= Photocurrent
{title2=$I_{\rm ph}$}
<Photocurrent> is the <electric current> attributable to illumination. Here $I_{\rm ph}\geq0$ denotes its magnitude after <background subtraction>. For a <photodiode> without internal multiplication, let $P$ be incident <radiant flux> concentrated at <wavelength> $\lambda$, and let $\eta$ be external <quantum efficiency>, including losses before collection. An incident <photon> has <energy> $E_\gamma=hc/\lambda$, with <Planck constant> $h$ and <speed of light> $c$. Dividing <energy> per second by <energy> per <photon> gives the incident <photon> rate $\Phi_\gamma$. Multiplying by $\eta$ gives the mean collected pair rate $\dot N_{\rm pair}$; multiplying by <elementary charge> $q$ gives
$$
\Phi_\gamma=\frac{P\lambda}{hc},\qquad
\dot N_{\rm pair}=\eta\Phi_\gamma,\qquad
I_{\rm ph}=q\dot N_{\rm pair},\qquad
R(\lambda)=\frac{I_{\rm ph}}P=\frac{\eta q\lambda}{hc}.
$$
The factor is $q$: each collected pair replenishes an <Electron> at one contact and removes an <Electron> at the other. A cross-section of the external wire therefore counts one transferred <Electron> per completed pair, consistent with <charge conservation>. The <Electron> and <electron hole> are two internal <charge carriers>, not two independent transfers through that wire.
Choose an illustrative <photodiode> model with $\lambda=650\,\mathrm{nm}$, $\eta=0.75$ and $P=1.00\,\mathrm{\mu W}$. Using the exact SI values $h=6.62607015\times10^{-34}\,\mathrm{J\,s}$, $c=299792458\,\mathrm{m\,s^{-1}}$ and $q=1.602176634\times10^{-19}\,\mathrm C$ gives
$$
\begin{aligned}
E_\gamma&=3.05607055\times10^{-19}\,\mathrm J,\\
\Phi_\gamma&=3.27217577\times10^{12}\,\mathrm{s^{-1}},\\
\dot N_{\rm pair}&=2.45413183\times10^{12}\,\mathrm{s^{-1}},\\
R(650\,\mathrm{nm})&=0.393195267\,\mathrm{A\,W^{-1}},\\
I_{\rm ph}&=0.393195267\,\mathrm{\mu A}.
\end{aligned}
$$
A mean fraction $0.75$ does not require each fourth <photon> to be lost in a repeating pattern. It specifies a mean conversion rate. Nor does $0.75$ mean $0.75\,\mathrm{A\,W^{-1}}$: <quantum efficiency> is dimensionless, whereas <spectral responsivity> compares <electric current> with <power>.
\Image[/photodiode-responsivity-and-photon-current.png]
{title=Calculated <spectral responsivity>, <photon> rate and <photocurrent>}
{description=Original model, not a measured device spectrum. Left: constant external <quantum efficiency> $\eta=0.75$ is assumed only on the displayed <wavelength> <interval> $450$–$800\,\mathrm{nm}$. Right: the $650\,\mathrm{nm}$ example at $1\,\mathrm{\mu W}$, with <photon> and collected-pair rates distinguished.}
At fixed <radiant flux>, longer-<wavelength> <photons> have less <energy>, so more arrive per second. This explains the rising <straight line> when <quantum efficiency> is held constant. A real <photodiode>'s <quantum efficiency> varies with <wavelength>; the plotted assumption cannot be extended past its <band gap> absorption cutoff. At fixed incident <photon> rate instead, $I_{\rm ph}=\eta q\Phi_\gamma$ has no additional factor of $\lambda$.
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