1. Introduction

Metal halide perovskite semiconductors have been receiving much interest during the last decade. Recently, perovskite based solar cells reached an efficiency level of 29% [1]. Perovskites have also found applications in optoelectronics including light emitting devices [2,3], photodetectors [4], and lasers [5,6]. These materials exhibit high absorption coefficients [7], direct band gap [8] and a sharp optical band edge. They can be deposited by several types of techniques some of these are, one-step deposition from a solution processable precursor solution [7], or a two-step process in which a metal halide is deposited and then converted to perovskite by exposure to a volatile organic compound [9]. These fabrication techniques which provide an opportunity to tune the band gap over the range 1.1- 3.3 eV simply by varying the anion (X = Cl^-, Br^-, I^-), metal (Pb, Cs etc.) and cation (MA, FA etc.) composition and ratios [10]. This is undoubtedly an advantage over conventional semiconductor materials, which are limited by the lattice mismatch and strained layer epitaxy. Furthermore, using perovskite lasers [11], the so called “green-gap” [12] in the existing semiconductor gain media can be overcome. Another important advantage of perovskites over conventional semiconductor materials is the presence of predominant Van der Waals interactions among the halide atoms and hydrogen bonding, which render them “soft materials”. Consequently, perovskites can be directly patterned by thermal nanoimprint lithography (NIL), a technique which cannot be directly used with conventional inorganic semiconductor (AlAs, GaAs, GaN etc.). The use of NIL not only improves the film quality and reduces scattering but also offers a high throughput for the device fabrication [13].

In virtue of the high optical gain of perovskites, various configurations of lasers have been demonstrated. The resonators used for feedback include Fabry-Perot cavities [14], spherical resonators [15], random laser cavities [16], photonic crystal cavities [17], and more. Compared to all other structures, distributed feedback (DFB) cavities received much attention due to their lasing wavelength flexibility and narrow linewidth properties. Particularly, the wavelength can be tuned by varying several factors such as the gratings periodicity, the thickness and refractive index of the gain material, the surrounding refractive index etc. [18]. Such lasers also exhibit very low threshold levels, high-quality factors and mirror free design.

DFB lasers are realized in two main common configurations, utilizing 1^st or 2^nd order Bragg reflectors. 2^nd order lasers (which are based on 2^nd order Bragg grating) exhibit strong vertical emission (perpendicular to the surface) and are often used as surface emitting laser. In contrast, 1^st order DFB lasers (which are based on 1^st order Bragg grating) only emit along the surface plane, exhibiting edge emission properties, as well as superior quality factor [19]. In fact, only for a very narrow range of duty cycles, the 2^nd order grating exhibit dominant edge emission properties. This is in contrast to 1^st order grating structures which emit only broadside for a large range of duty cycles. Finally, 1^st order lasers are more suitable for integration in optical devices such as waveguides, modulators, etc. Despite the abovementioned advantages, 1^st order DFB edge emitting lasers based on perovskite have not been demonstrated yet. It should be noted that the Bragg mirrors used for perovskite based VCSELs are quarter-wavelength thick. Thus, such VCSELs can be considered as 1^st order lasers. Nonetheless, the mirrors used in such devices where either dielectric [20] or consist of conventional semiconductor materials GaN/NP-GaN [21], thus requiring additional fabrication and processing steps. Furthermore, VCSELs are inherently surface emitting devices and unsuitable of edge emitting applications.

2. Results and discussion

In this paper, we design and fabricate, using nano-imprint lithography (NIL) 1^st and 2^nd order perovskite lasers and characterize them experimentally under pulsed optical pumping. The lasing properties of 1^st (pitch of 180 nm) order and 2^nd (pitch of 360 nm) order lasers are compared, showing that 1^st order lasers exhibit mainly edge emission characteristics. The dependence of the properties of both 1^st and 2^nd order DFB lasers on the excitation angle is also studied in details. The nano-imprint lithography used to fabricate the lasers enables a facile and inexpensive way to fabricate DFB resonators, which is feasible to upscaling and mass production.

DFB lasers are formed by exploiting the high reflectivity of a periodic structure in the vicinity of their photonic bandgap edges. These cavities can be realized by precise nano-structuring of the gain medium or by deposition of that medium on a pre-corrugated surface [22]. If the corrugations are shallow (weak index perturbations) lasing occurs very close the wavelength satisfying the Bragg condition, ${{\lambda} _{Bragg}}$: $2{n_{eff}}\Lambda = m{{\lambda} _{Bragg}}$, where ${n_{eff}}$ is the effective refractive index of the waveguide optical mode, $\Lambda $ is the periodicity of the corrugated structure, and m is the diffraction order. For a waveguide structure consisting of a 200 nm perovskite core, SiO₂ substrate and air clad, the Bragg condition for $m = 2$ and grating period of $\Lambda = 360\; \textrm{nm}$ leads to ${\lambda _{Bragg}} = 784.4\; nm$ [23]. Clearly, a first order ($m = 1$) grating with half that period (i.e., $\Lambda = 180\; \textrm{nm}$) yields the same Bragg wavelength.

The thickness of the perovskite layer must be chosen carefully. If the thickness is too large, the device might support many modes of the perovskite slab waveguide. Consequently, higher order modes have lower ${n_{eff}}$ compared to that of lower order modes and, hence, exhibit different lasing wavelengths. A multimode laser can result in either broadening of the lasing peak or lasing with multiple wavelengths. These additional lasing modes peaks will also compete over the optical gain and may lead to higher threshold and mode switching effects. On the other hand, a thin layer below the cutoff condition will not support any modes. Figure S1.2b (see supporting info.) depicts the dependence of the effective index of the two fundamental TE and TM mode on the waveguide thickness. This calculation is made for a perovskite slab waveguide on a SiO₂ substrate and air clad. Our aim is to find a thickness, which supports a single guided mode in the vertical direction while sufficiently away from the cutoff region. From figure S1.1 (see supporting info) it is clear that the confinement factor for 100 nm thick waveguide is very poor and expect to yield low modal gain. On the other hand, 300 nm thick perovskite core supports a second, undesired, TE mode (TE₁, see S1.1 with ${n_{eff}} = 1.7256$). A waveguide with a 200 nm thick core supports only the two fundamental TE₀ and TM₀ modes where the ${n_{eff}}$ of the TE₀ mode is 2.173. Nevertheless, only the reflectivity bandwidth of the TE₀ exhibits good overlap with the gain curve and expected to lase in practice. Thus, core thickness of 200 nm seems to be a good compromise between spatial confinement and single mode operation.

It should be noted that there is no lateral confinement in the structure and, in principle, many transverse modes can be supported. Nevertheless, the lasing spectrum exhibits a single peak and the linewidth of wide DFB lasers is identical to that of a laterally confined one [23]. We attribute this to the combination of mode suppression in the laser (due to the homogeneously broadened asymmetric gain profile) and the resolution of the spectrometer. Thus, it is possible that the laser emits several spatial modes of almost identical wavelength which are not resolved by the spectrometer, though the fact that laterally confined lasers exhibit similar linewidth does not support this possibility. While lateral confinement can be readily introduced (see e.g., Ref. [23]), it is unnecessary as the main objective of this work is to compare the impact of the grating order (1^st or 2^nd) on the laser properties.

We performed FDTD simulations to identify the optimal etch-depth of the grating in the gain (perovskite) medium. We found that 1^st order grating shows a sharp reflectivity peak for etch depth thicker than 10 nm whereas 2^nd order grating shows good reflectivity (>60%) for etch depth larger than 60 nm (Supporting info Sec. 2). Consequently, in our optimized design we use an etch depth in the range of 60–70 nm.

In order to compare the lasing characteristics of 1^st and 2^nd order DFB perovskite lasers, there are several design parameters that should be considered. In particular, varying the gratings duty-cycle can substantially modify the value and bandwidth of the reflectivity and hence, the lasing wavelength and threshold. Generally speaking, the coupling coefficient between the forwards and backwards propagating waves exhibit double hump curve dependence on the duty cycle for a 2^nd order grating where the two local maxima are at ∼20% and at ∼70–80% (see Figure S3.1b, c) [24]. On the other hand, the coupling coefficient of the 1^st order Bragg grating exhibits a single maximum (as a function of the duty-cycle – see Figure S3.1a, c). Referring to Figure S3.1, the 1^st order laser shows a single humped curve with a maximum reflectivity at duty cycle of 60% and lasing at 790 nm whereas the peak reflectivity for the 2^nd order devices is obtained at duty-cycle of ∼85%. Consequently, we choose duty cycle of 60% and 85% for the 1^st and 2^nd order lasers respectively.

In order to obtain lasing at 790 nm we choose to use gratings periodicity of 180 nm and 360 nm for the 1^st and 2^nd order devices respectively. The gratings are imprinted into the perovskite layer using a set of lithographic techniques (Fig. 1). First, E-beam lithography and reactive ion etching (RIE) are used for fabricating a master. Then, sol-gel lithography is utilized for fabricating a stamp from the master and finally, nano imprint lithography (NIL) is used for realizing the final device. The etch depth of the final DFB lasers are ∼60 nm And their lateral dimension are either 200×500 µm² or 500×500 µm² . The patterned length along the grating vector (Λ) is kept fixed at 500 µm. The number of periods for the 1^st and 2^nd order periods are 2777 and 1388 respectively, corresponding to the angular dispersion of 5.56 mrad/nm and 2.78 mrad/nm respectively. The duty cycles (DC) are 59% and 85% for 1^st order and 2^nd order lasers respectively. The complete details of the fabrication steps are provided in the Supporting info.

 

Fig. 1. Fabrication process flow and characterization of perovskite DFB lasers.

Download Full Size | PDF

To account for potential fabrication errors and tolerances we realized four perovskite based 1^st order DFB laser designs having dimension of 200 µm × 500 µm and periodicities of 170 nm, 175 nm, 180 nm, and 185 nm. To ensure compatibility with our measurement set-up we cut the chip with a scriber along the grating period (Fig. 1) and measured the emission characteristics in two configurations. First, excitation and emission collection from the top. Second, excitation from the top and emission collection from the edge of the device (Fig. 1). The DFB lasers with gratings periods of 170 and 185 nm did not lase. In contrast, the devices with gratings periods of 175 nm and 180 nm do show lasing under pulsed optical pumping (5 ns pulses, 20 Hz rep-rate, λ_p= 532 nm). The spectrum of the DFB laser with periodicity $\Lambda = 175{\; }nm$ exhibits two competing peaks at 780.19 nm and at 794.15 nm (Figure S4a, b) and is unsuitable for single mode lasing operation.

Figure 2(a) shows the evolution of lasing in a 1^st order laser ($\Lambda $ = 180 nm, top excitation, side collection geometry). The excitation scheme included a 20X objective with an additional lens (before the objective) in order to increase the spot size, leading to a spot size of ∼100 µm in radius. Figure 2(b) shows the FWHM as a function of excitation flux corresponding to Fig. 2(a). The threshold is found to be 300 µJ/cm² and FWHM at threshold is 1.2 nm. Figures 2(c) and 2(d) depicts similar plots for the top excitation - top collection geometry. The threshold in this case is found to be around 539 µJ/cm² and the FWHM at threshold is also 1.2 nm. The lasing wavelength of the 1^st order DFB laser is 794 nm, very close to the desired wavelength of 790 nm.

 

Fig. 2. (a) Emission from a 1st order DFB ($\varLambda = 180{\; }nm)$ when collected from side with an optical fiber of comparable mode field diameter. b) Peak intensity/FWHM vs excitation fluences for a side collection set-up. c) Same as (a) but when collected from top with a 20X objective. d) Same as (b) when collected from top.

Download Full Size | PDF

We note, that although the fabricated devices are standard DFB lasers (i.e., without a λ/4 phase-shift), the observed lasing spectrum includes only a single peak. We attribute this to the strong asymmetry of the material gain profile which highly overlaps with its the absorption profile. This complex gain/absorption spectra results in an asymmetric net gain profile which favors one of the solutions and suppresses the other.

In order to compare the threshold characteristics between 1^st and 2^nd order lasers, the 1^st order and 2^nd order DFB lasers are fabricated on the same chip with the same process to minimize variations that may arise from parameters tolerances (e.g., thickness, etch depth, defect density etc.).

Figure 3 shows experimentally obtained collected output power and FWHM as a function of the pump level for 1^st and 2^nd order lasers. All measurements were obtained from devices fabricated simultaneously on the same chip (note that the 1^st order lasers of Fig. 3(a) and Fig. 2 are of the same design but from different batches). The lasers were excited from the top with 20X (NA 0.42) objective. When the emission is collected from the edge of the chip, the emission collected from the edge of the 1^st order lasers is substantially larger than that collected from the top (approximately by a factor of 10). This is expected as the 1^st order gratings do not scatter light efficiently in the vertical direction. It should be noted that the side collection is less efficient than the top collection (the top collection utilizes a 20X objective with NA of 0.42 whereas the side collection utilizes an optical fiber with NA of 0.22), which means that the difference is even larger. Consequently, the difference between the intensity emitted broadside and that emitted vertically is considerably larger and the 1^st order laser is indeed mainly edge-emitting. In contrast, the emission collected from the edge of the 2^nd order lasers is lower than that collected from the top (by a factor of 5). However, as the difference is not as dramatic as in the case of the 1^st order DFB lasers and considering the higher efficiency of the top collection, it seems that the edge and top emissions of the 2^nd order DFB lasers are of similar order of magnitude. To evaluate the threshold levels, we consider the measurements with the best SNR, i.e., side collection for the 1^st order DFB lasers and top collection for the 2^nd order devices. The thresholds are found to be 239 µJ/cm² and 310 µJ/cm² for the 2^nd and 1st order devices respectively. Thus, in contrast to what one may expect, the threshold level of the 2^nd order lasers is lower than that of the 1^st ones.

 

Fig. 3. (a) Emission intensity maxima versus excitation energy (532 nm, 5 ns. 20 Hz) gray stars and black spheres (left axis), and FWHM (red stars and red spheres) versus pump energy for a 1st order (stars) and spheres when excited from (top) and collected from side. (b) Similar to (a) for 2nd order lasers.

Download Full Size | PDF

The fact that the threshold levels of the 2^nd order DFB lasers is lower than that of 1^st order ones is rather surprising as the later are expected to exhibit higher quality factor or at least similar one to that of the former. A possible explanation for that discrepancy is that the gain in the 2^nd order DFB lasers is larger than that of the 1^st order devices. Such difference could stem from differences in the coupling efficiency of the pump to the guided mode of the slab due to the gratings. In particular, if the 2^nd order grating couple the pump into the waveguide mode more efficiently than the 1^st order grating then the threshold of the former would be lower.

Figure 4(a) depicts FDTD-based calculations of the coupling efficiency of the pump into the waveguide mode as a function of the incidence angle for the 1^st and the 2^nd order devices. We note that the coupling efficiency of the pump into the 2^nd order devices is substantially larger than that of the 1^st order ones for incidence angle smaller than ∼12°. For incidence angle smaller than 5°, the difference between the coupling efficiency is of several orders of magnitudes. These calculations support the hypothesis that the lower threshold levels of the 2^nd order DFB laser originate from better coupling into the waveguide mode. Intuitively, it does not seem to be surprising that the 2^nd order gratings provide better input efficiency than that of 1^st order ones. 2^nd order gratings exhibit efficient vertical emission and thus, due to reciprocity, should facilitate efficient coupling into the waveguide mode. However, as the grating periodicity is designed according to the wavelength of emission (and not of the pump), it is not that obvious that the gratings will exhibit efficient in-coupling at the pump wavelength. Furthermore, one may intuitively expect to see enhanced in-coupling efficiency at discrete angles (corresponding to the Bragg order), which is not the case.

 

Fig. 4. a) FDTD simulation showing the coupled power in the waveguide (for λ = 532 nm) as a function of incidence angle. b) Emission intensity maxima versus excitation energy (532 nm, 5 ns. 20 Hz), white circles and gray stars (left axis), and FWHM (red stars and red circles) versus pump energy for a 1st order (stars) and 2nd order (circles) when excited from top and collected from top with a 5X, 0.21 NA objective. (c) Similar to (b) but when excited and collected from top with a 20X, 0.42 NA objective.

Download Full Size | PDF

In order to further verify that the pump coupling efficiency is indeed the reason for the threshold levels properties, we take advantage of the large difference in the coupling efficiencies at small angles. When the DFB lasers are excited with a 20X objective lens, the pump beam consists of components with incidence angle of up to ±25°. Thus, significant part of the pump beam can couple efficiently to both type of devices. However, if the devices are excited with an objective with lower NA, then the pump coupling efficiency into the 2^nd order devices is expected to be substantially larger and their lasing threshold should be much lower than that of the 1^st order devices. To verify that, we replaced the 20X objective lens with a 5X one (NA ∼0.21). This lens supports excitation angles of up to ±12°. Figure 4(b) compares the corresponding P_in-P_out curves of the two types of DFB lasers. For the experiment, we chose to use 500 × 500 µm² devices, with the optimal grating configuration for each laser type (i.e., duty cycle of 60% and 85% for the 1^st order and 2^nd order devices respectively). The threshold of the 2^nd order devices has reduced to 92.45 µJ/cm² while the 1^st order ones do not exhibit lasing even at pumping levels as high as 350 µJ/cm². The reduction of threshold for the 2^nd order is attributed to a larger pumping spot size which increases the reflectivity of the grating.

The observed threshold levels with the 5X objective lens pumping scheme are in full agreement with the pump beam coupling efficiency hypothesis. The lower NA of the lens enhances the pump beam coupling efficiency into the waveguide mode of the 2^nd order devices, thus yielding a lower threshold that observe with the 20X lens. In conjunction, the use of the 5X lens reduces dramatically the pump beam coupling efficiency into the waveguide mode of the 1^st order devices, leading to complete extinguishing of lasing action.

3. Conclusion

We have designed, fabricated, and characterized 1^st and 2^nd order DFB lasers based on nanoimprint lithography of MAPbI₃. To our knowledge, this is the first demonstration of perovskites-based 1^st order devices. The 1^st order lasers exhibit strong edge emitting properties while the 2^nd order one’s exhibit both edge and surface emission. We have studied the lasing thresholds and output power characteristics of the two types of lasers and found that, in contrast to what can be expected, the 2^nd order DFB lasers exhibit lower threshold levels under optical pumping. We showed that this phenomenon is attributed to better coupling of the pump beam into the laser waveguide mode, which yields substantially larger modal gain for the 2^nd order devices. It should be noted, however, that the lower lasing threshold of the 2^nd order DFB lasers originates from the use of optical pumping and that under electrical pumping conditions the 1^st order devices are expected to exhibit lower threshold levels than those of 2^nd order devices. The edge emitting properties of 1^st order DFB lasers render them of great potential for integrated optics in conjunction with waveguide configuration. Furthermore, the ability to tune continuously the emission from 1.1 to 3.1 eV render such devices highly valuable for telecommunication, medicine, and numerous other applications.