 Photoconductor response time

Photoconductor response time describes how quickly the electrical signal follows a change in illumination under stated bias, temperature, background and readout conditions. A rise time, fall time and modulation bandwidth summarize different features and require definitions. The manufacturer’s PbS description notes that sensitivity, response speed and dark resistance vary with temperature, so a timing number is not independent of operating conditions.^[ref]

An original one-lifetime model takes excess carrier density $n_e$ to obeyWith constant mobility and fixed detector bias, suppose the excess current is proportional to $n_e$. After a step from zero to generation $g_0$, the normalized signal is $1-e^{-t/\tau }$. The times to reach ten and ninety percent of its final value are $-\tau \ln 0.9$ and $-\tau \ln 0.1$, givingThe time from zero to ninety percent is instead $\tau \ln 10$. A quoted rise time without its thresholds is therefore incomplete.

For small sinusoidal generation changes, the normalized frequency response isThe half-power frequency is $f_c=1/(2\pi \tau )$, so this single-pole model gives $t_{10\text{–}90}{f}_c=\ln 9/(2\pi )\approx 0.3497$. This relationship is a consequence of the stated model, not a universal identity for arbitrary detectors.

For $\tau =100\mu \mathrm{s}$, the rise time is about $219.7\mu \mathrm{s}$ and the cutoff about $1.592\mathrm{kHz}$. At $1\mathrm{kHz}$, the signal amplitude is about $0.8467$ of its low-frequency value and its phase lags by $32.14^{\circ }$. The signal can therefore have a substantial phase delay before reaching the half-power point.

A readout adds its own dynamics. If the detector response is cascaded with a separate first-order electronic response of the same time constant, the overall magnitude is $1/[1+(2\pi f\tau {)}^2]$. Its half-power frequency is $\sqrt{\sqrt{2}-1}/(2\pi \tau )$, about $0.6436$ times the single-pole cutoff. Assigning that combined bandwidth entirely to the material would give an incorrect carrier-lifetime estimate.

Photoconductor rise and fall asymmetry tests another limitation of the simple model: linear one-lifetime dynamics predict equal normalized rise and fall behavior, but trap occupancy, changing background or a nonlinear circuit can produce different transients. A long relaxation tail should be measured rather than compressed into an unsupported single time constant.

A proposed experiment switches or modulates a monitored optical source, records detector current and actual bias, and measures ten-to-ninety and ninety-to-ten crossings after settling the initial illumination state. Repeat the modulation sweep with a characterized faster readout or independently measured amplifier response. Vary temperature and optical background while holding the wavelength and spot fixed. Agreement between step and frequency-response fits tests the one-pole approximation; disagreement identifies missing dynamics without by itself proving which physical mechanism caused them.