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. 2021 Feb 17;6(8):5297–5309. doi: 10.1021/acsomega.0c05414

Achieving Optical Gain of the CsPbBr3 Perovskite Quantum Dots and Influence of the Variable Stripe Length Method

Saif M H Qaid †,‡,*, Hamid M Ghaithan †, Bandar Ali Al-Asbahi †,§, Abdullah S Aldwayyan †,∥,⊥
PMCID: PMC7931209  PMID: 33681570

Abstract

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High-quality inorganic cesium lead halide perovskite quantum dot (CsPbBr3 PQD) thin films were successfully deposited directly from a powdered source and used as an active laser medium following the examination of their distinctive surface and structural properties. To determine the suitability of the CsPbBr3 PQDs as an active laser medium, amplified spontaneous emission (ASE) and optical gain properties were investigated under picosecond pulse excitation using the variable stripe length (VSL) method. The thin film of CsPbBr3 PQDs has exhibited a sufficient value of the optical absorption coefficient of ∼0.86 × 105 cm–1 near the band edge and a direct band gap energy Eg ∼2.38 eV. The samples showed enhanced emission, and ASE was successfully recorded at a low threshold. The light emitted from the edge was observed near 2.40 and 2.33 eV for the stimulated emission (SE) and ASE regimes, respectively. The nonradiative decay contributes excitons dominant over biexcitons in the sample edge emission above the ASE threshold, making it practical for CsPbBr3 PQDs to be used as optical gain media without undergoing repeated SE processes above the threshold over long periods. A high value of the optical gain coefficient was recorded at 346 cm–1.

Introduction

In the past decade, hybrid organic/inorganic metal halide perovskites have emerged as a new class of photovoltaic materials. They outperformed other materials in photonic applications owing to their high absorption coefficients (exceeding 104 cm–1 near the band edge), long-range balanced electron- and hole-transport lengths, and high carrier mobility.1−7 Based on these properties, the absorption coefficient of perovskites exceeds that of the famous semiconductors in high-performance commercial optoelectronic devices and even that of GaAs.8 The photoluminescence (PL) quantum yield (PLQY) is the ratio of the absorbed light to emitted light. Thus, a semiconductor that exhibits strong absorption can cause high light-to-electricity conversion efficiency corresponding to high luminescence efficiency. It can also be used to create lasers. In other words, many of the basic physical properties of perovskite materials, which improved the photovoltaic efficiencies, enhanced the performance of light-emitting devices. These properties have prompted the researchers to use perovskite as an active laser medium to achieve greater optical gain. The optical gain in semiconductors plays a significant role in the evaluation of the potential of a given semiconducting material in photonic applications. Thus, a positive optical gain is necessary (albeit insufficient) to realize a semiconductor laser diode.

Based on the above perovskite features, amplified spontaneous emission (ASE) and perovskite laser will be having a big growth spurt. Based on the composition, structure, and morphology engineering, for example, perovskite micro–nanolasers have achieved rapid advancements.1,9−14 Owing to the flexibility of structure-based-perovskite materials, their shapes and sizes can be easily manipulated as quantum dots (QDs),10 nanowires (NWs),11 nanoparticles (NPs),12 etc. Recently, perovskite QDs have emerged as the new generation of optical gain materials for ASEs and lasers owing to their high PLQYs.15,16 Moreover, some studies have confirmed that an inorganic cesium lead halide (CsPbX3) system exhibits a relatively higher thermal stability (∼500 °C) compared with the MAPbX3 system.17,18 There are some strategies to improve the stability of the PL intensity of the CsPbX3 QDs by ligand engineering19,20 (lengths of ligands—the short branched chains) or by incorporation into hydrophobic polymer matrices.21 Compared with CsPbI3 and CsPbCl3, CsPbBr3 exhibits significant PLQY features and improved stability; therefore, most reports focused on the low-threshold ASE of CsPbBr3 QDs22 or equipped them with external optical cavity configurations to obtain coherent laser output.14

However, laser/ASE threshold is dependent on the excitation stripe length because the change of stripe length L is implemented as a change of photon cavity loss, which is inversely proportional to L. But apart from the excitation stripe length, ASE threshold also depends on film thickness, film roughness, pump pulse width, excitation stripe width, collection optics, etc. Therefore, the ASE threshold only judges the presence of ASE under certain experimental conditions and should not be used to characterize materials for lasers and amplifiers. Also, ASE parameters are affected with laser pulse duration due to the unique properties of the short and ultrashort laser pulse durations to create a more excited state. With a short pulse duration, the threshold fluence will become lower. The ultrashort pulse duration yields better results and typically allows a lower threshold, high optical gain, higher photostability of the active materials.

Historically, the ASE performance of CsPbBr3 QD thin films was reported by Yakunin et al.23 with the ASE thresholds of 5 and 450 μJ cm–2 under femtosecond and nanosecond laser excitation, respectively. Pan et al. have reported the ASE threshold of the CsPbBr3 thin films to be 192 μJ cm–2 and 12 mJ cm–2 under single-photon and two-photon pump laser, respectively.10

A series of studies were conducted to further reduce the ASE or lasing threshold of the CsPbBr3 QD thin films.24−29 The ASE thresholds were reported to be 12,9 22,22 and 60 μJ cm–2 under 150 fs, 70 ps, and 2 ns excitation of pumping conditions,24,25 respectively. These values are comparable to the leading values of semiconducting polymers,26 colloidal quantum dots (CQDs),27 and colloidal nanoplates28 under the same excitation conditions.

However, \low-dimension crystals have promising applications as optical amplifiers.30−34 Optical amplification can be investigated by photoexciting the gain medium and measuring its spectral absorption on time (ultrafast transient absorption). The net modal gain indicates the efficiency of light amplification per unit length in the material and the quality of the resonator needed, which plays a significant role in the evaluation of a semiconductor material that can be used for creating laser and photonic devices.23 There are common methods to determine the optical gain in active material, such as variable stripe length (VSL) method,35 transmission method,36 and ultrafast transient absorption method. The VSL method is a very popular tool to obtain reliable gain values and used in the quantitative studies of the optical gain properties of thin films acting as an active layer in photonic devices. Among these methods, the stripe length method is the most widely used. Moreover, it can be studied using the VSL method to report the gain/offset with propagation loss as the net modal gain, as the optical amplification is given as gain per unit length. The VSL method has been applied to perovskite materials used as thin films. Using this method, the net modal gains were found to be in the range of 66–250,9 125,24 and 6–10 cm–1.37 Subsequently, CsPbBr3 perovskite nanocrystals (NCs) have emerged as an efficient solution-processed gain medium, with a net modal gain that is greater than 450 cm–1.23,38

As far as we know and according to our best knowledge, up to date, this field lacks reports that study the investigation of the ASE under picosecond pumping excitation of perovskite NC films.

In this paper, to achieve a successful examination, we study the ASE parameters and optical gain properties of high-quality inorganic cesium lead halide perovskite quantum dot (CsPbBr3 PQD) thin films under picosecond pulse excitation. The VSL method was also employed to evaluate the net modal gain (optical gain factor) by relating the measured variation in the light output with the variation in the length of the excitation beam. Subsequently, the optical gain properties were also investigated in detail and an interpretation of the optical gain nature was proposed, i.e., the discussion on the optical gain of the so-called “exciton” and “biexciton” to show the dominance of excitons or biexcitons in both regimes.

Results and Discussion

Structural and Surface Morphology Characteristics

To investigate the structural properties, morphology characteristics, and chemical compositions of the cesium lead bromide CsPbBr3 PQD material, measurements via high-resolution transmission electron microscopy (HR-TEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS), as well as atomic force microscopy (AFM) characteristics, were obtained. Figure 1a and its inset present the typical low- and high-resolution (enlarged image) TEM images of CsPbBr3 PQD after dilution in hexane solution, which shows the structure of the QD, with an average particle size of ∼6 nm, confirming the quantum confinement effect.

Figure 1.

Figure 1

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(a) TEM image of monodispersed CsPbBr3 PQD. (b) XRD pattern of the CsPbBr3 PQD thin film.

From the XRD pattern (Figure 1b), a set of strong diffraction peaks is seen with distinct peaks located at approximately 2θ = 15.33, 21.70, 30.87, 34.45, 37.90, 43.93, and 59.03° corresponding, respectively, to diffractions from (100), (110), (200), (210), (211), (220), and (321) planes of the CsPbBr3 perovskite. The XRD pattern of the crystalline structure of the CsPbBr3 PQD material represents a cubic phase at room temperature (RT), which is attributed to the combined effect of the PQD surface, high reaction temperature, and surface energy contributions.22,39 The crystallite size has been estimated from the XRD pattern for the (100), (200), (211), and (220) peaks. The crystallite size (D) is given by D = 0.9λ/(β cos θ), where λ is the X-ray source wavelength, θ is the Bragg angle, and β is the full width at half-maximum (FWHM) of the peak.4 XRD estimation gives a QD size of around 9.3 nm. The XRD results confirmed the particle size, which can be observed from the TEM image. Furthermore, to check the in-depth chemical states of the CsPbBr3 PQD thin film, measurements via XPS were conducted to analyze the binding status of the CsPbBr3 components. The XPS data, presented in Figure 2, also indicate the presence of CsPbBr3 in the film, and the full XPS spectra of the prepared sample are presented in Figure 2a and expanded in Figure 2b–d. Moreover, the XPS spectrum of CsPbBr3 indicates that most of the strong XPS peaks reveal the presence of cesium, lead, bromide, and carbon. The XPS results reveal that the film has successfully deposited from high-quality perovskite CsPbBr3 PQDs. The corresponding peak of carbon (C) appeared due to the adsorption of C atoms on the surface of the CsPbBr3 PQD thin film. The peak of C, as a charge reference to rectify the XPS spectra presented in Figure 2a (insets) at a binding energy of around 284.8 eV, is a typical peak of chemisorbed carbon C 1s.40 The results of the XPS analysis and the electronic effects of spin–orbit coupling are presented in Table S1. The XPS spectral lines are identified by the shell from which the electron was ejected (1s, 2s, 2p, etc.). Then, the atom releases energy through the emission of an Auger electron. As can be seen from the AFM image and cross-section analysis (Figure 3a,b), the surface morphologies of the CsPbBr3 PQD thin films exhibit high surface coverage and low roughness (surface defect) (root mean square (RMS) Rq = ∼5.44 nm and average surface roughness Ra = 4.22 nm). In optical studies, the good surface morphology of the film is an important factor affecting its optical characteristics. The active layer requires surface smoothing to reduce the loss of the incident angle of pumping light at the air–CsPbBr3 PQD thin-film interface to achieve high-performance light emission when it used in the creation of ASE, lasing applications, and the active layer in photonic devices. Therefore, the TEM, XRD, XPS, and AFM investigation of the CsPbBr3 PQDs confirmed that PQDs were successfully obtained from powder and were uniformly distributed in the alloying, small size, and stable cubic phase.

Figure 2.

Figure 2

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(a) XPS survey spectrum of CsPbBr3 PQD; the inset presents the XPS spectrum for C as a charge reference using the peak at a binding energy of around 284.8 eV. (b–d) High-resolution XPS spectra of (b) Cs 3d, (c) Pb 4f, and (d) Br 3d of CsPbBr3 PQDs.

Figure 3.

Figure 3

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AFM images: (a) two-dimensional (2D) topography and (b) a cross-section analysis of CsPbBr3 PQDs.

Optical Properties

Figure 4a presents the absorbance, PL, and ASE spectra of the sample. The absorbance spectrum tends to increase with an increase in photon energy. Moreover, it shows an absorption edge at ∼502 nm (2.47 eV) with a sharp peak at 508 nm (2.44 eV). This peak indicates the occurrence of an exciton transition and indicates the high quality of the film41 crystal, which agrees with the results of TEM, XRD, and AFM. CsPbBr3 PQDs have a very similar range of absorption to inorganic semiconductor NCs, such as GaAs, CdSe, and PbSe,42−44 and the absorption coefficient (α) of the QDs film, surpassing even that of GaAs, which is a leading semiconductor in high-performance commercial photonic devices, with α ∼ 1.48 × 105 and 0.86 × 105 cm–1 at 410 nm and near the band edge, respectively. Therefore, CsPbBr3 PQDs with higher absorption can efficiently convert light into electrical current; thus, they can support higher optical gain.

Figure 4.

Figure 4

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(a) Experimental absorbance spectra of the CsPbBr3 PQD thin film. The calculated band gap and exciton absorption spectra along with their summed spectrum are presented. Two PL spectra (PL and ASE) at low and high pump energy densities are presented in green for comparison. (b) PLQY evolution of the CsPbBr3 PQD measured at different storage times in air.

The absorption spectrum was recalculated using the Elliot formula, following the procedure proposed by Sestu et al.45 The results are also presented in Figure 4a. The best-fitting parameters result in a direct band gap energy of 2.51 eV, which is in close agreement with the value in the previous reports,10,12,46,47 an exciton binding energy of 58 meV, which is comparable to the values reported, and an exciton peak broadening of 68 meV. The dimensions of the QDs are comparable to the de Broglie wavelength of electrons; thus, the energy difference between the two consecutive states exceeds the multiplied values of the absolute temperature (T) and Boltzmann’s constant (kB), which causes a quantum confinement effect that imposes a limitation to the mobility of electrons and holes. Based on this, the exciton binding energy is 58 meV, which is sufficiently high for the enhancement effects to be observed at RT; given that for T = 297 K, the characteristic thermal energy is kBT = 25.63 meV.48,49 Thus, the CsPbBr3 PQDs have features of both perovskite materials and quantum confinement.

The observed PL signal centered at 2.40 eV, with a full width at half-maximum (FWHM) of 77 meV, and the band-edge PL peak is symmetric under 471 nm continuous-wave excitation (Figure 4a). The symmetric PL peak and narrower FWHM could reflect the distribution condition of the PQDs in size and morphology, which results in a more uniform PQD thin film and better monochromaticity.50 In semiconductors with a direct band gap, it can be found that two types of photoexcitation are possible near the band edge. The prevailing type of photoexcitation is dependent on the magnitude of the Coulomb attraction between positively charged holes and negatively charged electrons, which are screened by the dielectric properties of the materials.51 The two types of photoexcitation are the free electron–hole pairs and bound electron–hole pairs (excitons) or trions (charged excitons) even at RT.52

The absorption edge and PL peak of CsPbBr3 PQD are located at ∼508 and 516 nm, respectively, with an ultrasmall Stokes shift (37 meV) indicative of a sharp band edge and minimal vibrational relaxation, which is capable of sustaining optical gain close to the band edge. A low Stokes shift plays a significant role in the reduction of energy loss due to heat during pump downconversion in laser applications. Furthermore, the light emitted from the edge was observed near 2.40 and 2.33 eV for the photoluminescence (spontaneous emission) and ASE regimes, respectively. The ASE peak corresponds to the end of the shallow absorption tail (Urbach tail) (Figure 4a). Storing the film for 1 year under ambient conditions causes the CsPbBr3 PQD thin film to exhibit a 20% drop in the PLQY after 6 months and around 35% photobleaching after 1 year, which reflected from a reduction in the time-dependent PL intensity of the PQDs (Figure 4b). The improved stability can be ascribed to the short branched chains, which will increase the binding energy between the ligands and QDs and the lengths of ligands, which is related to the strength of the van der Waals (VDW) interactions among the ligands, and the strength is dominant to determine the crystalline structure and follow the optical properties of PQDs.20,53,54 This indicates that the as-synthesized CsPbBr3 PQDs can be appealing as luminescent materials for lasing. Moreover, they can function as suitable building blocks in high-efficiency light-emitting diode (LED) applications. In terms of the initial wavelength, the blue shift was presented by the time-dependent PL of the PQDs, which was attributed to the reduction in particle sizes with time due to light emission, depending on the particle sizes or the effect of oxidation by singlet oxygen for the same compositions.55−57 The PL blue shift and photobleaching of PQDs are believed to be attributed to the irreversible photo-oxidation of PQDs. The enhanced optical and chemical stability of the CsPbBr3 PQD sample is attributed to the absence of organic cations in the perovskite and the combined effect of the QD structure and the QD surface as well as the surface energy contributions.

ASE Characterizations

The characterization of films via TEM and XRD exhibited better film quality and crystallization and lower film surface defects, corresponding to the roughness value in AFM results. All of these results confirmed the quantum confinement effect of CsPbBr3 PQDs. Surface smoothing can decrease the loss of incident angle of pumping light at the air–PQD thin film interface. Surface defects are any imperfection, damage, or deformation at or near the film surface and are defined sometimes as roughness that can be caused, for example, by moisture. These surface defects play a major role in deciding the optical and electrical properties. In other words, the roughness induces an increase in surface defects and hence enhances defect emission. So, we expected that the smoother surface will decrease the loss of incident pumping light at the interface of air and thin film, which may be beneficial when it is used as an active layer in photonic devices or to the creation of ASE in the CsPbBr3 thin films. Adverse effects such as a large number of pin holes and poor surface coverage in the thin films could result from large-size crystallite agglomeration of CsPbBr3 QDs.20 This will definitely result in a higher level of emission, which can be useful to improve the performance in ASE and lasing applications and the creation of thin films and active layer photonic devices. Also, the higher level of emission will lead to highly qualified lasing features of low threshold and narrow linewidth attributed to the reduction of PL loss (optical gain) of the material. This will be discussed later in section Optical Gain Calculations Using the Variable Stripe Length Method. Other reasons for the small capture cross-sections of trap states are “slow” Auger recombination probability and low bimolecular recombination.58 The Auger recombination probability increases with the quantum confinement effect due to the relaxed momentum conservation requirement.58−60 Another parameter that is strongly dependent on the quantum confinement effect is the biexciton binding energy; a biexciton consists of two neutral bound excitons red-shifted compared to the unbound excitons because of Coulombic effects.58

The ASE values provide a better benchmark for the comparison of the materials in terms of their intrinsic suitability in gain applications. The ASE can be explained as follows: if stimulated emission (SE) is achieved at a certain threshold and two features are typically seen, first, the emission of the material as a function of pump laser energy will encounter a drastic change in the slope at a certain threshold, and second, one of the emission spectra usually observes line narrowing. Again, this indicates a transition from ASE to SE. Other indicators also exist, including the reduction of carrier lifetime. The realization of all of the above-mentioned benefits can be verified from Figure 5a,b. From Figure 5b and its inset, it can be seen that at low pump fluence, the PL spectra exhibit a Gaussian profile with an emission maximum that is red-shifted by ∼9 nm at high pump fluence. As the excitation intensity increases, a sharp and spectrally narrow peak (FWHM of ∼0.138 meV) emerges in the lower-energy side of the fluorescence peak and rapidly increases at higher pump fluence.

Figure 5.

Figure 5

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(a) PL emission spectra recorded at a pump fluence below and above Eth and incorporated into the plots to distinguish between ASE and PL. The inset presents the respective recombination kinetics of PL and ASE that were extracted for part (a). (b) Corresponding PL spectra for pump fluences above and below the ASE threshold. The inset presents the plots of the integrated emission intensity versus pump fluence in the CsPbBr3 PQD thin films. (c) ASE intensity in the CsPbBr3 PQD thin films under continuous ASE operation as a function of the number of laser shots at an excitation intensity of ∼2Eth. The left and right insets present the PL spectra of the sample to distinguish between before and after ∼33 000 shots, respectively. The shaded regions indicate the respective scaled PL emission spectra recorded at a pump fluence below Eth.

It is worth mentioning that the operational stability of ASE was verified by tracking the measurements of the PL spectra above the ASE threshold in sufficient time during continuous pumping under ambient conditions (the excitation density was set at 2Eth) for at least 32 400 laser shots. In real laser applications, the ASE operational lifetime, which is quantified as the number of pump laser pulses required to achieve an ASE intensity reduction of factor 1/e. To examine the operational stability of ASE, the laser device is operated at an excitation density that allows sufficient light amplification, and the ASE threshold determines the lowest excitation density required to achieve light amplification. From the extrapolation of the experimental data, Figure 5c presents an evidently higher ASE intensity stability of up to ∼23 000 laser pulses; then, a progressive intensity gradually decreases after a long time. After 33 000 pulses, the ASE intensity of the film is still 90% of the initial value, therefore, we can expect a long ASE lifetime (1/e) when the QDs films operate in the air, demonstrating the remarkable photo-stability. Thus confirming significant photostability of the QDs films under continuous picosecond pulsed-laser excitation. Apart from the effect of lengths of ligands and branched chains,20 our results located within between results of those fond by a nanosecond laser21 and a femtosecond laser,20 which confirmed that the ultrashort pulse duration of pumping laser typically allows higher photostability of the active materials.

Based on the above, our results suggest that the CsPbBr3 PQD gain medium is an excellent material platform for perovskite laser diodes. Moreover, the small size and large surface strain of QDs cause a substantial size and strain broadening. Thus, owing to the robustness of PQD, we were able to induce ultrastable ASE in PQD films. The ultralow pump threshold (22 μJ cm–2) and increased stability induce stable ASE under picosecond laser shots, thus paving the way for the use of these QDs as viable optical gain media.29 A comparison with other higher performance perovskite gain media is summarized in Table S2. For this reason, and to explore the potential of CsPbBr3 PQDs in laser application, the ASE characteristics from the CsPbBr3 PQD thin film were investigated by evaluating the PL with different pumping energies and calculating the optical gain using the VSL method as conventional excitation.

Optical Gain Calculations Using the Variable Stripe Length Method

Here, CsPbBr3 PQD as an active material was pumped by a homogeneous line of a laser beam emitted from a high-energy pulsed laser. Then, the emitted light was collected from the edge of the sample as the line widths of the edge PL spectra are narrower than those of the surface PL spectra. This is because the amplification degree in the edge PL is much greater than that in the surface PL due to the much longer optical pass in the edge PL configuration, even though their optical gains are identical.61 When the laser modes emanating from the active material propagate, they suffer from additional loss per unit length. The gain with propagation loss is recorded and provided as the net modal gain. It is measured using the VSL method. To measure the optical gain and its properties and to obtain high-efficiency optical output, a sufficient thickness of the thin films is required. In the quantitative studies of the optical gain properties of CsPbBr3 PQDs, the VSL method was based on the excitation of a semiconductor specimen with a picosecond laser beam of ∼70 ps and pumping energy that is 5 times the threshold energy of ≈112 μJ cm–2 and λex of 410 under ambient conditions at RT. The VSL configuration is presented in Figure S6 (Supporting Information), and the photograph of the CsPbBr3 PQD thin film excited above the ASE threshold is presented in the inset of Figure 6a. The variations of the edge-emitting light output as a function of increasing pump light excitation intensity by increasing the stripe length between 0 and 500 μm in a CsPbBr3 PQD thin film with a 20 μm increment are collected using a spectrometer. The PL intensity increases in the linear form by evaluating l in the first region (spontaneous emission) up to lth = 280 μm and then shows a fast, exponential increase above lth in the second region (stimulated emission), as presented in Figure 6b. The ASE threshold is clearly observed in the plot of the PL intensity (I) versus the stripe length as a sharp increase in the slope at l > lth with a narrow peak at 535 nm. A sharp ASE peak can be detected to split PL evaluation into two regions, indicating that the ASE process occurs in this CsPbBr3 PQD. A further increase in the excitation length from ls (ls: length of saturation in ASE intensity) results in a subexponential increase in the ASE intensity owing to the gain consumption phenomenon,61 with clear regions of PL, ASE, and saturation. Also, ls is defined as the gain lifetime multiplied by the speed of light within the gain medium. Also, the development of ASE can be attributed to an increase in the absorption rate of optical gain.

Figure 6.

Figure 6

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(a) PL spectra of a CsPbBr3 PQD thin film excited at λ = 410 nm by picosecond laser pulses and recorded using the VSL method to estimate the optical gain of the CsPbBr3 PQD thin film. (b) Data from (a) showing the plotted PL intensity as a function of the stripe length. A threshold stripe length and length saturation are indicated.

Now, to derive the magnitude of modal or net gain g of the CsPbBr3 PQD thin film using the standard VSL method, the I versus l dependence is usually analyzed, and the exponential data are fitted to the plot of the PL intensity (I) versus the stripe length using the VSL expression and the boundary condition IASE (0) = 0, as well as the below equation23,63−68

graphic file with name ao0c05414_m001.jpg VSL 1

where l, g, A, and IASE denote the excitation stripe length, optical gain coefficient, cross-sectional excited area mapped by the penetration depth, and detected ASE intensity, respectively.

Both the SE spectra and gain studies were described under optically pumped conditions, and the saturation of the amplification process is presented in Figure 5b. This saturation plays a significant role in the determination of the spectral distribution of the SE and in the determination of the narrow linewidth of the ASE spectrum. These studies suggest that the net gain in high-purity material, as in our case, does not result from band-to-band recombination; thus, an interpretation in terms of another type is suggested. However, if the VSL expression above does not allow one to simultaneously fit both regimes. This can be attributed to the fact that in QDs, both spontaneous and stimulated emissions arise from two types of excitations (luminescent quasiparticles), namely, excitons and biexcitons,67,68 respectively. The contributions of the exciton and biexciton to the emission intensities are determined to quantify the optical gain magnitudes. The excitons are bound electron–hole pairs, whereas the biexciton, formed from binding two excitons together in condensed exciton systems, two-photon absorption, or excitation from the single exciton state to the biexciton state. Biexcitons are of practical importance for quantum information due to their features for constructing coherent combinations of quantum states.52,58,68−71 The effects of both the exciton and biexciton become more prominent as the size of the NC decreases. The short lifetime of biexciton (doubly excited) emission (which is limited by non-radiative Auger recombination in low-dimensional structures) is not pronounced in the spontaneous emission regime, because non-radiative decay acceleration contributes excitons dominant over that of biexcitons in the sample edge emission below the ASE threshold. In other words, Auger recombination is not dominant at low pump fluence, whereas manifests under high pump fluence. Generally, to observe the biexciton, emission high excitation energy density or/and low temperature are required because the biexciton emission is a nonlinear process. The materials that emit biexciton at low excitation energy density will contribute to biexciton-associated optoelectronic applications. Auger recombination occurs where the excess energy from the recombination of electron–hole is transferred to electrons or holes that are subsequently excited to higher energy states within the same band instead of giving off photons (the radiative process).58,70

The biexciton emitter decays very quickly, which is associated with the cooling of the hot excitons into the band-edge state.58,72,73 Therefore, this biexciton state has been used to study the carrier energy relaxation in traditional semiconductor QDs and perovskite materials. In traditional semiconductor QDs such as CdSe or PbSe, the optical gain may be due to only the biexciton–exciton transition that is a result of double degeneracy of the electronic states. By comparing CsPbBr3 PQDs to traditional QDs, we expect different behavior because of the fast recombination lifetime in perovskites compared to that in the semiconductor QDs.58,70 And to ascertain if the fast recombination in perovskite comes from the biexcitons, we used a procedure based on the characterization of the recombination time at the exciton and biexciton emission energies and provide an estimation of Auger recombination losses.

From data of the optical gain in PQDs calculated from the VSL method, we will discuss if the observed ASE can be explained by the biexcitonic emission (i.e biexciton–exciton transition) or no. To elucidate the dominant above the threshold (excitons or biexcitons), the previous VSL formula can be re-rewritten as follows67,68

graphic file with name ao0c05414_m002.jpg VSL 2

where Gbx denotes the biexciton net gain and Abx and Ax denote the constants proportional to the ASE intensities of biexcitons and excitons, respectively. These experimental parameters can be extracted by fitting the experimental results with the above equation in the SE region.

The application of the last equation enables the fitting of the experimental points below and above the lth, including saturation. Now, the fitting processes of the experimental data with the (VSL eq 1) and (VSL eq 2) equations in different regions (Figure 7) extract the net gain of g = (346, 167, and 94) cm–1 and Gbx = 318, 110, and 30 cm–1. The spectra in the inset of Figure 7f was added with a log y scale, to evidence the eventual presence of exponential increase. The solid line in Figure 7a indicates the results obtained from the fitting process. The fitting is highly sensitive to the range of data selected and would only work if there are sufficient data points in both PL and ASE regions but not in the saturation region, which also makes it difficult to compare results from different experimental set-ups. In general, we observed that the net gain values obtained from the fitting of the experimental data with the first equation are greater than those obtained from the fitting with the second equation, which allows one to elucidate the contribution of excitons dominant over that of biexcitons in the sample edge emission below and above the ASE threshold. This method of comparing and conclusions is similar to what has been done in previous reports reports.9,63,68,74−76 In our case, the saturation effect is negligible due to IASE(L) ≪ IASE(ls). So, the net model gain was measured at lth < l ≪ ls without saturation term, with extract the net gain of g = 346 cm–1 and Gbx = 318 cm–1 for excitons and biexcitons, respectively. This shows the dominance of excitons over the biexcitons without neglecting the contribution of the biexcitons in the ASE emission. In particular, appeared the superlinear increase in the integrated PL of the narrow band with the intensity, which can be understood because the PL comes from biexcitonic recombination in addition to the dominant recombination in this region (excitonic recombination). Also, the overlap of the absorption band edge with the PL emission spectrum (in the spontaneous emission) suggests that the self-absorption effect should take place in explaining the ASE state. The biexcitons emission reduced the self-absorption effect compared to conventional excitonic emission.

Figure 7.

Figure 7

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PL intensity as a function of the stripe length. The solid line indicates the best-fitting curve based on the VSL method to (a–c) equation Inline graphic, and (d–f) equation Inline graphic.

From the above, it becomes clear that the estimated net optical gain of the CsPbBr3 PQD thin film reveals a large g = 346 ± 8 cm–1, primarily caused by the exciton gain. This means that CsPbBr3 PQDs exhibit a large optical gain due to their large absorption coefficient for photons with energy higher than the bandgap energy because the propagating light can be attenuated via absorption and they also exhibit optical losses. The great optical gain and a low surface defect of perovskite film strongly promise high-performance laser devices in the future. Also, this result suggests the feasibility of miniature, solid-state laser devices based on chemically synthesized PQDs. A region of linear variation on this logarithmic plot of output intensity with increasing length (Figure 8a) corresponds to the values of L, which is large enough for the exponential factor in the equation (VSL eq 1) to dominate. In such a region, g can be determined from the slope of the curve. The net optical gain was estimated to be 177 cm–1. Also, attenuation inside the active medium or the loss characteristics have been measured. The propagation losses in a medium can be quantified with a propagation loss coefficient, which is the sum of contributions from absorption and scattering. Also, the loss coefficient of QDs film in the planar waveguide structure determines the robustness of the CsPbBr3 NCs film as the active lasing media. In these measurements, the detected light intensity at lASE as a function of the stripe distance from the sample edge is plotted in Figure 8b. The data were fitted assuming an exponential dependence on length ∼as appropriate for absorption losses through equation IPL = A1 exp(−x/lp) to extract the effective propagation length and losses. The loss coefficient of CsPbBr3 PQDs by utilizing this method is found to be 7.69 cm–1 as a very small value and the total optical gain was estimated to be ∼353.69 cm–1.

Figure 8.

Figure 8

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(a) PL Intensity as a function of the stripe length and linear fitting to determine the modal optical gain. (b) PL Intensity as a function of the distance of the stripe to the edge of the sample (when the whole stripe is illuminating the sample) and fitting to equation IPL = A1 exp(−x/lp) to extract the effective propagation length and losses.

In summary, the characteristics of the optical net gain of CsPbBr3 PQDs were assessed using the VSL method at RT. CsPbBr3 PQDs had a large optical net gain of 346 ± 8 and 318 cm–1 for the excitons and biexcitons, respectively. From a wider perspective, we have developed the non-radiative decay in the SE regime, which contributes excitons dominant over that of biexcitons in the sample edge emission above the ASE threshold. Thus, the optical gain of CsPbBr3 PQDs is dominated by excitons, unlike the ASE regime in which the likelihood of predominantly biexciton-based gain is small in general due to the short lifetime of the biexciton (fast Auger recombination in low-dimensional structures). This makes it practical for such CsPbBr3 PQDs to be utilized as gain media as biexcitons are not needed, as well as repeated SE processes at above-threshold pump intensities over long periods.

Finally, it should be noted that the exponential shape of the VSL curve, followed by a saturation region, is not sufficient to prove the presence of gain. Thus, a full investigation of the emission spectral changes was conducted to show the break in the slope of variation of the emission intensity as a function of pump intensity.

Figure 9 shows two peaks in PL spectrum that make a proper determination of the FWHM difficult in the normal calculation. So, we use the Peak-Fit program to fitting the huge data.

Figure 9.

Figure 9

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PL spectra show two peaks and fitting by the Peak-Fit program.

Figure 10a presents the behavior of integrated PL and FWHM versus the increasing pump energy density by excitation stripe length in the VSL configuration. When the stripe length is short, the PL spectrum is broad. But, as the stripe length increases, the emitted intensity increases superlinearly, and the spectrum becomes narrower, as presented in Figure 10a. The same behavior is observed when the pump energy is increased at a constant stripe length, as presented in Figure 5b. The PQD samples exhibited narrow emission linewidths which are important for both LEDs and lasers since the laser should be monochromatic. The LEDs can benefit from the narrow linewidth to achieve high color purity. The narrowing of PL by increasing the length of the stripe is caused by a phenomenon called ASE. The photons produced by the ASE are not directly emitted; they pass through the gain medium and are amplified numerous times before being emitted from the edge of the sample. Finally, the resulting emission has a bandwidth narrower than that of ASE and exhibits a threshold-like behavior versus pump energy. The exciting region is treated as a one-dimensional optical amplifier. As presented in Figure 10b, the ASE peak is ∼12 nm redshifted with respect to the maximum PL, where the absorption and optical gain are balanced. This can be attributed to the exciton binding energies in the strong self-absorption of PQDs during exciton lasing. Therefore, we can state here the same thing mentioned in the discussion of Figure 10b. In addition, the increase in the excitation length induced a redshift due to the gain consumption and the consequent saturation of the ASE. Thus, the peak energy was redshifted at l > ls (Figure 10b), which may be a consequence of gain consumption due to a higher excitation, which excluded a thermal effect from the redshift mechanism due to the constant excitation pumping energy density in all measurements.61

Figure 10.

Figure 10

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(a) Integrated PL intensity and FWHM behavior versus stripe length. (b) ASE peak position versus stripe length, for the CsPbBr3 PQD thin film under 410-nm excitation.

Conclusions

In conclusion, the CsPbBr3 PQD thin films were successfully deposited directly from a powdered source. They exhibited excellent optical properties and significant long-term photo-stability with time under ambient conditions for more than 1 year. Besides, the ASE regime was recorded under picosecond pulsed-laser operation for an ultralow ASE threshold and narrow emission line widths. Furthermore, the continuous ASE operational stability against photo-degradation and highly optical gain property characteristics were showed in PQDs thin films. Then the optical gain was evaluated using the VSL method around 346 cm–1, which allows the achievement of resonant conditions for lasing. The ASE saturation indicates that the gain consumption induces a PL redshift. The achievement of ultralow ASE thresholds of CsPbBr3 PQDs has important implications for the realization of electrically pumped stimulated emission. The higher level of emission and gain coefficient achieved under picosecond laser for CsPbBr3 PQDs is considered one of the highest values obtained to date. This is expected, given the CsPbBr3 PQDs have a high absorption coefficient, high QD purity, QD surface energy contributions, photo-stability, good film quality, quantum confinement effect of CsPbBr3 PQDs. By considering these merits, our results suggest that PQD is an excellent material that can be used to create a true-green light-emitting device for lighting applications. We conclude that the ASE observed from the PQD thin film is primarily caused by the exciton gain.

Experimental Section

Materials

A high-quality green-emitting cesium lead bromide (CsPbBr3) QD (product number: QD-P-510 powder and oleic acid and oleylamine as capped ligands on the surface) used as the powder was purchased from Quantum Solutions Company (Thuwal, Saudi Arabia, www.qdot.inc). It was prepared through a modified hot injection. Details of the CsPbBr3 QD preparation are presented in ref (19). N-Hexane AR solution with a purity of 99.9%, was purchased from (Avonchem, U.K.), was used to dissolve CsPbBr3 PQD powder.

Synthesis of CsPbBr3 QD Thin Films

For all stages, the glass substrate was washed with a detergent solution (2% micro-90 liquid soap, International Product Corporation, Burlington, NJ), water, acetone, and isopropyl alcohol for 15 min under the ultrasonicator. Then, the glass was dried. About 50 mg of high-quality CsPbBr3 QD used as the powder was dissolved in 1 mL of hexane to obtain a concentration of 50 mg mL–1 and was left to stand overnight to achieve complete dissolution and better dispersion. Finally, the CsPbBr3 QD thin films were prepared using the drop-casting method. 100 μL of the QD solution was dropped on a microscope slide (1 × 2 cm2). Then, the solution was vacuum-dried for 1 h to completely remove the solvent.

TEM Experiment

For TEM characterization, samples were prepared by dilution of 10 μL from CsPbBr3 QDs solution with 2 mL of hexane followed by placing several drops of a dilute CsPbBr3 QDs solution onto a carbon-coated copper grid.

Film Characteristics

Structure and Morphology Characterization

Characterization via high-resolution transmission electron microscopy (TEM) was conducted using TEM-JEOL 2100 HRTEM (JEM-2100F, JEOL, Tokyo, Japan) at an acceleration voltage of 200 kV. The crystal phases of the CsPbBr3 PQD thin films were characterized via XRD. XRD was performed using Rigaku MiniFlex 600 (Tokyo, Japan) and Cu Kα radiation. The scanning angle 2θ was changed between 10 and 80° in steps of 0.01°. To check the in-depth chemical states of the film morphology and investigate the chemical composition and structure of CsPbBr3 PQDs, the measurement was performed using an XP spectrometer (JPS-9030, JEOL, Tokyo, Japan). Moreover, an aluminum anode was utilized to generate the Al Kα (photon energy = 1486.7 eV) as the monochromatic radiation source. Charge compensation was performed using adventitious C 1s peak (284.6 eV). Before the measurement, the surface of the film was cleaned by sputtering to clear the oxidation. Spectra background was fitted and subtracted using an integrated Shirley function. XPS curves were deconvoluted using the Voigt peak function for the metal-core electron spectra and the Gaussian peak function for the others. The XPS peaks were fitted using the CasaXPS software after Shirley’s type of background subtraction.

Surface Characterization

Advanced imaging modes have been developed via AFM characterization using MultiMode scanning probe microscope (Nanoscope V, Veeco, Santa Barbara) in tapping mode to examine surface morphologies. The thin-film thickness was measured using a surface profilometer (Bruker’s Dektak 150, Veeco, New York).

Optical Characterization

After the preparation of the solution from perovskite powder, CsPbBr3 PQD was dispersed onto a microscope glass substrate for optical characterization. The absorption spectra of the PQD thin films were recorded under ambient conditions at room temperature (RT) using an ultraviolet–visible (UV–vis) spectrophotometer (V-670, JASCO, Japan). The PL spectra of the perovskite films were obtained using a fluorescence spectrophotometer (FP-8200, JASCO, JASCO, Japan) at a wavelength range of 350–800 nm.

ASE Experiments and Optical Gain Measurements

To investigate the ASE properties, power-dependent ASE spectra were obtained from the sample edge in correspondence with the end of the excitation stripe using a β-barium borate optical parametric generator (OPG) (tunable range: 425–2300 nm) (LT-2215 OPG-PC, LOTTIS II, Minsk, Belarus) operated and pumped by a Q-switched Nd: YAG picosecond laser (LS-2151, LOTTIS II, Minsk, Belarus). The pulse duration was 70–80 ps, with a repetition rate of 15 Hz. The output signal emitted from the sample was collected using an optical fiber with a collimating lens attached to a spectrograph (QE65 Pro, Ocean Optics, Dunedin), with a spectral resolution of 0.78 nm in all ASE measurements. All measurements were performed in atmosphere air and at RT (293 K).

ASE Measurements

The beam size of the pump laser was shaped to a diameter of ∼2 mm by using a small hall. Then, the incident beam was focused on the sample surface using a cylindrical lens with a focal length of 10 cm onto the sample surface in a rectangular stripe (∼10 mm × 200 μm), with an excitation spot having an area of 0.02 cm2. The signal emitted from the sample was collected using an optical fiber. The pumping laser energy density was changed using a variable neutral density (ND) filter wheel. The pump laser energy was measured using a thermal sensor head (S470C, Thorlabs). Moreover, the pumping laser energy density was attenuated. This configuration enables us to study and elucidate the dependence of the threshold on the pumping laser energy density.

Optical Gain Measurements

In the quantitative studies of the optical gain coefficient and properties of PQD thin films, measurement of ASE intensities using the VSL method was performed through shaped into a stripe on the sample surface by a cylindrical lens, and the length of the stripe was varied using a tunable micrometer slit. To study the ASE regime, CsPbBr3 PQD thin films fabricated on microscope glass slides via drop-casting from hexane solutions were used. Moreover, for a high-efficiency optical output, sufficient thin-film thickness is required, which is 400 nm. In this investigation, the VSL method was based on the excitation of a semiconductor specimen with the picosecond laser beam at a fixed excitation density of about 5 times the ASE threshold and λex of 410 nm which focused onto the sample by using a cylindrical lens into a narrow stripe length of l. The length of this pumped is let to vary and light output ASE is measured as a function of the stripe length l. The variations of the edge-emitting light (PL spectra) caused by the excitation length (with a 20-μm increment between 0 and 500 μm) in a CsPbBr3 PQD thin film were collected using a spectrometer and were detected as presented above. All measurements were performed at an excitation energy density of 112 μJ cm–2 and under ambient conditions at RT. VSL configuration was performed, as presented in the inset of Figure 6a, to record the output emission spectra to enable the increase in pump light excitation intensity with the increase in the stripe length. A schematic diagram and details of the experimental setup of the VSL method are presented in ref (61). An image of the CsPbBr3 PQD thin-film excited above the ASE threshold is presented in the inset of Figure 6a.

Optical Loss Characteristics

To measure the attenuation inside the active medium or the loss characteristics, In these measurements, the length of the pump stripe was kept constant (2 mm), but the stripe itself was gradually moved away from the sample edge in steps of 25 μm. Since the output intensity from the end of the excitation stripe will be constant, observed decreases in the detected signal would be due to losses through mainly absorption and scattering within the un-pumped region. The ASE intensity as a function of the distance (x) between an un-pumped region of the sample and the edge of the excitation strip, can be fitted with the following equation I = I0 exp(−αx), where I0 is the initial ASE intensity, and α is the corresponding loss.71

Data Analysis

Analysis of the huge data obtained from this research was conducted using a software package built in our research lab. A Python-based programming code, which enables a rapid Gaussian peak fitting of the dual PL emission peaks from multiple data files, was used to analyze part of the PL data files.

Acknowledgments

The authors extend their appreciation to the Deputyship for Research & Innovation, “Ministry of Education” in Saudi Arabia for funding this research work through the project no. IFKSURG-1440-038.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c05414.

  • More details about the properties of CsPbBr3 QD perovskite films (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao0c05414_si_001.pdf (698.1KB, pdf)

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