Article pubs.acs.org/journal/apchd5
Excitation Energy Dependent Ultrafast Luminescence Behavior of CdS Nanostructures Christian Karras,*,† Robert Röder,‡ Wolfgang Paa,† Carsten Ronning,‡ and Herbert Stafast† †
Leibniz Institute of Photonic Technology, Albert-Einstein-Str. 9, D-07745 Jena, Germany Institute of Solid State Physics, Friedrich Schiller University Jena, Max-Wien-Platz 1, D-07743 Jena, Germany
‡
S Supporting Information *
ABSTRACT: Selected semiconductor nanostructures provide extremely localized coherent light sources. Here an ensemble of CdS nanostructures was excited by UV/vis femtosecond laser pulses and their ultrafast luminescence characteristics were investigated as functions of the pulse energy fluence and the photon quantum energy. All optical Kerr gating enabled studies of the emission dynamics with a time resolution of 150 fs avoiding any influence on the CdS emission. The initially observed emission built up after a delay of 0.1−3 ps and decayed rapidly in a biexponential way, strongly dependent on both the laser energy fluence and the quantum energy. The central wavelength of the emission spectrum revealed a significant blue-shift within the first few ps followed by a transient red-shift relative to spontaneous excitonic emission of CdS. All findings are mainly attributed to stimulated radiative carrier recombination in the laser excited electron−hole plasma after its thermalization with the CdS lattice. KEYWORDS: stimulated emission, lasing, CdS, nanostructures, ultrafast relaxation, hot charge carriers
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addition, the randomly oriented semiconductor nanostructures on the sample surface show random lasing at high pump powers8,9 and lasing of individual nanoscale structures already at moderate pump power.10 The ultrafast emission dynamics of nanostructured CdS with respect to its potential as optical gain material has only been rarely studied.11,12 A detailed knowledge of these properties is, however, essential in order to establish nanoscale laser sources for innovative applications such as ultrafast on-chip devices. In particular, fast elementary processes in the subps regime, like the generation and relaxation of free charge carriers, are of utmost importance, as they control the luminescence kinetics as well as the spectral emission characteristics. During optical pumping of the nanoscale light sources, the free carrier concentration is directly governed by the excitation pulse energy fluence Φ. Carrier thermalization, typically in the time range from several 100 fs to a few ps, depends also on the excess energy Eexce(h) of the excited carriers, which is related to the excitation photon energy hνex. The values Φ and Eexce(h)
ighly excited compound semiconductors are promising optical gain materials, as they benefit from several stimulated intrinsic recombination processes.1,2 In particular, II−VI compound semiconductors such as CdS and ZnO generate robust optical gain and stimulated emission supplied by the formation of an electron−hole plasma (EHP) with tremendously high gain values above 1 × 104 cm−13 and 7 × 103 cm−1,4 respectively. Furthermore, CdS attracted a lot of interest, as it emits efficiently in the green spectral region due to its direct band gap around 2.4 eV. However, establishing stimulated recombination processes of electron−hole (eh) pairs in CdS requires excellent single crystal quality and low defect densities. Semiconductor nanostructures fulfill these requirements, as they grow without any extended defects, almost strain-free, and with exceptionally high optical quality.5 In addition, CdS nanostructures can be easily synthesized using vapor transport techniques on arbitrary substrates without any restriction for an epitaxial relation between the substrate and the nanostructure materials. The morphology of grown CdS nanostructure ensembles adds further advantages for the use as stimulated emitter: it leads to efficient absorption of the pump light compared to that by thin film or bulk material.6,7 In © XXXX American Chemical Society
Received: October 1, 2016 Published: April 3, 2017 A
DOI: 10.1021/acsphotonics.6b00755 ACS Photonics XXXX, XXX, XXX−XXX
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Figure 1. Spectro-temporal luminescence behavior of the CdS nanostructure ensemble upon fs laser excitation at λex = 440 nm as a function of the laser pulse fluence Φ and the delay time Δt between the sample excitation and the detection time window (OKG pump pulses). The vertical line on the left indicates the maximum response time of the excitation/detection system; the dashed white curve guides the eye along the Φ dependent luminescence onset; the white lines in the luminescence traces indicate the position of the central emission wavelength λemc.
Figure 2. (a) Temporal development of the spectrally integrated CdS emission upon fs laser excitation (pulse shape indicated by dashed line at Δt = 0) at λex = 440 nm and three laser energy fluences Φ; the straight dashed lines indicate the determination of ton. (b) Rate constant kon = 1/ton as a function of Φ for λex = 440, 400, and 380 nm and emission wavelengths λem = 500 (squares), 511 (circles), and 525 nm (triangles); kon and Φ are displayed on logarithmic scales; the solid lines indicate the overall trend. Inset: kon(λem) values recorded at Φ ≈ 1 mJ/cm2 for the three λem values as a function of the excess excitation energy Eexc = hνex − Eg. (c) Logarithm ln(S/S0) of the normalized luminescence signal S describing the kinetics of the spectrally integrated emission obtained at λex = 440 nm and Φ = 0.33, 1.2, and 3.5 mJ/cm2 and (d) luminescence kinetics obtained at λem = 500, 511, and 525 nm upon excitation at λex = 440 nm and Φ = 3.5 mJ/cm2.
the CdS luminescence and revealed a delay between the exciting fs laser pulse and the observed emission. This delay is incompatible with spontaneous fluorescence and turned out to depend on both parameters, hνex and Φ. The observed temporal and spectral emission behavior of the CdS nanostructure ensemble is mainly attributed to stimulated emission processes originating from an EHP after equilibration with the CdS lattice. This assignment is corroborated by a simple statistical two-step model of the radiative and nonradiative free charge carrier relaxation.
both are therefore crucial parameters of such nanoscale coherent light sources. The present study aims for a comprehensive understanding of the temporal and spectral luminescence characteristics of a CdS nanostructure ensemble upon femtosecond laser pulse excitation at different photon energies hνex and fluences Φ. Its ultrafast detection was achieved by applying highly efficient all optical Kerr-gating (OKG) of >50% transmittance.13 In contrast to frequently applied pump−probe techniques, OKG prevented unwanted interference between the investigated processes and the applied (purely passive) detection method. The high OKG time resolution allowed to follow the buildup of B
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Figure 3. Fluence Φ dependences of the kinetic emission constants (a) kon (dashed lines) and krise (dotted lines) for λem = 500 nm and (b) kfast (squares) and kslow (triangles) obtained at λem = 500, 511, or 525 nm upon excitation at λex = 380, 400, or 440 nm; the values given near the traces are (λem /λex).
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RESULTS The experimental setup (see Methods) allows to acquire luminescence spectra of the laser excited CdS nanostructures as a function of the delay time Δt after excitation for various excitation laser pulse energy fluences Φ, and the excitation laser wavelengths λex (photon energy hνex). A representative series of such emission spectra as a function of Φ and Δt is displayed in Figure 1 for the excitation wavelength λex = 440 nm (hνex = 2.82 eV). Obviously, the luminescence onset is delayed relative to the exciting laser pulse particularly at low Φ values (Figure 1). The delay time ton is defined as the time interval between the sample excitation at Δt = 0 and the onset of measured sample emission. The onset is determined as the point where the extrapolated linear slope of the rising emission trace I(Δt) hits the Δt axis (also compare Figure 2a). The obtained values as a function of the impact fluence Φ and the emission wavelength λem range from 0.1 ps ≤ ton ≤ 3 ps, being mostly longer than the time resolution δt ≈ 150 fs of the OKG detection system. The ton value evidently decreases with increasing laser fluence Φ, as shown in Figures 1 and 2a,b. Furthermore, the shape of the emission spectra and their respective central wavelengths λemc change with the delay time Δt, in particular, for high fluence Φ. The evolution λemc (Φ,Δt) is highlighted by white lines in Figure 1. In the beginning, the emission maximum recorded at Φ = 3.5 mJ/cm2 is positioned at the short central wavelength λemc ≈ 501 nm, then shifts to λemc ≈ 518 nm and ends up at λemc ≈ 511 nm for long delay times (c.f. Figure 5b). Similar spectro-temporal series were recorded at excitation wavelengths of λex = 400 nm and λex = 380 nm (cf. Supporting Information). Insight into the nature of the observed light can be derived from the luminescence kinetics characterized by the onset time ton, the emission rise time trise, and the decay constants kfast and kslow together with their energy dependences. For a consistent description, the kinetic data preferably are given as rate constants such as kon = 1/ton and krise = 1/trise enabling a direct comparison and discussion of their energy dependences k(hνex) and k(Φ). Apparently, the rate constant kon = 1/ton is very small at low excitation laser energy fluence Φ and exhibits almost the same value for all three excitation wavelengths λex, as shown in Figure 2b. However, kon increases with increasing fluence Φ by about a factor of 10 for the excitation wavelength λex = 400 nm and by 25 for λex = 440 nm. The kon values recorded at different λex values but identical incident fluence Φ ≈ 1 mJ/cm2 are displayed in the inset of Figure 2b and clearly decrease with increasing excess energy Eexc = hνex − Eg.
The luminescence rise and decay kinetics are shown in Figure 2c,d as logarithmic plots ln(S/S0) of the emission intensity S normalized to its maximum value S0. The krise values increase with increasing laser energy fluence Φ (Figure 2c) and with decreasing emission wavelength from λem = 525 nm to λem = 500 nm for a constant pulse fluence Φ (Figure 2d). The luminescence traces can roughly be divided into two decay regimes leading to two decay rate constants (kfast and kslow) at the selected λem values of 500, 511, and 525 nm. It is pointed out that the kfast values in Figure 2d severely depend on the observed emission wavelength λem, whereas the kslow values are identical within the error limits. An overview over kon, krise, kfast, and kslow as functions of λex, λem, and Φ is depicted in Figure 3. In both diagrams of Figure 3, the highest k values are obtained at the shortest emission wavelength λem = 500 nm upon excitation at the longest excitation wavelength λex = 440 nm. This finding reflects the temporal change in the luminescence spectrum and reveals the strongest change on the short wavelength edge. In Figure 3a, the kon values appear to approach “saturation” with rising fluence Φ whereas the krise values surpass a maximum at ≈1.5 mJ/cm2 with λex = 440 nm and ≈3.5 mJ/cm2 with λex = 400 nm. In Figure 3b, all kslow values are found in the 0 ≤ kslow ≤ 0.5 ps−1 range, whereas the maximum kfast value amounts to 4.5 ps−1. It is pointed out that the ranges of the applied fluences Φ differ considerably for the excitation wavelengths λex = 380 nm (0.25 mJ/cm2 ≤ Φ ≤ 1.1 mJ/cm2), λex = 400 nm (0.35 mJ/cm2 ≤ Φ ≤ 6.7 mJ/cm2), and λex = 440 nm (0.3 mJ/cm2 ≤ Φ ≤ 3.5 mJ/cm2). Figure 3a focuses on the results obtained at λem = 500 nm, whereas Figure 3b displays the k values (fast and slow) for all selected emission wavelengths.
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DISCUSSION In principle, both spontaneous and stimulated photon emission processes are conceivable in the applied CdS nanostructures depending on the exciting laser pulse fluence (e.g., refs 4, 5, 10, and 14). Stimulated processes may lead to amplified spontaneous emission (ASE) and/or lasing of single nanostructures (e.g., nanowire lasing) as well as random lasing. To achieve insight into the nature of the observed light its spectrotemporal behavior will be considered in some detail, at first by a close look to the luminescence spectra and then to the emission kinetics. Luminescence Spectra. The energy of the detected photons 2.48 eV ≥ hνem ≥ 2.36 eV is close to the nominal CdS band gap energy of 2.4 eV, but between 0.3 and 0.9 eV away from the excitation photon energies of 3.26 eV ≥ hνex ≥ 2.82 eV. Furthermore, the central wavelength λemc of the C
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Figure 4. Simplified scheme of the energy dependent photo excitation of the direct semiconductor CdS and its relaxation: (a) Initial density distribution functions n(E) of the excited CB electrons and related VB holes for two photon energies hν1 and hν2 and in case of hν1 for two laser energy fluences Φ1 (high, red lines) and Φ2 (low, filled green areas) displayed along the energy scales Ee, Eexce, and Eexch; the dashed lines indicate the density of states (DOS) in the CB and VB. (b) Distributions ne(k) of the excited electrons and nh(k) of the excited holes as functions of the wave vector k after relaxation step 1 (T ≫ T0, dashed lines) and step 2 (T = T0, solid lines) for λex = 440 nm and Φlow = 0.33 mJ/cm2 (blue, upper part) and Φhigh = 3.5 mJ/cm2 (black, lower part).
Figure 5. (a) Product distribution functions ne(k)·nh(k) of electrons and holes after relaxation steps 1 (dashed lines) and 2 (solid lines) for λex = 440 nm at Φ = 0.33 mJ/cm2 (blue) and Φ = 3.5 mJ/cm2 (black) in comparison to the CdS emission spectra measured for the given Φ values. The spectra were integrated between 0.1 and 0.2 ps (Φ = 3.5 mJ/cm2, green trace) and between 2.5 and 3 ps (Φ = 0.33 mJ/cm2, red trace), as indicated by the hatched areas in part (b). (b) Time evolution of the λemc traces (white solid lines in Figure 1) upon CdS excitation at λex = 440 nm, Φ = 0.33, 1.2, and 3.5 mJ/cm2.
Statistical Two-Step Model. The initial distributions of photo excited hot electrons in the conduction band (CB) and hot holes in the valence band (VB) are affected by both the incident pulse energy fluence Φ and the photon energy hνex. The photon energy hνex determines the excess energy Eexce(h) of the charge carriers in their respective bands following the relation10,15
luminescence (white solid lines in Figure 1) changes during the emission over the 501 to 518 nm wavelength range (Δhν ≤ 0.08 eV). Both findings prove relaxation of the photo excited charge carriers between the laser excitation and the observed emission. Prior to the following discussion it is pointed out that even the moderate development of the central emission wavelength λemc in time Δt (Figures 1 and 5b) cannot be explained by a chirp of the ultrashort laser pulse exciting the CdS sample and dispersion of the sample emission light. The latter passes through the dispersion-free off-axis parabolic mirror (OAPM) system, the 0.5 mm thin polarizer, and the OKG sample only. Furthermore, dispersion should not show a fluence Φ dependence like that seen in Figures 1−3 and 5. Therefore, the spectroscopic results will be compared to a simple statistical model describing the optical excitation of the CdS nanostructures as well as their radiative and nonradiative relaxation processes (Figures 4 and 5).
e(h) Eexc
−1 ⎛ me(h) ⎞ ⎟⎟ = (hνex − Eg )⎜⎜1 + mh(e) ⎠ ⎝
(1)
with Eg being the band gap energy and me(h) the effective electron (hole) mass. The fluence Φ, on the other hand, controls the densities ne(Eexce) and nh(Eexch) of the hot carriers. These initial distributions of the nonequilibrium semiconductor state relax by various processes such as carrier−phonon, carrier−defect, or carrier−carrier scattering (cf., for example, D
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charge carrier gases after step 1 (dashed lines) is expected at higher emission photon energy hνem (shorter emission wavelength λem) than that of the cold charge carrier gases after step 2 (solid lines). Comparison of Model with Experimental Results. The measured emission spectra in Figure 5a were time-integrated over the hatched areas of Figure 5b, that is, between the onset of the observed luminescence and a noticeable shift of the central emission wavelength λemc (0.33 mJ/cm2: 2.5 ps ≤ Δt ≤ 3 ps; 3.5 mJ/cm2: 0.1 ps ≤ Δt ≤ 0.2 ps). These experimental spectra are found to be very close to the emission spectra expected from the product ne(k)nh(k) distribution functions after relaxation step 2. This suggests that step 1 is much faster than the buildup of the observed emission. The differences between the emission spectra obtained at low and high Φ values are compatible with their differences in band filling (e.g., ref 11): After excitation at low fluence Φ (0.33 mJ/cm2) band filling is weak and the observed emission spectrum with λemc ≈ 510 nm at the beginning is very close to the “final” value of 511 nm (Figure 5b). At high fluence, Φ = 3.5 mJ/cm2, on the other hand, band filling is strong at the onset of the luminescence leading to an emission band extension to short wavelength down to λemc ≈ 501 nm (Figure 5b). Band filling decreases, however, rapidly during emission by radiative eh pair recombination. This decrease shows up in the shift of the emission spectrum maximum toward long wavelengths during the luminescence decay (“final” value λemc ≈ 511 nm). In addition, the time evolution of the emission spectra, as displayed by λemc(Δt) in Figure 5b is characterized by a second phenomenon: At an intermediate stage, λemc exceeds its “final” value and passes through a maximum. This maximum value increases with the applied fluence Φ, that is, λemc(max) ≈ 515 nm for Φ = 1.2 mJ/cm2 compared to λemc(max) ≈ 518 nm for Φ = 3.5 mJ/cm2. This transient λemc maximum is attributed to band gap renormalization (cf., for example, ref 2). This is also inherent in Figure 5a: The modeled emission spectra were shifted along the ordinate scale such that each maximum after relaxation step 2 coincided with the maximum of the related measured spectrum. As a result, the onsets of the modeled spectra at the low hνem value edge differ by 30 meV for the selected Φ values. Each spectral onset represents the effective band gap Egeff after band gap renormalization. As expected, Egeff(3.5 mJ/cm2) at high eh pair density is smaller than Egeff(0.33 mJ/cm2) at low carrier density. The same energy difference is obtained in Figure 5b when comparing the lowest emission photon energies, that is, hν c em,min (0.33) − hνcem,min(3.5) = 2.42 eV − 2.39 eV = 0.03 eV. Looking at the “final” λemc values after some few ps they still differ from the values of 505 to 508 nm5,17,18 expected from the (completely relaxed) CdS band gap value at room temperature. The deviations from the “relaxed” emission amount to about 2−7 nm. This finding may be interpreted as the result of local transient heating of the irradiated sample volume on the ps to ns time scale followed by heat dissipation until the subsequent excitation laser pulse after 1 ms. Emission Kinetics. As a first approach to reveal the kinetics of the observed luminescence, its build-up and decay each are described by two empirical kinetic constants kon and krise as well as kfast and kslow, respectively. While the discrimination between the two decay regimes (kfast and kslow) appears to be a selfevident approximation (Figure 2c,d), the relations of kon and krise to different physical phenomena deserve to be briefly discussed. This discussion is based on the assumption that the
ref 2). The fastest process is energy redistribution within the hot electron (hole) gas. This equilibration (thermalization) of the photo excited carrier gases leads (approximately) under energy conservation to Fermi−Dirac (FD) distributions with a high electron (hole) temperature Te (Th). Figure 4a depicts three selected examples of photoexcitation, that is, the generation of the initial distributions of hot electrons and hot holes for a photon energy hνex and an energy fluence Φ. Before optical excitation, the valence band (VB) should be nearly filled by electrons following the distribution function ne(Ee) ≈ DOS(Ee), with ne(Ee) and DOS(Ee) being the density of electrons and the density of states at electron energy Ee, respectively. The wave vector k of the optical transition fitting the resonance condition hνex = Eg + Eeexc + Ehexc (energy conservation) as well as the selection rule Δk = 0 (momentum conservation) can easily be determined. The width of the distribution functions of the photo excited charge carriers reflects the coherence bandwidth of the applied laser pulses as visualized in Figure 4a. Thus, optical excitation leads to an ensemble of photo excited electrons in the conduction band (CB) of a defined average excess energy Eexce per electron and the total excess energy Eexce(total) of the electron gas depending on the fluence Φ. Due to the optical generation of electron/hole (eh) pairs there is a 1:1 relation between the number of CB electrons at Eexce and the number of VB holes at Eexch, as depicted in Figure 4a. With respect to the nonradiative relaxation processes following the photo generation of eh pairs, the excited CB electron and VB hole ensembles are considered as separate systems with their excess energies Eexce,h relative to their band edge energies E0(CB) and E0(VB), respectively. Both systems develop independently on different kinetic time scales. Two idealized relaxation steps after laser excitation are regarded (Figure 4b): Step 1: Both photoexcited charge carrier systems in Figure 4a separately undergo collisional redistribution (thermalization) of e e their excess energies Eexc (total) = ntot(Φ)Eexc (e−) and Ehexc(total) = ntot(Φ)Ehexc(h+) assuming constant ntot(Φ) values and adiabatic conditions, that is, energy redistribution without energy losses by, for example, radiative eh pair recombination and carrier−phonon coupling. Eventually, the density of photoexcited eh pairs in the irradiated CdS material is ntot(Φ) tot = ntot e (Φ) = nh (Φ). Step 1 results in two Fermi−Dirac (FD) distributions of very high temperatures Te, Th ≫ T0, with T0 ≈ 300 K being the ambient temperature.16 Step 2: In the second step, the very hot electron and hole gases equilibrate with the CdS lattice by carrier-phonon coupling at ambient temperature T0 and are severely cooled due to the very large heat capacity of the lattice compared to the very small heat capacities of the charge carrier gases. Again, ntot(Φ) is kept constant. The charge carrier distribution functions ne(k) and nh(k) in Figure 4b were derived for the two photoexcited states with the distribution functions ne(Eexce) and nh(Eexch) after excitation by hν1 = 2.82 eV (λ = 440 nm) at Φ = 0.33 and 3.5 mJ/cm2 (cf. Methods and, for example, ref 16). The resultant FD distributions for the hot and the cooled charge carrier gases are depicted in Figure 4b as a function of the wave vector k. This presentation allows to estimate the properties of the CdS luminescence, that is, the radiative eh pair recombination with Δk = 0. As a first approach for the expected emission spectra, the product distribution functions ne(k)nh(k) are displayed in Figure 5a. They show that the emission maximum of the hot E
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observed luminescence dominantly originates from stimulated photon emission (compare “Spontaneous versus Stimulated Emission” below). In case of purely spontaneous emission the luminescence should start during the exciting fs laser pulse and then typically decay in a single exponential function on the ∼ns time scale (e.g., refs 11 and 17−19). Figures 1 and 3a show, however, a pronounced delay ton = 1/kon between the laser excitation and the observation of luminescence. The kinetic constant kon may a priori be determined by two processes, step 2 in the above relaxation model and the buildup of stimulated emission in the CdS sample. The buildup of stimulated emission should, however, dominantly show up in krise and therefore kon is tentatively attributed to relaxation step 2. It is useful to look at the different developments kon(Φ,λex,λem) and krise(Φ,λex,λem) in Figures 2 and 3 in order to support such a separation. These figures not only visualize the results derived from Figure 1 (λex = 440 nm), but also those from the equivalent emission traces obtained at λex = 400 and 380 nm (Supporting Information). Figures 2b and 3a reveal that kon increases with the fluence Φ and the excitation wavelength λex. Step 2 should, of course, be fast at high charge carrier density (high collision rate), which is achieved at high energy fluence Φ. On the other hand, kon values are small for high excess energy Eexc = hνex − Egap (inset of Figures 2b and 3a). This can be rationalized by assuming a maximum amount of energy that can be redistributed between the collision partners per interaction process. Consequently, the redistribution of a high excess energy Eexc requires many scattering processes and much time. The development of krise (buildup of stimulated emission) in Figure 3a appears to show a maximum with increasing Φ values. The required population of eh pairs can readily build up at a large fluence Φ and should be largest shortly after the exciting laser pulse. The emission decay is much faster than that of purely spontaneous emission and shows a biexponential behavior. Spontaneous fluorescence is relatively slow (kf ≈ 109 s−118) and therefore very weak providing only a very small undetected signal in the applied, very short detection time window of δt ≈ 0.15 ps opened by the OKG switch (kf·δt ≈ 1.5 × 10−4 photon emission probability during the OKG time window (c.f., Supporting Information, Figure SI 6). Auger recombination might lead to an accelerated emission decay by the rapid depopulation of the conduction band. Typical time constants of Auger recombination in CdS amount to several tens of ps15 and are much larger than those of the observed decays. A more detailed analysis of the Auger recombination based on ref 15 is given in the Supporting Information (part G, Figure SI 7). Therefore, it is considered to play a minor role in our observations only and would not explain the significant delay of the emission build-up. Spontaneous versus Stimulated Emission. The following arguments support the assignment of the observed luminescence to stimulated emission, that is, amplified spontaneous emission (ASE), lasing of individual CdS nanostructures, and random lasing: (i) The decay time constants of spontaneous emission in CdS nanowires (0.1 to several nanoseconds17,18) are much larger than those of the observed luminescence (≤10 ps, Figure 3b). Auger recombination can accelerate the emission decay but is not expected to reduce the emission lifetime to 10 ps or even below.
(ii) The delay ton of the observed luminescence relative to the excitation laser pulse (Figures 1, SI 1, and 3a) is incompatible with spontaneous emission, which typically starts immediately after or even during the excitation pulse. On the other hand, ton is compatible with the thermalization between the photoexcited hot charge carriers and the cold CdS lattice. The thus thermalized electron−hole plasma (EHP) provides the medium of stimulated emission, as confirmed by the spectral emission properties discussed below. (iii) The 510 nm ≤ λemc ≤ 520 nm range of central emission wavelengths (time integrated value of Figures 1 and SI 1, and SI 2b) overlap considerably with the laser emission spectra over 510 to 525 nm of single CdS nanowires (Figures SI 3b and SI 4) but deviate considerably from the spontaneous emission spectra of the nanowire (Figures SI 3b and SI 4) centered around 502 nm. (iv) The spectral bandwidths (fwhm) 7 nm ≤ Δλ ≤ 13 nm (time integrated value of Figures 1 and SI 1, and Figure SI 2b) are comparable to the related values of the lasing emission spectra of single CdS nanowires (Figure SI 2d,e), but are smaller than the values 16 nm ≤ Δλ ≤ 19 nm of the spontaneous emission spectra of the nanowire (Figures SI 3b and SI 4). (v) The transient redshift in the measured spectra (Figure 5b) indicates band gap renormalization particularly at large energy fluence Φ. Band gap renormalization originates from an electron−hole plasma of sufficient density, which is known to generate stimulated emission. The difference between band gap renormalization at Φ = 0.33 and 3.5 mJ/cm2 amounts to 0.03 eV (Figure 5), being in the several 10 meV range of the estimated literature values.20,21 The spectral behavior described in (iii)−(v) strongly supports stimulated processes as origin of the observed emission: A stimulated build-up requires a “steady-state” population inversion such as the thermalized and cooled electron−hole plasma after step 2. Furthermore, the band gap renormalization indicates the presence of the necessary carrier concentration for stimulated processes in the plasma.2 Both the measured spectral width and the spectral centroid agree better with stimulated than with spontaneous emission characteristics. (vi) It is pointed out, that lasing in an optical cavity (e.g., nanowire), as one stimulated process, typically leads to resonant cavity modes, that is, individual narrow emission lines (cf., e.g., refs 5 and 10 and Figure SI 3b). If, however, many modes from differently sized nanostructures are excited simultaneously, their emission lines at various emission wavelengths may overlap and form a broad almost unstructured emission spectrum as is shown in the Supporting Information, Figure SI 5. Furthermore, the emission spectra in the present case (e.g., in Figures 1 and 5) represent the sum of laser emission lines obtained by many excitation laser pulses. The laser line positions and pulse energies may fluctuate from pulse to pulse and their time-integrated record thus yields smeared-out average emission spectra (Figure SI 5). Within this description, the λemc values (white solid lines in Figure 1) can be correlated to the spectral position of the highest average optical gain and its temporal development after the excitation laser pulse. F
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Figure 6. (a) Scheme of the fs laser setup with OKG and detection system; LBO: Li triborate; Fi: optical filters, OPA: optical parametric amplifier, Ii: iris apertures, f i: focusing lenses of focal lengths f i, OAPMi: off-axis parabolic mirrors of focal lengths f Pi (details cf. text). (b) Representative scanning electron microscopic (SEM) image of the investigated CdS nanostructures.
some few ps passing through a maximum at λemc ≈ 518 nm (Figure 5). Part of the experimental findings are rationalized by a simple statistical two-step model to describe separately the Fermi gases of the photoexcited electrons in the conduction band and of the excited holes in the valence band (Figures 4 and 5): Step 1 addresses the redistribution of the energy deposited in the electron and the hole gases leading to two Fermi−Dirac (FD) distributions of very high temperatures Te,Th ≫ T0 (T0 = 300 K), that is, partial thermalization within the charge carrier gases only. Step 2 includes carrier-phonon coupling leading to cooled FD distributions of Te = Th = T0, that is, complete thermalization within the irradiated CdS material. Looking at the relevant FD distributions and taking into account Δk = 0 for radiative electron−hole (eh) pair recombination, it turns out that the CdS luminescence spectra expected after relaxation step 2 are very close to the measured spectra (Figure 5a).
(vii) Spontaneous fluorescence of the CdS nanostructures is assumed to lie below the detection limit of the applied experimental setup (previous paragraph). The overall interpretation of the above experimental findings is depicted in the scheme sketched out in the Supporting Information (Figure SI 6). Summarizing (i)−(vii), the observed emission is attributed to stimulated emission processes such as ASE, nanowire lasing, and random lasing, leaving open their final assignment. As lasing requires very efficient radiative eh pair recombination it seems more likely at high fluences whereas ASE might dominate at low excitation fluence. A tentative assignment of kfast to lasing and kslow to ASE would be supported by the large variation in the kfast values in Figures 2d and 3b contrasted by the identical kslow values for different excitation fluences.
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SUMMARY An experimental setup (Figure 6a) has been established allowing to excite semiconductor samples by a focused femtosecond (fs) laser beam (pulse width τp ≈ 50 fs) tunable in the 380 nm ≤ λex ≤ 440 nm wavelength region and observe their luminescence simultaneously in the 490 nm ≤ λem ≤ 530 nm range using a dispersion-free imaging system. The build-up and decay kinetics of the luminescence can be detected with a time resolution of about δt ≈ 0.15 ps applying an optical Kerr gate (OKG) pumped by fs laser pulses (τp ≈ 50 fs, λex = 800 nm) at variable delay Δt relative to the sample excitation pulse. This setup has been used to investigate an ensemble of CdS nanostructures (Figure 6b). Most strikingly, the onset of the observed CdS luminescence shows a delay 0.1 ps ≤ ton ≤ 3 ps relative to the excitation laser pulse (Figures 1−3) depending on the applied laser photon energy hνex and the laser pulse energy fluence Φ. The emission build-up is in a first approach characterized by two kinetic constants 0.5 ps−1 ≤ kon = 1/ton ≤ 10 ps−1 (Figures 2 and 3) and 1 ps−1 ≤ krise ≤ 4 ps−1 (Figure 3) with kon describing the delay and krise the increase of the luminescence signal. The subsequent biexponential emission decay is determined by 0.1 ps−1 ≤ kfast ≤ 4.5 ps−1 and 0 ≤ kslow ≤ 0.5 ps−1 (Figures 2 and 3). At high Φ values, the luminescence spectrum is initially centered at λemc ≈ 501 nm and shifts to about 511 nm within
CONCLUSIONS The observed delay between the exciting fs laser pulse and the observed luminescence is attributed to two processes, thermalization of the photo excited hot charge carriers with the cold CdS lattice and the buildup of stimulated emission. Auger recombination is considered negligible under the applied experimental conditions. The luminescence delay as a function of the photon quantum energy hνex and the laser energy fluence Φ can be rationalized by assuming a (nearly) constant amount of energy to be redistributed within one electron−phonon interaction process. Spontaneous fluorescence is excluded as an essential contribution to the observed emission. The observed fast biexponential decay as well as the variations of the luminescence spectra on the ps time scale support the conclusion of stimulated processes to be the origin of the observed emission. The spectral variations are tentatively attributed to effects of band filling and band gap renormalization. The application of the ultrafast optical Kerr gate (OKG) switch of δt ≈ 150 fs provides a purely passive diagnostics method as distinguished from, for example, pump−probe methods. It opens up many options for ultrafast and dispersion free detection of broadband luminescence spectra and their kinetics. On this basis, the dynamical behavior of highly excited G
DOI: 10.1021/acsphotonics.6b00755 ACS Photonics XXXX, XXX, XXX−XXX
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to the growth parameters given in ref 5. The randomly orientated CdS nanostructures had typical lengths in the 15 ± 5 μm range. Wire-shaped structures showed a diameter of 0.5 ± 0.1 μm and band shaped structures a thickness of 3 ± 2 μm. A two-step statistical model has been applied to describe intermediate relaxation states of the irradiated CdS nanostructure ensemble. The total excited charge carrier density ntot(Φ) = nehtot(Φ) = netot(Φ) = nhtot(Φ) in the irradiated sample volume is calculated for a selected Φ-value (cf. below). Furthermore, the excess energies Eexce in the CB and Eexch in the VB are calculated for the photon quantum energy hνex by use of eq 1 applying the effective masses me = 0.2m0 and mh = 0.8m0 (free electron rest mass m0 = 9.109 × 10−28 g).24 Knowing the values Eexce in the CB and Eexch in the VB per charge carrier, the total energy content of the hot electron and hot hole gases is calculated, that is, Eexce(tot) = netot(Φ)Eexce and Eexch(tot) = nhtot(Φ)Eexch. Subsequently, the calculations for the electron and the hole gases are performed completely separately (separate systems) but follow equivalent procedures. Therefore, it is sufficient to sketch out the proceeding of the electron gas calculation. For a selected Φ-value the total electron density ntot(Φ) in the irradiated sample volume is calculated for the absorption coefficient α = α(hνex) assuming the validity of Beer’s law (linear 1-photon absorption only) and applying it for simplicity to an irradiated CdS cube of length a:
semiconductors like the CdS nanostructures of this paper can now be investigated in depth, experimentally and theoretically.
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METHODS The setup for excitation and diagnostics of the CdS nanostructure ensemble is sketched in Figure 6a. The photoexcitation source consists of a fs laser oscillator/amplifier unit (Coherent, Mantis oscillator and Legend Elite amplifier) emitting at λ = 800 nm, τp = 50 fs pulse duration, and 1 kHz pulse repetition rate. The amplified laser pulses were divided by a beam splitter and partially frequency doubled (SHG: second harmonic generation) in a lithium triborate (LBO) crystal to generate 400 nm radiation, which was filtered from the fundamental laser light by dichroic mirrors (Layertec GmbH, Mellingen, Germany). The SHG pulse energy was varied by rotating the LBO crystal and thus changing the SHG efficiency. Alternatively, the 800 nm pulses entered an optical parametric amplifier (OPA, Coherent, Opera solo) tuned to 440 or 380 nm output wavelength. The energy of the frequency shifted pulses was controlled by variation of the internal OPA settings. The frequency shifted laser pulses passed through an iris aperture (I1), were focused by a lens ( f 2 = 100 mm) and directed orthogonally onto the CdS sample by a small plane mirror. The sample emission was collimated by an off-axis parabolic mirror (OAPM1, Edmund optics, #84−565, 30°, f P1 = 76.4 mm) and focused by a second off-axis parabolic mirror (OAPM2, Edmund optics, #47−087, 30°, f P2 = 50.8 mm) through a polarizer (1 mm separated thin films, Edmund optics, #86−178) into the OKG medium (beam radius in focal plane wem(1/e2) ≈ 50 μm, 1 mm SAL 4 glass manufactured at IPHT Jena22,23). The OKG medium was optically pumped by the other part of the 800 nm fs laser pulse (wOKG(1/e2) = 100 μm) having passed a variable beam attenuator, a variable time delay unit (−1 ps ≤ Δt ≤ 35 ps), a f1 = 500 mm lens, and a highly reflective mirror. After transmission through the OKG medium the pump pulse was blocked by a beam stop. The sample emission light behind the OKG was collected by a microscope objective (Zeiss 20X NA 0.4 LP Achroplan), passed through a second polarizer (Zeiss polymer thin film polarizer (analyzer), rotated by 90° relative to polarizer 1), and a stack of dichroic filters (F2, Semrock, Brightline FF01 550/88 nm fluorescence filter, Omega Optical, third millennium 630SP and Thorlabs FES0750−1). Finally, it was focused into an imaging spectrograph (ANDOR, SR303i-B, fiber coupled) equipped with a cooled camera system in combination with a microchannel plate (ANDOR i-Star, cooled to −18 °C). The angle between the gate pulse beam and the emission signal beam amounted to about 1°. The camera signal was recorded by a PC for further data analysis. The spot size of the excitation laser beams on the sample ranged from radius w(1/e2) values of 23−86 μm (in detail: λex = 380 nm: wx = 78.0 ± 0.5 μm, wy = 85.8 ± 0.4 μm; 400 nm: wx = 23.0 ± 0.6 μm, wy = 22.8 ± 0.6 μm; 440 nm: wx = 46.4 ± 0.2 μm, wy = 47.6 ± 0.7 μm). The time resolution of the OKG detection system was determined to δt ≈ 150 fs (part (H) of Supporting Information). Figure 6b shows a typical scanning electron microscopy (SEM) image of the CdS nanostructure ensemble, which was synthesized using the vapor−liquid−solid (VLS) mechanism described in ref 5. Briefly, a thermal transport technique of atomic species was exploited for the growth of the nanostructure batches in a horizontal tube furnace according
Φ [1 − exp(−αa)] · hν a Φα ≈ for αa ≪ 1 hν
ntot(Φ) =
(2)
for Φ being the average pulse energy fluence over the cube cross section σcube = a2. The distribution function of the thermalized electrons ne(Eexce) is determined by the density of states ρ(Eexce) and the Fermi−Dirac distribution function16 according to e ne(Eexc )=
e 3/2 Eexc 1 ⎛ 2meff ⎞ ⎜ ⎟ e − μ)/kTe] 2π 2 ⎝ ℏ2 ⎠ 1 + exp[(Eexc
(3)
with μ = μ(Te) being the chemical potential of the excited electron gas in the CB. Under the above assumptions the number (density) of excited electrons is conserved, that is, ntot(Φ) =
∫0
∞
e e ne(Eexc )dEexc
(4)
Furthermore, energy conservation in the electron gas is valid during the adiabatic step 1, that is, e e Eexc (tot) = netot(Φ)Eexc =
∫0
∞
e e e ne(Eexc )Eexc dEexc
(5)
Therefore, the calculation of the distribution function ne(Eexce) requires to know the values of Eexce, ntot(Φ), μ(Te), and Te. The first two values are known from eqs 1 and 2. In the special case, Te = 300 K after relaxation step 2 the chemical potential μ(300 K) is calculated analytically for given Eexce(tot) and ntot(Φ) values.16 In the general case of unknown μ(Te) and Te for given Eexce(tot) and ntot(Φ) values, however, there is no analytical solution and the numerical Gaussian algorithm is applied (Numpy-library of programming language Python, Python version 3.3). Representative results of distribution functions ne(Eexce) obtained in these ways for excitation at 440 H
DOI: 10.1021/acsphotonics.6b00755 ACS Photonics XXXX, XXX, XXX−XXX
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(7) Oh, J.; Yuan, H.-C.; Branz, H. M. An 18.2%-efficient black-silicon solar cell achieved through control of carrier recombination in nanostructures. Nat. Nanotechnol. 2012, 7, 743−748. (8) Hsu, H.-C.; Wu, C.-Y.; Hsieh, W.-F. Stimulated emission and lasing of random-growth oriented ZnO nanowires. J. Appl. Phys. 2005, 97, 064315. (9) Li, G.; Zhai, T.; Jiang, Y.; Bando, Y.; Golberg, D. Enhanced FieldEmission and Red Lasing of Ordered CdSe Nanowire Branched Arrays. J. Phys. Chem. C 2011, 115, 9740−9745. (10) Röder, R.; Sidiropoulos, T. P. H.; Tessarek, C.; Christiansen, S.; Oulton, R. F.; Ronning, C. Ultrafast Dynamics of Lasing Semiconductor Nanowires. Nano Lett. 2015, 15, 4637−4643. (11) Puthussery, J.; Lan, A.; Kosel, T. H.; Kuno, M. Band-Filling of Solution-Synthesized CdS Nanowires. ACS Nano 2008, 2, 357−367. (12) Prasankumar, R. P.; Upadhya, P. C.; Taylor, A. J. Ultrafast carrier dynamics in semiconductor nanowires. Phys. Status Solidi B 2009, 246 (9), 1973−1995. (13) Karras, C.; Paa, W.; Litzkendorf, D.; Grimm, S.; Schuster, K.; Stafast, H. SiO2-Al2O3-La2O3 glass - a superior medium for optical Kerr gating at moderate pump intensity. Opt. Mater. Express 2016, 6, 125−130. (14) Bohnert, K.; Anselment, M.; Kobbe, G.; Klingshorn, C.; Haug, H.; Koch, S. W.; Schmitt-Rinck, S.; Abraham, F. F. Nonequilibrium Properties of Electron-Hole Plasma in Direct-Gap Semiconductors. Z. Phys. B: Condens. Matter Quanta 1981, 42, 1−11. (15) Shah, J. Hot Electrons and Phonons under High Intensity Photoexcitation of Semiconductors. Solid-State Electron. 1978, 21, 43− 50. (16) Kittel, C.; Kroemer, H. Thermal Physics, 2nd ed.; W.H. Freeman & Co.: U.S.A., 1980. (17) Xu, X.; Zhao, Y.; Sie, E. J.; Lu, Y.; Liu, B.; Ekahana, S. A.; Ju, X.; Jiang, Q.; Wang, J.; Sun, H.; Sum, T. C.; Huan, C. H. A.; Feng, Y. P.; Xiong, Q. Dynamics of Bound Exciton Complexes in CdS Nanobelts. ACS Nano 2011, 5, 3660−3669. (18) Liang, S.; Li, M.; Wang, J.-H.; Liu, X.-L.; Hao, Z.-H.; Zhou, L.; Yu, X.-F.; Wang, Q.-Q. Silica-coated and annealed CdS nanowires with enhanced photoluminescence. Opt. Express 2013, 21, 3253−3258. (19) Pan, A.; Liu, R.; Yang, Q.; Zhu, Y.; Yang, G.; Zou, B.; Chen, K. Stimulated Emissions in Aligned CdS Nanowires at Room Temperature. J. Phys. Chem. B 2005, 109, 24268−24272. (20) Kreissl, A.; Bohnert, K.; Lyssenko, V. G.; Klingshirn, C. Experimental investigation on the complex dielectric function of CdS in the exciton and in the plasma limit. Phys. Status Solidi B 1982, 114 (2), 537−544. (21) Bohnert, K.; Kalt, H.; Klingshirn, C. Intrinsic absorption optical bistability in CdS. Appl. Phys. Lett. 1983, 43 (12), 1088−1090. (22) Karras, C.; Litzkendorf, D.; Grimm, S.; Schuster, K.; Paa, W.; Stafast, H. Nonlinear refractive index study on SiO2-Al2O3-La2O3 glasses. Opt. Mater. Express 2014, 4, 2066−2077. (23) Schuster, K.; Unger, S.; Aichele, C.; Lindner, F.; Grimm, S.; Litzkendorf, D.; Kobelke, J.; Bierlich, J.; Wondraczek, K.; Bartelt, H. Material and technology trends in fiber optics. Adv. Opt. Technol. 2014, 3, 447−468. (24) Brus, L. E. Electron−electron and electron-hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state. J. Chem. Phys. 1984, 80, 4403−4409.
nm are used to calculate the distribution functions ne(k) for ntot(Φ) = 1.7 × 1019 cm−3 and 0.16 × 1019 cm−3 for Φ = 3.5 and 0.33 mJ/cm2, respectively, using Eexce(k) = 0.358 eV and Eexch(k) = 0.090 eV.10,15,16 These functions are sketched out in Figure 4b for Te ≫ T0 after relaxation step 1 and Te = T0 = 300 K after step 2.
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.6b00755. (A) Spectro-temporal luminescence traces of CdS nanostructures upon femtosecond laser excitation at λex = 440, 400, and 380 nm; (B) CdS nanostructure ensemble and time integrated stimulated emission spectra; (C) Single CdS nanowire and its spontaneous and stimulated emission spectra; (D) Comparison of spectral emission properties of a single CdS nanowire and an ensemble of CdS nanostructures; (E) Superposition of individual CdS nanowire (NW) lasing spectra; (F) Scheme of emission by CdS nanostructure ensemble and its detection; (G) Auger recombination in CdS nanowires; (H) Temporal resolution of the excitation and detection system (PDF).
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Christian Karras: 0000-0001-6935-0795 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Institutional funding by the Thuringian Ministry of Economic Affairs, Science and Digital Society is gratefully acknowledged. Two authors (C.R. and R.R.) thank the German Research Foundation for financial support via Grant FOR1616. The IPHT authors thank Dr. K. Schuster and D. Litzkendorf (IPHT) for providing the SAL glass sample.
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REFERENCES
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