Photoconductive detector (photoconductive gain)

A photoconductive detector, or photoconductor, is a slab or film of semiconductor between two ohmic contacts, held at a bias voltage. Absorbed photons with energy above the bandgap (or above an impurity level, in extrinsic detectors) create free carriers, the conductivity rises, and the extra current through the bias circuit is the signal. Because carriers can circulate through the external circuit several times before they recombine, a photoconductor has internal gain, from below 1 in fast devices to 10⁴ and more in slow ones such as CdS light-dependent resistors. Common examples are PbS and PbSe for 1–5 µm, photoconductive HgCdTe for the long-wave infrared, extrinsic germanium and silicon for longer wavelengths, and low-temperature-grown GaAs in the photoconductive antennas used for terahertz generation.

The term should be kept apart from the "photoconductive mode" of a photodiode, which means a reverse-biased p-n or p-i-n junction. A reverse-biased photodiode has no photoconductive gain; each absorbed photon contributes at most one electron to the external current.

Photoconductive gain

When a carrier drifts out of one contact, charge neutrality requires another to enter at the opposite contact, so the current continues for as long as the excess carrier population survives. The gain is therefore the ratio of the carrier lifetime $\tau$ to the transit time $\tau_{tr}$ of the faster carrier across the electrode gap $L$:

$$G = \frac{\tau}{\tau_{tr}}, \qquad \tau_{tr} = \frac{L^2}{\mu V}.$$

For a 10 µm gap at 1 V bias and an electron mobility of 8500 cm²/(V·s), as in GaAs, the field is 1 kV/cm, the drift velocity is 8.5 × 10⁶ cm/s and the transit time is 118 ps. With $\tau$ = 1 ns the gain is 8.5. The responsivity is the photodiode value multiplied by the gain:

$$\mathcal{R} = \eta\,\frac{q\lambda}{hc}\,G.$$

At 850 nm with a quantum efficiency of 0.5, the factor $\eta q\lambda/hc$ is 0.34 A/W and the photoconductor gives 2.9 A/W.

Gain-bandwidth product

The photocurrent decays with the carrier lifetime once the light is removed, so the 3 dB bandwidth is $1/(2\pi\tau)$, 159 MHz for $\tau$ = 1 ns. The product of gain and bandwidth is $1/(2\pi\tau_{tr})$, 1.35 GHz in the example, and depends only on the transit time: a longer lifetime buys gain and loses bandwidth in equal proportion. Raising the bias shortens the transit time only until the drift velocity saturates, near 10⁷ cm/s in common semiconductors, which limits a 10 µm gap to about 100 ps. Fast photoconductive switches and terahertz antennas instead use material with sub-picosecond lifetimes, accepting a gain well below 1.

Trapping complicates the picture. If minority carriers are captured by traps while the majority carriers keep circulating, the effective lifetime and the gain both grow, and the response acquires slow tails that depend on illumination level. Many photoconductors therefore show a gain and a time constant that change with background light.

Noise

The random generation and recombination of carriers produces generation-recombination (g-r) noise, with a current spectral density

$$\overline{i_{gr}^2} = \frac{4qGIB}{1 + (2\pi f\tau)^2},$$

where $I$ is the DC current and $B$ the bandwidth. Compared with an ideal amplified shot noise $2qG^2 I_{ph} B$ of the primary photocurrent $I_{ph} = I/G$, the g-r noise is larger by a factor of 2 in power, √2 in current, because both generation and recombination are random. In the example, 1 µW at 850 nm gives 2.9 µA and a g-r noise of 4.0 nA in a 1 MHz bandwidth. The detector also has its own dark resistance, so its thermal noise adds, and the dark current from thermally generated carriers is why infrared photoconductors are cooled. Many also show strong flicker noise at low frequencies, which is one reason they are often used with a chopped source and a lock-in amplifier.

The best achievable specific detectivity of a background-limited photoconductor is lower than that of a background-limited photodiode by a factor of √2, a direct consequence of the g-r factor.

Pitfalls

The gain multiplies signal and dark current alike, so a high responsivity does not by itself mean a low noise-equivalent power. Responsivity measured with a chopped source depends on the chopping frequency through $\tau$, and a quoted value is meaningful only with the frequency, bias and background stated. At high flux, recombination becomes faster and the response sublinear, which distorts Fourier-transform spectra recorded with photoconductive HgCdTe.

Common questions

Is a photoresistor the same as a photoconductive detector?

Yes. A light-dependent resistor, usually CdS or CdSe, is a photoconductor with a very long carrier lifetime: high gain, response times of milliseconds, and a resistance that changes by orders of magnitude between dark and bright conditions.

Why use a photoconductor instead of a photodiode?

In some materials and wavelength ranges good junctions are hard to make, and a photoconductor needs only two ohmic contacts. Its gain also helps where the following amplifier would otherwise dominate the noise.

References: B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); E. L. Dereniak and G. D. Boreman, Infrared Detectors and Systems (Wiley, 1996); A. Rogalski, Infrared Detectors, 2nd ed. (CRC Press, 2011); S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. (Wiley, 2007).