**2. Characterization of a Quantum Cascade Detector**

A schematic of the conduction band of the QC detector with a coupled-quantum-well design is shown in Figure 1a [7,11,21]. The response wavelength was determined by the energy separation between levels 7 and 1 (*E*<sup>71</sup> = 289 meV). An incident light that has an energy corresponding to *E*<sup>71</sup> associated with the electron excitation was absorbed. Due to the asymmetric conduction-band potential, the excited electrons were transferred in a preferential direction in line with the step-like energy levels formed in the sequential quantum wells. In the coupled-quantum-well design, the center of the wavefunction for the upper absorption level 7 was slightly shifted from that of level 1 to the thin well side. Consequently, longer longitudinal optical phonon scattering times (τ71~3 ps) were obtained, while the dipole length (*d*71~1.1 nm) remained almost unchanged. Additionally, reverse currents caused by electron transitions from levels 6–4 to 1 were prevented by the spatial separation via the thin well between the absorption and transport regions. As the level 7 wavefunction extended to the transport region and overlapped with that of level 6, photoexcited electrons could escape from the absorption region across the thin well and thick barrier.

All of the layer structures consisting of 90 cascade modules were grown on a semiinsulating InP substrate via metal–organic vapor-phase epitaxy. The wafer was processed into a 25-μm-wide mesa stripe and cleaved to a 100-μm length. The cleaved facet was used as the acceptance surface for strong absorption of the incident light propagating along the stripe direction. Both the thick active region of the 90 cascade modules and the narrow 25 μm × 100 μm mesa were essential to reducing the parasitic capacitance. Furthermore, to cut the device inductance, air-bridge wiring was used for electrical connection to the signal-output electrode. The device capacitance was 0.19 pF, as determined with a *C*-meter (4280A, Hewlett-Packard, Palo Alto, CA, USA), and the inductance was 0.21 nH, as calculated from the geometry of the air-bridge wiring [11]. The 3-dB cutoff frequency was estimated to be ~23 GHz, based on an equivalent circuit model, including the 1-ps ultimate electron transition time across one cascade module [11]. The experimental confirmation of the frequency response of the QC detector is shown later.

**Figure 1.** (**a**) Schematic of the conduction band and moduli squared of the relevant wavefunctions of the quantum cascade detector. The In0.53Ga0.47As/In0.52Al0.48As layer sequence of one period of the active regions, in angstroms, starting from the absorption well, is 44/**25**/9/**40**/13/**33**/14/**36**/15/**28**/25/**27**/28/**30**, where InAlAs barrier layers are in bold, InGaAs quantum-well layers are in roman type, and the doped layer (Si, 4 <sup>×</sup> <sup>10</sup><sup>17</sup> cm−3) is underlined. (**b**) Photoresponse spectrum of the device measured without cooling. (**c**) Dark current–voltage characteristics over the temperature range 220–300 K. (**d**) Arrhenius plot of the measured differential resistance. The red line is the fit of the Arrhenius model, *L* = Aexp[*E*act/*k*B*T*], where *L* is lifetime, A is a constant, *E*act is the activation energy, *k*<sup>B</sup> is Boltzmann's constant, and *T* is the device temperature.

Figure 1b shows a response spectrum of the uncooled QC detector obtained with a Fourier-transform infrared spectrometer (Nicolet 8700, Thermo Fisher Scientific, Waltham, MA, USA). The peak response wavelength was 4.6 μm (2160 cm<sup>−</sup>1, 267 meV), and *E*<sup>71</sup> was less than the calculated value of 287 meV. The reason for this difference was because of the insufficient band offset for the higher 7 and 8 energy levels. The energy difference for the second peak, which appeared at a shorter wavelength region, was ~30 meV because of weaker quantum confinement near the top of the barrier height. This difference between design and experiment could be reduced by applying a strain-compensated condition in the InGaAs/InAlAs or by using other wide-bandgap materials, as in shorter-wavelength QC detectors [8,10].

The dark voltage–current characteristics measured at various temperatures over 220–300 K, with 20 K intervals, are shown in Figure 1c. An asymmetric behavior originating from the band structure was observed. Figure 1d is an Arrhenius plot of the differential resistances at zero bias. The estimated activation energy of the device was 251 meV, which corresponded to the transition energy between *E*<sup>61</sup> (264 meV) and *E*<sup>51</sup> (228 meV). This indicated that the dark current induced by the transition from the ground level 1 to the 5–2 levels in Figure 1a was suppressed in the coupled-quantum-well design.

Figure 2a plots the output photocurrent as a function of the incident light power. The incident light was the 2220 cm−<sup>1</sup> continuous wave (CW) distributed-feedback QC laser described below. The photoresponse exhibits good linearity with the incident light power up to 250 mW; the slope derived from the linear fit was estimated to be 4.7 mA/W for the specific wavelength of 2220 cm−<sup>1</sup> (without compensation for the coupling losses from the focusing lens, surface reflections of the optics, and the cleaved facet acceptance area of the QC detector). Simultaneously, the peak responsivity at 2160 cm−<sup>1</sup> was 5.7 mA/W, determined from the ratio of the signal intensities between the two wavelengths in the response spectrum in Figure 1b. Figure 2b plots the current noise power spectrum density of the QC detector at room temperature, obtained with a low-noise current amplifier (LCA-40K-100M, FEMTO, Berlin, Germany) and an audio analyzer (SR1, Stanford Research Systems, Sunnyvale, CA, USA). At frequencies higher than 100 Hz, the measured flat noise level matched the calculated Johnson–Nyquist noise level for an 89-kΩ device resistance. Due to the excellent low noise in bias-free operation, the detectivity was improved despite the low responsivity relative to other MIR detectors. The calculated noise-equivalent power was 7.7 × <sup>10</sup>−<sup>11</sup> W/Hz1/2, with a peak responsivity and flat noise level of 4.4 × <sup>10</sup>−<sup>13</sup> A/Hz1/2.

**Figure 2.** (**a**) Measured photocurrent vs. incident light power of the 2220-cm−<sup>1</sup> distributed-feedback quantum cascade (QC) laser. The measured results are plotted as square black dots, and the red line is a linear fit. (**b**) Current noise power spectrum density of the QC detector at room temperature (no cooling). The red dashed line indicates the Johnson–Nyquist noise level calculated from 4*k*B*T*/*R*, where *k*<sup>B</sup> is Boltzmann's constant, *T* is the device temperature, and *R* is the device resistance.
