Generation-recombination noise and thermal noise
In photoconductors, there are two main noise mechanisms:
Generation-recombination noise caused by the statistical fluctuation of the number of carriers (generation and recombination) in a photoconductor following a Poisson distribution . The generation-recombination noise current is expressed as: = √4 0 [A] (2.12), where 0 is the average current flowing across the photodetector, and is the frequency integration bandwidth ( = 1 withthe integration time).
Thermal noise or Johnson-Nyquist noise  . It is an electrical noise present in all resistive devices caused by the thermal fluctuations of the velocity of charge carriers. The thermal noise current is given by: 11 = √4 ⁄ [A] (2.13), where R is photoconductor resistance.
For a detector under illumination, the total noise is then given by: √ 4 ⁄ = √ 2 + 2 = ( + 4 ( + )) ∗[A] (2.14), where we have made a distinction between the dark current and the photogenerated current = ℛ × .
Noise equivalent power, Detectivity, and BLIP regime
We define the signal-to-noise ratio as:= (2.15).⁄ ⁄.
The noise equivalent power (NEP) is defined as the incident power yielding a signal-to-noise ratio equal to 1 for a frequency integration bandwidth, i.e. it represents the minimum detectable power: = [W/Hz1/2] (2.16). ℛ√∆. Since = × , where = × is the detector surface and the noise current density, is clear, from Eq. (2.14) and Eq. (2.16), that the NEP is proportional to√ . To eliminate the dependence from these parameters, and allow to classify detector materials according to a more objective figure of merit, we introduce the detectivity D*, defined as: ∗ = √ [cm Hz1/2 W-1 or Jones] (2.17).
Interband and intersubband MIR photodetectors
Semiconductor photodetectors involve two kinds of transitions: interband transitions and intersubband (ISB) transitions. Interband transitions take place between the valence band and the conduction band, therefore the transition energy has a minimum cut-off limited by the bandgap. In ISB transitions the optical excitation takes place between quantized energy levels within the conduction or valence band of a semiconductor heterostructure. As a result, the excitation energy is not limited by the bandgap but rather by the band offset between the different semiconductor materials of which the heterostructure is made.
The Quantum Well Infrared Photodetector (QWIP) is a semiconductor device based on ISB transitions. Another type of MIR detector relying ISB transitions is the so-called photovoltaic quantum cascade detector (QCD), which, thanks to a built-in field produced by a ladder of subbands, does not require an external bias . Besides QWIPs, there are several other types of MIR semiconductor photodetectors, such as InSb, PbSe, and HgCdTe (MCT) detectors. These detectors have their own strengths and weaknesses, and their target absorption wavelengths are different too. Fig. 2.4 shows a general comparison of the detectivity of various infrared detector technologies in the range of 1-40 µm. The dashed line corresponds to the maximum achievable detectivity for an ideal photodetector (photovoltaic, photoconductor, thermal detector). A photovoltaic detector consists of a junction between two opposite-polarity semiconductors (a p-n junction). Photons absorbed at or near the junction cause the emission of charge carriers. These are separated by the built-in electric field producing a photo-voltage. The magnitude of the voltage is proportional to the number of incident photons.
Figure 2.4. Comparison of the D* of various commercially available infrared detectors when operated at the indicated temperature. The chopping frequency is 1000 Hz for all detectors except the thermopile (10 Hz), thermocouple (10 Hz), thermistor bolometer (10 Hz), Golay cell (10 Hz), and pyroelectric detector (10 Hz). Each detector is assumed to view a hemispherical surround at a temperature of 300 K. Theoretical curves for the background limited D* for ideal photovoltaic and photoconductive detectors and thermal detectors are also shown (adapted from ). PC indices photoconductive detectors; PV is photovoltaic detectors; PEM means photo electromagnetic detectors. Below, we give a brief survey of the main semiconductor photodetectors, namely Lead Salt (PbSe and PbS), InSb and MCT detectors.
Lead salt detectors
Lead salts such as PbS and PbSe were the first compound semiconductors used to fabricate MIR photodetectors since the 1940s . As shown in Fig. 2.4, at room temperature the wavelength operating ranges are ~1-3µm for PbS, and ~1-5µm for PbSe. Unlike most semiconductors, the bandgaps of PbS and PbSe decrease with decreasing temperature, producing a red shift of the spectral response. As shown in Fig. 2.4, at 77K this results into extended operating ranges up to ~4 µm and ~6 µm respectively for PbS and PbSe.
Unlike most other semiconductor IR detectors, lead salt photoconductive materials are used in the form of polycrytalline films approximately 1 μm thick and with individual crystallites ranging in size from approximately 0.1–1.0 μm . They are usually prepared by chemical deposition [9, 10, 11, 12, 13, 14], which generally yields better uniformity of response and more stable results than the evaporative methods [15, 16, 17, 18, 19, 20].
Lead salt detectors offer the highest detectivities at room temperature with typical values of ~1011 cmHz1/2/W (PbS) and ~109 cmHz1/2/W (PbSe). Together with their low cost, this makes of PbSe and PbS polycrystalline thin films the materials of choice for uncooled infrared detector systems in the 1-3 µm and 1-5 µm spectral ranges . Their response speed is limited by Auger recombination, with typical lifetimes in the µs range (PbS~20 µs, PdSe~2 µs  ), making them unsuitable for high-speed operations.
Indium antimonide (InSb) is a semiconductor material from the III-V group, discovered in the 1950s. At the time it presented the smallest known semiconductor energy gap, therefore its application to MWIR detection became obvious. Moreover, InSb offers good fabrication and material quality (high uniformity over large areas, high yield, controllability of dopants…).
The main operating range is ~1-5 µm, which corresponds to that of PbS and PbSe detectors. While lead salts materials are only used as photoconductors, InSb is used to realise both photoconductive and photovoltaic detectors. The smaller energy gap of InSb brings a higher thermal noise at high temperature. As a result, unlike lead salt detectors which can reach high detectivities at room temperature, typical operating temperatures of InSb are ~200K and ~77K when operated respectively as photoconductor (D*~109 cmHz1/2/W) , or photovoltaic detector (D*~ 1010 ÷ 1011 cmHz1/2/W) .
The interest for InSb as a material for IR detector stems not only from its small energy gap, but also from the fact that it can be prepared in single crystal form by conventional growth techniques. As a result the design of InSb detectors can be inferred directly from its bulk properties . On the contrary, the fabrication of lead salts thin films (see the previous Section) through either vacuum evaporation or chemical deposition is much less obvious and reproducible, hence their performance cannot be predicted from a study of their bulk crystal properties. Thanks to the high-quality growth and uniformity, InSb-based FPAs with large number of pixels are easy to realize [25, 26, 27, 28, 29, 30].
InSb detectors are commonly exploited in thermal imaging systems, infrared homing missile guidance systems, astronomy, and astrophysics. For applications in astrophysics, these devices are very often operated at 4-7 K with a resistive or capacitive transimpedance amplifier to achieve the lowest noise performance.
As for lead salts, the response speed of InSb is also limited by Auger recombination, with carrier lifetimes in the ~ns range (~µs for lead salts), thus preventing ultrafast operation.
In 1959, the first HgCdTe alloy was obtained by the group of Lawson . Mercury-Cadmium-Telluride (MCT) presents a widely tunable bandgap from 1µm to 30µm, obtained by controlling the proportion of Cd/Hg in the alloy. For this reason, combined with its excellent detection performance, MCT is the most favorable material for IR detection.
From the late 1950s to the early 1970s, the main growth method was bulk crystal growth. Then, with the surge of epitaxial growth, HgCdTe was fabricated by epitaxy on either CdTe or CdZnTe substrates. MCT is a compound of CdTe and HgTe, where CdTe is a semiconductor and HgTe is a semimetal. At room temperature, CdTe has a bandgap of approximately 1.5 eV, while the bandgap of HgTe is 0 eV. As a result, by controlling the proportion of Cd/Hg in the alloy, one can obtain any bandgap from 0 to 1.5 eV. As shown in Fig. 2.5, in the 3-7 m range the absorption coefficient of MCT is comparable to that of PbS/PbSe/InSb. At the same time, MCT detectors respond over a broader range of wavelengths, up to ~12.5 m, offering high sensitivities together with multicolor capabilities.
Table of contents :
1 General Introduction.
1.1 The mid-infrared spectral range
1.2 Blackbody radiation
1.3 MIR detectors: a brief historical overview
1.4 Main applications
2 Semiconductor infrared photodetectors
2.1 Semiconductor photodetectors
2.1.1 Photocurrent and responsivity
2.1.2 Generation-recombination noise and thermal noise
2.1.3 Noise equivalent power, Detectivity, and BLIP regime
2.1.4 Time response of photoconductor
2.2 Interband and intersubband MIR photodetectors
2.2.1 Lead salt detectors
2.2.2 InSb detectors
2.2.3 MCT detectors
2.2.4 QCD detectors
2.2.5 QWIP detectors
3 Quantum well infrared photodetectors
3.1 Basic QWIP concept and operation
3.2 Technology and main applications
3.3 Intersubband transitions in quantum wells
3.3.1 The envelope function Hamiltonian
3.3.2 The symmetric quantum well
3.4 Photoconductive QWIPs
3.4.1 Photocurrent and responsivity in QWIPs
3.4.2 Darkcurrent in QWIPs
3.4.3 Detector noise
3.4.4 Noise equivalent power and detectivity in QWIIPs
3.4.5 Patch antenna QWIPs
126.96.36.199 Comparison between the figures of merit of PARs and “mesa” QWIPs
3.5 Ultrafast QWIPs
3.5.1 Response time
3.5.2 Heterodyne detection
3.5.3 QWIP heterodyne detection in a photoconductor: an electrical circuit model
4 Ultrafast QWIPs based on patch antennas: design and fabrication
4.2 Design and simulation
4.2.1 Active region design
4.2.2 Patch array design and simulations
4.3 Fabrication process
4.3.1 Epitaxial layer transfer
4.3.2 Silicon nitride coating
4.3.3 Wafer bonding by Au-Au thermocompression technique
4.3.4 Coplanar waveguide
4.3.5 Air bridges
5 Ultrafast QWIPs based on patch antennas: electro-optical characterization
5.1 Spectral and dc characterization
5.1.1 Reflectivity measurements
5.1.2 Spectral response and polarization dependence
5.1.3 dc photocurrent and responsivity under continuous wave laser excitation
5.2 Frequency response
5.2.1 Heterodyne measurement set-up
5.2.2 Electrical circuit model of PARs QWIP
5.2.3 Measurement and analysis of PARs QWIP impedance
5.2.4 Measurement and analysis of PARs QWIP frequency response
5.2.5 Determination of small-signal circuit parameters
5.2.6 Evaluation of carriers capture and transit times
5.2.7 Power dependence
5.2.8 dc characterization and frequency response ofQWIP-2 PARs detector
6 Conclusions and outlook
6.1 Summary of the main results
6.2 Improving the performance of the PARs QWIP
6.3 PARs QWIPs as MIR photomixers for sub-mm and THz generation