Design and performance of GaSb-based quantum cascade detectors

2.1 Principles and growth analysis

Due to the intersubband character of QCDs, they are only sensitive to illumination polarized parallel to the growth direction (out-of-plane polarization) [25]. In contrast to the 300 K band gap of 0.36 eV [21] of InAs substrates, the larger 0.73 eV [21] band gap of GaSb allows for illumination through the substrate in the standard 45°-facet double-pass method for wavelengths ≳1.7 µm, compared to 3.44 µm for InAs. On GaSb substrates, InAs layers have a tensile mismatch of 0.62 %, and AlSb layers have a compressive mismatch of −0.64 %. The critical layer thickness on GaSb, calculated with the formula of Matthews and Blakeslee’s [26], is for both materials approximately 35 nm. A strain-compensated growth of InAs/AlSb on GaSb is therefore achieved with an InAs:AlSb layer-thickness-ratio of 0.96:1, which would result in approximately equally thick barriers and wells. Considering the necessary InAs well thicknesses of a QCD design for 4.3 µm is between 2.95 and 7.2 nm, equal-thickness AlSb barriers would drastically reduce the QCD’s figures of merit, due to an insufficient extraction efficiency. To optimize a QCD design, it is necessary to change the well and barrier thicknesses independently of each other, especially because of the high CBO, the AlSb barriers need to be thinner than conventional designs. One trick to achieving this lies in designing the interfaces. Since InAs and AlSb do not have any constituents in common, one of two interfaces can form at the interface between the well and barrier, either InSb or AlAs. To achieve strain-balancing with decreasd AlSb barrier thickness, one needs a material with a compressive mismatch to GaSb, which is given for InSb with a −5.92 % mismatch. Previous studies on InAs/AlSb superlattices found increased carrier mobility for InSb interfaces compared to AlAs interfaces [27], thus making them the preferred interfaces. Due to the high mismatch of InSb to GaSb, submonolayer thick InSb layers are sufficient to strain-balance an optimized InAs/AlSb QCD design, with the advantage that such thin InSb layers do not influence the band structure design. For the QCD growth, the submonolayer thick InSb layers were first calculated and then experimentally calibrated by strain-balanced test structures. The process proved itself to be reproducible, as determined by HR-XRD. To achieve sharp interfaces and limit the As-for-Sb exchange [28], shutter sequences and shutter opening times were developed similarly to Refs. [27, 29, 30].

In the following, the results of the four InAs/AlSb QCD designs on GaSb ranging from 3.65 to 5.5 µm are presented. The QCDs are designed using an eight-band k⋅p-method, including scattering mechanisms such as longitudinal optical (LO) and acoustic phonon scattering, as well as interface roughness scattering, and alloy scattering. Figure 1 shows the active region band structure design for each QCD, where (a) is the 3.65 µm design, (b) the first design for 4.3 µm, referred to as the 4.3a µm design, (c) the second design for 4.3 µm, referred to as the 4.3b μm design, and (d) the 5.5 µm design. The conduction band edge is depicted in dark gray, and the valence band edge is in blue. The designs are based on a vertical optical transition. The optical well is the first well of each structure. The blue contour of the probability density, mainly in the first well, corresponds to the electron occupation. Once the transition occurs due to photon absorption, the electrons are extracted from the first excited state in the first well, which is nearly resonant to the first state of the extraction region. The energy separation of the next states and the thin barriers allow for sub-picosecond scattering times along the extractor ladder. To ensure reduced thermal backfilling, the lowest extractor state has a higher energy separation from the ground state of the next optical transition. This increases the electron lifetime in the ground level of the optical well and benefits the absorption efficiency. Design 4.3b μm corresponds to a refined version of design 4.3a µm with thinner barriers and a higher energy separation of the last extractor state to the next optical ground state, which allows for reduction of the active region by one well and barrier in the extractor, increasing the extraction efficiency. The blue lines extending into the InAs conduction band stem from the valence band of the submonolayer thick InSb strain-balancing layers. The layers are too thin to allow states in the InSb to form. The areas drawn in light gray correspond to the band gap. Due to the type-II band alignment of InAs/AlSb and the small band gap of InAs, interband transitions in the MIR to near-infrared (NIR) are expected.

Figure 1:

Band diagrams for the four designs from 3.65 to 5.5 µm. Shown are the probability densities of the energy levels, where the first well corresponds to the optical transition well. The blue contour, mainly in the ground state of the optical well, corresponds to the electron occupancy. The active region was repeated 20 times for all devices. The conduction band edge is dark gray, the valence band is blue, the dashed blue line is the light-hole valence band, and the solid blue line is the heavy-hole valence band of the InAs/AlSb material system, the band gap is light gray. The blue peaks reaching into the InAs conduction band are the submonolayer InSb layers valence bands. (a) 3.65 µm peak responsivity with the layer sequence in nm: 1.80, 6.30, 1.80, 2.55, 1.80, 2.65, 1.60, 2.70, 1.50, 2.90, 1.60, 3.20, 1.60, 3.35, 1.50, 3.50, 1.80, and 4.0. (b) 4.3 µm peak responsivity (design 4.3a) with the layer sequence in nm: 1.80, 7.20, 1.80, 2.95, 1.80, 3.20, 1.60, 3.30, 1.50, 3.40, 1.60, 3.50, 1.60, 3.60, 1.50, 3.80, 1.80, and 4.30. (c) 4.3 µm peak responsivity (design 4.3b) with the layer sequence in nm: 1.50, 7.20, 1.80, 2.95, 1.80, 3.20, 1.60, 3.30, 1.50, 3.40, 1.50, 3.45, 1.50, 3.75, 1.70, and 4.15. (d) 5.5 µm peak responsivity with the layer sequence in nm: 1.60, 8.85, 1.80, 3.70, 1.80, 3.80, 1.80, 4.0, 1.80, 4.20, 1.80, 4.40, 1.80, 4.80, 1.80, 5.20, 1.80, and 5.80. The boldly printed layers are the AlSb barriers, and the underlined well is Te doped 8 × 10¹⁷ cm⁻³.

The four QCDs were grown by molecular beam epitaxy with a Riber Compact 21 and are doped with Te, since Si exhibits strong amphoteric behavior in Sb-compounds. Therefore, Te avoids unwanted p-type doping in AlSb barriers that could result from Si dopant diffusion into the barriers. The active regions consist of 20 periods grown between 200 nm-thick short-period InAs/AlSb superlattice contacts, where the InAs wells are Te doped to 3 × 10¹⁸ cm⁻³. Additional transition layers from the GaSb substrate to the superlattice contact and from the superlattice contact to the active region were necessary for the final device design.

Figure 2 shows the growth analysis of all QCDs, where (a–c) correspond to the 3.65 µm design, (d–f) to the 4.3a µm design, (g–i) to the 4.3b μm design, and (j–l) to the 5.5 µm design. The growth was analyzed using three methods: High-resolution X-ray diffraction (HR-XRD) ω-2θ scans with a Philips MRD Pro, left column, HR-XRD (224) reciprocal space maps, middle column, and atomic force microscopy (AFM) with a Veeco Dimension V, right column.

Figure 2:

Growth analysis of the InAs/AlSb QCDs on GaSb of (a), (b), & (c) design 3.65 µm, (d), (e), & (f) design 4.3a µm, (g), (h), (i) design 4.3b μm, and (j), (k), & (l) design 5.5 µm: left: HR-XRD (004) ω-2θ scans, middle: HR-XRD 0.5° × 0.5° (224) reciprocal space maps, and right: 3 × 3 µm AFM scans with a root-mean-square surface roughness of (c) 0.188 nm, (f) 0.171 nm, (i) 0.197 nm, and (l) 0.165 nm.

As observed in the HR-XRD ω-2θ scans, the highest intensity peak is the substrate followed by the zeroth-order active region peak, where good strain balancing is observed for all QCDs. The third peak to the left corresponds to the zeroth-order short-period contact superlattice peak. The modulation between 29.6 and 30.0° stems from a 20 nm-thick highly-doped InAs layer top contact. The sharp peaks observed in all scans indicate low interface roughness. The (224) reciprocal space maps of the QCDs show a perfectly vertical intensity contour, which indicates a fully strained material growth. From the intensity maxima, no increased mosaic spread (which shows high crystal quality), interface roughness, or growth rate fluctuations are apparent, which would result in horizontal or vertical broadening of higher-order peaks [31]. AFM scans of a 3 × 3 µm surface of the QCDs confirm the low interface roughness with low root-mean-square surface roughness values of 0.188 nm for the 3.65 µm design, 0.171 nm for the 4.3a µm design, 0.197 nm for the 4.3b μm design, and 0.165 nm for the 5.5 µm design.

2.2 Fabrication and optical characterization

The QCDs were fabricated into the 45°-facet double-pass geometry, a standard structure for intersubband device characterization, which allows a comparison to QCD devices in literature [10]. Figure 3 depicts a sketch of the measurement setup, including the fabricated QCD and its light-coupling mechanism. For this configuration, a facet under an angle of 45° is polished substrate-side onto the wafer edge of the QCD. The device is then illuminated through the substrate, with the facet oriented normal to the light source. Due to the intersubband selection rule, the QCD structure is only sensitive to light polarized out-of-plane, with respect to the quantum well. However, due to the 45° measurement geometry of the QCD, out-of-plane polarized light is coupled in at an angle of 45° and therefore still contains both polarizations (mixed).

Figure 3:

Schematic measurement setup for responsivity measurements of QCDs. The measurements were performed using an FTIR with a MIR Globar source. The QCDs were fabricated into the 45°-facet double-pass configuration. The current output of the QCDs is fed as an analog voltage signal back to the FTIR by the transimpedance amplifier. For mixed (both)/in-plane polarization measurements, a MIR polarizer is placed before the lens.

The QCDs are fabricated into 150 × 150 µm mesas, which were defined by a Cl/Ar dry etching process using an inductively coupled plasma (ICP) process, resulting in smooth, slightly positively sloped sidewalls. The top contact (10/380 nm Ti/Au) is on top of the mesa, and the bottom contact (10/380 nm Ti/Au) is on the backside of the n-type 1–4 × 10¹⁷ cm⁻³ doped GaSb substrate.

Next, the QCDs were optically characterized with a Bruker Vertex 70v Fourier-transform infrared spectrometer (FTIR) with a Globar as a broadband unpolarized light source and a Thorlabs PDA200C transimpedance amplifier to obtain the responsivity and detectivity. For this, the following steps were performed at ambient conditions [32]:

The spectrum of the Globar, its beam spot profile, and the power of the entire beam spot were recorded in the measurement configuration with an Ophir Laserstar detector. As the Globar beam spot is significantly larger than the QCD mesa, only the incident light intensity P _ω on the mesa area was considered, using the highest intensity area of the beam spot. For each QCD, the spectrum of 3–4 mesas was recorded under the same conditions, and current–voltage (I–V) characteristics in aligned and dark conditions were measured with a Keithley 2612B. To obtain the responsivity, the photocurrent I _p was extracted from the aligned I–V measurements at 0 V, where the dark current at 0 V was subtracted.

The responsivity spectrum R _p is obtained by

where I(f) is the spectrally resolved photocurrent, with I _p = ∫I(f)df, and P(f) is the spectrally resolved Globar incident light intensity with P _ω = ∫P(f)df. The specific Johnson noise limited detectivity D was obtained using [10]:

where R ₀ A is the differential resistance optical area product of the device at zero bias, k _B is the Boltzmann constant, and T is the temperature.