ZnS Quantum

May 16, 2007 - The gain was measured systematically for close-packed films of rods and dots under quasi-CW nanosecond optical pumping, using the ...
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J. Phys. Chem. C 2007, 111, 7898-7905

Temperature Dependence of Optical Gain in CdSe/ZnS Quantum Rods Miri Kazes, Dan Oron, Itzhak Shweky, and Uri Banin* Department of Physical Chemistry, the Farkas Center for Light Induced Processes and the Center for Nanoscience and Nanotechnology, The Hebrew UniVersity of Jerusalem, Jerusalem 91904, Israel ReceiVed: January 4, 2007; In Final Form: March 16, 2007

We studied the optical gain characteristics of CdSe/ZnS core/shell colloidal quantum rods, investigated their temperature dependence, and compared the gain properties with quantum dots (QD). The gain was measured systematically for close-packed films of rods and dots under quasi-CW nanosecond optical pumping, using the variable stripe length method measuring the amplified spontaneous emission (ASE). Tunable ASE can be achieved by changing the rod diameter. Optical gain factors of up to 350 cm-1 at a temperature range of 10-120 K were measured for quantum rods. Above 120 K, the gain decreased sharply, but by increasing the pump power, ASE was easily achieved also at room temperature. The temperature dependence was assigned to the Auger heating process and phonon assisted thermal relaxation. QD of similar diameters as the rods showed much smaller gain values (∼50 cm-1) and a sharp decrease in gain at lowered temperatures (∼50 K), and ASE could not be detected at room temperature even at high pump powers. The significantly improved gain values in quantum rods as compared with dots were attributed to the slower Auger relaxation rates, the higher absorption cross-section, and the reduced self-absorption due to the larger Stokes shift. The temperature dependence of the threshold power for the quantum rods, used to characterize the thermal insensitivity of the system, showed two distinct temperature regions. In the low-temperature region, a very high T0 value of 3500 K was measured, as predicted for a low-dimensional quantum confined system.

Introduction Semiconductor nanocrystals are interesting materials for lasing and optical gain due to their size and composition tunable emission and the ability to manipulate them chemically.1 Lasing in 0-D quantum dot (QD) systems, due to the discrete density of states, was expected to occur at low thresholds and show an insensitivity to temperature.2,3 However, in spherical QDs with diameters of a few nanometers, the gain performance is compromised by the rapid and strongly size-dependent Auger relaxation processes. In systems where the electron and hole are confined to the core (type I band alignment), a biexciton was required for population inversion and the onset of lasing,3-5 and the Auger relaxation process leads to fast decays of few tens of picoseconds.6 Yet, lasing and gain in various geometries such as in films distributed feedback cavities, and various microcavities were achieved.7-13 Quantum rods (QRs), intermediate between 0-D dots and 1-D wires, provide improved gain characteristics as compared with the spherical QDs and exhibit significantly reduced lasing thresholds.9,14 This improvement is assigned to slower nonradiative recombination of multiexcitonic states via Auger processes in the QR,14 to their increased oscillator strength, and to the increased Stokes shift that reduces losses due to reabsorption. Here, we report a study of optical gain in QR films and its dependence on rod size, temperature, and pump intensity. We use the variable stripe length method (VSLM)15 to extract gain values for different QR samples at variable temperatures and compare these results to those of QD films. Since the excitation of multiple excitons is crucial for the achievement of optical gain, gain in CdSe nanocrystals was * Author to whom correspondence should be addressed. E-mail: [email protected].

extensively studied using subpicosecond excitation.1,14 This is typically required to overcome the picosecond scale Auger relaxation processes mentioned previously.6,16 While these experiments enable the study of gain characteristics, and have even led to the observation of room temperature gain, real-life applications require the achievement of gain for durations much longer than the typical Auger lifetimes. In this study, we investigated gain characteristics of close-packed semiconductor nanoparticle films under nanosecond pumping. Unlike ultrafast pumping, this pumping regime leads to an effective quasi-CW excitation of the semiconductor nanocrystals and to prolonged gain since the pulse duration is significantly longer than the typical Auger relaxation times of the biexciton.17 Because of the competing Auger mechanism, however, the parameter space enabling achievement of gain is much more restrictive, as compared with that under ultrafast pumping. In particular, significantly increased pump energies are needed to achieve gain, and the gain performance is sensitive to temperature. Moreover, as will be shown next, the effects of Auger heating18,19 and the ensuing thermalization cannot be neglected. We conducted a size- and temperature-dependent study of the gain in QRs. We also compared the results for those of QDs under similar conditions. Experimental Procedures Chemicals and Materials. Dimethylcadmium (Cd(CH3)2) was purchased from Strem, vacuum transferred from its original cylinder to remove impurities, and stored in a refrigerator inside a glovebox. Tetradecylphosphonic acid (TDPA, 98% purity) was purchased from Alfa. Trioctylphosphine (TOP, 90% purity), trioctylphosphine oxide (TOPO, 90% purity), hexadecylamine (HDA, 90% purity) selenium (Se), hexamethyldisilathiane {(TMS)2S}, and 1 M diethylzinc {Zn(Et)2} in hexane solution

10.1021/jp070075q CCC: $37.00 © 2007 American Chemical Society Published on Web 05/16/2007

Temp Dependence of Optical Gain in CdSe/ZnS Quantum Rods were purchased from Aldrich. TOP was purified by vacuum distillation and kept in a glovebox. Nanocrystal Synthesis. The CdSe/ZnS QRs were grown using the method of colloidal nanocrystal synthesis utilizing high-temperature pyrolysis of organometallic precursors in coordinating solvents and were overcoated by HDA, TOPO, and phosphonic acids.20,21 The core/shell configuration was chosen since the growth of a few monolayers of ZnS on the organically coated CdSe QRs enhanced the fluorescence quantum yield (QY) from ∼1% to ∼20-30%. The shell thickness was estimated to be 1.5-2 monolayers. The shell, composed of ZnS that has a band gap enclosing that of CdSe, passivates surface traps that in the organically coated CdSe rods lead to nonradiative decay of the excited state competing with the buildup of optical gain. Nanorods were compared also with CdSe/ZnS QDs that were synthesized using the method described in ref 22 followed by a shell synthesis using a layerby-layer growth method (ref 23), which results in an almost monodispersed sample with 60% quantum yield. Film for Gain Studies. Films for the gain studies were prepared by spin coating from a toluene solution on a glass substrate. The glass substrates were pre-cleaned and treated with hexamethyldisilazane at 70 °C overnight to silanize the surface. Prior to deposition, we performed twice a separation procedure to clean the rod solutions from excess organic ligands to allow for the formation of a close-packed film. This was performed by dissolving ∼1 g of the as-prepared sample (in the growth solution) in 2 mL of toluene followed by dropwise addition of methanol up to the point of flocculation and separating by centrifuging. Following the cleaning, the samples were redissolved in toluene by sonicating for ∼10 min. As a result of this processing, the quantum yield of the samples decreased to about 5%. Following this separation, the films were deposited by dropping 50 µL of a concentrated rod solution in toluene onto the glass substrates using a spin speed of ∼600 rpm for 5 min. Films obtained were of medium optical quality, as during the drying process cracks were formed. However, on a length scale of the optical gain measurement by the variable stripe method (∼1 mm), we could easily find regions of sufficient optical quality. Figure 1e shows a scanning electron microscope (SEM) picture of such a film, demonstrating the long-range quality in regard to the smoothness and thickness of the film. The film thicknesses reported here were measured by an optical microscope to be ∼20 µm (Figure 1f). The volume ratio of the nanoparticles, calculated from optical density measurements, was found to be about 3% and 6% for typical rod and dot samples, respectively. The density of the films was calculated to be about 1 × 1017 and 1 × 1018 particles per cubic centimeter for the rod and dot samples, respectively. Optical Gain Measurements. The spectroscopic measurements of amplified spontaneous emission (ASE) were carried out using VSLM commonly used for the investigation of gain in solid-state systems.15 The experimental scheme, as described in the inset of Figure 1b, consists of a 532 nm, 5 ns doubled Nd:YAG excitation laser beam that was focused into a stripe of 100 µm width by a cylindrical lens. The stripe was gradually exposed by an adjustable barrier mounted on a stepper motor. The excitation stripe was positioned on the edge of the film, and the emission was collected perpendicular to the edge of the film into a monochromator coupled to a CCD detector. All measurements were carried out in a variable temperature Heflow cryostat. Typically, measurements were carried out using a single shot pump mode, and each data point was averaged over 10 shots.

J. Phys. Chem. C, Vol. 111, No. 22, 2007 7899 Results and Discussion Optical Gain in Semiconductor QRs. To investigate the size dependence of optical gain in QRs, we examined four samples with varied diameters and lengths. The absorption spectra of the samples are shown in Figure 1a, demonstrating that the spectral tunability in QRs was achieved by controlling the rod diameter.24 Note also that the 4 nm × 14 nm and 4 nm × 24 nm rod samples show a similar band gap as the length already in this size regime hardly affects the spectrum. This is because the exciton Bohr radii of CdSe is ∼5.6 nm, and already at 14 nm, the long axis exhibits only weak quantum confinement. Representative transmission electron microscope (TEM) images of two QR samples are also presented in Figure 1c,d for the 4 nm × 24 nm sample and for the 5.8 nm × 35 nm sample, respectively. Statistical analysis of the TEM pictures gives a size distribution of (10% for the diameters and (15% for the lengths. Optical gain measurements were conducted using VSLM. Figure 2 shows ASE spectra at variable exposure lengths for the 4 nm × 24 nm CdSe/ZnS QR sample for a film with an optical density of 0.43 and a film thickness of 15 µm (T ) 30 K). The sample was excited using the 532 nm laser at an excitation intensity of ∼50 mJ/cm2, just above the ASE threshold. A narrowed emission peak at the blue side of the photoluminescence (PL) emission spectrum emerged at a stripe length of ∼20 µm and was attributed to ASE. As the gain developed, the ASE peak became dominant over the broad PL emission Here, we used a nanosecond pump source, much longer than the nonradiative Auger relaxation lifetimes of biexcitons involved in the ASE (tens of picoseconds).1,16 Time-resolved emission measurements that we performed show a strong transient emission component during the excitation pulse followed by a slower relaxation characteristic to exciton emission (Figure S1 in the Supporting Information). The fast component was assigned to the ASE, which lasts only during the pulse duration, while the slower decay reflected the lifetime of excitons in the QRs. This indicated a ladder climbing population model in which state filling takes place, where exciton, bi-exciton, and multi-exciton states were gradually built during pumping. The gain was thus limited by a fast relaxation process, corroborating its assignment to a fast multi-excitonic state.25 Excitation was therefore performed under a quasi-CW pumping regime, unlike many previous optical gain studies in QDs performed in transient excitation conditions. The number of photons absorbed per particle within the pulse duration was calculated using the density of the particles and the beam size to be about 350 photons/particle for the QR film characteristics described previously and a pump power fluence of 1 × 107 W/cm2 used in this experiment. Other results (ref 17) show that an efficient excitation of BX requires about 100 photons/particle, whereas an efficient excitation of triexciton (TX) requires about 1000 photons/particle, suggesting that the gain originates from BX emission. The larger number of photons per particle is needed to achieve optical gain because the ASE process itself is an additional loss mechanism for the BX population. As the gain begins to develop, a blue-shift of the ASE peak is observed, suggesting some contribution to gain from a higher excited TX level in the QRs. Unlike the QDs, the high degeneracy in QR states, due to the long axis, leads to a smaller shift for the TX state relative to the BX.26 At longer stripe lengths, the ASE becomes saturated, and there is a slight shift

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Figure 1. (a) Absorbance spectra of the different CdSe/ZnS quantum rod samples taken in a toluene solution at room temperature. The quantum rods’ dimensions are 3 nm × 17 nm (dashed line), 4 nm × 14 nm (solid line), 4 nm × 24 nm (dotted line), and 5.8 nm × 35 nm (dashed-dotted line). (b) Schematic diagram showing the experimental setup for the optical gain measurements. The excitation source is a doubled frequency, 5 ns Nd:YAG laser. The excitation beam was focused onto a stripe using a cylindrical lens, and the stripe length was controlled by an adjustable barrier. The signal was collected from the edge of the film into a monochromator coupled to a CCD detector. (c and d) TEM pictures of 4 nm × 24 nm and 5.8 nm × 35 nm CdSe/ZnS QRs, respectively (scale bar 100 nm). (e and f) SEM image and optical micrograph (cross-section) of a typical film, respectively.

to the red accompanied by an increase in the ASE line width. This might be attributed to the contribution from charged BX levels.17,27 The inset of Figure 2 shows the ASE peak intensity as a function of the stripe length plotted on a log scale. The emission intensity increases by about 4 orders of magnitude up to a stripe length of 400 µm, which represents the gain buildup region, and then saturates. Gain values were extracted by fitting the ASE intensity, I, as a function of stripe length with the equation15

g gL ) γI + log I+1 A

[( ) ]

(1)

where g is the gain factor (cm-1), L is the stripe length (cm), I is the ASE intensity, and A is the spontaneous emission coefficient. The saturation region is given by the linear term

where γ is the linear gain coefficient describing the contribution to the intensity resulting merely from the longer exposed region. Most gain values given here are extracted by fitting a simpler form with only the exponential gain region by the following equation:15

I)

(Ag)(e

gL

- 1)

(2)

Both fitting procedures were found to yield very similar gain values. The gain factor reported here is the modal gain, which takes into account the waveguide losses due to scattering and refraction index matching. To evaluate the optical losses, the film was excited with a fixed stripe length that was gradually moved from the edge of the film, and the emission was measured from its edge. A loss factor of the order of 10 cm-1 was

Temp Dependence of Optical Gain in CdSe/ZnS Quantum Rods

Figure 2. ASE spectra of 4 nm × 24 nm QR film at different stripe lengths at a temperature of 30 K and 0.1 mJ pump energy. The nominal stripe lengths from bottom to top are 50, 75, 125, 250, 500, 750, and 1250 µm. The PL emission at short stripe lengths is red-shifted with respect to the exciton emission position due to energy transfer in the high-density close-packed film. ASE is clearly seen as the peak appearing at 580 nm corresponding to the biexciton emission position. Inset: ASE peak intensity as a function of stripe length fitted by eq 1 (black line) to give a gain factor of 440 cm-1.

Figure 3. ASE intensity as a function of excitation pump fluence plotted in a log-log scale for 4 nm × 24 nm (squares) and 5.8 nm × 35 nm (circles) QR films. The change in slope (black lines) corresponds to the onset of gain at a full BX inversion at ∼0.01 J/cm2 and at high pump power a saturation of gain owing to fast TX buildup. Inset: gain factors as a function of pump fluence show similar saturation behavior.

measured, allowing us to neglect its contribution to the gain values reported here. The ASE intensity plotted as a function of pump power at a full stripe length of 1250 µm is presented in Figure 3 for 4 nm × 24 nm (squares) and 5.8 nm × 35 nm (circles) quantum rod films. Both samples show very similar behavior with increasing pump powers manifested by the different regions in the curve revealed by the change in slope. The 4 nm × 24 nm, 1.15 o.d. film shows a sublinear change in slope at 10 mJ/cm2, calculated to be at an excitation of ∼70 photons/particle, which correlates with the number of photons needed for full BX inversion and the onset of gain (assuming the BX lifetime to be 100 ps16). The saturation region begins from ∼200 mJ/cm2 (∼1300 photons/particle) that correlates with an efficient TX population buildup and saturation of the BX state. In this sample, we did not observe TX gain, although TX gain was measured for a 3 nm × 17 nm QR.17 This may be due to the fact that in the 3 nm × 17 nm particles, the 532 nm pumping is much closer to the TX electronic level, reducing the effect of the fast intraband nonradiative relaxation process.28 While increased excitation powers led to an increase in ASE intensity, they affected the gain to a much lesser degree. Indeed, the gain dependence on pump power, shown in the inset of Figure 3, was weak. The gain coefficient increased from about 120 cm-1 at a 0.03J/cm2 pump power to about 300 cm-1 for 0.8 J/cm2 pump powers.

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Figure 4. ASE (solid lines) and PL (dashed lines) spectra of various CdSe/ZnS quantum rod samples measured at a temperature of 30 K. The ASE feature is the narrow emission peak emerging at the PL central position as gain develops. PL is measured for films in 45° angle geometry. Quantum rods’ dimensions from left to right: 3 nm × 17 nm, 4 nm × 14 nm, 4 nm × 24 nm, and 5.8 nm × 35 nm.

The large increase in the ASE intensity with increasing pump powers is mainly due to the exponential dependence of the ASE intensity with optical gain as described in eq 2. Another consideration is the volume that supports ASE. Qualitatively, since the film is optically thick, increasing the pump intensity leads to an increased volume of the film contributing to the ASE intensity, while leaving the gain coefficient unaffected. To expand the study, the gain was also investigated for a wide range of QR samples with different sizes. We observe similar behavior, and Figure 4 shows ASE and PL spectra for QR samples with dimensions of 3 nm × 17 nm, 4 nm × 14 nm, 4 nm × 24 nm, and 5.8 nm × 35 nm, which generally vary in the spectral position. This demonstrates the wide spectral coverage afforded by controlling the size of the QRs. Although the PL peak positions are controlled mainly by the diameter of the rods and not the lengths, the ASE peak positions for the 4 nm × 24 nm and 4 nm × 14 nm rods do exhibit a noticeable shift. This is because the gain process is more selective, and as a result, the ASE peak position is more affected by size distribution and the biexciton emission position. We also note that PL measured by VSLM is red-shifted as compared to PL emission spectra measured from low-density films at a 45° angle geometry (Figure 4, dashed lines) due to energy transfer within the close-packed films. To reveal the specific gain behavior of QRs, the optical gain was investigated also for QDs in similar films showing distinct differences. ASE in QD films was hard to achieve and was only demonstrated for larger dots of 4 nm in diameter and with a threshold pump power nearly an order of magnitude higher than for QRs. The modal gain value we obtained at low temperatures is ∼50 cm-1 as compared with 350 cm-1 in the QRs. This is fully consistent with our previous reports of QR lasing in a cylindrical microcavity, which showed a significantly reduced threshold power for QRs9 as well as with other studies showing advantageous optical gain from QRs.14,16 There are several reasons for this difference: first, QRs have a much higher absorption cross-section as compared with QDs of similar diameter, and this enables gain in lower threshold pump powers. Second, the Auger recombination in QDs is faster as compared with rods of a similar diameter.16 For 4 nm × 24 nm QRs, the biexciton lifetime was estimated from ref 16 to be ∼100 ps, while it was only 50 ps for the QD sample,27 which facilitates the development of optical gain in the same spectral region. The larger absorption PL Stokes shift in QRs (20 nm for the

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Figure 6. Gain and PL intensity as a function of temperature for a 4 nm CdSe/ZnS QD film. The gain (filled circles) shows a sharp decrease at T ≈ 50 K. The PL intensity (crosses) shows a more moderate temperature dependence, starting only around 90 K. This is due to the effect of heating at the high pump powers used to achieve ASE threshold. See text for details.

Figure 5. (a) ASE intensity as a function of stripe length (squares) at different temperatures of a 4 nm × 24 nm QR sample using 50 mJ/ cm2 excitation power. The initial rise up to a stripe length of about 400 µm is the gain region, followed by a saturation of the ASE intensity at longer stripe lengths. The gain region is fitted by eq 2 as described in the text (lines). (b) Extracted gain factor as a function of temperature. A gain value of about 350 cm-1 is maintained up to a temperature of 120 K and then decreases rapidly. The gain factor shows a crossover into loss at a temperature of 225 K. We emphasize that it is possible to observe gains also at the higher temperatures but only at higher excitation powers.

4 nm × 24 nm QRs vs 10 nm for the QDs) also reduces losses due to reabsorption. Comparing the gain values obtained in this study with other CdSe systems shows an interesting correlation. Other measurements on colloidal CdSe QDs in closed-packed films29 and in QDs incorporated into titania matrices30 report similar gain factors. Low-temperature VSLM of CdSe QD stacks grown by molecular beam epitaxy (MBE) with lateral dimensions of 510 nm and heights of 2 nm measured at similar conditions also gave a maximum gain factor of 400 cm-1.31 Although lowdimensional systems as QRs are expected to show an advantage over the bulk, much higher gain factors of 1000 cm-1 are reported for CdSe bulk for similar excitation powers.15 While measurements done on CdSe/ZnS quantum wells give gain factors as high as 2900 cm-1 with even smaller excitation powers,32 gain factors measured for CdSe QRs are smaller. One possible reason for the decreased gain value in QRs is the lack of alignment in our films. QRs show polarized emission33-35 and lasing.9 Therefore, alignment could lead to significantly enhanced gain factors. Additionally, clearly, the fast nonradiative Auger process plays a central role in reducing gain. The details of the mechanism through which gain is inhibited will be further elucidated in the following section dealing with the temperature dependence of the gain. Temperature Dependence of Gain in QRs. We next turn our attention to a study of the temperature dependence of the optical gain. Figure 5a shows the temperature dependence of

the ASE intensity as a function of stripe length for the 4 nm × 24 nm QR sample. Figure 5b shows the gain factors extracted by eq 2 versus temperature. A gain factor of ∼350 cm-1 is maintained nearly constant up to a temperature of ∼120 K and then drops rapidly. The same low excitation power is maintained throughout the experiment while measuring gain in the same area. We emphasize that for QRs, it is also possible to extend the ASE range to higher temperatures and even to room temperature by using higher excitation powers. The temperature dependence of gain in QDs shows an even sharper decrease with temperature than for QRs. Figure 6 shows the optical gain as a function of temperature (circles) for the QD sample. QDs give very small gain values of no more than 80 cm-1 and show a much more pronounced dependence on temperature with a sharp decrease in gain at a temperature of ∼50 K. In this case, a pump fluence of 320 mJ/cm2 (as compared with 50 mJ/cm2 for the QR sample) was needed to achieve stable ASE emission for a film thickness of 20 µm and an optical density of 1.55 (0.43 in QRs) at the excitation wavelength. This sharp decrease differs significantly from the temperature dependence of the exciton PL of CdSe/ZnS QDs embedded in a polystyrene matrix, measured by Anni et al.36 They observed a moderate decrease in PL intensity in the temperature range of 70-195 K, which was assigned to a thermally activated nonradiative process due to carrier trapping in defects and surface states. They also assigned the much more significant decrease above 195 K to thermal escape by coupling to LO phonons.36 However, the temperature dependence of ASE emission investigated here shows a much stronger dependence on temperature. For both the QD and the QR samples, a significant decrease in gain was observed at a temperature range where thermally assisted nonradiative relaxation was relatively weak (in the weak excitation regime). To account for this, we considered the dynamics of the temperature change within the gain medium under strong excitation. We first considered the expected rise in the film temperature within the duration of the excitation laser pulse, assuming full thermal equilibrium of the QDs with the surrounding matrix. Indeed, thermal relaxation times in a close-packed organic matrix can be approximated to 10 ps.37 The rise in temperature, an effect relevant only for quasi-CW conditions, is given by38 ∆T ≈ RF/CF, where R is the linear absorption coefficient, F is the excitation pump fluence, C is the specific heat capacity, and F is the film density. Taking the heat capacity of a 4 nm diameter CdSe QD sample at 50 K to

Temp Dependence of Optical Gain in CdSe/ZnS Quantum Rods be 4 J/g K as calculated from ref 39 and estimating the TOPO heat capacity,40,41 which consists of much of the medium, to be ∼2 J/gK, give a significant temperature rise, leading to an estimate of 115 K for the film temperature under the excitation pulse (while the measured temperature inside the cryostat is 50 K). As can be seen, since most of the film heat capacity is due to the organic matrix, the temperature rise is predominantly dependent on the threshold pump fluence. This effect can account for the observed discrepancy between the temperature at which the low-intensity PL and the high-intensity ASE begin to decrease in the QD sample (as shown in Figure 6). The PL peak intensity decreases at a temperature of 90 K in comparison to 50 K for the ASE peak intensity. The 40 K difference agrees well with the estimated 60 K increase in temperature at the peak of the excitation pulse. For the QRs, we can use a much lower pump intensity and hence maintain a much more stable temperature performance as explained next. The previous analysis still does not account for the relatively low temperature at which a decrease in gain is observed. Moreover, for the QR film, taking the heat capacity as 2 J/g K (deduced by crystal volume considerations from ref 39) gives a temperature rise of only 15 K, which does not explain the decrease in ASE emission intensity already at 120 K. Since overall heating of the sample at the measured pump powers causes only a minor temperature rise, the origin of the decrease in gain must lie elsewhere. In particular, the assumption of local thermal equilibrium has to be reexamined. The ASE emission, as previously discussed, originated from a BX emission, which implies different excitation conditions and different thermal dissipation mechanisms than studied by Anni et al. The BX recombination is accompanied by a fast nonradiative Auger recombination process in which the electronhole recombination energy is transferred to an electron or a hole, thus in fact causing the actual heating of the carriers in the nanocrystal. This excess energy has been shown to rapidly thermalize with the LO phonons. Thus, following an Auger recombination event, a transient rise of up to several hundreds of degrees in their temperature occurs.19 The LO phonons, in turn, dissipate this heat to acoustic phonons on a longer time scale of several picoseconds. During this time window, the LO phonon temperature can exceed the threshold for strong nonradiative relaxation of the remaining charge carriers via coupling to LO phonons (i.e., above 195 K, as shown in Anni et al.36). Note that the time scale for thermalization of the LO phonons is comparable to the BX Auger lifetime. This implies that under the illumination conditions required for achievement of gain, the LO phonon temperature is higher than the ambient temperature for a significant time within the excitation pulse. At yet stronger excitation, the LO phonon temperature will be maintained at a higher value than the ambient during the entire excitation pulse. To examine this, we show in Figure 7 the normalized integrated PL intensity (open symbols) plotted as a function of temperature for different excitation powers translated to the number of photons per particle. All measurements show an increase in intensity in the temperature range of 10-50 K that might be due to a crossover from a dark to a bright exciton state.42 However, higher temperatures show different behaviors for different pump powers. The PL at the pump powers correlating mostly to exciton emission (35 photons/particle) shows almost no change with temperature (high noise level is due to the low intensity in this measurement). As the pump power increases to a region of full BX inversion (100 photons/ particle) and higher, the PL intensity shows a decrease by a

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Figure 7. Normalized integrated PL intensity (open symbols) plotted as a function of temperature for different excitation powers for 4 nm × 24 nm QRs. The excitation powers are translated to the number of photons per particle (see legend). While the emission intensity at low pump powers (35 photons/particle) that correlates to exciton emission shows almost no change with temperature, the BX emission at higher pump powers (correlating to 100 photons/particle and higher) show an initial decrease at about 120 K. At even higher pump powers correlating to efficient buildup of TX population (2000 photons/particle), the intensity reduction begins at a lower temperature of 80 K due to efficient Auger heating. Gain values (solid squares) extracted from the VSLM measured at a pump power that correlates to 350 photons/particle show similar behavior with temperature as the BX emission. This is consistent with our assignment of gain to the BX emission.

factor of 2 from about 120 K to room temperature. At yet higher pump powers, in the regime of high TX emission (2000 photons/ particle), the PL begins to drop at even lower temperatures. Thus, the Auger process not only plays a role in the depletion of the BX state, and hence the gain, but also causes the opening of nonradiative decay routes by the electron-LO phonon interaction. Under the conditions required for gain, the nanocrystal system no longer can be regarded to have one defined temperature, but rather, the time scale for thermal equilibrium is determined by an initial subpicosecond LO phonon decay time followed by a slower relaxation through acoustic phonons (tens of picoseconds).19 The cooling dynamics in this system is dependent on the balance between the excitation rate controlling in effect the Auger heating rate and the thermal relaxation rates through phonon interactions. Gain values (Figure 7, solid squares) extracted from the VSLM for the same QR sample are plotted as a function of temperature measured at a pump power that correlates to 350 photons/particle. Although both the gain and the PL measured at the same excitation power (350 photons) show a decrease with temperature at about 120 K, while the PL shows a decrease of a factor of 2, the gain turns into a loss. The stronger dependence of gain with temperature, in comparison with the PL at the same excitation power, is explained by the exponential behavior of the optical gain process and the stochastic manner in which the ASE is developed. As already mentioned, gain in QRs can be achieved also at elevated temperatures, but it requires higher excitation powers. Gain measurements for the QR sample at room temperature gave a gain factor of ∼100 cm-1 but required pump powers an order of magnitude larger and a longer stripe length at threshold (0.1 cm) as compared with ∼350 cm-1 gain values and ∼50 mJ/cm2 pump fluence at cryogenic temperatures. In this case, ASE was not stable, and the emission degraded over the time of the measurement probably due to poor heat dissipation in the film. Room temperature gain was also measured for a longer rod sample of 4 nm × 40 nm. In this case, a lower threshold power of 250 mJ/cm2 was needed to achieve the

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Figure 8. Temperature dependence of the pump power at the onset of gain (solid squares). Shown are a logarithmic plot of threshold pump power normalized by the threshold at the lowest temperature (10 K) and the gain factor (open squares) normalized similarly for the 4 nm × 24 nm QR film. The gain and threshold power temperature dependence show a similar behavior. The gain factor begins to decrease at a temperature of 120 K, while the pump power needed to reach gain begins to increase at this temperature as well. The dependence of the threshold pump power on temperature can be expressed by eq 3 to give an effective temperature T0. The two different temperature regions were fitted separately. T0 for the lower temperatures is very high (3500 K) as is theoretically expected for particles with 0-D such as QRs.

development of ASE. We assign this to the higher absorption coefficient and the slower Auger rates of the longer rods. For systems with decreased dimensionality, due to the discrete states, the threshold power is predicted theoretically to show insensitivity to temperature.2 We studied this also by measuring the temperature dependence of the excitation threshold for ASE in the QRs (Figure 8, solid squares). We observed two distinct regions depicted by the change in slope at 80 K. At low temperatures, the threshold power was independent of the temperature, whereas for temperatures above 80 K, the threshold power shows an exponential increase. The two temperature regions can be fitted separately (Figure 8, black lines) by

Pth (T) ) Pth(T0) exp(T/T0)

(3)

where Pth(T0) is the threshold excitation power at low temperature, and Pth(T) is the threshold at higher temperatures. Using this formula, the influence of the temperature on the threshold power for ASE can be expressed in terms of an effective temperature T0.2 In the temperature region below 80 K for QRs, we find T0 ) ∼3500 K. For the higher temperature region, above 80 K, a T0 of 70 K is calculated. This abrupt change in behavior is probably due to the opening of nonradiative routes competing with gain through electron-phonon coupling as discussed previously. Our T0 measurements agree well with T0 measurements for MBE grown CdSe QD stacks that also show two distinct regions with similar T0 values.31 This corresponds with the prediction for high T0 values in 0-D systems. In an ideal 0-D system, T0 should approach infinity due to the discrete density of states. Conclusion Although colloidal semiconductor nanocrystals have attracted much attention as potential gain media, most gain experiments to date were performed using subpicosecond pumping, which circumvents many of the problems associated with achieving prolonged optical gain in colloidal semiconductor devicess in particular, those associated with thermal effects. Here, we

showed that achievement of optical gain is possible under nanosecond (quasi-CW) illumination. However, the conditions for its achievement, in terms of the pumping fluence and of the temperature range, are more restrictive. In particular, a detailed comparison between the temperature dependence of the optical gain and the temperature dependence of spontaneous emission at low pump fluence, both in CdSe/ZnS QD and in QR, reveals the effect of sample heating during the excitation pulse. The temperature rise places a practical limit on the pump fluence, the ambient temperature, and the nanocrystal volume fraction. We see that these effects are pronounced in CdSe/ZnS QD because a higher volume ratio and a higher threshold power are required for gain but hardly affects the QRs. This points to the suitability of large QRs, having large absorption crosssections and Auger relaxation times of several hundreds of picoseconds for achieving gain in the regime of long pump pulses and high temperatures. The lasing wavelength can still be controlled by varying the QR diameter while maintaining a high aspect ratio or changing the QR composition. This also emphasizes the role of the Auger process not only in the depletion of the biexciton state but also in the transient temperature rise caused by the Auger heating effect that allows for the opening of nonradiative decay routes through electron LO phonon relaxation. Our work further established the considerable advantages of QRs over QDs in gain performance. This is due to the slower Auger rates, the increased absorption cross-section, and the larger Stokes shift typical for QRs versus QDs. Therefore, choosing the right nanocrystal system (i.e., size, shape, and composition) may allow controlling the Auger rates and realization of stable room temperature optical gain even under quasi-CW pumping conditions. Acknowledgment. M.K. was supported by the Israel Ministry of Science and Technology via the Eshkol scholarship program. This work was partially supported by the James Franck Program and the German Israel Program (DIP). Supporting Information Available: Time-resolved measurement of ASE in QRs (Figure S1). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Klimov, V. I.; Mikhailovsky, A. A.; Xu, S.; Malko, A.; Hollingsworth, J. A.; Leatherdale, C. A.; Eisler, H.-J.; Bawendi, M. G. Science 2000, 290, 314. (2) Arakawa, Y.; Sakaki, H. Appl. Phys. Lett. 1982, 40, 939. (3) Asada, M.; Miyamoto, Y.; Suematsu, Y. IEEE J. Quantum Electron. 1986, 22, 1915. (4) Ivanov, S. A.; Nanda, J.; Piryatinski, A.; Achermann, M.; Balet, L. P.; Bezel, I. V.; Anikeeva, P. O.; Tretiak, S.; Klimov, V. I. J. Phys. Chem. B 2004, 108, 10625. (5) Efros, A. L.; Rodina, A. V. Solid State Commun. 1989, 72, 645. (6) Klimov, V. I.; Mikhaliovsky, A. A.; McBranch, D. W.; Leatherdale, C. A.; Bawendi, M. G. Science 2000, 287, 1011. (7) Gindele, F.; Westpha¨ling, R.; Woggon, U.; Spanhel, L.; Ptatschek, V. Appl. Phys. Lett. 1997, 71, 2181. (8) Moller, B.; Artemyev, M. V.; Woggon, U.; Wannemacher, R. Appl. Phys. Lett. 2002, 80 (18), 3253. (9) Kazes, M.; Lewis, D. Y.; Ebenstein, Y.; Mokari, T.; Banin, U. AdV. Mater. 2002, 14, 317. (10) Sundar, V. C.; Eisler, H.-J.; Bawendi, M. G. AdV. Mater. 2002, 14, 739. (11) Moller, B.; Woggon, U.; Artemyev, M. V.; Wannemacher, R. Appl. Phys. Lett. 2003, 83 (13), 2686. (12) Cha, J. N.; Bartl, M. H.; Wong, M. S.; Popitsch, A.; Deming, T. J.; Stucky, G. D. Nano Lett. 2003, 3, 907. (13) Kazes, M.; Lewis, D. Y.; Banin, U. AdV. Funct. Mater. 2004, 14, 957.

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