Fundamental Detector Performance Limits
This chapter discusses the fundamental limitations to IR detector performance imposed by the statistical nature of the generation- recombination processes, and by radiometric considerations. We will try to establish the ultimate theoretical sensitivity limit that can be expected for a detector operating at a given temperature.
Photon detectors are fundamentally limited by generation-recombination noise arising from photon exchange with a radiation background. Thermal detectors are fundamentally limited by temperature fluctuation noise arising from radiant power exchange with a radiating background. Due to fundamentally different types of noise, these two classes of detectors have different dependencies of detectivities on wavelength and temperature. The photon detectors are favored at a long wavelength infrared spectral range and at lower operating temperatures. The thermal detectors are favored at a very long wavelength spectral range.
In this chapter, we first examine fundamental infrared detection processes for both categories of detectors. To start with, comparative studies of thermal and photon detectors are carried out.
Photon Detectors
In general, the photon detector can be considered as a slab of homogeneous material with actual “electrical” area, Ae, thickness, t, and volume, Aet (see Fig. 2.9). Usually, the optical and electrical areas of the device are the same or similar. However, the use of some kind of optical concentrator can increase the AJAC ratio by a large factor.
The detectivity, D of an infrared photodetector is limited by generation and recombination rates G and R (in m'V1) in the active region of the device [1,2]. It can be expressed as:
where 2 is the wavelength, h is Planck’s constant, c is the velocity of light, and /7 is the quantum efficiency.
For a given wavelength and operating temperature, the highest performance can be obtained by maximizing the ratio of the quantum efficiency to the square root of the sum of the sheet thermal generation and recombination rates i]/[(G + R)t]V2. This means that high quantum efficiency must be obtained with a thin device.
A possible way to improve the performance of IR detectors is to reduce the physical volume of the semiconductor, thus reducing the amount of thermal generation. However, this must be achieved without a decrease in the quantum efficiency, optical area, or field of view (FOV) of the detector.
At equilibrium, the generation and recombination rates are equal. If we further assume Ae=A0, the detectivity of an optimized infrared photodetector is limited by thermal processes in the active region of the device. It can be expressed as:
where
The ratio of the absorption coefficient to the thermal generation rate, a/G, is the fundamental figure of merit of any material intended for infrared photodetection. The a/G ratio versus temperature relationship for various material systems capable of bandgap tuning is shown in Fig. 3.1 for a hypothetical energy gap equal to 0.25 eV (2 = 5 pm) [Fig. 3.1(a)] and 0.124 eV (2 = 10 pm) [Fig. 3.1(b)]. Procedures used in calculations of a/G for different material systems are given in [3]. Analysis shows that
FIGURE 3.1 a/G ratio versus temperature for (a) MWIR (/ = 5 pm) and (b) LWIR (A =10 pm) photodetectors based on HgCdTe, QWIP, Si extrinsic, and type-II superlattice (for LWIR only) material technology (adapted after Ref. [4]).
narrow-bandgap semiconductors are more suitable for high-temperature photodetectors than competing technologies, such as extrinsic devices, QWIP (quantum well IR photodetector), and QDIP (quantum dot IR photodetector) devices. The main reason for the high performance of intrinsic photodetectors is the high density of states in the valence and conduction bands, which results in strong absorption of infrared radiation. Figure 3.1(b) predicts that the emerging competing IR material, the type-II superlattice, is the most efficient material technology for IR detection in the long-wavelength region, theoretically perhaps even better than HgCdTe if the influence of the Shockley-Read-Hall lifetime is not considered. It is characterized by a high absorption coefficient and relatively low fundamental (band-to-band) thermal generation rate. However, this theoretical prediction has not been confirmed by experimental data. It is also worth noting that, theoretically, AlGaAs/GaAs QWIP is also a better material than extrinsic silicon.
The ultimate performance of infrared detectors is reached when the detector and amplifier noise are low, compared with the photon noise. The photon noise is fundamental in the sense that it arises, not from any imperfection in the detector or its associated electronics, but rather from the detection process itself, as a result of the discrete nature of the radiation field. The radiation falling on the detector is a composite of that from the target and that from the background. The practical operating limit for most infrared detectors is not the signal fluctuation limit but the background fluctuation limit, also known as the background-limited infrared photodetector (BLIP) limit.
The expression for shot noise can be used to derive the BLIP detectivity:
where /7 is the quantum efficiency, and Фв is the total background photon flux density reaching the detector, denoted as:
where в is the detector field-of-view angle.
Planck’s photon emittance (in units of photons cm 2 s"1 pm-1) at temperature TB is given by:
Equation (3.3) holds for photovoltaic detectors, which are shot noise limited. Photoconductive detectors that are generation-recombination noise limited have a D’blw lower by a factor of 21/2:
Once background-limited performance is reached, quantum efficiency tj is the only detector parameter that can influence a detector’s performance.
Figure 3.2 shows the peak spectral detectivity of a background-limited photodetector, operating at 300, 230, and 200 K, versus the wavelength calculated for 300 К background radiation and hemispherical field-of- view (FOV) (0=90 deg). The minimum D'BUP (300 K) occurs at 14 pm and is equal to 4.6 XlO10 cmHzI/2/W. For some photodetectors, which operate under near-equilibrium conditions, such as non-sweep-out photoconductors, the recombination rate is equal to the generation rate. For these detectors, the contribution of recombination to the noise will reduce DBlip by a factor of 21/2. Note that DBUP does not depend on area or the AJAe ratio. As a consequence, the background-limited performance cannot be improved by making AJAe large.
The highest performance possible will be obtained by the ideal detector with unity quantum efficiency and ideal spectral responsivity; P(A)
FIGURE 3.2 Calculated spectral detectivities of a photodetector limited by the hemispherical FOV background radiation of 300 К as a function of the peak wavelength for detector operating temperatures of 300, 230, and 200 К (after Ref. [2]).
increases with increasing wavelength to the cutoff wavelength Ac> at which point the responsivity drops to zero. This limiting performance is of interest for comparison with actual detectors.
The detectivity of BLIP detectors can be improved by reducing the background photon flux, Фь. Practically, there are two ways to do this: a cooled or reflective spectral filter to limit the spectral band, or a cooled shield to limit the angular field of view of the detector (as described above). The former eliminates background radiation from spectral regions in which the detector need not respond. The best detectors yield background-limited detectivities in quite narrow fields of view.
