Metal halide perovskite semiconductors are a promising platform to realize a nonepitaxial laser diode because they are e cient light emitters with a tunable bandgap that can be solution-processed on a wide range of substrates. 1 They have demonstrated low threshold optically-pumped lasing, [2][3][4] light-emitting diodes (LEDs) that operate under high current injection, [5][6][7][8] LEDs that lase under optical pumping and, very recently, electrically-assisted amplified spontaneous emission (ASE) from LEDs under combined optical and electrical excitation. 9 This last milestone by Elkhouly et al. 9 is especially significant because it shows that injecting 3 kA cm -2 can reduce the optically-pumped ASE threshold by about 13 %, which establishes the remaining improvement that will be required to achieve stimulated emission under pure electrical pumping.

Here, we take an important next step by fabricating a full distributed feedback (DFB) perovskite laser diode and demonstrating that it achieves electrically-assisted lasing under short, high current pulsing at low temperature. The device architecture employs a mixed formamidinium lead iodide and methylammonium lead bromide ((FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 ) active layer with a 2 nd order SiO 2 DFB grating and doped organic transport layers to reduce series resistance. Using a custom impulse circuit, we are able to inject an estimated carrier density of 6 × 10 17 cm -3 during 20 ns electrical pulses, which amounts to roughly one quarter of the optical threshold at 230 K. Under these conditions, we observe a ⇠24 % decrease in the optically-pumped laser threshold when the optical pulse overlaps the first few ns of the electrical pulse. These results indicate that roughly an order of magnitude reduction in the threshold carrier density will be required to achieve pure electrically-pumped lasing in (FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 at low temperature.

Figure 1(a) illustrates the device architecture, which consists of an 80 nm-thick SiO 2 grating patterned via e-beam lithography on indium-tin-oxide (ITO; 120 nm thickness with a sheet resistance of 15 Ω/⇤)-coated glass. The grating period is ⇤ = 410 nm and its f ⇠ 0.3 duty cycle is optimized to reduce the threshold gain via rigorous coupled wave analysis (RCWA) simulations described in the Supplementary Material. The hole transport 4 layer (HTL) consists of poly(2,4,6-trimethyltriphenylamine-4',4"-diyl) (PTAA) p-doped with 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F 4 TCNQ). 10 The HTL is spin-coated at a nominal thickness of 20 nm on a flat reference wafer; however, the actual thickness between the grating ridges in Fig. 1(b) is likely thicker.

The subsequent (FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 layer is also spin-coated and planarizes the grating with a thickness of approximately 140 nm between the ridges (Fig. 1(b)). It is important to note, however, that the thickness of the (FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 layer varies by ⇠20 nm over the 15 µm × 100 µm active device area windowed in the SiO 2 . Accounting for this thickness variation is important to correctly tune the resonant mode of the grating to the peak of the (FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 gain spectrum. The (FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 layer is followed by a 40 nm-thick electron transport layer (ETL) consisting of 2,4,6-tris(3-(diphenyl phosphoryl)phenyl) triazine (PO-T2T) co-evaporated with the n-dopant (pentamethylcyclopentadienyl) (1,3,5-trimethylbenzene)ruthenium dimer ([RuCp*Mes] 2 ). The stack is completed with a 100 nm-thick Ag cathode, and a graphite heat spreader is subsequently added on top of the device, similar to Zhao et al. 5 .

The devices are characterized in a continuous flow liquid N 2 cryostat using a home-built microscope equipped with a long working distance objective as shown in Fig. 1(c). The entire system mounted to three motorized linear stages to control position and focus. High voltage electrical pulses with controllable duration in the range <1 to 100 ns are generated using the impulse circuit described in the Supplementary Material. The pulses are delivered via mini-coax cables and a custom printed circuit board connector with 50 Ω transmission lines that terminate on the anode of each device through pogo pins that press the substrate against the cryostat cold head (Fig. 1(c)). Optical excitation pulses ( = 532 nm, 22 ps duration) are focused through the microscope to a ⇠50 µm-wide stripe that overlaps the device active area as shown in Fig. 1(c). Emission is collected exclusively from a small spot at the center of the device active area using a 50 µm multimode fiber optic cable connected to a streak camera that is synced to both the optical and electrical pulses using a digital 5 6 Page 5 of 19 ACS Paragon Plus Environment ACS Photonics delay generator. Time-averaged emission spectra are recorded by plugging the collection fiber into a cooled CCD grating spectrometer. Full details on the electrical interconnection and timing scheme are provided in the Supplementary Material. While this level of electrical injection is not su cient to achieve lasing by itself, it does yield a measurable assist under combined optical+electrical co-pumping as shown in Fig. 3.

In this case, the optical pulse fluence is set just below threshold and timed to reach the sample 1 ns before or after the start of the electrical pulse (Fig. 3(a), inset). The associated spectra in Fig. 3(a) show that this 2 ns timing di↵erence has little e↵ect on the background EL+PL 8 spontaneous emission, but has a significant e↵ect on emission at the laser line, implying that the electrical pulse boosts the device above threshold. Figure 3(b) shows the threshold characteristic acquired for each timing sequence, which confirms that coincident co-pumping reduces the threshold optical pulse fluence by about 24 % relative to the non-overlapped case. The magnitude of the threshold reduction is smaller (about 10 %) when compared to the optical-only measurement in Fig. 2(b) because the latter does not include accumulated heating from the electrical pulse train that increases the threshold carrier density. 12 Since the optical-before-electrical co-pumping case does account for this, it represents the more meaningful reference point.

Crucially, Fig. 4(a) shows that the lasing assist in Fig. 3 only occurs within the first few ns of the electrical pulse. When the optical pulse arrives 10 ns into the electrical pulse, emission at the laser line is quenched, presumably due to the buildup of heat. The fact that a few ns timing di↵erence separates assistance from quenching indicates that these observations are not related to field-induced ion migration, which alters laser threshold on a much longer timescale (i.e., commensurate with the time average of the electrical pulse train). 13 The dependence of the lasing assist on electrical pulse amplitude for an optimally-delayed optical pulse is more nuanced (Fig. 4(b)). Although the stimulated emission signal is enhanced on average relative to optical-only pumping over the 30 to 50 V range, the signal is volatile. Neither the volatility nor the absence of lasing above 52 V is due to device degradation, as both were repeatably cycled between di↵erent voltages and each data point represents the average over more than 200 electrical pulses. The spontaneous emission background, by contrast, displays a steady decrease with increasing voltage, which suggests that higher pulse amplitude actually reduces the total rate of radiative recombination, likely due to heating. Taken together with the behavior in Fig. 4(b), the message is that letting heat accumulate for too long, 12 or generating it too fast (at a rate / V 2 ) quickly overwhelms the ability to assist lasing.

In this context, it is worth discussing and justifying the pulsing conditions and choice of 9 (a) (b)

Figure 3: (a) Time-average emission spectra for electrical+optical co-pumping of a 100 µm × 100 µm square device at T = 230 K. The optical pulse fluence is set to 90 % of threshold and timed to arrive just before (opt.!elect.) or just after (elect.!opt.) the electrical pulse as depicted in the inset. The electrical pulse amplitude is 52 V. (b) Full input-output characteristics recorded for each timing sequence as a function of optical pulse fluence. The optical contribution to the carrier density is shown on the top axis assuming the optical pulse is fully absorbed in the (FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 layer. 10 T = 230 K as the measurement temperature. The latter was chosen because it is the lowest temperature (and thus lowest threshold carrier density; see Supplementary Fig. S2) at which we could maximize electrical injection without irreversibly damaging the devices. Since the device impedance is a strong function of temperature, it is di cult to match to the pulsing circuit a priori. Therefore, at the beginning of an experiment, one of the devices on the substrate was typically sacrificed to determine the maximum electrical pulse amplitude that could be tolerated without causing irreversible degradation.

The temperature-dependent impedance mismatch also makes it di cult to accurately determine both the voltage and current at the device because a portion of the electrical pulse is reflected. Figure 4(a) provides a measurement of the voltage and a calculation of the current derived from the voltage monitor output of the pulsing circuit. However, the pulses are short enough that there is an appreciable time lag between the voltage and current leaving the pulser, and each quantity at the device. This issue arises for any high speed pulsing measurement where the voltage and current are not probed near the device. The integrated measurement resistor described by Chime et al. 14 could resolve this issue, but was not straightforward to implement in these particular devices. Consequently, we rely on the PL-calibrated EL intensity from Fig. 2(c) as the best measure of injected carrier density in this work.

Looking ahead to the ultimate goal of pure electrically-pumped lasing, there are several near-term opportunities to improve the device architecture. Better impedance matching, the addition of an integrated measurement resistor (to simplify current measurement), and redesign of the DFB resonator to eliminate the electrical dead spots that currently exist above the SiO 2 grating ridges would all help to increase the gain. However, it seems clear from Fig. 4(b) that simply injecting more current without also addressing heat dissipation (e.g., by reducing series resistance in the device) is counterproductive, particularly since Fig. 4(a) implies that heat buildup becomes problematic within just a few ns. To this point, we tried a series of co-pumping measurements on (FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 LEDs with electrical 11 (a) (b)

Figure 4: (a) Stimulated emission signal recorded from a square device in a co-pumping experiment similar to that in Fig. 3, but with varying optical pulse delay. The lasing assist peaks and then disappears over the first few ns of the electrical pulse. When the optical pulse arrives more than ⇠8 ns into the electrical pulse, no lasing is observed. The red trace shows the voltage monitor from the impulse circuit together with the pulser current density calculated by dividing the voltage monitor by a 50 Ω load and normalized to the area of the device (right-hand axes). The rise time of the red trace is limited by the 100 MHz bandwidth of the oscilloscope used to measure it. (b) Stimulated emission signal recorded from a rectangular device as a function of pulse voltage at an optimal electrical!optical pulse delay of 0.7 ns. No lasing is observed for pulse amplitudes higher than ⇠52 V.

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pulse widths of just 3 ns, but were unable to achieve an assist for amplified spontaneous emission; see the Supplementary Material for details.

The overwhelming priority, therefore, is to reduce the threshold carrier density, by approximately an order of magnitude, to n th ⇠ 10 17 cm 3 . This has been achieved in opticallypumped halide perovskite lasers [15][16][17] but not, to our knowledge, in a diode laser architecture.

Possibilities to help reach this goal include adopting a mixed order grating 18 or a low loss ring resonator architecture, hot-pressing or nanoimprinting the perovskite to reduce its surface roughness-induced scattering loss, 17 and replacing the top Ag contact with a lower loss transparent conducting oxide as in Elkhouly et al. 9 . Finally, 140 nm of (FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 is simply a large amount of material to invert. Confining recombination to a smaller volume of active layer material (e.g., small, lower band gap inclusions in a mixed phase perovskite 2 ) in the same spirit as III-V quantum well lasers would be beneficial, but only after the dominant extrinsic optical losses above have been eliminated.

In summary, we have shown that electrically-injected carriers can assist lasing in (FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 under short, high current electrical pulsing at low temperature. This result reinforces recent observations of electrically-assisted ASE, 9 adding momentum to the worldwide e↵ort to realize a perovskite laser diode. By systematically increasing the electrical assist fraction through reduction of the threshold carrier density, this goal finally appears to be within reach.

Materials. Formamidium iodide (FAI), methylammonium bromide (MABr), and methylammonium chloride (MACl) were purchased from Greatcell Solar Materials. PbI 2 and PbBr 2 were purchased from Tokyo Chemical Industry (TCI). PTAA was purchased from Solaris Chem. PO-T2T was purchased from Xi'an Polymer Light Technology. F 4 TCNQ was purchased from Ossila. [RuCp*Mes] 2 was synthesized as described elsewhere. 19 Dimethyl-13 formamide (DMF), dimethyl sulfoxide (DMSO) and chlorobenzene were purchased from Sigma-Aldrich. The graphite sheet (50 µm) with an insulating adhesive layer (6 µm) was manufactured by Panasonic. All materials were used as received.

Device Patterning and Grating Fabrication. The device layout design is similar to our previous work. 5 A narrow ITO anode strip with a width of 200 µm is patterned by a wet etching process. Then, a patterned Au layer (200 nm, deposited by electron-beam evaporation) connected to the ITO strip is formed by a lift-o↵ process to reduce series resistance. A thin film of SiO 2 was grown by PECVD at 70 °C on top of the ITO and Au layers. To form both the DFB grating and device active area, the SiO 2 films were patterned and completely etched using electron-beam lithography (50 nm of PMMA was used as a resist layer, followed by development at -20 °C to enhance resolution) and an inductively coupled plasma etching process. The device active area is defined by the windowed region in the SiO 2 containing the DFB grating, which is smaller than the area of the overlap between the bottom ITO anode strip and the top Ag cathode strip.

Perovskite Device Fabrication. The perovskite precursor solution was prepared in an N 2 -filled glovebox that contains PbI 2 (613.14 mg mL -1 ), FAI (228.72 mg mL -1 ), PbBr 2 (25.69 mg mL -1 ), MABr (7.84 mg mL -1 ), and MACl (33.08 mg mL -1 ) using DMF/DMSO mixed solvent (the volume ratio of DMF to DMSO is 8:1) to obtain 0.5 M (FAPbI 3 ) 0.95 (MAPbBr 3 ) 0.05 . The devices were fabricated on the patterned ITO/glass substrates described above. The substrates were cleaned in air sequentially with soapy water, deionized water, acetone, and isopropyl alcohol, and were then dried by N 2 and treated with O 2 plasma for 10 min prior to film deposition in an N 2 -filled glovebox. PTAA (5 mg mL -1 in chlorobenzene) with the F 4 TCNQ dopant (0.2 mg mL -1 in chlorobenzene) was then spincoated at 1500 rpm for 60 s andthermally annealed at 110 °C for 20 min. The samples were then treated with O 2 plasma for 15 s to improve wettability for the subsequent perovskite layer, which was spin-coated initially at 1,000 rpm for 10 s (with an acceleration rate of 200 rpm/s), and then 5,000 rpm for 30 s (with an acceleration rate of 2000 rpm/s). A solvent-14 quenching step was performed 20 s after spinning by dropping chlorobenzene (0.2 mL) on the spinning samples. The samples were then annealed at 100 °C for 30 min and loaded into a thermal evaporator to deposit 10 nm of undoped PO-T2T followed by 30 nm of PO-T2T doped with [RuCp*Mes] 2 in a 5:1 volume ratio via co-evaporation. The device was completed by depositing a 100 nm-thick Ag cathode through a shadow mask.

Characterization. At the start of testing, devices were illuminated with a Xe arc lamp for 20 min at room temperature to activate doping by [RuCp*Mes] 2 20 in the cryostat prior to lowering the temperature. Devices were measured within 8 h of this step. Most measurements of a given device were completed within one hour, though this sometimes extended to 4 h for streak camera measurements. Because of the small device size and collection spot, the temperature in the cryostat had to stabilize completely so that thermal expansion/contraction of the cold finger did not move the device under study by more than 1 µm in 30 min relative to the microscope. Following thermal stabilization, one device was selected for a sacrificial measurement in order to establish the upper bound on electrical pulse amplitude that could be tolerated before the onset of degradation. As long as the electrical pulses were kept within the limit determined from the sacrificial device, no degradation was observed over the course of testing on the other devices, consistent with previous high current pulsing measurements. 5 The repetition rate of all optical and electrical pulses was 20 Hz. Full details of the synchronization and timing setup are provided in the Supplementary Material.