On Specific Detectivity of Photonic Infrared Detectors

In this section, we consider various possibilities to maximize the D f product of photonic IR detectors. To this purpose we proceed to analyze separately specific detectivity and response time. 

We start from the phenomenological expression for the current of a photocon-ductive detector, described in literature as the fundamental equation of photoconductivity [7]. This expression is valid both for intrinsic and extrinsic detectors in stationary state and is given as 

This is actually the increase of the dark current due to illumination and is a dc value (valid for/= 0 Hz). Here rj denotes the quantum efficiency of the detector, ) is the incident photon flux density, A is the detector active area. The factor T denotes the photoelectric gain or photogain (the ratio between the number of electrons flowing through the electric circuit and the number of absorbed photons). The fundamental equation of photoconductivity is also valid without changes for the short circuit current of a photovoltaic detector (photodiode operating in photo-conductive mode). In that mode of operation T = 1 in most of the cases. 

Using the fundamental equation of photoconductivity and the definition of the current responsivity given in Table 1.1 

In the case when the surface of the detector receiving the incident optical flux is not equal to the detector active area, i.e., when some kind of concentrator is used to collect radiation from a larger area and direct it to the active area, a factor of optical concentration [8] may be formally introduced into the expression for the specific detectivity. This factor is equal to the square root of the ratio between the optical and active ( electrical ) detector area. 

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