Chapter 3 The InAs-Based nbn Photodetector and Dark Current

68 Chapter 3 The InAs-Based nbn Photodetector and Dark Current The InAs-based nbn photodetector, which possesses a design that suppresses surface leakage current, is compared with both a commercially available InAs-based photodiode and an InAs-based photodiode grown and fabricated in the Molecular Beam Epitaxy (MBE) Laboratory. Data, taken at 0 Field of View (FOV) and for device temperatures, T, between 320 and 140 K, are presented. The InAs-based nbn photodetector achieves at 140 K, through the virtual elimination of surface leakage current, a dark current as much as 6 orders of magnitude lower than that of the commercial photodiode and 4 orders of magnitude lower than that of the photodiode fabricated in the MBE Laboratory. Neither the commercial photodiode nor the photodiode grown and fabricated in the MBE Laboratory achieves background limited photodetection (BLIP) 6,40 conditions at any measured temperature. This is a consequence of the high levels of surface leakage current in both photodiodes. In contrast, the nbn photodetector operates in the BLIP regime for device temperatures as high as 200 K. The composition of the low-temperature dark current of a device is especially significant as pixel sizes are reduced to satisfy the needs of advanced imaging systems. As will be shown, reducing the dimensions of photodetectors limited by surface leakage current, such as these cooled p-n junction photodiodes, will worsen performance. However, decreasing the pixel sizes of photodetectors limited by bulk current, such as the nbn photodetector, does not impact performance. 3.1 The nbn and p-n Junction Photodetectors: Device Descriptions Surface leakage current in narrow-bandgap semiconductors, including InAs, is enabled by the presence of surface states. Surface states pin the Fermi level of exposed InAs surfaces in the conduction band, as illustrated in Figure 3.1.1b, and this occurs regardless of doping in the bulk. 82-84 In the case of an InAs diode, a p-n junction forms not only between the bulk p- type and n-type materials, but also between the bulk p-type material and the n-type inversion layer at the exposed surface. As depicted in Figure 3.1.1a, the inversion layer forms an n- type surface channel spanning the entire exposed surface of the semiconductor; it is a lowresistance current shunt path aligned parallel to the heterojunction. Mobile carriers may flow through the device as bulk current and be regulated by the built-in potential across the

3.1 nbn and p-n Junction Photodetectors 69 heterojunction, or they may take advantage of the low resistance current shunt path and bypass the potential barrier as surface leakage current. Tunneling from the p-type material to the n-type surface inversion layer is more efficient when the p-type bulk material is more highly doped. This is partially the result of a narrower depletion region. It is also a consequence of better overlap between the states in the valence band of the bulk p-type material and the states in the conduction band of the surface inversion layer. 85,85 Surface passivation is commonly performed to reduce surface leakage current, 7 and the use of gate electrodes has also been shown to reduce surface leakage current, 48,87 but having the option of using less complex methods is desirable. (a) (b) Figure 3.1.1 Surface inversion layer and energy band diagram of InAs. (a) Is a diagram of an InAs p-n junction. The entire exposed surface is an n-type. (b) An energy diagram of the Fermi level pinned in the conduction band at the surface of bulk p-type material. One relatively simple approach to reducing surface leakage current in narrow-bandgap semiconductor photodiodes is the insertion of a wide layer of intrinsic material between the p-

3.1 nbn and p-n Junction Photodetectors 70 type and n-type layers, which yields a p-i-n photodetector. 86,88,89 Although the p-i-n photodiode is observed to have lower levels of surface leakage current then p-n junction photodiodes, the p-i-n photodiode is typically chosen for a given application based on the strength of other attributes. Two of the more commonly cited advantages, realized for some p-i-n photodiodes, are improved quantum efficiencies and lower junction capacitances. 24,88 3.1.1 The nbn Photodetector The nbn photodetector (n-type active layer, wide-gap Barrier, n-type contact layer) is an advanced photodetector structure originally developed to eliminate dark current arising from both Shockley-Read-Hall generation mechanisms (SRH) and the flow of majority carriers through the bulk material. 6 The data presented in this chapter also show the AlAs x Sb 1-x barrier in the InAs / AlAsSb nbn photodetector architecture effectively breaks the surface conductivity path and suppresses surface leakage current. Figure 3.1.2 is an energy diagram of the InAs / AlAsSb nbn photodetector and a reproduction of Figure 1.6.3. Ideally, there is no energy barrier in the valence band obstructing the free flow of the minority carrier holes, while a large energy discontinuity in the conduction band impedes the flow of majority carrier electrons. Both the zero valence band and the large conduction band energy discontinuities in an InAs-based nbn photodetector are achieved with an AlAs x Sb 1-x barrier with a specific composition, x. The precise composition is not known, but experimental data and modeling, which are presented in Chapter 2, suggests the composition is 0.14 < x < 0.17. A composition resulting in a nonzero valence band energy discontinuity on the order of kt or less does not appreciably impact the performance. 43 The composition of the AlAs x Sb 1-x barrier layer producing a zero valence band energy offset with InAs optimally also possesses a lattice constant that matches or is closely similar to that of the InAs layer; this allows the AlAs x Sb 1-x to be grown as a pseudomorphically strained epilayer. A barrier composition of AlAs 0.16 Sb 0.84 lattice matches InAs. 32 The nbn photodetector architecture simply and effectively suppresses surface leakage current. The large conduction band discontinuity between the absorption and barrier layers obstructs the flow of n-type majority carriers. Fabrication of an nbn photodetector requires etching through the n-type contact layer, but not through the insulating barrier. With the barrier intact, there is no exposed surface on the pixel oriented parallel to the barrier, and this

3.1 nbn and p-n Junction Photodetectors 71 provides no opportunity for surface states to form a shunt path bypassing the barrier. In the case of the InAs / AlAsSb nbn photodetector, preliminary experiments indicate that it is also possible to etch through the AlAs x Sb 1-x barrier layer without creating a current shunt path. Unlike InAs, the surface Fermi level of the wide-bandgap AlAs x Sb 1-x layer is expected to be located deep in the bandgap, as is the case for AlAs and AlSb, 90,91 and to be highly resistive. The presence of the AlAs x Sb 1-x barrier layer is expected to block the n-type current shunt path that would otherwise connect the InAs absorption and contact layers. The dark currents of the nbn photodetector are therefore mainly bulk diffusion currents. These are thermally activated and decrease with temperature at a rate approximately proportional to exp(-e g /kt), as shown in Chapter 1, with E g the bandgap of InAs. Figure 3.1.2 Sketch of an nbn photodetector. The energy diagram of the voltage biased nbn photodetector is shown below the sketch of the structure. E f, E c, and E v are the Fermi level, conduction band, and valence band energies, respectively. For this work, the nbn photodetector, referred to as Benchmark and diagrammed in Figure 3.1.2, is grown on an n-type InAs (100) substrate. It is fabricated from growth G2-563; Shimon Maimon performed the crystal growth of this sample and processed it into nbn

3.1 nbn and p-n Junction Photodetectors 72 photodetectors. The growth was conducted on a Varian Gen II molecular beam epitaxy machine. A Veeco Mark IV arsenic cracker source delivers As 2, and conventional evaporative effusion cells supply Sb 4, the group III elements, and the dopants. The InAs active layer is 2 microns thick, the AlAs 0.18 Sb 0.82 barrier layer is 2000 Angstroms thick and pseudomorphically strained, and the InAs contact layer is 1000 Angstroms thick. The unintentionally doped InAs absorbing layer is n-type with a carrier concentration of 1.2 x 10 16 cm -3, and it is in ohmic contact with the substrate. The AlAs x Sb 1-x barrier layer grows with an unintentional acceptor carrier concentration of 1.8 x 10 15 cm -3, 92 and the layer is depleted of mobile carriers in the nbn structure. The InAs contact layer possesses a graded n-type doping profile with a maximum doping concentration of 1x10 18 cm -3 at the surface. The barrier layer material, AlAs 0.18 Sb 0.82, is an indirect-gap semiconductor; at 200 K it has a minimum a bandgap energy of 1.7 ev at the X point in the Brillouin zone, which corresponds to wavevector K = 2π/a(0,0,1) with lattice constant a. InAs is a direct gap material with a minimum bandgap energy of 0.38 ev at 200 K at the Γ point, which corresponds to K = 2π/a(0,0,0). (All material parameters are calculated using the material parameters collected in Reference 32.) Gold contacts are evaporatively deposited and provide electrical contact to the InAs substrate and contact layers. A pixel is defined by wet etching through the InAs contact layer; the AlAs x Sb 1-x barrier layer is used as an etch-stop. The nbn photodetector operates under an applied reverse bias, which is defined as applying a negative voltage to the contact layer and the common to the substrate. 3.1.2 The Photodiodes Two InAs-based photodiodes are tested and the resulting data are compared with those taken for the InAs-based nbn photodetector. One photodiode is acquired from a commercial vendor, 22 and the other is grown and fabricated by the author in the MBE Laboratory and is designed to have lower levels of surface leakage current than conventional p-n junction photodiodes. The doping levels and architectures of p-n junction based devices are generally tailored to best suit the requirements of the application. One method used to make room temperature operation of MWIR p-i-n photodiodes possible is the incorporation of a p + -type barrier layer between the p-type and intrinsic layers. 93 The p + -type barrier layer has a large conduction band offset with the p-type layer. The barrier layer blocks the diffusion current generated in

3.1 nbn and p-n Junction Photodetectors 73 the p-type layer by the Auger 7 process, which can be significant. High n-type doping levels may be used to suppress the Auger 1 diffusion process in the n-type layer, but it is not practical to use a similar approach to suppress the Auger 7 process. It would require prohibitively high levels of p-type doping to result in degeneracy in the p-type layer. The barrier layer is capable of suppressing the diffusion current in MWIR photodiodes so that Shockley-Read-Hall (SRH) generation current becomes the primary contributor to dark current at room temperature. This is shown to improve the R o A measured at room temperature by a factor of 16 in an InAs 0.89 Sb 0.11 based photodiode. 10 The focus of this study is surface leakage current; measurements are conducted to quantify and compare the magnitude of the surface leakage current in a cooled InAs-based nbn photodetector with those in two cooled and unpassivated InAs-based photodiodes. The design of the nbn photodetector is expected to suppress the magnitude of surface leakage current to negligible levels, while cooled and unpassivated InAs-based photodiodes are known to possess high levels of surface leakage current. As BLIP, rather than room temperature, operation is examined, photodiodes designed to suppress diffusion current at warmer temperatures are not of interest to this work. It would be preferable to perform measurements using photodiodes that are designed to suppress surface leakage current, but which are not passivated. As it is not known whether the commercially acquired photodiode is constructed to minimize surface leakage current, the author fabricated and tested an InAsbased photodiode possessing a design intended to exhibit reduced levels of surface leakage current. The design of the photodiode grown and fabricated in the MBE Laboratory is guided by reports that a wide layer of intrinsic material in p-i-n photodiodes acts to suppress surface leakage current. 86,88,89 Lin et. al find the magnitude of the surface leakage current in a p-i-n photodiode correlates with the width of the intrinsic layer; a wider intrinsic layer produces a greater reduction in the magnitude of surface leakage current. They cite two aspects of the intrinsic layer contributing to this effect. The first is that there is a reduced probability of carriers tunneling into the surface inversion layer from the unintentionally doped intrinsic layer, as compared with a doped p-type layer. 86 The depletion layer between the intrinsic bulk and n-type surface inversion layer is wider, and there is a larger energy difference between the valence band edge in the intrinsic bulk and the conduction band edge in the n- type surface inversion layer. The intrinsic layer is expected to contribute fewer free carriers to the shunt current than a p-type layer, as fewer free carriers are likely to be routed from the

3.1 nbn and p-n Junction Photodetectors 74 intrinsic layer to the surface. The second effect they identify is the attenuation of the surface leakage current as it travels, from the p-type layer to the n-type layer, along the intrinsic layer. The intrinsic layer is not anticipated to be a primary contributor to surface leakage current, but it also does not inhibit carriers in the p-type bulk layer from tunneling to the surface n-type inversion layer and then travelling along the shunt channel. Lin et al. posit that the high density of surface defects in the n-type surface shunt channel, combined with the wide intrinsic layer lengthening the distance between the n-type and p-type layers, increases the probability the free carriers travelling along this shunt channel will recombine before entering the n-type layer; the greater the distance the surface leakage current must travel along the intrinsic layer, the greater the overall attenuation of the surface leakage current. They find the difference in R o A, at 160 K, between an unpassivated p-n junction with no intrinsic layer and an unpassivated p-i-n junction with a 0.72 micron thick intrinsic layer, to be in excess of two orders of magnitude. Thermal activation energies for all samples are calculated to be ~0.33 ev. 88,89 The apparent utility of the intrinsic layer in the p-i-n photodiode influences the design chosen for crystal growth G4531, which is referred to as MBELabPN(Riber). Growth G4531 is performed on an undoped and n-type InAs (100) substrate from Wafer Technology Inc. Sample MBELabPN(Riber) possesses a 2 micron, unintentionally doped, InAs n-type layer and is capped with a beryllium-doped InAs p-type layer. This structure omits an intentionally doped n-type InAs layer, but, as the unintentionally doped layer grows n-type with a carrier concentration of 1-2 x 10 16 cm -1, a rectifying junction occurs despite the absence of the intentionally doped n-type layer. The absence of the doped n-type layer is intended to produce a device with fewer defects, as the process of doping causes defects, and consequently reduce levels of SRH current. The p-type layer is graded to a carrier concentration of 1x10 18 cm -3 over 700 Angstroms, and then a 2000 Angstrom layer is grown at this doping level. The p-type contact layer is created by first grading the doping level from 1x10 18 cm -3 to 2.5x10 19 cm -3 over 500 Angstroms and then growing a final 1000 Angstroms at this highest doping level. Processing includes photolithographic techniques and wet etching through the p-type layer and into the intrinsic layer to a total depth of approximately 1.7 microns. Contacts to the device are gold, and these are evaporatively deposited. The 2 micron width of the intrinsic layer and the etch depth are intended to minimizes surface leakage current. The overall device design is expected to result in diffusion current, rather than SRH current, being the dominant component of dark current at higher temperatures.

3.2 Current vs. Temperature 75 The commercial InAs photodiode is acquired from Teledyne Judson Technologies and is one of the J12 series photodiodes. 22 Information concerning the fabrication method and architectural details of this photodiode have not been made available, but the photodiode likely has a conventional p-n junction structure. Data published by Teledyne Judson Technologies specify the 0.25 mm diameter device, which was purchased without a cooling system, has a cutoff wavelength of 3.6 microns and a minimum D* of 3.7 x 10 9 cm Hz 1/2 /W. 3.2 Temperature-Dependent Current Measurements Dark current and photocurrent measurements are performed for the InAs-based nbn photodetector and the photodiodes over a range of device temperatures: 140 K < T < 320 K. The Teledyne Judson Technologies (TJT) photodiode has a 0.049 mm 2 active area, 22 the G4531 photodiode, which is processed from growth MBELabPN(Riber), has a 0.018 mm 2 active area, and the nbn photodetector, which is processed from growth Benchmark, has a 0.041 mm 2 active area. All have cutoff wavelengths of ~3.3 microns at T = 200 K. The 0.6 Volt reverse bias on the nbn photodetector locates the most photosensitive portion of the I-V curve. The 0.05 V reverse bias on the TJT photodiode enables operation in the narrow range over which the current is approximately independent of voltage. The 0.04 V reverse bias chosen for the MBELabPN(Riber) photodiode corresponds to the lowest voltage for which the current is approximately independent of voltage. Dark current measurements are made with the photodetectors enclosed within the 77 K walls of a cryostat. Photocurrents are measured while the photodetectors are illuminated from the top by a 295 K blackbody source through a FOV of 146º. 3.2.1 R o A of the Photodiodes The resistance area product, R o A, is a figure of merit commonly applied to photovoltaic detectors. It is discussed in Chapter 1. In the case of photovoltaic photodetectors dominated by bulk current, R o A is an inherent material property and does not depend on the dimensions of the pixel. When the primary contributors to the dark current in the photodetector are temperature-dependent, the noise current is reduced and the R o A is improved by cooling the device. 19

3.2 Current vs. Temperature 76 R o A may be directly determined from the current density data of the diode, when it is a function of voltage: it is the reciprocal of the slope of the curve, and it is taken at zero voltage bias. Larger values of R o A indicate better detectors; devices with lower values of R o A possess more detector noise. It is possible to calculate D*, the specific detectivity, from R o A as is shown in Chapter 1. Figure 3.2.1 R o A of the TJT photodiode as a function of temperature. Data points plotted in magenta are used to calculate the values of the slopes, indicated on the plot by dashed lines. The corresponding thermal activation energies, E A, are noted. The R o A data plotted in Figure 3.2.1 are calculated for the TJT photodiode under dark current conditions. Over the warmer temperature range, in which bulk current is the primary contributor to the dark current, R o A improves as the photodetector is cooled. The rate of improvement decreases significantly at approximately 200 K and essentially ceases for lower

3.2 Current vs. Temperature 77 temperatures. The thermal activation energy of the higher temperature slope is 0.384 ev and that of the lower temperature slope is 0.001 ev. The former agrees well with the energy of the InAs bandgap, which ranges from 0.35 ev at 300 K to 0.38 ev at 200 K. 32 This indicates diffusion current is the primary contributor to the dark current for these warmer temperatures, as is discussed in Chapter 1. The slope of the lower temperature data is indicative of a temperature-insensitive current, which is consistent with surface leakage current being the primary contributor to dark current. 7 Over this cooler temperature region, the R o A associated with the surface leakage current contribution to dark current is the smallest. By pinning the value of R o A for these lower temperatures, surface leakage current prevents additional device cooling from further reducing the noise current and subsequently improving the SNR and D* of the photodiode; R o A is limited to a value between 25 and 30 Ω cm 2. Figure 3.2.2 is a plot of R o A computed for the MBELabPN(Riber) photodiode. The data points follow a trend similar to that exhibited by the TJT commercial photodiode: a steep initial slope over warmer temperatures, with a thermal activation energy approximately equal to the bandgap of InAs, followed by a shallow slope and correspondingly reduced thermal activation energy over lower temperatures. The thermal activation energy over the cooler temperature range is larger than that of the TJT photodiode, but it is also an order of magnitude smaller than the bandgap of InAs. This indicates the primary current over this temperature range is not diffusion current or SRH current, which has a thermal activation energy approximately equal of half of the bandgap energy. As is true of the TJT photodiode, surface leakage current is the dominant component of dark current for the cooler temperatures. The dominance of surface leakage current limits the values of R o A of both photodiodes at lower temperatures, however the best value of R o A for the MBELabPN(Riber) photodiode is over 30 times higher than that for the TJT photodiode. This is attributed to the design of the MBELabPN(Riber) photodiode reducing the magnitude of the surface leakage current. The difference between the maximum values of R o A for the two photodiodes suggests the TJT photodiode does not possess an architecture intended to minimize surface leakage current. The ideality factor, n, is computed for both diodes. This factor appears in the current density equation of a diode: 43 J = J S exp qv nkt, (3.2.1)

3.2 Current vs. Temperature 78 where J S is the saturation current density. The value of n is 1 for an ideal diode in which diffusion current dominates the bulk current, and n is 2 when SRH current dominates. The ideality factors are found to be 1.04 and 1.08 for the TJT and the MBELabPN(Riber) photodiodes, respectively. Figure 3.2.2 R o A of the MBELabPN(Riber) photodiode as a function of temperature. Data points plotted in magenta are used to calculate the values of the slopes, indicated on the plot by dashed lines. The corresponding thermal activation energies, E A, are noted. 3.2.2 Current Measured as a Function of Temperature Figure 3.2.3 plots current as a function of inverse temperature for the conventional TJT InAs photodiode and for the InAs-based nbn photodetector, Benchmark. The dark current data for the TJT photodiode may be divided into two temperature regimes. Bulk current is dominant

3.2 Current vs. Temperature 79 over the warmer temperature range, and it is reduced as the diode is cooled. Surface leakage current is the primary contributor to dark current over the colder temperature range, where the magnitude of the measured current is largely independent of temperature. This behavior is consistent with the R o A data. Figure 3.2.3 I vs. 1000/T for the TJT photodiode and nbn photodetector. Plotted are current measurements of an InAs-based nbn photodetector, from Benchmark, and a commercial InAs photodiode. Both the dark current (dark current) and the current produced when the device is exposed to a 295 K blackbody radiator (blackbody + dark current) are plotted for each detector. These two curves overlap for the case of the p-n photodetector. Dotted and dashed lines are guides for the eye. No surface leakage current is detected for the nbn photodetector over the range of measured temperatures. The dark current measured for the nbn photodetector decreases monotonically over the entire temperature range. The thermal activation energy of the nbn photodetector is calculated to be E A = 0.39 ev based on the slope of the dark current data

3.2 Current vs. Temperature 80 over 180 K < T < 320 K. This closely matches the bandgap of InAs, which increases from 0.35 ev at 300 K to 0.39 ev at 150 K, and is consistent with diffusion current being the dominant component of dark current over the entire range of measured temperatures. The magnitude of the dark current of the TJT photodiode is pinned by surface leakage current. This is in contrast to the monotonic decrease of the dark current measured for the nbn photodetector, and it leads to a six order of magnitude difference between the two measured dark currents at 145 K. This is significant as the magnitude of dark current determines the magnitude of the noise current in the photodetector, which determines the weakest signal the device may detect. Also plotted in this figure are the current data measured for the TJT photodiode and the nbn photodetector while radiation from a 295 K blackbody source is incident on the detectors. A photodetector achieves BLIP conditions if exposure to background radiation produces a photocurrent with a magnitude larger than that of the internal dark current. For this work, a 295 K background simulates radiation emitted by the Earth. In the case of the TJT photodiode, the magnitude of the current measured in the presence of this radiation essentially matches that taken under dark current conditions. Diffusion current is dominant for T > ~220 K, while surface leakage current is dominant for T < ~220 K; for no device temperature is the dark current small enough for the background-stimulated photocurrent to dominate. The surface leakage current component of the dark current masks the photocurrent stimulated by the radiation from the 295 K blackbody source, the target is not detected, and the TJT photodiode does not achieve BLIP conditions. Device cooling does not enable BLIP operation in the photodiode. Surface leakage current is not a primary contributor to the dark current in the InAs-based nbn photodiode, and as a result the photodetector is able to detect weaker radiation sources than the TJT photodiode. When the nbn photodetector is cooled to temperatures below 200 K and exposed to the same 295 K blackbody radiation, the measured current is notably elevated over the corresponding dark current. This photocurrent measured for the cooled nbn photodetector is approximately invariant with temperature. BLIP operating conditions are achieved for device temperatures below 200 K, where the measured current is dominated by the photocurrent. Diffusion current dominates for T > 200 K.

3.2 Current vs. Temperature 81 Figure 3.2.4 plots the current data measured for the MBELabPN(Riber) photodiode with that taken for the nbn photodetector. The surface leakage current measured for the MBELabPN(Riber) photodiode is approximately 2 orders of magnitude below that measured for the TJT photodiode; at 145 K, the difference between the dark currents of the nbn and MBELabPN(Riber) photodetectors is four orders of magnitude, which is an improvement over the of six orders of magnitude difference measured for the case of the TJT photodiode. Figure 3.2.4 I vs. 1000/T for the MBELabPN(Riber) Photodiode and nbn Photodetector. Plotted are current measurements of an InAs-based nbn photodetector, from Benchmark, and the MBELabPN(Riber) photodiode. Both the dark current (dark current) and the current produced when the device is exposed to a 295 K blackbody radiator (blackbody + dark current) are plotted for each detector. These two curves overlap for the case of the p-n photodetector. The solid, dashed, and dotted lines are guides for the eye.

3.2 Current vs. Temperature 82 Despite exhibiting reduced levels of surface leakage current, the MBELabPN(Riber) photodiode is not able to achieve BLIP operating conditions. The current measured for the MBELabPN(Riber) photodiode, when it is exposed to the 295 K blackbody radiator, is indistinguishable from the recorded dark current. As with the TJT photodiode, diffusion current is dominant for T > ~220 K, while surface leakage current is dominant for T < ~220 K. While the dark currents measured for the MBELabPN(Riber) photodiode over the cooler temperature range are lower, they are significantly higher than the dark currents measured for the nbn photodetector. The dark currents measured for the MBELabPN(Riber) photodiode, for temperatures below 200 K, are between five and ten times higher than the current measured for the nbn photodetector when it is exposed to the 295 K blackbody source. 3.2.3 Implications for Specific Detectivity, D* Incorporating smaller pixels into higher spatial resolution imagers is a current development trend. 2 The nbn photodetector and TJT photodiode investigated for this work have pixel side lengths of approximately 200 microns, and the MBELabPN(Riber) photodiode has an equivalent side length closer to 130 microns, but pixels with side lengths at least ten times smaller than these are required. Reducing the pixel size of photodetectors degrades the performance when surface leakage current, rather than bulk current, is the dominant component of dark current. Specific detectivity, D*, is a figure of merit commonly applied to infrared photodetectors, and it can be used to quantify the relationship between the pixel size and the performance of the detector. It is proportional to the reciprocal of the square root of the sum of the magnitudes of the current density components, 94 D * i 1 J i Dark + J Background (3.2.3) and this relationship is valid for both photodiodes and the nbn photodetector at all temperatures. Σ J Dark i is the sum of all contributors to the dark current density, and J Background is the magnitude of the photocurrent density simulated through the detection of background radiation. The measured currents of the nbn and TJT photodetectors differ by approximately two orders of magnitude at T 200 K. Consequently, the D * of the nbn photodetector is

3.2 Current vs. Temperature 83 greater than that of the TJT photodiode by approximately 10. Similarly, the D* of the nbn photodetector exceeds that of the MBELabPN(Riber) photodiode by a factor of approximately 10 at T 200 K. The D * of the nbn photodetector, which is limited by bulk dark current over the entire measured range of temperatures, is independent of detector size. Bulk current also dominates the dark current of the two photodiodes for temperatures warmer than 220 K. The D* of the photodiodes over this warmer temperature range is accordingly independent of the size of the detector, but this is not true for the photodiodes when they operate at temperatures below 220 K. Over this cooler temperature regime, the specific detectivities of the photodiodes are limited by surface leakage current, and under these conditions the D* scales as the square root of the linear dimension of the pixel. The D* of the nbn photodetector and these photodiodes are dependent on the combined conditions of pixel size and temperature as described in Table 3.2.1. From the relations summarized in this table, the D* of a cooled photodiode, in which surface leakage current dominates the dark current, decreases by a factor of 4.5 as the pixel side length is reduced from 200 microns to 10 microns. The D* of the nbn photodetector remains constant under these same conditions. Device Type Dependence of D* on Pixel Dimension Temperature Range nbn D* invariant all T Photodiode D* invariant T > 220 K Photodiode D * 4S = Perimeter T < 220 K Table 3.2.1 Relationship among pixel dimensions, D*, and temperature. S is the side length of the pixel. These temperature-dependent relationships for D* reflect the results of measurements made on the InAs-based photodetectors discussed in the text. A dependence exists when surface leakage current is the dominant contributor to dark current.

3.2 Current vs. Temperature 84 Restricting the field of view (FOV) increases the value of D* for photodetectors operating under BLIP conditions, as is discussed in Chapter 1. The relationships between the FOV and the D* of the nbn photodetector and the photodiodes are summarized in Table 3.2.2. The nbn photodetector, when operating in the BLIP regime at temperatures cooler than 200 K, experiences a factor of 2 increase in D* when the FOV is decreased from 146 to 60. Decreasing the FOV of the photodiodes has no effect, regardless of the temperature, as surface leakage current prohibits both from achieving BLIP conditions. The nbn photodetector is not limited by surface leakage current at any temperature examined in this chapter, while surface leakage current is the primary contributor to dark current in these cooled photodiodes. At 200 K and under the conditions imposed by this investigation, this results in the nbn photodetector possessing a value of D* larger than those of the TJT and MBELabPN(Riber) photodiodes by factors of 10 and 10, respectively. The differences in D* between the cooled nbn photodetector and the TJT and MBELabPN(Riber) photodiodes are expected to increase as the pixel sizes and FOV are reduced. This is a consequence of the D* of the cooled photodiodes worsening with reduced pixel dimensions, and the inability of these photodiodes to achieve BLIP operating conditions and subsequently benefit from a smaller FOV. Device Type Dependence of D* on FOV BLIP Status (Temperature Range) nbn D* invariant not BLIP (T > 200 K) nbn D* 1 Sin FOV /2 ( ) BLIP (T < 200 K) Photodiode D* invariant not BLIP (all T) Table 3.2.2 Relationship among FOV, D*, and temperature. The D* of a nbn photodetector or a photodiode operating under BLIP conditions improves with reduced FOV. For the photodetectors tested in this chapter, only the nbn photodetector achieved BLIP operating conditions.