Responsivity

Table of Contents:

The responsivity of an infrared detector is defined as the ratio of the root- mean-square (rms) value of the fundamental component of the electrical output signal of the detector to the rms value of the fundamental component of the input radiation power. The units of responsivity are volts per watt (V/W) or amperes per watt (A/W).

The voltage (or analogous current) spectral responsivity is given by

where V_s is the signal voltage due to Ф_е, and Ф_е(Х) is the spectral radiant incident power (in W).

An alternative to the above monochromatic quality, the blackbody responsivity, is defined by the equation

where the incident radiant power is the integral over all wavelengths of the spectral density of power distribution Ф_е(А) from a blackbody. The responsivity is usually a function of the bias voltage, the operating electrical frequency, and the wavelength.

Noise Equivalent Power

The noise equivalent power (NEP) is the incident power on the detector, generating a signal output equal to the rms noise output. Stated in another way, the NEP is the signal level that produces a signal-to-noise ratio (SNR) of 1. It can be written in terms of responsivity:

The unit of NEP is watts.

The NEP is also quoted for a fixed reference bandwidth, which is often assumed to be 1 Hz. This “NEP per unit bandwidth” has a unit of watts per square root hertz (W/Hz^1/2).

Detectivity

The detectivity D is the reciprocal of NEP:

It was found by Jones [13], that, for many detectors, the NEP is proportional to the square root of the detector signal, which is proportional to the detector area, A_d. This means that both NEP and detectivity are functions of electrical bandwidth and detector area, so a normalized detectivity D* (or D-star), suggested by Jones [13], is defined as:

The importance of D* is that this figure of merit permits comparison of detectors of the same type, but having different areas. Either a spectral or blackbody D* can be defined in terms of the corresponding type of NEP. Useful expressions equivalent to Eq. (2.6) include:

where D* is defined as the rms signal to noise ratio (SNR) in a 1-Hz bandwidth per unit rms incident radiant power per square root of detector area. D* is expressed in unit cmHz^1/2W^_1, a unit which recently has been referred to as a “Jones”.

Spectral detectivity curves for several commercially available IR and THz detectors are shown in Fig. 2.7. Interest has focused mainly on the

FIGURE 2.7 Comparison of the D* of various available detectors when operated at the indicated temperature. Chopping frequency is 1000 Hz for all detectors except for 10 Hz for the thermopile, thermocouple, thermistor bolometer, Golay cell, and pyroelectric detector. Each detector is assumed to view a surrounding hemisphere (2 л field of view) at a temperature of 300 K. Theoretical curves for the background-limited D* (dashed lines) for ideal photovoltaic and photoconduc- tive detectors and thermal detectors are also shown. PC: photoconductive detector; PV: photovoltaic detector; PEM: photoelectromagnetic detector; and HEB: hot electron bolometer (after Ref. [14]).

two atmospheric windows 3-5 pm (medium-wavelength IR, MWIR) and 8-14 pm (long-wavelength IR, LWIR); atmospheric transmission is the highest in these bands and the emissivity maximum of the objects at T« 300 К is at the wavelength /I» 10 pm. In recent years, there has been increasing interest in longer wavelengths, stimulated by space and terahertz applications. The spectral character of the background is influenced by the transmission of the atmosphere that controls the spectral ranges of the infrared for which the detector may be used when operating in the atmosphere.

Quantum Efficiency

A signal whose photon energy is sufficient to generate photocarriers will continuously lose energy as the optical field propagates through the semiconductor. Inside the semiconductor, the field decays exponentially as energy is transferred to the photocarriers. The material can be characterized by an absorption length a and a penetration depth 1 la. Penetration depth is the point at which lie of the optical signal power remains.

The power absorbed in the semiconductor as a function of position within the material is then:

The number of photons absorbed is the power (in W) divided by the photon energy (E = hv). If each absorbed photon generates a photocarrier, the number of photocarriers generated per number of incident photons for a specific semiconductor, with reflectivity r, is given by:

where 0

Figure 2.8 shows the quantum efficiency of some of the detector materials used to fabricate arrays of ultraviolet (UV), visible, and infrared detectors. Photocathodes and aluminum gallium nitride (AlGaN) detectors in the UV region are being developed. Silicon p-i-n diodes are shown with and without antireflection coating. Lead salts (PbS and PbSe) have

FIGURE 2.8 Quantum efficiency of different detectors (after Ref. [3]).

intermediate quantum efficiencies, whereas PtSi Schottky barrier types and quantum-well infrared photodetectors (QWIPs) have low values. InSb can respond from the near-UV out to 5.5 pm at 80 K. A suitable detector material for the near-IR (1.0-1.7 pm) spectral range is InGaAs lattice, matched to the InP. Various HgCdTe alloys, in both photovoltaic and photoconductive configurations, cover from 0.7 pm to over 20 pm. InAs/GaSb strained-layer superlattices have emerged as an alternative to the HgCdTe. Impurity-doped (Sb, As, and Ga) silicon BIB detectors operating at 10 К have a spectral response cut-off in the range of 16 to 30 pm. Impurity-doped Ge stressed detectors can extend the response out to 100-200 pm.

There are different methods of light coupling in a photodetector to enhance quantum efficiency [15]. A notable example of a method described for thin-film solar cells [16,17] can be applied to infrared photodetectors. In general, these absorption enhancement methods can be divided into four categories that use either optical concentration, antireflection structures, optical path increase, or light localization, as shown in Fig. 2.9. They are briefly described in Chapter 8 of monograph Antimonide-based Infrared Detectors: A New Perspective [3].

Different methods of absorption enhancement in a photodetector use of an optical concentrator, an antireflection structure, structures for optical path increase

FIGURE 2.9 Different methods of absorption enhancement in a photodetector use of an optical concentrator, an antireflection structure, structures for optical path increase (cavity enhancement), and light localization structures.

References

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