= 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>.<How does a PbS photoconductive detector work? by Shimadzu Scientific Instruments>[temperature-dependence paragraph]{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 $\tau\ln9$. 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 and
$$
\dot n=g-\beta n^2,\qquad \beta>0.
$$
Under constant $g_0$, let $n_\infty=\sqrt{g_0/\beta}$ and $\tau_*=1/(\beta n_\infty)$. Starting at zero gives $n/n_\infty=\tanh(t/\tau_*)$. Starting at $n_\infty$ and setting $g=0$ gives $n/n_\infty=(1+t/\tau_*)^{-1}$. Direct substitution verifies both solutions.
For an output proportional to $n$, the resulting durations are
$$
t_r=\tau_*[\operatorname{artanh}(0.9)-\operatorname{artanh}(0.1)]\approx1.3719\tau_*,
\qquad
t_f=\tau_*\left(\frac1{0.1}-\frac1{0.9}\right)\approx8.8889\tau_*.
$$
With stipulated $\tau_*=1\,\mathrm{ms}$, 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 $V_sR_LG/(1+R_LG)$ 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.
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