels, measures actual detector bias and current, waits for the same initial equilibrium, and repeats in both directions. Compare current-derived conductance with divider output, then vary background, temperature and step size. A slow reference source or readout can imitate a detector tail. Asymmetry alone does not uniquely identify trapping or any other microscopic mechanism.