Detector performance: figures of merit

Before we turn towards a classification of optical detectors in terms of their operational principle, we will summarize commonly used figures of merit, which allow us to compare the relative performance between detectors. These quantities also constitute the link between the radio-metric quantities of radiation impinging on the detector material and the final electrical detector output.

Quantum efficiency. Quantum efficiency η(λ)relates the number of photons incident on the detector to the number of independent elec-trons generated. It counts only primary charge carriers directly related to the initial absorption process and does not count electrical amplifi-cation. Quantum efficiency takes into account all processes related to photon losses, such as absorptance of the detector material, scattering, reflectance and electron recombination.

In a more general sense, the CIE vocabulary defines quantum effi-ciency as the ratio of elementary events contributing to the detector output to the number of incident photons. This also accounts for de-tectors in which no charge carriers are directly released by photon ab-sorption. The quantum efficiency can be expressed as

η(λ)= no

np (4.24)

wherenp is the number of incident photons; no defines the number of output events, such as photoelectrons in photodiodes, and electron-hole pairs in semiconductors (Section4.5.2).

4.5 Detecting radiance 95 a

η

λ_c λ b

R

λ_c λ

Figure 4.5: Response of an ideal photodetector. aQuantum efficiency; andb responsivity. Solid lines correspond to ideal detectors and dashed lines to typical departures from ideal curves (After [3]).

The quantum efficiency is always smaller than one and is commonly expressed in per cent. Figure4.5a shows the spectral quantum effi-ciency for an ideal photodetector. The ideal quantum effieffi-ciency is a binary function of wavelength. Above a certaincutoff wavelengthλc, photons have insufficient energy to produce photogenerated charge carriers (Section4.5.2). All photons with higher energy (smaller wave-lengths) should produce the same output. Real photodetectors show a slightly different behavior. Nearλc the thermal excitation of the de-tector material can affect the production of charge carriers by photon absorption. Thus, the sharp transition is rounded, as illustrated by the dashed line. Another typical behavior of photodetectors is the decreas-ing quantum efficiency at short wavelengths.

Responsivity. An important quantity relating the final detector out-put to the irradiance is theresponsivity Rof the detector. It is defined as the electrical output signal divided by the input radiative fluxφ:

R(λ,f )= V (λ,f )

φλ(f ) (4.25)

whereVdenotes the output voltage andf is the temporal frequency at which the input signal is chopped. The frequency dependency accounts for the finite response time of detectors and shows the detector’s re-sponse to fast changing signals. If the detector output is current, rather than voltage,V has to be replaced by currentI. Depending on the type of detector output, the units are given as V W⁻¹(volts per watt) or A W⁻¹ (amperes per watt).

For a photon detector (Section 4.5.2), the responsivity can be ex-pressed by the quantum efficiencyηand the photon energyep =hc/λ

as

R(λ)= ηλqG

hc (4.26)

whereq denotes the electron charge,q =1.602×10⁻¹⁹C. The photo-conductive gain G depends on the geometrical setup of the detector element and material properties. The frequency dependent responsiv-ity is given by

R(λ,f )= ηλqG hc

2πf τ (4.27)

whereτ denotes the time constant of the detector.

The ideal spectral responsivity of a photodetector is illustrated in Fig.4.5b. AsRis proportional to the product of the quantum efficiency ηand the wavelengthλ, an ideal photodetector shows a linear increase in the responsivity with wavelength up to the cutoff wavelengthλc, where it drops to zero. Real detectors show typical deviations from the ideal relationship as illustrated by the dashed line (compare to Fig.4.5a).

Noise equivalent power. Another important figure of merit quanti-fies the detector noise output in the absence of incident flux. The signal output produced by the detector must be above the noise level of the detector output to be detected. Solving Eq. (4.25) for the incident ra-diative flux yields

φλ=V

R (4.28)

whereRis the responsivity of the detector. Thenoise equivalent power NEP is defined as the signal power, that is, radiative flux, which cor-responds to an output voltageV given by the root-mean-square (rms) noise output,σn:

NEP= σn

R (4.29)

In other words, NEP defines the incident radiant power that yields a signal-to-noise ratio (SNR) of unity. It indicates the lower limit on the flux level that can be measured. It depends on the wavelength of the radiation, the modulation frequency, the optically active detector area, the noise-equivalent electrical bandwidth∆f, and the detector oper-ating temperature. Thus, it depends on a large number of situation-dependent quantities.

4.5 Detecting radiance 97 Detectivity. The detectivity D of a detector is the reciprocal of the NEP:

D= 1

NEP (4.30)

A more useful property can be obtained by incorporating the detec-tor area and the noise-equivalent bandwidth∆f. The corresponding quantity, callednormalized detectivity D^∗ or D-star is defined as:

D^∗=

A_d∆f

NEP (4.31)

whereAd denotes the optically active detector area. It normalizes the detectivity to a 1-Hz bandwidth and a unit detector area. The units of D^∗are cm Hz^1/2W⁻¹, which is defined as the unit “Jones.” The normal-ized detectivity can be interpreted as theSNR of a detector when 1 W of radiative power is incident on a detector with an area of 1 cm².

Again, the normalized detectivity depends on the remaining quan-tities, the wavelength of the radiation, the modulation frequency, and the detector operating temperature.