INTRODUCTION

Quantum-cascade lasers (QCLs) in the mid-infrared range are of particular interest for systems used to detect chemical elements and various gases [1–5]. Small geometrical dimensions allow the integration of several ring QCLs and hollow waveguides on one substrate, letting us build systems capable of detecting multiple gases in a mixture. The compactness of the QCL ring resonator and the absence of mirrors allows continuous generation at room temperature with the extraction of surface radiation [6]. Selecting the period of the second-order diffraction grating ensures the surface extraction of radiation along the normal to the QCL surface [7, 8]. Using a double phase shift in a second-order diffraction grating yields focused radiation with maximum intensity at the center of the far field [9–11].

This work presents results from manufacturing and studying the characteristics of surface-emitting QCLs in the spectral range of 7.5–8.0 μm, equipped with a ring resonator and a second-order diffraction grating with a double phase shift to extract radiation. We used focused ion beam etching (direct ion lithography) to create a diffraction grating that had an elevated coefficient of coupling and covered the entire surface of the ring resonator. Such lithography is an alternative to the reactive ion etching of the upper plate of the waveguide [6, 12–15] or the selective liquid etching of the InGaAs layer of with the subsequent deposition an InP layer [16].

EXPERIMENTAL

Our QCL heterostructure was grown via molecular beam epitaxy on an InP substrate with crystallographic orientation (100) ± 0.5° and a doping level of (1–3) × 1017 cm−3. In contrast to QCLs operating in the 4–6 μm spectral range [17, 18], long-wavelength QCLs do not encounter the problem of the above-barrier ejection of charge carriers due to transitions from the direct-gap Γ valley to the indirect-gap X and L valleys of quantum wells [19]. This allows the use of an In0.53Ga0.47As/Al0.48In0.52As heteropair matched in the crystal lattice constant with the substrate material [20] in constructing QCL active regions in the spectral range of 7–8 μm. The active region included 50 periods epitaxyed on the surface of a In0.53Ga0.47As buffer layer 500 nm thick. The upper cladding of the waveguide was formed from an InP layer 3.9 μm thick with a silicon doping level of 1.0 × 1017 cm−3. In0.53Ga0.47As layers with a total thickness of 120 nm were used as contact layers. This design of the waveguide yielded an optical confinement factor for the fundamental mode (the value of the Γ factor) on the order of 76%, according to results from the numerical calculation. A mesa design with a double groove was used to form QCL crystals, [6, 12]. The width of the ring resonator near the surface was 26 µm. The QCL crystal was mounted on a copper heat sink with the substrate down using indium solder.

The coefficient of coupling in a diffraction grating was calculated numerically for different depths of the etching of lines. Coefficient of coupling κ over length of coupling L was determined within the theory of coupled waves as a jump of the real part of the effective index of refraction in the etched and unetched regions for grooves in the diffraction grating without subsequently filling them with metal [6]. Based on calculations of the effective index of refraction for these two regions, the coefficient of coupling was estimated for different depth of etchings using the equation

$$k = {{\pi {{\Delta }}{{n}_{{{\text{eff}}}}}} \mathord{\left/ {\vphantom {{\pi {{\Delta }}{{n}_{{{\text{eff}}}}}} {{{\lambda }_{{\text{B}}}}}}} \right. \kern-0em} {{{\lambda }_{{\text{B}}}}}},$$
(1)

where Δneff is the change in the real part of the effective index of refraction, and λB is the wavelength of Bragg resonance.

The values typically used to obtain a single-frequency mode of generation in ring QCLs are k ~ 12–16 cm−1 and the product kL ~ 1.4–1.6 [21, 22]. Calculations show that raising the depth of etching to 2.8 μm (allowing for the thickness of metallization) yields values of k ~ 12 cm−1 and kL ~ 1.4 for the considered resonator length. The profile of the distribution of the electromagnetic field across the formed waveguide (the intensity distribution profile of the fundamental mode) was considered in calculating the value of neff. Figure 1 presents the refractive index (left ordinate) and the intensity distribution profiles of the fundamental mode (right ordinate) for the unetched regions (Fig. 1a) and regions etched to a depth of 2.8 μm (Fig. 1b).

Fig. 1.
figure 1

Refractive index profile (left ordinate) and distribution of the intensity of the fundamental mode in the resonator (right ordinate) for (a) unetched and (b) etched regions.

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Before creating a diffraction grating via direct focused ion beam (FIB) lithography, we used electron and ion microscopy to analyze the ring laser for the ellipticity of the resonator and measured the diameter of the latter (374 μm) along the middle circle. No ellipticity was found in the resonator. The diffraction grating was formed in an ultrahigh vacuum using a focused ion beam of gallium ions with an energy of 30 keV. The main technological parameters of the lithographic etching of the grating are given in Table 1. The depth of etching required for a metallization thickness of 600 nm was fixed at 2800 ± 100 nm. The lithographic pattern consisted of rectangular grooves 1.183 × 16 µm in size, running along the middle circle of a ring laser with a radius of 187 µm. The duty cycle of the grooves was 50%. The diffraction grating had a phase shift of π at angles of 90° and 270°. The grooves of the diffraction grating were etched using a NanoMaker lithographic system. The grating grooves were represented in the lithographic structure in the form of lines that determined the trajectory of the ion beam when the surface was exposed. The diameter of the hole in the laser surface formed by an ion beam with an operating current of 2500 pA and a 1 μs period of exposure was ~600 nm. Multiple exposures were used to etch to a greater depth (~3 μm). The width of the grating line on the surface of the laser was ~1.2 µm when the required depth of etching was reached, regardless of the thickness of metallization. Lateral etching was done using the contribution from ions in the tails of the spatial distribution of the beam. By representing the grooves of the grating in the lithographic structure as lines rather than rectangles, the time spent on lithography of the diffraction grating over the entire surface of the ring resonator was shortened to ~1.5 versus ~3 h [23]. A scanning electron microscope (SEM) image of a QCL crystal (top view) after creating diffraction grating grooves via direct ion lithography is shown in Fig. 2. A Tescan MIRA-3 scanning electron microscope was used to take high-resolution SEM images of the QCL crystal.

Table 1.   Main technological parameters of the process during the formation of a diffraction grating by FIB lithography. The calculated depth was determined on the basis of earlier experiments on etching rates
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Fig. 2.
figure 2

SEM images of a QCL with a ring resonator after creating a diffraction grating in the layers of the upper shell of the waveguide via FIB lithography. The red square in the left panel marks the region with one of the phase shifts (by π) of the diffraction grating, an enlarged image of which is shown in the right panel.

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The spectral characteristics of the lasers were measured on a Bruker Vertex 80v Fourier-transform spectrometer at a temperature of 77 K. To record the signal in the stepped mode of scanning, we used a high-speed HgCdTe photodiode cooled to the boiling point of liquid nitrogen with a typical photoresponse time of ~100 ns. The resolution of the obtained spectra was 0.5 cm−1. When studying the spectral characteristics of lasers and the dependence of the characteristic intensity of radiation on the level of current pumping, the durations of the current pumping pulses were 100 and 70 ns, respectively. The rate of pulse repetition was fixed at 15 kHz.

RESULTS AND DISCUSSION

Figure 3 shows the measured current–voltage characteristics and the dependence of the characteristic intensity of radiation P on current pump level I. Threshold current Ith was ~80 mA, which corresponds to a threshold current density of jth ~ 0.3 kA/cm2 and threshold voltage Uth ~ 12 V. The low value of the threshold voltage in terms of the period (0.24 V) shows there was no additional contribution from the drop in voltage across the contacts. The region of the injector in the period of the cascade causes an additional drop in voltage in the cascade. The equivalent of this value expressed in millielectron-volts (meV) is called the defect voltage, since it is additional energy, relative to the quantum energy spent on heating the heterostructure [24]. The estimated value of the defect voltage, defined as the difference between the threshold voltage (expressed in meV and reduced to one period of the cascade) and the quantum energy was 78 meV, which corresponds to the calculated energy between the lower laser level and the upper level of the next cascade (77.4 meV).

Fig. 3.
figure 3

Current–voltage characteristic (left ordinate) and dependence of the integrated intensity of radiation on the level of current pumping (right ordinate), measured at a temperature of 77 K.

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The threshold current was 170 mA (jth ~ 1.4 kA/cm2) for semi-ring QCLs of the same radius, [25]. Raising the current pump level to 15Ith (Fig. 3) did not saturate the dependence of the characteristic intensity of radiation on the former.

We estimated total internal loss αi in a ring laser, which is defined as the product of the threshold current density and the differential gain reduced to the optical overlap factor (product gΓ). According to [25], the differential gain is described as

$$\begin{gathered} g = {{\;}}{{4{{\pi eabs}}\left( {z_{{43}}^{2}} \right){{\;}}} \mathord{\left/ {\vphantom {{4{{\pi eabs}}\left( {z_{{43}}^{2}} \right){{\;}}} {\left( {{{\varepsilon }_{0}}{{n}_{{{\text{eff}}}}}{{\lambda }_{0}}\left( {2{{{{\gamma }}}_{{43}}}} \right){{L}_{{\text{p}}}}} \right)}}} \right. \kern-0em} {\left( {{{\varepsilon }_{0}}{{n}_{{{\text{eff}}}}}{{\lambda }_{0}}\left( {2{{{{\gamma }}}_{{43}}}} \right){{L}_{{\text{p}}}}} \right)}} \\ \times \,\,{{{{\tau }}}_{4}}\left( {1 - {{{{{{\tau }}}_{3}}} \mathord{\left/ {\vphantom {{{{{{\tau }}}_{3}}} {{{{{\tau }}}_{{43}}}}}} \right. \kern-0em} {{{{{\tau }}}_{{43}}}}}} \right), \\ \end{gathered} $$
(2)

where ε0 is the dielectric constant in a vacuum, e is the electron charge, 2γ43 is the width (FWHM) of the spontaneous emission spectrum, Lp is the thickness of the layers of one period of the cascade, z43 is the interaction matrix element, τ4 is the lifetime at the upper level, τ3 is the lifetime at the lower level, and τ43 is the ratio of periods. According to numerical estimates, τ4 = 1.96 ps, τ3 = 0.28 ps, τ43 = 4.94 ps, z43 = 2.43 nm, and neff = 3.215. The differential gain was therefore g ~ 59 cm/kA. The product is then gΓ ~ 45 cm/kA for calculated value Γ = 76% in the considered design for a QCL waveguide. Based on the obtained value of gΓ, the estimated value of the total internal loss αi [26] in the ring laser was ~14 cm−1. The Q factor is determined using the expression [27]

$$Q = {{2{{\pi }}{{n}_{{{\text{eff}}}}}} \mathord{\left/ {\vphantom {{2{{\pi }}{{n}_{{{\text{eff}}}}}} {{{\lambda }}{{{{\alpha }}}_{{\text{i}}}}}}} \right. \kern-0em} {{{\lambda }}{{{{\alpha }}}_{{\text{i}}}}}}$$
(3)

was 1900.

Results from measuring the lasing spectra are shown in Fig. 4. Near the threshold current, the spectrum is represented by three lines spread over wavelength λ = 7.6 μm corresponding to wavenumber ν = 1316 cm−1 (Fig. 4). This wavelength corresponds to a quantum energy of 163 meV, which is in good agreement with the calculated value of the energy of radiative transitions at a temperature of 77 K for the structure of the active region under study. The intermode distance corresponds to whispering gallery modes for a ring laser with a radius of 187 μm. Group refractive index ngr was estimated to be 3.36. The lasing spectrum for semi-ring QCLs of the same radius was represented by 10 whispering gallery modes near the threshold value [26]. Raising the level of current pumping to 1.0 A resulred in additional higher-order azimuthal modes and a considerable increase in the total width of the lasing spectrum (up to 400 nm or 71 cm−1 [26]). This effect of lasing spectrum broadening for semi-ring QCLs was not observed in our lasers, due to additional mode selection caused by the formation of a diffraction grating on the surface of the ring cavity (an additional selective optical loss). The position of the optical modes shifted toward the region of long wavelengths upon an increase in the level of current pumping, due possibly to a drop in the conduction band offset at the heterojunction in combination with the Stark effect [24]. In light of the coefficient of the shift of the wavelength of laser generation along with temperature for a similar heterostructure (−0.09 cm−1/K [28]), the laser heating resulting from the action of a pump pulse was estimated at 10 K at a pump level of 1 A.

Fig. 4.
figure 4

Spectra of multimode laser generation measured at a temperature of 77 K.

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CONCLUSIONS

Surface lasing near 7.6 μm was performed in quantum-cascade lasers with a ring resonator by raising the coefficient of diffraction grating coupling and the optical mode to 12 cm−1. The single-frequency lasing regime was not achieved despite the observed selection of whispering gallery modes, due possibly to insufficient verticality of the etched grooves of the diffraction grating. This will be the subject of further studies.