Temperature Dependence Study of Electrical and Electro-Optical Performances of Midwave Infrared Ga-Free T2SL Barrier Photodetector

: In this paper, we report on temperature dependence performances of a midwave infrared (MWIR) Ga-free InAs/InAsSb type-II superlattice (T2SL) barrier (XBn) photodetector grown by molecular beam epitaxy on n-type GaSb substrate. The T2SL structure, with a 3 µ m thick active region, was processed in a mesa device in order to perform dark current measurements and spectral photoresponse as a function of temperature. Analyses of these temperature dependence characterizations help us to improve the design of Ga-free T2SL MWIR XBn detectors. PL measurements, we can extract the peak position to verify the bandgap energy of the T2SL structure, the full-width-at-half-maximum (FWHM) and integrated intensity to evaluate the material quality, and the temperature-dependent spectra. PL measurements of these samples placed in a liquid nitrogen (LN2)-cooled JANIS cryostat, optically pumped with an 835 nm ﬁber-coupled GaAs diode laser, were collected using a Nicolet-870 Nexus Fourier transform infrared (FTIR) spectrometer. The absorption spectrum was deduced from the transmission measured by the FTIR spectrometer and the absorption coefﬁcient was extracted from the ratio with the transmission measurement performed on the same GaSb substrate alone with no epilayers deposited on it.

Temperature dependence investigation of dark current measurements and quantum efficiency is an efficient way to characterize an infrared photodetector, and consequently to understand the transport of minority carriers in the T2SL device. Indeed, in a well-designed XBn detector, the dark current should be diffusion-limited whatever the temperature, and the depletion region must be confined only to the barrier layer. If not, the identification of additional current mechanisms, such as generation-recombination (GR), trap-assisted tunneling (TAT) and leakage currents, is important to determine the reasons for malfunctioning. At a given temperature, the operating voltage (Vop), for which the photoresponse (PR) value saturates, must be as low as possible. In this XBn structure, the Vop value is directly linked to the presence of a valence band offset between the barrier layer (BL) and the absorbing layer (AL), impeding the transport of minority carriers. Moreover, the PR value and its evolution as a function of temperature is essential to determine the optimized AL thickness inducing the highest quantum efficiency (QE).
We studied the influence of temperature on the electrical and electro-optical performances of a MWIR Ga-free T2SL XBn detector, grown by MBE on n-type GaSb substrate, in order to improve the design and fabrication of the structure and device, compatible with an operating temperature as high as 150 K.

Materials and Methods
The Ga-free InAs/InAsSb T2SL structure, strained balanced to GaSb substrate, must be chosen in terms of superlattice period (p) and antimony (Sb) composition to address the full MWIR domain but also to optimize the absorption coefficient, as the InAs/InAsSb heterostructure presents a type II-b band offset where electrons are confined in the binary layer (InAs) while holes are strongly confined in the InAsSb alloy [4,11,29]. The chosen T2SL structure consists of InAs (4.17 nm)/InAs 0.63 Sb 0.37 (1.42 nm). Two types of T2SL structure samples were grown on 2-inch n-type (Te-doped) GaSb (100) substrate by MBE using a 412 RIBER Machine.
The goal of first structure sample (Figure 1a) is to study material properties as a function of temperature. Such samples, consisting of a 3 µm thick InAs/InAsSb T2SL layer on GaSb substrate, are dedicated to absorption and photoluminescence (PL) measurements. From PL measurements, we can extract the peak position to verify the bandgap energy of the T2SL structure, the full-width-at-half-maximum (FWHM) and integrated intensity to evaluate the material quality, and the temperature-dependent spectra. PL measurements of these samples placed in a liquid nitrogen (LN2)-cooled JANIS cryostat, optically pumped with an 835 nm fiber-coupled GaAs diode laser, were collected using a Nicolet-870 Nexus Fourier transform infrared (FTIR) spectrometer. The absorption spectrum was deduced from the transmission measured by the FTIR spectrometer and the absorption coefficient was extracted from the ratio with the transmission measurement performed on the same GaSb substrate alone with no epilayers deposited on it. 3 of 12 analyzed with a Yokogawa oscilloscope. Following the approach of Donetsky et al. [33], minority carrier lifetime as a function of temperature was extracted.

FOR PEER REVIEW
(a) (b) From epitaxial T2SL structures, circular mesa photodetectors with diameters ranging from 60 to 310 µm were fabricated using standard photolithography techniques. Mesa The second structure of interest is the XBn T2SL detector structure (Figure 1b). From bottom to top, the XBn structure consists of a 400 nm Te-doped (n-type) GaSb buffer layer, which is followed by a 100 nm thick n-type doped InAs (4.17 nm)/InAs 0.63 Sb 0.37 (1.42 nm) T2SL and by non-intentionally doped (nid) 3 µm thick AL (536 periods) made of the same T2SL structure. A BL is then made from 120 nm nid AlAs 0.09 Sb 0.91 , and finally, the contact layer (CL) of the structure is composed of an 80 nm thick nid T2SL. The AL, CL and BL are undoped, and the residual doping is expected to be n-type for the two first layers and p-type for the third one [18].
Prior to device fabrication, several material characterizations were routinely performed, such as high-resolution X-ray diffraction (HR-XRD) scanning to evaluate the structural quality of the XBn sample and its lattice mismatch with the GaSb substrate, atomic force microscope (AFM) images to assess the surface roughness and morphology, additional PL spectra and time-resolved photoluminescence (TRPL) measurements to extract the minority carrier lifetime. For TRPL measurements, a 1.55 µm laser pulse with a FWHM less than 1 ns was used to generate excess carriers. The power of the laser is tunable and measurements were performed at a given laser pulse fluence. The photoluminescence signal was detected with a HgCdTe photodiode from Vigo (PVMI-3 TE-8) and analyzed with a Yokogawa oscilloscope. Following the approach of Donetsky et al. [33], minority carrier lifetime as a function of temperature was extracted.
From epitaxial T2SL structures, circular mesa photodetectors with diameters ranging from 60 to 310 µm were fabricated using standard photolithography techniques. Mesa photodetectors were realized by isotropic wet chemical etching using a citric acid solution and with no use of specific surface treatment. Deep-etched mesa devices below the AL were performed and polymerized photoresist was spun after the wet etching to protect the mesa surface from ambient air. Metal coatings were finally applied on top of the mesa (n-type T2SL cap layer) and on the back of the n-type GaSb substrate, in Ti/Au (40/150 nm) and Pd/AuGeNi (5/200 nm), respectively.
Next, the samples were wire-bonded onto a pin leadless chip carrier (LCC) and placed in the LN2-cooled JANIS cryostat ready to perform electrical and electro-optical measurements. Dark current density-voltage (J-V) measurements (under a 0-degree field of view) were performed using a KEITHLEY 6517A Electrometer to apply the bias voltage and measure the current density delivered by the device. Capacitance-voltage (C-V) characterizations were carried out using a Boonton 72B coupled with a programmable source meter (Keithley 2400) and a programmable multimeter (Keithley 2000). The measurements were performed at fixed AC voltage (15 mV) and frequency (1 MHz). Photoresponse measurements were performed in front-side illumination using a VERTEX 70v FTIR spectrometer. The quantum efficiency (QE) was measured using a black-body source cavity CI Systems SR-200 with temperatures ranging from 973 K to 1273 K and a narrow bandpass filter [3 µm; 3.5 µm]. The QE value was then extracted from the slope of the photocurrent versus the incident flux [34].
Absorption, PL, TRPL, QE and dark current density measurements were performed as functions of temperature, and the results are discussed in the next section. Figure 2 shows the absorption coefficient for temperature ranging from 90 K to 220 K. At λ = 3.4 µm, the absorption coefficient α reaches 4800 cm −1 at 150 K, in agreement with other values reported elsewhere [7,20,28]. The absorption band edge shows a wavelength red-shift with increasing temperature, while the absorption value remains relatively constant. PL spectra, presented in Figure 3, display a shift in PL peak from 4.89 µm to 5.70 µm in the temperature range (77-250 K). Such values confirm that the Ga-free T2SL structure is relevant for the MWIR spectral domain.   PL spectra, presented in Figure 3, display a shift in PL peak from 4.89 µm to 5.70 µm in the temperature range (77-250 K). Such values confirm that the Ga-free T2SL structure is relevant for the MWIR spectral domain. PL spectra, presented in Figure 3, display a shift in PL peak from 4.89 µm to 5.70 µm in the temperature range (77-250 K). Such values confirm that the Ga-free T2SL structure is relevant for the MWIR spectral domain.   The T2SL's bandgap energy, extracted from the PL peak, as a function of temperature (E g (T)) is shown in the inset of Figure 3, and a fitting curve (solid line) was plotted using the Einstein Oscillator model [8] through the equation E g (T) = E 0 -α × (T E /(exp(T E /T) − 1)), where α = 2.013 × 10 −4 meV/K stands for the slope of the high-temperature linear asymptote, E 0 = 258 meV stands for the energy gap at T = 0 K, T E = 117.6 K stands for the Einstein temperature and T is the absolute temperature. This fitting of the bandgap as a function of temperature will be used to analyze dark current density measurements performed on devices (see Section 3.3).

Absorption, Photoluminescence and Time-Resolved Photoluminescence Measurements
TRPL measurements were performed on the XBn T2SL structure (Figure 1b) to determine the minority carrier lifetime as a function of temperature ( Figure 4). A lifetime value of 1 µs was extracted from these measurements for temperature ranging from 90 K to 220 K. As a consequence, since this value remains constant in this range of temperature, the minority carrier lifetime is limited by SRH processes [35]. Moreover, a lifetime value as high as 1 µs at 150 K validates the MBE growth of the Ga-free XBn InAs/InAs 0.63 Sb 0.37 T2SL structure sample ready for device processing.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 5 of 12 The T2SL's bandgap energy, extracted from the PL peak, as a function of temperature (Eg(T)) is shown in the inset of Figure 3, and a fitting curve (solid line) was plotted using the Einstein Oscillator model [8] through the equation Eg(T) = E0 -α × (TE/(exp(TE/T) − 1)), where α = 2.013 × 10 −4 meV/K stands for the slope of the high-temperature linear asymptote, E0 = 258 meV stands for the energy gap at T = 0 K, TE = 117.6 K stands for the Einstein temperature and T is the absolute temperature. This fitting of the bandgap as a function of temperature will be used to analyze dark current density measurements performed on devices (see Section 3.3).
TRPL measurements were performed on the XBn T2SL structure (Figure 1b) to determine the minority carrier lifetime as a function of temperature (Figure 4). A lifetime value of 1 µs was extracted from these measurements for temperature ranging from 90 K to 220 K. As a consequence, since this value remains constant in this range of temperature, the minority carrier lifetime is limited by SRH processes [35]. Moreover, a lifetime value as high as 1 µs at 150 K validates the MBE growth of the Ga-free XBn InAs/InAs0.63Sb0.37 T2SL structure sample ready for device processing.  Figure 5a,b displays the QE as a function of temperature for two operating bias voltages Vb equal to −0.2 V and −0.4 V, respectively. The detector cut-off wavelength is 5 µm at 150 K, and a QE value higher than 50% is extracted (without anti-reflection coating (ARC)), which is a remarkable value considering the absorption coefficient and the low hole mobility in the T2SL structure [31,32]. Nevertheless, it may be observed that the QE values are strongly dependent on the applied voltage in the considered temperature range (77-220 K).

Quantum Efficiency Measurements
For Vb = −0.2V, we can observe (Figure 5a) that the 50% QE value is not reached for temperatures below 200 K. This may be due to the presence of an unwanted valence band offset (VBO) between the AL and BL which impedes the transport of hole minority  Figure 5a,b displays the QE as a function of temperature for two operating bias voltages Vb equal to −0.2 V and −0.4 V, respectively. The detector cut-off wavelength is 5 µm at 150 K, and a QE value higher than 50% is extracted (without anti-reflection coating (ARC)), which is a remarkable value considering the absorption coefficient and the low hole mobility in the T2SL structure [31,32]. Nevertheless, it may be observed that the QE values are strongly dependent on the applied voltage in the considered temperature range (77-220 K). carriers. This is not the case for Vb = −0.4V (Figure 5b), where this barrier seems to be overcome, resulting in higher QE values at low temperatures before saturation at 200 K.  Figure 6 displays the QE values measured at λ = 3.4 µm for different applied biases in the temperature range (77-220 K). The QE increases from 32% at T = 77 K and Vb = −0.4 V to reach 54% at T = 200-220 K and Vb = −0.3 V. This evolution with temperature is due to an increase in the hole minority carrier vertical diffusion length (along the growth axis), since absorption and lifetime measurements (Figure 2 and Figure 4, respectively) showed no significant evolution in this temperature range. Moreover, a slope of the QE can be observed, mainly at low temperature. This slope is a signature of a non-optimized device in the considered range of temperature. Indeed, if the AL thickness is longer than the vertical diffusion length of the minority carriers, some of the photo-generated carriers For Vb = −0.2V, we can observe (Figure 5a) that the 50% QE value is not reached for temperatures below 200 K. This may be due to the presence of an unwanted valence band offset (VBO) between the AL and BL which impedes the transport of hole minority carriers. This is not the case for Vb = −0.4V (Figure 5b), where this barrier seems to be overcome, resulting in higher QE values at low temperatures before saturation at 200 K. Figure 6 displays the QE values measured at λ = 3.4 µm for different applied biases in the temperature range (77-220 K). The QE increases from 32% at T = 77 K and Vb = −0.4 V to reach 54% at T = 200-220 K and Vb = −0.3 V. This evolution with temperature is due to an increase in the hole minority carrier vertical diffusion length (along the growth axis), since absorption and lifetime measurements (Figures 2 and 4, respectively) showed no significant evolution in this temperature range. Moreover, a slope of the QE can be observed, mainly at low temperature. This slope is a signature of a non-optimized device in the considered range of temperature. Indeed, if the AL thickness is longer than the vertical diffusion length of the minority carriers, some of the photo-generated carriers recombine before reaching the CL. Thus, an increase in the depletion width with the bias is necessary to promote the full collection of minority carriers. However, the QE begins to saturate at high temperature ( Figure 6). Indeed, taking into account minority carrier lifetime and mobility values in the Ga-free T2SL structure [32], the vertical diffusion length increases with the temperature, allowing better collection of photo-generated carriers. At 150 K, a slight QE slope remains, while at 220 K, the QE completely saturates for biases lower than the operating bias (Vb= −0.4 V). A QE value higher than 55% highlights that the transport of hole minority carriers is optimized at this temperature, but not completely at the 150 K targeted temperature operation. Indeed, at this temperature, the hole vertical diffusion length was estimated at around 3 µm [32], in agreement with the chosen AL thickness.

Quantum Efficiency Measurements
Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 1 recombine before reaching the CL. Thus, an increase in the depletion width with the bia is necessary to promote the full collection of minority carriers. However, the QE begins to saturate at high temperature ( Figure 6). Indeed, taking into account minority carrier life time and mobility values in the Ga-free T2SL structure [32], the vertical diffusion length increases with the temperature, allowing better collection of photo-generated carriers. A 150 K, a slight QE slope remains, while at 220 K, the QE completely saturates for biase lower than the operating bias (Vb= −0.4 V). A QE value higher than 55% highlights tha the transport of hole minority carriers is optimized at this temperature, but not completely at the 150 K targeted temperature operation. Indeed, at this temperature, the hole vertica diffusion length was estimated at around 3 µm [32], in agreement with the chosen AL thickness.  Figure 7 shows typical J-V characteristics carried out for a 210 µm diameter detecto in the temperature range (120-270 K). At the 150 K targeted temperature operation, dark current density as low as 3.5 × 10 −5 A/cm 2 is recorded. Such a result must be improved since when compared to the MCT state-of-the-art photodiode limited by diffusion dark current [36], the current is 20 times higher at the corresponding cut-off wavelength. Nev ertheless, this value remains in agreement with the most recent results reported on Ga free T2SL detectors [14,15,[17][18][19][20][21].

Dark Current-Voltage and Capacitance-Voltage Measurements
From the dark J-V characteristics, transport regimes in the barrier detector can b identified by plotting the dynamic resistance area product RdA = (δJ/δV) −1 , where A is th area of the device (210 µm diameter). Through the shape of the displayed curves in Figur 8, we can identify the main dark current regimes and analyze the QE spectra recorded ( Figure 5).
The first significant bias value is the turn-on voltage (Von). This bias is located at th first RdA minimum and its value decreases when the temperature increases, from 260 mV to 85 mV in the temperature range (130-210 K). Below Von, the minority carriers ar blocked due to the presence of the VBO in addition to the possible potential barrier du to the difference in doping between AL and CL. Above the reverse bias Von, the minority  Figure 7 shows typical J-V characteristics carried out for a 210 µm diameter detector in the temperature range (120-270 K). At the 150 K targeted temperature operation, dark current density as low as 3.5 × 10 −5 A/cm 2 is recorded. Such a result must be improved, since when compared to the MCT state-of-the-art photodiode limited by diffusion dark current [36], the current is 20 times higher at the corresponding cut-off wavelength. Nevertheless, this value remains in agreement with the most recent results reported on Ga-free T2SL detectors [14,15,[17][18][19][20][21].

Dark Current-Voltage and Capacitance-Voltage Measurements
From the dark J-V characteristics, transport regimes in the barrier detector can be identified by plotting the dynamic resistance area product R d A = (δJ/δV) −1 , where A is the area of the device (210 µm diameter). Through the shape of the displayed curves in Figure 8, we can identify the main dark current regimes and analyze the QE spectra recorded (Figure 5).
At the targeted temperature of 150 K, Vop = −400 mV and the corresponding RdA product is equal to 2.5 × 10 4 Ω.cm 2 (Figure 8). Then, over Vop, the next visible RdA minimum VGR indicates the beginning of the generation-recombination (GR) regime. At this bias, the barrier is fully depleted and the depletion region expands into the absorber, which explains the appearance of the electric field-related GR current. Such behavior is only observed at low temperature since the device is diffusion current-limited for temperatures higher than 170 K.  is equal to 2.5 × 10 4 Ω.cm 2 ( Figure 8). Then, over Vop, the next visible RdA minimum VGR indicates the beginning of the generation-recombination (GR) regime. At this bias, the barrier is fully depleted and the depletion region expands into the absorber, which explains the appearance of the electric field-related GR current. Such behavior is only observed at low temperature since the device is diffusion current-limited for temperatures higher than 170 K.   The first significant bias value is the turn-on voltage (Von). This bias is located at the first R d A minimum and its value decreases when the temperature increases, from 260 mV to 85 mV in the temperature range (130-210 K). Below Von, the minority carriers are blocked due to the presence of the VBO in addition to the possible potential barrier due to the difference in doping between AL and CL. Above the reverse bias Von, the minority carriers can flow unimpeded through the barrier detector, and the quantum efficiency value becomes higher than 80% of its maximum value ( Figure 6). We can remark that the higher the temperature, the lower the required voltage.
Next, the device reaches the operating voltage Vop. It is defined as the bias at which the maximum R d A product is obtained and is linked to the photoresponse spectra. At this particular Vop bias, the photonic current/quantum efficiency begins to saturate (Figure 6). At the targeted temperature of 150 K, Vop = −400 mV and the corresponding R d A product is equal to 2.5 × 10 4 Ω.cm 2 (Figure 8). Then, over Vop, the next visible R d A minimum V GR indicates the beginning of the generation-recombination (GR) regime. At this bias, the barrier is fully depleted and the depletion region expands into the absorber, which explains the appearance of the electric field-related GR current. Such behavior is only observed at low temperature since the device is diffusion current-limited for temperatures higher than 170 K.
Finally, extracted from J-V curves of Figure 7, dark current densities at Vop = −400 mV are reported as a function of 1/k B T (Arrhenius plot) in Figure 9, where k B is the Boltzmann constant.  A fit over the temperature range (150-270 K) using the expressio yields an activation energy Ea = 230 meV, which is approximately bandgap (Eg) in this temperature range, signature of a diffusion-limite temperature range (120-150 K), the activation energy is 117 meV, appro of the T2SL bandgap (Eg/2), indicating that the dark current is GR-limite ence of a depletion region extending into the AL.
To determine residual carrier concentrations, both in the nid p-ty type AL (Nres), C-V measurements were performed [18]. From these me ical 1/C 2 curve as a function of voltage at T = 150 K is shown in Figure 10 Von, the extracted slope leads to Pres = 2.7 × 10 16 cm −3 in the BL while t reverse voltage,(above the operating voltage Vop) leads to Nres = 3.2 × 1 A fit over the temperature range (150-270 K) using the expression A exp(-E a /k B T) yields an activation energy E a = 230 meV, which is approximately the T2SL energy bandgap (E g ) in this temperature range, signature of a diffusion-limited behavior. In the temperature range (120-150 K), the activation energy is 117 meV, approximately one half of the T2SL bandgap (E g /2), indicating that the dark current is GR-limited, due to the presence of a depletion region extending into the AL.
To determine residual carrier concentrations, both in the nid p-type BL (P res ) and n-type AL (N res ), C-V measurements were performed [18]. From these measurements, a typical 1/C 2 curve as a function of voltage at T = 150 K is shown in Figure 10. For biases below Von, the extracted slope leads to P res = 2.7 × 10 16 cm −3 in the BL while the slope at higher reverse voltage,(above the operating voltage Vop) leads to N res = 3.2 × 10 15 cm −3 in the AL. The residual doping, one order of magnitude higher in the BL, induces the presence of the electric field in the AL, even when no bias is applied.
ical 1/C 2 curve as a function of voltage at T = 150 K is shown in Figure 10. For Von, the extracted slope leads to Pres = 2.7 × 10 16 cm −3 in the BL while the slo reverse voltage,(above the operating voltage Vop) leads to Nres = 3.2 × 10 15 cm The residual doping, one order of magnitude higher in the BL, induces the pr electric field in the AL, even when no bias is applied.

Conclusions
The temperature dependence performances of MWIR Ga-free T2SL barrier photodetector have been reported.
At the expected temperature operation (T = 150 K), the quantum efficiency of the device, with no ARC, as high as 50% was achieved, but it is necessary to apply −400 mV (Vop) to reach this QE value. This means that there is a valence band barrier blocking the minority heavy hole carriers remaining at the AL/BL interface. A dark current density of the device as low as 3.5 × 10 −5 A/cm 2 was recorded. This result is on par with the state of the art, but the Arrhenius plot extracted from J-V measurements as a function of temperature shows that at temperatures lower than 150 K, the device is GR-limited, evidencing the presence of an unwanted electric field in the T2SL AL. Such a presence is consistent with C-V measurements showing higher residual doping in the BL.
The results obtained in this study highlight that the main problems are the presence of the electric field in the AL and a valence band offset at the BL-AL interface impeding the flow of minority carriers. To overcome these problems, a study of the AlAsSb BL must be conducted in terms of doping, thickness layer and alloy composition. This will be the subject of forthcoming investigations. Funding: This work was partially funded by the French "Investment for the Future" program (EquipEx EXTRA, ANR 11-EQPX-0016) and by the French ANR under project HOT-MWIR (ANR-18-CE24-0019-01).

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author upon reasonable request.