Efficient heat dissipation perovskite lasers using a high-thermal-conductivity diamond substrate

Efficient heat dissipation that can minimize temperature increases in device is critical in realizing electrical injection lasers. High-thermal-conductivity diamonds are promising for overcoming heat dissipation limitations for perovskite lasers. In this study, we demonstrate a perovskite nanoplatelet laser on a diamond substrate that can efficiently dissipate heat generated during optical pumping. Tight optical confinement is also realized by introducing a thin SiO2 gap layer between nanoplatelets and the diamond substrate. The demonstrated laser features a Q factor of ∼1962, a lasing threshold of 52.19 µJ cm−2, and a low pump-density-dependent temperature sensitivity (∼0.56 ± 0.01 K cm2 µJ−1) through the incorporation of the diamond substrate. We believe our study could inspire the development of electrically driven perovskite lasers.

Perovskite lasers have rapidly achieved progress in developing continuous-wave excited lasing from a femtosecond pulse excited lasing, which is considered a critical step towards electrically excited lasing [19,22,23]. After continuous-wave lasing at room temperature, the next goal is to realize electrically driven lasing [24][25][26]. In commercially available electric injection lasers, traditional epitaxial grown single crystal semiconductors with both large thermal conductivity κ and high charge carrier mobility m usually exhibit small resistive heating under large current flow [27][28][29]. While perovskites possess large and balanced charge carrier mobilities, they suffer from small κ values [11]. The thermal conductivity of MAPbI 3 is 1-3 W m −1 K −1 , which is inferior to that of GaAs (50 W m −1 K −1 ) [20]. Hence, heat converted from energy loss through nonradiative pathways cannot be effectively dissipated. This failure will increase the lasing threshold as carriers occupy a broader energy range at a higher temperature, diluting the population inversion of any given transition along with other problems such as degradation and heat-induced defects [30]. The lowest electric excitation threshold of a distributed-feedback (DFB) perovskite laser would be as high as 24 mA cm −2 [20]. Moreover, owing to high current injection in conventional perovskite light-emitting diode architectures used for laser devices, the external quantum efficiency would be significantly restricted under high current injection conditions owing to Joule heating [31]. Hence, heat management is a bottleneck for developing perovskite-based electrically driven lasers.
In a perovskite laser, temperature rising from absorptions of excitation light can be described by [32] 2 where ρ, C, κ, and q are the density, specific heat, thermal conductivity, and heat source inside the device. For a pulsed pumped laser, where Δt is the period used for the time integration of one laser pulse, v is the pulse repetition frequency, and η is the quantum efficiency of perovskites. a p and a s are absorption coefficients of perovskites and the substrate, respectively. P p and P s are energy densities in the perovskite layer and substrate, respectively. For a continuous-wave pumped laser, q can be expressed as q a I a I = (1 ) + , p p s s where I p and I s are light intensities in the perovskite layer and substrate, respectively. Normally, pump light propagates through the perovskite layer and substrate sequentially.
According to the Beer-Lambert law, 90% of the pump light is absorbed by the perovskite layer as a p can be as high as 3 × 10 5 cm −1 [33]. Therefore, P p is much higher than P s . To avoid further heat accumulation from the substrate, a s should be much smaller than a p . High-thermal-conductivity substrates are usually considered as solutions for tackling the above issue in perovskite lasers. Equation (1) shows that substrates with high thermal conductivities are capable of efficient heat dissipation for lasers with different injection mechanisms. The resonant wavelength λ of an optical microcavity is determined by λ = 2nL / p, where p is an integer, n is the refractive index, and L is the cavity length. Hence, the resonant wavelength of a whispering gallery mode (WGM) microcavity laser is only determined by the refractive index and cavity length. As both n and L are temperature sensitive, the wavelength shift induced by temperature is as follows: where dn/ndT is the thermal optical coefficient, and dL/LdT is the thermal expansion coefficient. This characteristic makes monitoring the resonant wavelength shift of a laser ideal for temperature-sensing applications [3,34]. For more efficient heat dissipation, a low-temperature continuous-wave perovskite laser was demonstrated using a sapphire substrate with high thermal conductivity (~25 W m −1 K −1 ). With improved heat dissipation, the demonstrated lasing shows a thermally induced peak wavelength shift of~0.9 nm as the pump intensity increases from 17.5 to 18.4 kW cm −2 [35]. Using a silicon substrate (~150 W m −1 K −1 ) and high-quality gain medium, even roomtemperature continuous-wave lasing can be realized [36]. Ascribed to the efficient heat management, the laser shows a thermally induced center wavelength shift of~0.4 nm as the pump intensity increases from 2.5 to 22.5 W cm −2 . To achieve optical confinement, we can introduce a low-refractive-index gap layer between the perovskite and silicon substrate. Using a YAG crystal-fiber scheme, thermal dissipation is improved by spreading heat over a crystal fiber that has high thermal conductivity (9.48 W m −1 K −1 [37]). Other high-thermal-conductivity materials, such as silicon carbide (490 W m −1 K −1 ), have also been reported to be used as substrates [38]. Among all natural materials, the diamond substrate has the highest thermal conductivity (2400 W m −1 K −1 ), which has already been widely applied as an ideal heat spreader for highpowered electronics [39]. However, it has never been employed for developing high-performance perovskite lasers. Moreover, the lower refractive index of diamond (~2.40) compared with silicon is beneficial for realizing a lower effective refractive index for the substrate and may enable better optical confinement while improving heat dissipation [40]. In this study, we report a perovskite laser with efficient heat dissipation based on a diamond substrate, which can successfully control the temperature elevation during optical pumping. We fabricated perovskite nanoplatelets through a chemical vapor deposition method on mica substrates. These nanoplatelets were then transfer-printed by thermal release tapes onto the diamond substrate covered with a low-refractive-index SiO 2 gap layer [41,42]. Benefitting from efficient thermal management and improved optical confinement, the perovskite laser exhibited a quality factor Q of 1962 and lasing threshold of 52.19 μJ cm −2 , with a pump density (P)-dependent temperature sensitivity as low as 0.56 ± 0.01 K cm 2 μJ −1 . The sensitivity is one to two orders of magni-tude lower than values for previously reported perovskite nanowire lasers on glass substrates [43]. This study facilitates the development of electrically driven perovskite lasers.

EXPERIMENTAL SECTION
Perovskite nanoplatelets were synthesized on mica substrates through chemical vapor deposition [42]. They were transferprinted onto square-shaped diamond substrates with SiO 2 gap layers with various thicknesses through thermal release tapes [41]. The absorption spectra of the diamond substrate were obtained at room temperature using a Shimadzu UV-2600 UV-VIS spectrometer. Then the electric field distribution in the equilateral triangular nanoplatelets was analyzed using a finiteelement method. We obtained optical images of MAPbI 3 nanoplatelets using a Nikon LV150 optical microscope. Atomic force microscopy (AFM) images were collected on an FM-Nanoview 1000 AFM (FSM Precision) which sampled 512 points in x and y directions, respectively. Perovskite nanoplatelet lasers were then excited using a 343-nm femtosecond laser. Room temperature was controlled at 293 K with a fluctuation of less than 0.1 K to avoid air fluctuations. Emission signals were collected through a home-built microscope setup. Signals were measured using an Ideaoptics PG2000-Pro spectrometer with a working range in the wavelength of 700-900 nm [42]. Temperature-dependent photoluminescence (PL) was obtained by heating the perovskite nanoplatelet through a high-temperature station (KeyFactor). Fig. 1a shows the schematic of the proposed optically pumped MAPbI 3 whispering gallery mode (WGM) laser comprising a triangular MAPbI 3 nanoplatelet, a SiO 2 gap layer, and a diamond substrate. In a WGM cavity, light confinement is achieved through total internal reflection (TIR) at the boundaries of the high refractive index MAPbI 3 nanoplatelet. Fig. 1b shows the wave propagation inside the triangular MAPbI 3 nanoplatelet in the transverse plane. Evidently, optical paths remain constantly parallel to one of the triangular sides. Light confined in the WGM cavity should obey ray optics theory, where each light ray reflected at the interface should fulfill TIR. Fig. 1c shows that the refractive index of the nanoplatelet n p (~2.56) is higher than that of the surrounding air n a (~1.00) [44]. Hence, TIR is satisfied in the transverse plane. The diagram in Fig. 1d represents the optical paths of TIR in the vertical direction. At the boundary between the nanoplatelet and the air, TIR can be readily fulfilled. The other boundary that locates between the nanoplatelet and substrate must have a high refractive contrast as well (Fig. 1e), which is crucial in realizing TIR in high-quality cavities. As the refractive index of the diamond is~2.40, only slightly lower than that of MAPbI 3 (~2.56), loading the nanoplatelet directly on the diamond causes the leakage of light at the interface. In our design, a SiO 2 gap layer with a low refractive index of~1.454 is introduced between MAPbI 3 nanoplatelet and diamond substrate for achieving TIR in MAPbI 3 nanoplatelet [45].

RESULTS AND DISCUSSION
To investigate the vertical mode confinement in nanoplatelet-SiO 2 -diamond structures, we first calculated electric field distributions inside the structures with different SiO 2 gap layer thicknesses. Fig. 2a shows the electric field profile inside a nanoplatelet-SiO 2 -diamond-structured WGM cavity with a 50nm-thick SiO 2 gap layer. Hence, the MAPbI 3 nanoplatelet does not support optical resonance anymore owing to the large portion of leakage field in the diamond substrate. With the increase of the gap layer thickness, the leakage field in the diamond substrate can be suppressed significantly. In Fig. 2b, the electric field profile of the structure with a 100-nm-thick SiO 2 gap layer clearly manifests an increase in electric field intensity of waveguide mode in the nanoplatelet along with a decrease in leakage field in the diamond substrate compared with a 50-nmthick SiO 2 gap layer. Fig. 2c shows that a wide SiO 2 gap of 200 nm in thickness produces evidently less leakage field in the diamond substrate, simultaneously proposing better mode confinement within the MAPbI 3 nanoplatelet. However, a thicker SiO 2 gap layer will weaken the heat dissipation capacity of the diamond substrate. Q is widely used to characterize a cavity's sharpness or its ability to store energy. It can then be defined as Q = λ / Δλ, where Δλ is the full-width at half-max-imum (FWHM) linewidth [1]. In the experiment, nanoplatelet-SiO 2 -diamond structures with different SiO 2 thicknesses were prepared to compare their heat dissipation abilities and quality factors. To maximize the heat dissipation effect, we selected nanoplatelets with a thickness of~80 nm [46].
To maximize the heat dissipation of the diamond substrate during the MAPbI 3 nanoplatelet lasing, self-heating from the substrate should first be minimized. Fig. 3a shows the image of the square diamond substrate, indicating that it is transparent in the visible spectrum region. In the ultraviolet-visible (UV-vis) absorption spectrum of the substrate (Fig. 3b), the light absorption of the substrate is much smaller than that of the perovskites within the 330-800 nm spectrum region, greatly minimizing its self-heating. In nanoplatelet transfer, adhesion forces between nanoplatelets and the substrates are typically dominated by van der Waals interaction. The root mean square (RMS) roughness of both the nanoplatelets and substrates should be on the~nm level. Hence, enough adhesion forces between nanoplatelets and the substrate can be generated to overcome residual adhesion forces from the thermal release tape [41]. For heat dissipation, smooth surfaces are ideal owing to their improved thermal conduction efficiency. The AFM indicated smooth surfaces with small RMS roughnesses of~0.7 nm on the pristine diamond substrate (Fig. 3c) and~0.8 nm on the SiO 2 gap layer (Fig. 3d).
The microscopy image of an 80-nm-thick transfer-printed nanoplatelet on the SiO 2 -coated diamond substrate shows an maintained nanoplatelet morphology without any mechanical damage or impurity induced by transfer (Fig. 3e). Fig. S1a shows that some crystalline nanostructures have heights of several nanometers, which should be residual MAPbI 3 molecular islands from coalescence processes that form a continuous film. Thanks to the well-controlled MAPbI 3 molecular islands, we achieved nanoplatelets with smooth surfaces. AFM image of the transfer printed nanoplatelet (Fig. S2) shows that the RMS roughness is 1.7 nm, which is consistent with that of the initial nanoplatelet deposited on mica substrate. This further confirms the intact morphology of the nanoplatelet WGM cavity.
PL spectra were then measured using a 343-nm femtosecond laser as a pumping source. The WGM cavity was uniformly

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excited from its top surface. Emission from the cavity was then collected through a microscopic objective lens. The collected emission light beam was split into two beams and sent into a spectrometer and a camera concurrently. Fig. 4a shows a twodimensional (2D) pseudo-color plot of the emission spectra as a function of P for the nanoplatelet laser on a diamond substrate with a 100-nm-thick SiO 2 gap layer. P in μJ cm −2 was used throughout the study to make the evaluation of lasers easy. At a low pump density (P ≤ 52.19 μJ cm −2 ), each emission spectrum shows a broad Gaussian line profile with an FWHM of Δλ 47 nm, which is the typical linewidth of MAPbI 3 spontaneous emission. At a high pump density (P > 52.19 μJ cm −2 ), several sharp peaks with Lorentz line shape appear. Their amplitudes then grow rapidly with pump density, while the broad Gaussianprofile spontaneous emission peak remains almost unchanged. The clear threshold in linewidth is one of the key properties of lasing [47]. Fig. 4b plots the dependence of output intensities on P. Output intensity has a nonlinear dependence on P above the lasing threshold, with a kink at the threshold (52.19 μJ cm −2 ). The clear threshold in output intensity is the second key property of lasing [47]. The FWHM plot (Fig. 4c) shows a large value of~51 nm below the threshold and a sudden drop to 0.42 nm above the threshold. The narrow linewidth (Å) of emission is the third key property of lasing. Fig. 5a, b show the 2D emission spectra for a nanoplatelet on a diamond substrate with a 200-nm-thick SiO 2 gap layer and a mica substrate, respectively. Figs S3 and S4 show the microscopy and AFM images, respectively. The laser on the substrate with a 200-nm-thick SiO 2 gap layer shows a slightly lower lasing threshold of~43.58 μJ cm −2 , benefiting from higher refractive index contrast at the nanoplatelet/SiO 2 boundary. The sample on the mica substrate shows the lowest lasing threshold of 18.2 μJ cm −2 because of the highest refractive index contrast at the nanoplatelet/substrate boundary. Furthermore, the transferring process, wherein the thermal release tape needs to be baked to release the nanoplatelets, may also change the gain property of perovskites slightly [41]. This deficiency could be avoided in the future by directly preparing the perovskite lasers on the diamond-based substrate. Fig. 5c-e present their lasing spectral characteristics. The FWHM of the lasing peak of the nanoplatelet laser on the 100nm-thick SiO 2 gap layer at 784.8 nm is 0.4 nm with a P of 53.90 μJ cm −2 . The corresponding Q is~1962. The FWHM (~0.68 nm) of the lasing peak of the nanoplatelet laser on the 200-nm-thick SiO 2 gap layer at 777.8 nm is slightly larger than that of the nanoplatelet laser on the 100-nm-thick SiO 2 gap layer. This difference might be caused by inhomogeneities such as surface defects and uneven morphology from the CVD synthesis, regardless of the substrate used. These inhomogeneities impact nanoplatelets' PL quantum yields and scattering losses; hence, the lasing performances are different. The resonant wavelength difference should be from different edge lengths of nanoplatelets and effective refractive indices of substrates. The corresponding Q is~1143. The FWHM (~0.74 nm) of the lasing  peak of the nanoplatelet laser on the mica substrate at 778.5 nm is close to that on the 200-nm-thick SiO 2 gap layer at a P of 20.39 μJ cm −2 . The corresponding Q is~1052. Fig. S5 shows the PL images of MAPbI 3 nanoplatelets with different shapes above the lasing threshold and the corresponding optical mode simulations. Fig. S5a, b show that lasing mainly couples out at the cavity edge, suggesting good optical confinement from nanoplatelet WGM cavities. Owing to the large leakage energy loss, lasing did not occur in the perovskite nanoplatelet on diamond substrates with a 50nm-thick SiO 2 gap layer. Fig. S6 shows that emission from the nanoplatelet with an edge length of~30 μm and surface roughness of~1.0 nm remains in broadband spontaneous emission after excitation with a pump density of up to 53.7 μJ cm −2 . Simulation results show that lasing would not occur at even higher pump densities owing to the large portion of leakage field in the diamond substrate (Fig. 2a).
We evaluated the heat dissipation in perovskite nanoplatelet lasers on the diamond substrate by temperature variations under optical pumping conditions. This is obtained by monitoring the peak wavelengths (λ 0 ) of the WGM resonances as a function of P, which are affected by the thermal-optic and thermal expansion effects of the resonator materials and surrounding environment [34]. First, the temperature sensitivity of the fabricated MAPbI 3 perovskite nanoplatelet laser is determined to be~146 ± 6 pm K −1 from the temperature-dependent PL (Fig. S7). In our experiments, we set pump density above and below the lasing and damage thresholds, respectively. Fig. 6a-c show the pumpdensity-dependent lasing spectra of nanoplatelet lasers on the diamond substrate with 100-nm-and 200-nm-thick SiO 2 gap layers together with mica substrate, respectively. Among them, the sample on the 100-nm-thick SiO 2 gap layer exhibits the smallest blue shift of resonant peaks. Fig. 6a shows a 90-pm blue shift in the lasing peak as the pump density increases from 52.86 to 53.90 μJ cm −2 . As the exciton binding energy of MAPbI 3 is only~10 meV, much smaller than the room-temperature thermal energy of~26 meV, the exciton-polariton-related wavelength shift can be eliminated [48,49]. Furthermore, the wavelength of the pump laser is fixed at 343 nm, excluding the possibility of a band-filling effect [50,51]. Equations (1) to (4) show that wavelength shifts originate from a temperature increase (~0.6 K) induced by the absorption of pump energy that is transferred to nonradiative losses. However, the nanoplatelet laser with a 200-nm-thick SiO 2 gap layer shows a more evident blue shift of 280 pm as the pump density increases from 46.73 to 48.16 μJ cm −2 , which corresponds to a temperature increase of 2.0 K. While nanoplatelet lasers on the mica substrate have the lowest pump threshold, it still shows a blue shift of~280 pm as the pump density increases from 18.86 to 20.39 μJ cm −2 , which corresponds to a temperature increase of~2.0 K. Hence, a relatively high temperature increase should result from the low thermal conductivity (0.75 W m −1 K −1 ) of the mica substrate [52]. Fig. 6d-f depict the λ 0 of the three samples as a function of P. Fitting the λ 0 as a function of P shows that nanoplatelet lasers on the diamond substrate with a 100-nm SiO 2 gap layer have the lowest pump density sensitivity of~0.56 ± 0.01 K cm 2 μJ −1 . This value is one to two orders of magnitude lower than the previously reported results of lasers, which also used the MAPbI 3 as the gain medium but with a low thermal conductivity glass substrate [43]. Fig. S7b summarizes the pump density sensitivities of different MAPbI 3 perovskite lasers. Nanoplatelet lasers on the diamond substrate with a 200-nm-thick SiO 2 gap layer have higher pump-density-dependent temperature sensitivity of 1.1 ± 0.1 K cm 2 μJ −1 . Nanoplatelet lasers on the mica substrate have the highest pump-density-dependent temperature sensitivity of~2.20 ± 0.2 K cm 2 μJ −1 . This value is approximately three times higher than that of the sample transferred on a diamond substrate with a 100-nm-thick SiO 2 gap layer. These

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results confirm that efficient heat management has been realized in perovskite lasers by utilizing a diamond substrate with high thermal conductivity. While efficient heat dissipation has been demonstrated under pulsed laser excitation in this study, utilization of high-thermal-conductivity diamond substrate to alleviate heat accumulation of perovskite lasers would also be effective in continuous wave excitation cases. According to Equation (1), the heat dissipation principle is quite similar for perovskite lasers under different injection conditions.
We performed thermal diffusion simulations to further understand the heat dissipation effect of the diamond substrate. Fig. S8 shows the temperature variation of nanoplatelet lasers on diamond substrates with 100-and 200-nm-thick SiO 2 gap layers and a mica substrate pumped by a 343-nm femtosecond (290 fs) laser at an energy density of 84 μJ cm −2 . The heat of the nanoplatelet laser on the mica substrate dissipates slowly owing to the low thermal conductivity of mica compared with those on the diamond substrates with 100-and 200-nm-thick SiO 2 gap layers. At 50 ns, the device temperature decreases to~313.9 K. Due to the thicker SiO 2 gap layer, the heat reaches the diamond later in the nanoplatelet laser on the diamond substrate with a 200-nm SiO 2 gap layer compared with that with a 100-nm SiO 2 gap layer. Therefore, the temperature in the nanoplatelet laser on the diamond substrate with a 100-nm SiO 2 gap layer decreases faster than that with a 200-nm SiO 2 gap layer after 30 ns. At 50 ns, the temperatures of nanoplatelet lasers on the diamond substrates with 200-and 100-nm SiO 2 gap layers decrease to~303.6 and 300.8 K, respectively. Hence, the diamond substrate with a 100nm SiO 2 gap shows the most efficient heat dissipation in the three devices, which agrees well with the experimental results.

CONCLUSIONS
We demonstrate an efficient thermal management method wherein perovskite nanoplatelet lasers are mounted on a diamond substrate. The fabricated lasers achieved a Q factor of 1962, a lasing threshold of 52.19 μJ cm −2 , and a pump-densitydependent temperature sensitivity of~0.56 ± 0.01 K cm 2 μJ −1 . The sensitivity is one to two orders of magnitude lower than the values for previously reported perovskite nanowire lasers on glass substrates [43]. The high-thermal-conductivity diamond substrate enables the nanoplatelet laser to operate at a high pump density. Additionally, using the SiO 2 gap layer enables strong vertical confinement. Besides the success of our study on heat dissipation, more efforts will be needed for electric injection perovskite micro-/nanolasers with higher stability, including high-quality gain medium and large carrier mobilities.