Development of 13 $\mu m$ Cutoff HgCdTe Detector Arrays for Astronomy

Building on the successful development of the 10 $\mu m$ HgCdTe detector arrays for the proposed NEOCam mission, the University of Rochester Infrared Detector team and Teledyne Imaging Systems are working together to extend the cutoff wavelength of HgCdTe detector arrays initially to 13 $\mu m$, with the ultimate goal of developing 15 $\mu m$ HgCdTe detector arrays for space and ground-based astronomy. The advantage of HgCdTe detector arrays is that they can operate at higher temperatures than the currently used arsenic doped silicon detector arrays at the longer wavelengths. Our infrared detector team at the University of Rochester has received and tested four 13 $\mu m$ detector arrays from Teledyne Imaging Systems with three different pixel designs, two of which are meant to reduce quantum tunneling dark current. The pixel design of one of these arrays has mitigated the effects of quantum tunneling dark currents for which we have been able to achieve, at a temperature of 28 K and applied bias of 350 mV, a well depth of at least 75 $ke^-$ for 90% of the pixels with a median dark current of 1.8 $e^-/sec$. These arrays have demonstrated encouraging results as we move forward to extending the cutoff wavelength to 15 $\mu m$.


Introduction
Cryogens or cryo-coolers used to cool long wave infrared (LWIR) detector arrays on space missions take up valuable space and weight, and the limited volume of cryogens limits the lifetime of the LWIR detector array sensitivity. This project addresses these limitations, since the current ∼13 µm (LW13), and eventual 15 µm (LW15) wavelength cutoff HgCdTe arrays, can operate at temperatures that can be attained through passive cooling in space.
Instruments in past space missions that used LWIR detector arrays (wavelength cutoff above ∼5µm) required cooling to very low temperatures with on-board cryogens. For example, the Spitzer Space Telescope's Si:As impurity band conduction (IBC) LWIR arrays with a cutoff wavelength of ∼28 µm used in all three instruments (IRAC, MIPC, IRS) 1, 2 were operated at 6-8 K, and WISE's similar arrays (centered at 12 and 22 µm) 3 were cooled to 7.8 K. After cryogens ran out, due to good thermal design the focal plane of Spitzer Space Telescope warmed up and equilibrated to ∼ 28 K. The mid-wave IR InSb cameras continue to function at comparable sensitivity to that during the cryogenic phase, while the Si:As IBC LWIR large format detector arrays ceased to function due to high dark currents. Similarly, only the WISE mid-IR HgCdTe arrays continued to function once cryogen was depleted. Figure 1 shows the median dark current vs. temperature for all four ∼13 µm cutoff wavelength HgCdTe arrays presented here, where three of the arrays show a median dark current < 1 e − /sec at a temperature of 28 K and an applied bias of 150 mV.
Although the arrays presented here were developed for space missions, this technology can be important for ground based observatories. Instruments developed to explore the N-band that use 13 µm arrays HgCdTe arrays, would be able to operate with the use of a cryo-cooler, eliminating the need for cryogens. We have initiated a study of this with colleagues, where our colleagues are experimenting with one of the LW13 arrays (H1RG-18508) to see if a fast readout (full-frame time of 12.5 msec) brings the N-band signal on scale, enabling astronomical observations with the array.

Mercury Cadmium Telluride (HgCdTe)
Our group and Teledyne Imaging Systems (TIS) are working together to develop new 15 µm LWIR detector arrays that can operate at relatively elevated focal plane temperatures for low background astronomy. TIS manufactures and develops these LWIR detector arrays with substantial feedback from our group. The testing and characterization of these devices is carried out at the University of Rochester (UR). The alloy used for these detectors, Hg 1−x Cd x Te, has the x composition parameter (molar concentration of Cd) varied to reach different cutoff wavelengths. The band gap energy (in eV) of this semiconductor at a temperature in degrees Kelvin is given by 4 E g (x, T ) = −0.302 + 1.93x − 0.81x 2 + 0.832x 3 while the relationship between the band gap energy and the cut-off wavelength is given by where h is Planck's constant and c is the speed of light.

Prior Development / NEOCam
The UR infrared detector team has been working on the development and improvement of low background devices with a cut-off wavelength longer than about 5.4 µm since 1992. [5][6][7][8][9] By 2003, these early large format arrays were 512×512 pixels and had cut-off wavelengths of 9.3 and 10.3 µm (LW10 arrays), and showed low dark current, but could not support a large reverse bias which limited the well depth of these devices. Even with these limitations, the devices showed promise as they were both operable at a temperature of 30 K. 6,10 The Near Earth Object Camera (NEOCam) is a JPL proposed mission whose goal is to find and characterize near-Earth objects (asteroids and comets), some of which have Earth-crossing orbits and could be potentially hazardous. The mission will use the LW10 detector arrays discussed above to allow the telescope to observe from 6-10 µm. In addition to the instrumentation involving the LW10 arrays, NEOCam will also have a camera with lower cut-off wavelength arrays (5 µm) already developed for WISE and the James Webb Space Telescope. 11 To meet the requirements of the NEOCam project, TIS successfully increased the array format from 512×512 pixels to 2048×2048 pixels. The arrays have cut-off wavelengths of ∼ 10 µm, low read noise, high quantum efficiency (QE), and have operabilities (well depth of more than 44,000 e − and dark current less than 200 e − /s ) > 90% up to temperatures of 42 K, and have been proton irradiated and demonstrated the ability to withstand the cosmic ray radiation that they are expected to receive in space. [12][13][14] These devices have reached NASA Technical Readiness Level-6.

LW13 Detector Arrays
In order to reach the present 15 µm goal (composition parameter x ∼ 0.209, at a temperature of 30 K), we are completing an intermediate step by developing arrays with a cutoff wavelength of 13 µm (x ∼ 0.216, at a temperature of 30 K) to identify any problems that would prevent us from reaching the 15 µm goal. As the compound becomes softer (which is a consequence of increasing the mercury fraction with increased wavelength), there is an increased likelihood TIS provided measurements of the QE before anti-reflection coating and cutoff wavelength from mini-arrays on process evaluation chips (PECs) manufactured with the arrays, at a temperature of 30 K (Table 1). The QE as a function of wavelength was measured at UR using a circular variable filter, and we only quote the PEC QE measurements since we found a reasonable agreement with TIS measurements.

Operability
Operable pixels should have low initial dark current with sufficient well depth, high QE, and low read noise. The performance of the LW13 arrays has been shown to be limited by dark current and well depths during characterization.
These arrays have shown excellent QE (> 70% before anti-reflection coating) and low correlated double sample (CDS) read noise (∼ 23 e − shown for two arrays in Section 4.3) both at 30 K.
We will show that high dark currents and/or low well depths limit the performance of these arrays.
For this developmental project, we have focused our efforts in the reduction of high dark currents since their effects are expected to worsen when the wavelength is increased to the final goal of 15 µm. Therefore, pixels with low dark current and sufficient well depth will be considered operable.
We adopt the same dark current operablity requirements to that of the LW10 devices developed for the NEOCam mission. 14 Our imposed operability requirements include dark currents < 200 e − /s, and well depth of ∼ 40 ke − for an applied bias of 150 mV (larger well depth requirements are used for larger applied biases). The dark current requirement for NEOCam was established such that the mission's 6-10 µm channel will be background-limited by the thermal emission from the zodiacal dust cloud.
The operability requirements adopted for NEOCam are also specific to the filters, telescope size and throughput. Any future mission that intends to use these LW13 devices likely would have a modified set of requirements.
Though operability requirements depend on specific applications of these devices, the dark current and well depth requirements for operable pixels in the LW13 arrays are used as a benchmark to compare the performance of the different arrays at different temperatures and applied bias, and to determine the best pixel design that will be pursued when increasing the cutoff wavelength to 15 µm.

Sources of Dark Current and their Implications
Thermal (diffusion 18 and generation-recombination 19 ) and tunneling [20][21][22] (band-to-band and trapto-band) dark currents have been found to be the sources of dark current in these LW13 devices.
Tunneling currents are the primary dark current mechanisms limiting the operability of the LW13 arrays at low temperatures and moderate high applied reverse bias required for use with lowpower source-follower readout integrated circuit (ROIC) commonly used for astronomy focal plane arrays.
Both tunneling dark currents are strong functions of bias, and have large non-linear effects that can affect data calibration. In addition to the non-linear effects, the charge capacity of pixels with very large dark currents, due to trap-to-band tunneling, can be depleted leading to low well depths, where a subset of these pixels create a cross-hatching pattern in the operability map for all four arrays (see section 4.4.1).
The design of H1RG-18509 successfully lowered tunneling dark currents, where the median dark current and well depth at a temperature of 28 K and reverse applied bias of 350 mV is 1.8 e − /s and 81 ke − respectively, while the median dark current for the other three arrays was >200 e − /s. The effects of tunneling currents on calibration and operability for all four devices are shown in section 4.
The dark current of these devices has been modeled using the theory described in the following section. The results are shown in section 5, where we have shown that at biases >∼200 mV and low temperatures, band-to-band tunneling is the dominant component of dark current and is shown to be fairly uniform since all pixels are affected equally by this dark current mechanism.
Operating regimes in which thermal currents dominate would be ideal to avoid any non-linear dark current behavior as pixels debias due to integrating signal since both diffusion and generationrecombination dark currents do not vary significantly with a bias above 25 mV. These regimes will be further discussed in section 6.
2 Dark Current Theory

Diffusion Current
Diffusion dark current occurs when electrons in the valence band gain enough energy thermally to overcome the band gap and transition to the conduction band. This thermally induced current must occur within one diffusion length (much larger than the pixel width and depth in these arrays) from the depletion region, and is given by 18 where A is the diode junction area, n i is the intrinsic carrier concentration, d is the thickness of the n-type region, N d is the doping density, τ b is the minority carrier (hole in the n-type region) lifetime, k b is Boltzmanns constant, and T is the temperature. In reverse bias, the actual bias across the diode (V actual bias ) is negative and the exponential term is negligible for the applied biases that we typically apply (> 25 mV of reverse bias). It can be readily seen that diffusion dark current does not change appreciably with varying bias, while the strong temperature dependence comes in the form of the intrinsic carrier concentration 4 where x is the cadmium mole fraction.

Generation-Recombination
The second source of dark current that increases with temperature is Generation-Recombination (G-R). Traps in the depletion region with energy levels between the valence band and the conduction band can facilitate the indirect transition of an electron to the conduction band, where electrons in traps would have to overcome a smaller energy gap. G-R current is given in Sah (1957) 19 by E tgr is the trap energy level position with respect to the valence band which contributes the most to the G-R current, while E i is the intrinsic Fermi level (E g /2). τ GR is the depletion region lifetime for holes and electrons, and W D is the depletion region width given by 5 where 0 is the permittivity of free space, is the relative permittivity of HgCdTe, and V bi is the built-in voltage. G-R current also has a very weak dependence on bias (as long as the back-bias is greater than ∼25 mV).

Quantum Tunneling Currents
Tunneling currents are produced by electrons tunneling from the valence to the conduction band directly (band-to-band), or by traps with energies between the valence and the conduction band (trap-to-band). There are two different models for band-to-band currents; the first assumes a triangular barrier, while the second one uses a parabolic barrier. The equation corresponding to the parabolic barrier is omitted here as our data best matches the behavior of a triangular barrier, and it is given by 20,21 where m ef f is the effective mass of the minority carrier and E is the electric field across the depletion region given by 18 Trap-to-Band tunneling current for a triangular barrier is modeled by 20,22 where M is the mass matrix, E t is the energy of the trap level with respect to the valence band, and n t is the trap density in the depletion region at E t .
Data from pixels that appear to exhibit trap-to-band tunneling in the LW10 5,8,9 and the LW13 devices have also shown a soft breakdown in the I-V curves, prior to the onset of trap-to-band tun-neling. Other authors have observed soft breakdowns in 4H-SiC 23,24 and Silicon 25 diodes caused by screw dislocations and stacking faults respectively, which became electrically active at a certain "threshold voltage". Furthermore, Neudeck et al., 23 Ravi et al., 25 and Benson et al. 26 (for HgCdTe on Si) showed that there is no correlation between the degraded I-V characteristics and the trap density, because all traps associated with dislocations may not contribute to the soft breakdown due to the varying threshold voltage for dislocations within the same diode at which they become electrically active.
Though we cannot say with certainty what type of dislocation 10 causes the soft breakdown in the LW13 arrays presented here, we believe a defect associated mechanism, likely different from that described by the authors above is responsible for this early soft breakdown and the onset of trap-to-band tunneling as traps become electrically active. Bacon (2006) 8 parametrically fit the I-V curves by introducing a threshold voltage at which certain traps become active and contribute to trap-to-band tunneling as where n t i is an initial active trap density, n t d is the trap density due to activated dislocations at a voltage V a , and γ is a parameter which dictates how sharply the current increases due to the soft breakdown before reaching the current expected from trap-to-band tunneling. A small modification to the Eq. 2.29 in Bacon (2006) was made where we multiply the sum of the activation voltage and the actual bias by γ. This change was made so that the fitted γ parameter only affected the sharpness of the soft breakdown, and not the fitted activation voltage.
Although this is not a physical model since we do not know the trap identity, a more detailed  More data at lower biases would be needed to more accurately characterize the threshold voltage of the traps which contribute to the trap-to-band tunneling, while data at larger biases is needed to properly characterize pixels which only appear to show the soft break down, and there is no in-dication if the behavior before or after the soft breakdown is consistent with trap-to-band tunneling or any other form of dark current.

Data Acquisition
UR uses a liquid helium dewar with multiple chambers to test the arrays. The innermost chamber that houses the array and filter wheel has an aluminum cylindrical shield coupled to a liquid helium reservoir, allowing temperatures down to 4 K and below (by reducing the pressure in the liquid helium reservoir) to be reached. The filter wheel has several narrow band filters, two circular variable filters (covering a wavelength range between 4-14.3 µm), and a dark blocking filter. Attached to the filter wheel housing is a 67.6 µm diameter Lyot stop used to control the illumination of the array. The temperature inside the innermost chamber is regulated with a Lake Shore Cryotonics temperature controller, allowing the arrays presented here to be tested at different stable temperatures.
The inner chamber is surrounded by an aluminum cylindrical shield attached to a liquid nitrogen reservoir, shielding the liquid helium reservoir and inner chamber from the outer shell which is at room temperature. The outer shell has an anti-reflection coated ZnSe window in the line of sight of the array being tested.
The array controller used for data acquisition is based on an open source hardware design developed by the Observatory of the Carnegie Institute of Washington (OCIW). The version that we use is optimized for infrared arrays. It has programmable clocks and biases with four channels of amplification and analog to digital conversion for the output of the array. A detailed description of the array controller can be found in Moore et al. (2003). 27

Sampling Modes
The data presented here were obtained using either the Sample-Up-The-Ramp (SUTR) or Correlated Double Sample (CDS, or Fowler-1) sampling methods, [28][29][30] where the method used for specific data sets will be mentioned in the their description. The same reset mode is used for both sampling methods, where a reverse bias (V bias ) is applied to reset the array row by row (all columns in a row simultaneously). Immediately after the reset switch is turned off to allow the device to debias as signal and dark current are accumulated, a redistribution of charge (pedestal injection due to capacitive coupling to the reset FET) results in a change in the bias voltage across the diode to a value designated as V actual .
Following the reset, the first sampled image is referred to as the pedestal. The delay time to the pedestal sample ranges from circa 5.8 milliseconds to 5.8 seconds, depending on the row and column for a specific pixel. For CDS images, the pedestal is subtracted from an image sampled some integration time later. The SUTR method is used to obtain many non-destructive samples to study the behavior of the array as pixels debias over time. In this sampling mode, following the reset and pedestal frame (used to normalize the rest of the samples to a zero point), many samples are taken at equal time intervals without resetting the array.

Characterization
To characterize the performance of the LW13 arrays we measured the dark current and well depth (amount of charge collected at the integrating node when saturation is reached) per pixel at temperatures ranging from 28 to 36 K with applied reverse bias of 150, 250, and 350 mV, as well as the read-noise per pixel at a temperature of 30 K for two of the arrays. The node capacitance and signal linearity have also been measured at a temperature of 30 K with applied reverse bias of 150, 250, and 350 mV to calibrate the arrays.

Calibration
The first step in the calibration process is to measure the source-follower FET gain of signal in the multiplexer by turning on the reset switch, and varying the reset voltage while recording the output voltage. The source-follower FET gain was measured to be ∼0.9 for all four arrays, allowing us to convert between the output referred and input referred signal.
Next, to convert from volts to electrons we measure the nodal capacitance. Our data are recorded in analog to digital units (ADU), which can be converted to volts by dividing the 5 V range of the 16 bit A/D converter by 2 16 ADUs and the gain from our array controller electronics.
The nodal capacitance per pixel is obtained using the noise squared (σ 2 ) vs. signal method 31 shown in Fig. 3. Sets of 100 CDS images, each set at varying fluence levels, were used to obtain the signal and the rms noise. Figure 4 shows the nodal capacitance distribution per pixel for H1RG-18508 for three applied biases, where the median capacitance is then used to convert between the measured ADUs and the signal in electrons for the entire array.
The capacitance then has to be corrected for interpixel capacitance (IPC), determined through the nearest neighbor method. Pixels with a very high signal (due to very high dark currents) are used to determine the coupling parameter α between the high signal pixel and its nearest neighbors. 32 The nodal capacitance is then multiplied by a factor of 1 − 8α to correct for IPC. 32 The IPC coupling factor α and corrected capacitance for all four arrays are shown in Table 2 for three applied biases.
This method of converting the signal at the integrating node to electrons is only valid for low  These capacitances have not yet been corrected for interpixel capacitance. The spread in the capacitance distribution is due to noise. One standard deviation away from the mean for the 150 and 250 mV distributions is equal to 6.8 fF and 10.5 fF for the 350 mV distribution. signal data which minimizes debiasing as in Fig. 3. For large signals, we need to account for the non-linear diode capacitance resulting from the debiasing of the diode, leading to the reduction of the junction depletion region as signal is collected. 33 To measure the non-linearity of these devices, the signal collected from a constant illuminating flux is sampled in SUTR mode until saturation is reached. The non-linear collected signal rate is calculated by dividing the signal over the time it took to collect the signal. The signal is not corrected for dark current. Figure 5 shows the non-linearity curve for H1RG-18509 with an applied bias of 150 mV at 30 K, normalized to the first sampled signal. The normalized signal rate is also referred to as C 0 /C, where C 0 is the nodal capacitance at zero collected signal and C is the nodal capacitance. To correct for the non-linear capacitance, the slope of a fitted line to the non-linearity curve (between 20 and 80% of the saturating signal) is used. Correcting for the non-linearity can be difficult when dark currents are on the order of the collected signal, which can occur at biases larger than 150 mV. A further step is required at high bias, where the extrapolated line fit is normalized to unity at zero signal. Figure 6 shows the non-linearity curve for H1RG-18369 with an applied bias of 250 mV, where at low signals the rate at which the diode debiases is much faster than is expected from a constant flux illumination. This quick debiasing is due to elevated dark current levels at high bias attributed to quantum mechanical tunneling. The effects of tunneling dark currents which are dominant at A light leak in the test dewar has been ruled out because the anomalous dark current was not present in all data sets taken under similar conditions (without changes to the system setup). Figure  Fig 6 Non-Linearity curve obtained from a 50X50 box average of pixels in H1RG-18369 with an applied bias of 250 mV at a temperature of 30 K. The signal rate was normalized and shifted such that the fitted line has a y-intercept of unity. The difference between a value of unity (horizontal dashed line) and the non-linearity curve is the fraction of the signal that was not collected due to the debiasing of the device. The vertical dashed line corresponds to the mean saturating signal at an actual bias of zero for the entire device. The rapid debiasing of the detector at low signals is due to tunneling dark currents. 20 shows an instance where an elevated current affected the dark current and well depth data but was not present in the warm-up data (discussed in Sect. 5.1) taken at a similar temperature and same applied bias. Dark current has also been ruled out since the dark current mechanisms studied here do not increase by a factor of 10 or more by increasing the temperature by 1 K for H1RG-18367 and -18369 (see Fig. 1 or Tables 4 and 8). Instead, we believe this current could be a glow from the unit cell FETs in the multiplexer. This effect will be referred to as "mux glow" hereafter when describing the data that were affected. Further work is required to evaluate this anomalous behavior.

CDS Read Noise
The total noise per pixel was measured for two arrays, H1RG-18369 and H1RG-18509 at a tem-   The CDS read noise was obtained by subtracting the contribution from dark current or a signal flux from the total noise in a CDS image. The total noise is plotted for H1RG-18369 to show the contribution from the "mux glow" to the noise of the detector. The dark current contribution from H1RG-18509 to the total noise was minimal, and did not exhibit a "mux glow", therefore we only present the read noise distribution for this array.

Dark Current and Well Depth (Operability)
To measure the dark current and well depth, 200 samples-up-the-ramp in the dark were taken with an integration time of 5.8 seconds between each sample. Without resetting, we allow a radiative flux to uniformly saturate the array, where this saturating level includes a 10-20 mV forward bias contribution from the signal flux. 8 To determine the actual zero bias saturation signal for each pixel, the array is then read out 200 additional times in the dark, allowing the array to debias to actual zero bias. The initial dark current is the measured slope at the beginning of the signal vs.
time (SUTR) curve. The difference between the pedestal frame and the average of the last twenty frames (taken when the array is at zero bias) then gives us the well depth of each pixel.
Well depth and dark current are presented here concurrently because the initial dark current of The well depth requirement of 155 mV (∼ 41 ke − ) was chosen to include the majority of the good pixels, and we kept this requirement for higher temperatures with the same applied bias. Note that the well depth corresponds to the actual initial detector bias, ranging from 155 to 225 mV at the beginning of the integration among the operable pixels for this data set. a pixel may be heavily dependent on the actual bias (well depth) across the pixel when it is first sampled (referred to as pedestal). Quantum tunneling dark currents are exponentially dependent on bias, so large tunneling dark currents can debias a pixel considerably between reset and pedestal frame, thus showing a low initial dark current but with a depleted well. Figure 8 shows the distribution of initial dark current vs. well depth per pixel for H1RG-18367 at a temperature of 28 K and applied bias of 150 mV, where the operable pixels are below and to  the right of the dashed lines. The dark current distribution per pixel for this array peaks around 10 e − /s for an applied bias of 150 mV and a temperature of 28 K: we attribute this dark current to the "mux glow" discussed in section 4.2 given its uniformity across the entire array, and lack of bias dependence. The "mux glow" was also observed at temperatures of 30 and 32 K for this array, with a median "dark" current of 130 and 156 e − /s respectively with a bias of 150 mV. This accounts for some of the loss of operability at 30 and 32 K c.f. 28K. The percentage of operable pixels for different temperatures and applied biases are reported in Table 3, along with the well depth requirements. Median dark current and well depth measured for this array are shown in Table 4. Figure 9 shows the discharge history of a pixel in the dark at three different applied biases for this device. The initial larger curvature observed in the signal with an initial applied bias of 350 mV is a consequence of quantum tunneling dark currents which are exponentially dependent on bias. As the pixel debiases, tunneling dark currents decrease and the dark current approaches the constant behavior with bias expected from steady "mux glow".

H1RG-18367
The major limiting factor in the operability of these arrays at larger bias and low temperatures has been tunneling dark currents, and it is much more evident at biases of 350 mV since trap-toband and especially band-to-band tunneling are strongly dependent on the applied bias. 5, 6, 9 At higher applied bias, most of the pixels have dark currents exceeding 200 e − /s, giving very low operabilities. The trap-to-band dark current is highly variable from pixel to pixel, but the band-toband tunneling affects all of the pixels in the array.
The inoperability at low temperatures and low applied bias (∼ 28 K and 150 mV respectively)  This effect can be seen in the operability map for all four arrays (Fig.10 for H1RG-18367 35 and Chang et al. 36 Shapiro et al. 38 see the same pattern along the three cross-hatching directions as QE variation on sub-pixel scales on a 2.5 µm cutoff HgCdTe array, in addition to a cluster of high dark current pixels that lie along only one of the cross-hatching directions. H1RG-18508 has a higher operability (Table 5) at higher temperatures than its counterpart H1RG-18367 (both were grown and processed in the same way, and both have similar cutoff wavelengths), and "mux glow" was not detected for this array. The dark current vs. well depth distribution for this array at 28 K and an applied bias of 150 mV is shown in Fig. 12, where the majority of pixels had dark currents below 1 e − /s. Median dark current and well depths are presented in Table 6.
The operabilities at 350 mV of applied bias are below 1% at all temperatures, and have therefore been omitted from the operability table. The inoperability at larger applied bias is evidence of tunneling dark currents. The large curvature in the dark signal vs. time curve is observed with increasing bias in Fig. 13, which is a hallmark of tunneling dark currents. The SUTR data obtained with an applied bias of 150 mV are linear as is expected if thermal dark currents (diffusion and G-R, which are a weak function of bias), a light leak, or a mux glow are dominating the dark current as the pixel debiases.

H1RG-18369
This array has a similar dark current and well depth distribution as H1RG-18508, where the majority of the pixels achieved dark current levels less than 1 e − /s at a temperature of 28 K and an  0.0 * 0.0 * 0.0 * * The "mux glow" affected the noted operabilities for this array, increasing the median dark current by a factor of ∼100 when the temperature was increased from 33 to 34 K with an applied bias of 150 mV, and by a factor of ∼ 43 when increasing the temperature from 32 to 33 K with an applied bias of 250 mV, effectively making the entire array inoperable.   applied bias of 150 mV. Table 7 shows the operability for this array, where the unusual drop in operability when increasing the temperature by one degree with an applied bias of 150 mV and 250 mV is most likely due to "mux glow". Table 8 shows the median dark current and well depth for this array, where the increase in median dark current by a factor of ∼100 at a temperature of 34 K and 150 mV of bias cannot be explained by any of the known dark current mechanisms.
Additionally, the decrease in dark current with increasing temperature, for an applied bias of 350 mV from 28-32 K, is consistent with tunneling dark currents. If the increase in dark current at 33 K was due to thermal currents overtaking tunneling currents, we would expect the dark current to continue to rise with increasing temperature, and this is not the case. Figure 14 shows the dark current distribution for this array at 33 and 34 K with an applied bias of 150 mV.
Furthermore, despite the experimental design used to reduce tunneling dark currents, this array also exhibited low operabilities at 350 mV (< 1%) as did the standard growth arrays (H1RG-18367 and 18508).  To mitigate the effects of the tunneling dark currents, Teledyne developed several modifications to its baseline NEOCam design, designated as designs 1 and 2, shown in Table 1. H1RG-18509 was from the Design-2 lot split and outperformed the other LW13 arrays in terms of operability at all applied biases, but especially at 350 mV, and at higher temperatures (Table 9). Table 10 shows the median dark current and well depths measured for this array at different temperatures and applied bias. This array has a slightly shorter wavelength cutoff compared with the standard growth arrays. Design 2 had a positive effect on reducing the quantum tunneling currents as is readily apparent in curves of the time dependence of charge collected in the dark, where most of the individual SUTR curves for H1RG-18509 did not exhibit highly curved discharge behavior such as observed for the other arrays. Figure 15 shows the histogram of curvature values (initial second derivative of

Dark Current Model Fits
The effects of tunneling dark currents were shown in sections 4.4.1 -4.4.4, and comparing our measurements to theory will allow us to assess the degree to which each of the tunneling components is dominant and how we can mitigate these effects further as we continue to extend the cutoff wavelength for the second phase of this project.
Given the different dependences on temperature and bias for the dark current mechanisms, we fit the thermal currents, which are strongly temperature dependent, to dark current vs. temperature (I-T) data, while the tunneling currents are fit to dark current vs. bias (I-V) data given their strong dependence on bias.

Dark Current vs. Temperature
I-T data consist of two different data sets: (1) the initial dark current per pixel which was obtained at the stable temperatures reported in the operability tables in Sections 4.4.1 -4.4.4, and (2) the warm-up data taken when the liquid helium in our dewar runs out. Four full array frames are read after resetting the array in SUTR mode, immediately followed by an array reset and reading four sub-array (32 rows, all columns) frames in SUTR mode. This data-taking process continued until the temperature reached 77 K. The dark current was then obtained by subtracting the pedestal from the following three frames, taking the average signal from the pedestal subtracted frames and dividing by the average integration time.
The integration time between the full array data frames is 5.8 seconds, and 0.2 seconds for the sub-array frames. At lower temperatures, the amount of charge collected by pixels in 0.2 seconds is on the order of the read-noise (∼ 23 e − ); we therefore use the 5.8 second integration time data to form the I-T curve at these lower temperatures. As the temperature increases, so does the dark current, saturating the full array frames at a temperature of ∼ 40 K. At a point before the full frames saturate we used the sub-array frames which saturate at a higher temperature (∼ 50 K) because of the shorter integration time.

Dark Current vs. Bias
SUTR data sets taken to measure the dark current and well depth are used to obtain I-V curves.
The dark current is obtained by taking the difference between sequential data points along the dark The I-V curve for the 150 mV SUTR set is not used since the data for reasonably good pixels typically span less than 5 mV of bias. Instead, only the initial dark current and well depth are used as the lowest bias data point. The same is done for H1RG-18509 for the three applied biases since most pixels discharge less than 5 mV in the dark signal vs. time data.

Fitting Process and Caveats
Equations 9 and 11 in Section 2.3 show that tunneling currents are exponentially dependent on band gap and electric field in the junction region. The I-V curves of several operable pixels at large applied bias (> 200 mV) matched the trend of a fit to band-to-band tunneling, where the only parameter to fit is E 3/2 g /E ≡ β. If indeed these pixels (or the majority) are dominated by band-toband tunneling, this would allow us to get the most accurate estimate of the parameter β since other dark current mechanisms have several other parameters to fit, which can lead to a non-unique set of fitted parameters. Figure 16 (a) shows an example of an operable pixel in H1RG-18508. Inoperable pixels required the addition of trap-to-band tunneling to fit the I-V data. Figure 16 (b) shows an inoperable pixel in H1RG-18508, where the β parameter of the operable nearest neighbor pixels used to fit band-to-band tunneling current is shown to be orders of magnitude below the measured dark current and hardly contributes to the fit.
Unlike band-to-band tunneling where β is the only unknown parameter, trap-to-band tunneling requires the fitting of five additional parameters (see Sect. 2.3). Furthermore, the fitted trap-to-band tunneling heavily depends on the parameters' initial guess, which may not be unique.
Therefore, only band-to-band is initially fitted to the larger applied bias I-V data of operable pixels to estimate the value of β. The following step to model the dark current was to then fit the thermal dark currents (diffusion and G-R) to the higher temperature I-T data. Lastly, the test dewar light leak or "mux glow" is fitted, along with trap-to-band tunneling if necessary.
When estimating the value of β in H1RG-18367 and H1RG-18509, an additional constant current was added to the I-V data along with band-to-band tunneling (similar to that shown on Fig.   19 on individual pixels) because the large bias data was not completely dominated by band-to-band tunneling. In the case of H1RG-18367, the "glow" from the multiplexer (discussed in sections 4.2 and 4.4.1) has a considerable effect on the I-V data up to 300 mV of bias, while H1RG-18509 is dominated by a possible < 1 e − /s light leak in the test dewar and G-R up to a bias of ∼350 mV.
Since G-R current does not have a large bias dependence in the range of interest, the light leak plus the G-R current in H1RG-18509 were modeled as a constant current when estimating β. Figure 17 shows the distribution of fitted β values to a 32×400 pixel region in the four arrays presented here.  Fig. 17, while the single band-to-band tunneling curve is calculated from the mean β value of the 36 pixels.

Dark Current Model Results
The I-V data for the 36 pixels in Fig. 18 (b) follow the trend of band-to-band tunneling with slightly different β values at biases > 200 mV. The dark current models fitted to the I-T data shows that, up to a temperature of ∼32 K, the dark current of operable pixels is dominated by Fig 19 Dark current vs. bias data curves for 36 pixels which where operable at a temperature of 28 K and applied bias of 250 mV in H1RG-18367 at a temperature of 28 K. The constant leak current that was fitted corresponds to the "mux glow".
band-to-band tunneling. At higher temperatures G-R and diffusion currents are the dominating components.
Similar to H1RG-18508, the majority of the pixels in the other three arrays (Fig. 19-21) that were operable at a temperature of 28 K and 250 mV of applied bias were dominated by band-toband tunneling at larger biases The observed "mux glow" in H1RG-18367 is large enough to dominate the dark current up to a bias of ∼ 300 mV (see Fig. 19), and in the linear behavior of the SUTR curve for the pixel in Fig. 9. Thermal dark currents were not fitted to this array as warm-up data are not available.
The warm-up data for H1RG-18369 were obtained with an applied bias of 150 mV, where the I-T data in Fig.20 (a) show that at 28 K, the dark current is limited by a possible 0.3 e − /s light leak in the test dewar. The 34 and 35 K stable data points, which were affected by the "mux glow", do not follow the behavior expected from any of the dark current mechanisms, further confirming that the anomalous increase of dark current from 33 to 34 K is not due to thermal currents. The "mux The mean actual bias of 181 mV, corresponding to the 28 K stable data point, was used to fit the dark current models. (b) Individual dark current vs. bias (at 28 K) data curves for the same 36 pixels shown in (a). The 33 and 34 K stable temperature data points in (a) were affected by a "mux glow", increasing the dark current above the expected value from thermal dark currents.
glow" was not present in the warm-up data.
The increased tunneling currents in these devices, compared with the LW10 devices, was expected given the smaller bandgap. H1RG-18509 was designed to address this concern. A substantial decrease in band-to-band tunneling current in this array compared with the other three arrays can be seen in Fig. 21. The small curvature in the SUTR curves (shown in the double derivative at the beginning of the SUTR curves in Fig. 15) for the majority of the pixels for this array is due to the relatively small tunneling current found in the I-V data ( Fig. 21 (b)). As a consequence, we are able to achieve larger well depths by applying a large bias (∼75 ke − with an applied bias of 350 mV). The warm-up data for this array were taken with an applied bias of 250 mV. Dark current data for this array above 29 K is dominated by G-R and diffusion, while lower temperature dark current which is well below 1 e − /s approaches the light leak level.
The apparent dominance of band-to-band tunneling at higher biases in operable pixels for all ar- rays is very encouraging, as further enhancements in Teledyne's design to increase β will decrease this tunneling component in future longer wavelength devices.

Discussion on Linear Dark Current Regimes
We have shown that tunneling dark currents dominate the operabiilty of these devices, where the non-linear effects of these currents may present a problem in the calibration of low signal data.
The reduction of tunneling dark currents in H1RG-18509 allows for a linear dark current calibration at low signals since the dark current vs. time is nearly linear at biases as large as 350 mV.
The non-linear effects on collected signal vs. time due to large band-to-band tunneling currents seen in the other three arrays at large biases may be modeled for each of the operable pixels in an attempt to calibrate it, but the exact (or very close to) initial actual bias across each pixel is needed since the tunneling currents vary appreciably as pixels debias.
Alternatively, the three arrays that show large band-to-band currents can be operated in regimes where the dark current is not dominated by band-to-band tunneling.
In the low applied bias regime where band-to-band tunneling is negligible, thermal dark currents would be the dominant source of dark current and could be calibrated at stable temperatures since these currents are approximately linear (above ∼25 mV of reverse bias) as pixels debias. For applications that require larger well depths than can be attained with the Hawaii-XRG multiplexers at the biases needed to operate in this regime (∼< 200 mV), a capacitive transimpedance amplifier (CTIA) multiplexer could be used in its place. A CTIA multiplexer would allow the operation of these arrays at a constant voltage while signal is integrated, therefore maintaining a constant dark current, and with a much larger well depth at the expense of higher power dissipation and read noise.
Another solution to avoid non-linear dark currents as a function of bias is to increase the operating temperature. Tunneling currents decrease with increasing temperature since the bandgap energy increases. At higher temperatures, the dark current due to thermal currents may be comparable to those from band-to-band tunneling at lower temperatures. Figure 18(a) shows that with an applied bias of 250 mV, the dark current in H1RG-18508 at 35 K is dominated by G-R and is comparable to that at 28 K which is dominated by band-to-band tunneling.

Summary
We demonstrate the promising performance of four 13 µm cut-off wavelength arrays which all have high quantum efficiency, low read noise, and operabilities close to or greater than 90% for temperatures of up to 32 K for an applied bias of 250 mV. At lower temperatures the majority of pixels have dark currents below 1 e − /s for three of the four tested arrays, while the fourth has currents of ∼ 10 e − /s due to a probable glow from the mux.
The cross-hatching pattern associated with the intersection of slip planes and the growth plane in HgCdTe detector arrays was observed for all four LW13 arrays in pixels with high dark currents and/or low well depths due to trap-to-band tunneling dark current. Cross-hatch patterns are generally related to the formation of misfits, generated either during growth or fabrication; further optimization of the process could potentially result in further improvements. Pixels which were operable at a temperature of 28 K and 250 mV of applied bias (∼ 90% for all four arrays) appear to be dominated by band-to-band tunneling dark current at biases greater than about 200 mV for three of the four arrays. Band-to-band tunneling is also responsible for the inoperability of these three arrays with an applied bias of 350 mV. H1RG-18509 was shown to have an improved performance at larger applied biases with the mitigation of the band-to-band tunneling presumably because of Teledyne's experimental structure, and better operability at lower bias, due to less trapto-band tunneling. At a temperature of 28 K and an applied reverse bias of 350 mV, the median dark current and well depth for this array is 1.8 e − /s and 81 ke − respectively.
These long-wave arrays which can be passively cooled in space will provide cost-savings, offer a longer operational time-frame, and entail no decrease in sensitivity-thereby improving remote sensing capabilities and performance for future space missions.
TIS has completed the growth of several 15 µm cutoff wavelength arrays, and results on those arrays will be reported separately once characterization tests and analysis are complete.