Time-Resolved Stark Spectroscopy in CdSe ... - ACS Publications

Sep 20, 2016 - With the developed field-dependent population model treating all occurring ... Alexander W. AchtsteinOliver MarquardtRiccardo ScottMoha...
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Time-Resolved Stark Spectroscopy in CdSe Nanoplatelets: Exciton Binding Energy, Polarizability, and Field-Dependent Radiative Rates Riccardo Scott,*,†,∥ Alexander W. Achtstein,*,†,‡,∥ Anatol V. Prudnikau,§ Artsiom Antanovich,§ Laurens D. A. Siebbeles,‡ Mikhail Artemyev,§ and Ulrike Woggon† †

Institute of Optics and Atomic Physics, Technical University of Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany Optoelectronic Materials Section, Delft University of Technology, 2628 BL Delft, The Netherlands § Research Institute for Physical Chemical Problems of Belarusian State University, 220006, Minsk, Belarus ‡

S Supporting Information *

ABSTRACT: We present a study of the application potential of CdSe nanoplatelets (NPLs), a model system for colloidal 2D materials, as field-controlled emitters. We demonstrate that their emission can be changed by 28% upon application of electrical fields up to 175 kV/cm, a very high modulation depth for field-controlled nanoemitters. From our experimental results we estimate the exciton binding energy in 5.5 monolayer CdSe nanoplatelets to be EB = 170 meV; hence CdSe NPLs exhibit highly robust excitons which are stable even at room temperature. This opens up the possibility to tune the emission and recombination dynamics efficiently by external fields. Our analysis further allows a quantitative discrimination of spectral changes of the emission energy and changes in PL intensity related to broadening of the emission line width as well as changes in the intrinsic radiative rates which are directly connected to the measured changes in the PL decay dynamics. With the developed field-dependent population model treating all occurring field-dependent effects in a global analysis, we are able to quantify, e.g., the ground state exciton transition dipole moment (3.0 × 10−29 Cm) and its polarizability, which determine the radiative rate, as well as the (static) exciton polarizability (8.6 × 10−8 eV cm2/kV2), all in good agreement with theory. Our results show that an efficient field control over the exciton recombination dynamics, emission line width, and emission energy in these nanoparticles is feasible and opens up application potential as field-controlled emitters. KEYWORDS: Field-dependent PL, nanoplatelets, quantum confined Stark effect, Franz-Keldysh effect, exciton binding energy

R

excitons with rather weak exciton binding energy in contrast to the nanoplatelets. We provide a comprehensive study of the occurring effects in field controlled semiconductor nanoplatelet PL emitters: The Quantum Confined Stark Effect and FranzKeldysh Effect lead to a strong alteration of the exciton wave function resulting in a change of the emission intensity, the PL lifetime, line width, and emission energy. This goes in line with field-dependent changes of the exciton transition dipole moment and changes of the static exciton dipole moment. We will quantify these changes by a new global model involving both time-integrated and resolved field-dependent PL data on CdSe nanoplatelets28−30 as a model system and deduct the exciton binding energy. Up to now, it is for example still an open question to what extent the exciton binding energy and the field-induced changes of the radiative rates affect the field-dependent emission intensity and broadening of nanoplatelets. A detailed study

obust excitons are desirable for many photonic applications (e.g., lasing1) and are currently in the focus of interest as they occur in 2D semiconductor nanomaterials with strong confinement and high dielectric mismatch to the surrounding.2,3 We expect these high exciton binding energies to allow high spectral modulation while preventing field ionization in field-controlled nanoemitters and nanostructure based modulators. This has great application potential in miniaturized and integrated photonics such as modulated emitters, switchable single photon sources, or ultra high bandwidth modulators.4−12 We show that CdSe nanoplatelets exhibit high exciton binding energies of ≈170 meV in line with theoretical predictions. As those robust excitons are stable at room temperature and still efficiently polarizable, there is great application potential for field-dependent photoluminescence (PL) nanoemitters or modulators. While field-controlled electroabsorption based modulators have been studied intensively both in experiment and theory,8,9,13−22 fielddependent photoluminescence (PL) nanoemitters23−27 have been mostly discussed on a qualitative or semiquantitative level. However, these studies investigated field effects on Wannier © XXXX American Chemical Society

Received: August 3, 2016 Revised: September 16, 2016

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Figure 1. (a) Level scheme of the CdSe platelets’ electronic structure of crystal ground state |0⟩, ground |GS⟩, and excited state |ES⟩ exciton, with the radiative transition rates ΓrES/GS, the ES↔ GS zero temperature scattering or relaxation rate γ0, and the nonradiative rates Γnr ES/GS. (b) TEM image of the platelets embedded in polymer in the sandwich-like field-effect stucture shown in panel c. (d) Sketch of the dual ES and GS emission of CdSe F 0 F nanoplatelets centered at Ec,0/F ES/GS and separated by δE for zero and δE for finite field F. Voigt emission profiles (total fwhm wES/GS) with natural G Lorentzian line width wL,F ES/GS and Gaussian inhomogeneous line width wES/GS (due to field-independent inhomogeneous broadening by lateral size distribution of the nanoplates) are used to fit the field-dependent emission spectra in part e. The area under curve AFES/GS of each emission is proportional to the emission intensity IFES/GS. (e) Zero-field and field-dependent time integrated PL along with Voigt fits as well as the fielddependent differential emission spectra. Thin gray dotted line: Weak, red-shifted defect emission.

with respect to the external electrical and optical fields. Their volume fraction in the polymer was held well below 5% to avoid interplatelet coupling effects such as Förster resonant energy transfer (FRET) effects.32 A sandwich-like ITO/CdSeNPLs doped polymer/epoxy/ITO structure is obtained by attaching a second ITO electrode to the polymer (PMAO (polymaleic anhydride-alt-octadecene)) with embedded nanoplatelets using epoxy glue, see Figure 1c. A DC voltage power supply is used to apply the external electric field F, defined as the applied voltage divided by the exact distance between the ITO electrodes, measured to be 48 μm. For time integrated PL experiments a He−Cd laser at 441 nm was used as an excitation source in combination with detection by an 0.55 m spectrometer (Horiba IHR550) and attached cooled CCD via 0.4 N.A. PL collection optics. The PL emission in CdSe nanoplatelets is governed by the recombination of excited and ground state heavy-hole excitons,30,31 shown in Figure 1e first panel. The resulting field-dependent PL spectra of our nanoplatelets (NPLs) at room temperature are also shown in the same figure. Time resolved measurements were performed with a titanium-sapphire (Ti:Sa) 150 fs laser with 75.4 MHz repetition rate at 440 nm (frequency doubled) at an excitation density of 0.7 W/cm2. The transient PL emission was analyzed by a streak camera (Hamamatsu C5680) and is shown and discussed later in Figure 3. Changing the applied field in our nanoplatelet field-effect structure alters the emission strongly, as seen in Figure 1e. We observe a decrease of the emission intensity, a line broadening, and increasing spectral shifts with increasing applied electric fields. To analyze the changes more in detail we use the differential emission defined as

involving the above-mentioned effects at the same time is still missing. We use CdSe nanoplatelets (NPLs) as a model system as they exhibit a strong electrooptic response.12 They are characterized as colloidal quantum wells of finite size exhibiting both an excited state (ES) and ground state (GS) exciton emission and an LO-phonon bottleneck in-between the two states (see Figure 1a).31 Our investigation shows that the fielddependent change of the transition rates contributes more than the transition line width broadening to the strong fielddependent PL modulation. The former results in an alteration of the PL lifetime, which we investigate by time-resolved PL measurements, while the latter leads to a measurable broadening of the time-integrated PL spectra. Based on a rate equation model developed for the recombination dynamics in CdSe nanoplatelets31 (at zero field), we develop a formalism to connect the occurring field-induced changes in the PL lifetime, the transition energies, and the line width to the microscopic processes: They involve changes of the exciton transition dipole moment μ due to the transition dipole moment polarizability X and transition energy due to the exciton’s polarizability α as well as broadening of both ES and GS. We further show that the total modulation depth of our field-controlled platelet emitter can be up to 28%, a very high value for a nanoparticle emitter and only limited by the maximum field strength of our measurement setup. Results and Discussion. Zinc blend CdSe nanoplatelets with first exciton absorption at 550 nm (5.5 monolayers of CdSe thickness) where synthesized as in ref 12 and characterized by transmission electron microscopy obtaining a lateral size of 42 ± 7 nm × 8.7 ± 2.1 nm (Figure 1b). The NPLs were embedded in thin polymeric films deposited on the surface of indium−tin−oxide (ITO)-coated glass. The NPLs are thus randomly (isotropically) oriented in the polymer and B

DOI: 10.1021/acs.nanolett.6b03244 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters ⎛ ΔI ⎞ E , F I E , F − I E ,0 ⎜ ⎟ = ⎝ I ⎠ I E ,0

(1)

shown in the lower part of Figure 1e where IE,F is the emission at a spectral position (energy E) at an external field F. We observe a strong electromodulation behavior. The local minimum and maximum of the differential emission spectrum correspond to the ES and GS exciton transition energies9 of our CdSe nanoplatelets. We model the ES and GS emissions with Voigt profiles VE,F taking into account the homogeneous and inhomogeneous emission line width of our emitters so that we rewrite eq 1 as E ,F E ,0 E ,0 ⎛ ΔI ⎞ E , F − [VGS + VES V E , F + VES ] ⎜ ⎟ = GS E E ,0 ,0 ⎝ I ⎠ VGS + VES

(2)

which involves the Lorentzian (homogeneous) line width wL,F ES/GS, the field-independent inhomogeneous Gaussian broadening wGES/GS (related to the lateral size distribution of platelets), F and the centers Ec,F ES/GS of the emission profiles. AES/GS is the area under curve of each emission and proportional to the emission intensity IFES/GS. To avoid confusion by many variables we indicate field-dependent quantities always by a superscript F and the energy position in the spectrum E. Quantities related to the excited ES or ground state GS are indicated by a subscript ES or GS, respectively, see illustration in Figure 1d for the used nomenclature. Figure 1e shows the corresponding global fits to the field-dependent emission (upper panels) and differential emission (lower panels) which are fitted simultaneously (for each field-strength) with a shared set of parameters; see also Supporting Information (SI). The ES−GS energy spacing δEF can be sensitively determined due to the inclusion of the differential emission spectra. From the fits we obtain a zero field ES−GS energy spacing of δE0 = 23.9 meV, close to the LO phonon energy in zinc-blend CdSe of 25.4 meV.31 The results of these fits for the field-induced changes of the transition energies ΔEF and homogeneous (Lorentzian) broadening ΔwL,F ES/GS are shown in Figure 2. We observe a redshift of the excitonic emissions accompanied by a significant broadening. This is a characteristic of the quantum confined Stark and Franz-Keldysh effects, as has been observed in various quantum wells and quantum dots.9,13,15,17,33−35 The observed quantum confined Stark shifts mostly originate from a distortion of the square well confinement potential reducing the energetic difference between hole states in the valence band and electron states in the conduction band.13 The broadening is mostly due to the Franz-Keldysh effect for platelets having a preferential parallel orientation to the electric field13 which are polarizable due to the formation of spatially distorted excitons in the presence of an external field. We must note here that the used external field-strengths in our measurements are well below the expected exciton ionization fields so that we are not in a regime where exciton ionization contributes to the observed energy shift (see SI). The fielddependent energetic shift of the PL ΔEF can be modeled as10,23

Figure 2. (a) External field F dependent ES and GS transition energy shifts ΔEFES/GS and fits according to eq 3. (b) Field-dependent total time integrated PL intensity AFGS + AFES, normalized to the zero field emission intensity (A0GS + A0ES). (c) Field-induced homogeneous (Lorentzian) broadening ΔwL,F ES/GS. The solid lines are guides to the eye.

field in the nanoparticles (averaged angularly over 4π accounting for the random orientation of the nanoparticles in the host polymer) to the external field-strength F = U/d. U is the applied voltage and d the polymer thickness between the ITO electrodes of the field-effect structure. Hence the observed spectral Stark shift corresponds to the angularly averaged internal electrical field-strengths. (See also SI.) Figure 2 a shows that our measured field-dependence of the transition energies, obtained from our analysis of the data in Figure 1 e, is well fitted with the model eq 3 (solid lines). We obtain a dipole polarizability α for the GS of 8.6 ± 1.6 × 10−8eV cm2/kV2 (which equals 1.4 ± 0.3 × 10−36 Cm2/J in SI units, further always indicated in brackets for comparison). For the ES we find α to be 1.8 ± 0.2 × 10−6 eV cm2/kV2 (3.0 ± 0.3 × 10−35 Cm2/J). These values are substantiated by a comparison with theory and experiment. A rough estimate of the polarizability can be obtained from perturbation theory yielding α = 2e2⟨r2⟩/ΔE36,37 where ⟨r2⟩ is the expectation value of the position operator squared, e the elementary charge, and ΔE an average energy spacing of all allowed transitions. As the spatial extent of the exciton limits the dipole length we estimate the volume of the exciton as a cylinder with the height Lw = 1.67 nm (well width in perpendicular direction) and a radius equal to the Bohr radius aB = 1.41 nm. The expectation value of the position operator squared is then ⟨r2⟩ = (πLwa2B)2/3/4. ΔE is approximated by a typical exciton binding energy in CdSe nanoplatelets of EB ∼ 200 meV.38 This was also used to calculate aB = ℏ/(2μrEB)1/2 = 1.41 nm with the reduced exciton mass μr.30 From this perturbation theory approximation we find α = 1.9 × 10−36 Cm2/J, strengthening our experimental value. Kunneman et al.39 measured an imaginary part of the mobility of μI = 2.0 cm 2/(V s) in CdSe nanoplatelets, which corresponds to the sum of ES and GS polarizabilities, as the experiment cannot distinguish between the contributions of ES and GS. This imaginary mobility can be related to the

ΔE F = (p + pind )Fint = (p + αFint)Fint = (p + α|flf̃ |F )|flf̃ |F = p|flf̃ |F + α |flf̃ |2 F 2

(3)

with p the permanent exciton dipole moment and α its polarizability, resulting in a linear and quadratic term for the external field F dependence of the energy shift. The effective local field factor flf̃ = Fint/F = f lf/ϵr,poly is the ratio of the internal C

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The field-dependent transition dipole moments, which are F 2 related to the radiative rates of each state Γr,F ES/GS ∝ |μES/GS| , can be understood as an addition of a perturbation to the zero field transition dipole moment μ9

polarizability by α = 2πfμI/e where f is the used THz probe frequency in the experiment in ref 39. A value of ∼1.0 × 10−35 Cm2/J is obtained, which is in good agreement to our results as it corresponds to the sum of ES and GS polarizabilities. The trend that our GS polarizability is substantially smaller (by more than 1 order of magnitude) as compared to the ES is in line with calculations of the in-plane polarizability of infinite quantum wells by Pedersen.40 We further note that reducing the dimensionality of an exciton from bulk (D = 3) to D = 2 in a quantum well strongly reduces in general the exciton polarizability because the energy level spacings are increased and the dipole length is limited due to the spatial confinement. Pedersen40 has shown that the confinement-related decrease of the polarizability is stronger for the GS thus resulting in a lower polarizability of 2D GS excitons with respect to ES excitons. Therefore, the lower GS polarizability in our CdSe nanoplatelets is not unexpected. We would like to point out that the here discussed findings independently confirm beyond the analysis presented in ref 31 that the observed high energy PL emission in the CdSe nanoplatelets is from an excited state in the nanoplatelets. We observe no (measurable) permanent dipole moment p in the CdSe nanoplatelets, as the induced average shift in a random distribution of dipoles is expected to be zero. Furthermore, in a system with inversion symmetry (zinc blende CdSe) no permanent dipole moment is expected. The measured ground state exciton polarizability α can be related to the polarizability volume Vpol via Vpol = α/4πϵ0. The polarizability volume allows an estimate of the exciton binding energy. Assuming that the polarizability volume of a quasi 2D exciton is determined by its physical size (exciton volume), which can be approximated as a cylinder of height Lw and radius aB (with EB = ℏ2/2μra2B), we obtain EB ≈ ℏ2πLw/2μrVpol = 170 ± 31 meV. This experimentally obtained exciton binding energy is in good agreement with the aforementioned theoretical results of Benchamekh,38 predicting EB = 193 meV, and the predictions in ref 30 for the used platelet thickness. Therefore, we provide the first experimental proof for the predicted high exciton binding energies in colloidal CdSe nanoplatelets. This agreement on the other hand is an additional indirect confirmation of our measured polarizability. We show in the SI that the estimation of the exciton binding energy via the polarizability is also confirmed by an application of this method on reported field dependent data of CdSe quantum dots. Hence we have measured for the first time the exciton binding energy in CdSe nanoplatelets and provide a new method to estimate exciton binding energies in colloidal 2D systems. These robust excitons are highly desirable as they are stable at room temperature, which results in no coexisting electron−hole pair populations. Figure 2b shows the modulation of the total PL intensity. It reaches up to 22% for high fields. The magnitude of the PL reduction is in our case only limited to our experimentally accessible range of field; hence there is the potential to reach an even higher modulation depth (as well as spectral shift). As we demonstrate in the SI, the change of the emission intensity is clearly not related to the negligible changes of absorption of the exciting laser under applied field of below 0.1%. In contrast, the observed high modulation of the total emission suggests a strong alteration of the transition dipole moments of ES and GS under an applied external field which will be investigated in the following.

Fint μES/GS = μ + XFint

(4)

with X the transition dipole moment polarizability and Fint the internal field in the nanoparticle. The radiative transition rate Γr relates to the transition dipole moment μF via41

Γr ,F =

ω3n |fopt |2 3π ϵ0ℏc 3

|μ F |2 (5)

resulting in Γ

r ,F

=

=

ω3n |fopt |2 3π ϵ0ℏc 3

ω3n |fopt |2 3π ϵ0ℏc 3

|μ + X |flf̃ |F |2

(μ2 + 2μX |flf̃ |F + X2 |flf̃ |2 F 2)

(6)

using eq 4, so that we obtain an explicit field dependence of Γr,F. As the transition dipole moment polarizability X is negative (indicated by the decrease of the radiative rates with field in Figure 5) and the induced change (of the dipole moment) with respect to the zero-field case is small; the last simplification can be made in eq 6. fopt is the optical local field factor at the transition energy, n the refractive index of the surrounding matrix, and ω the transition frequency (see also SI). In the following we will derive the field dependence of the radiative rates of ES and GS from time-resolved PL (TR-PL) and timeintegrated PL (TI-PL) measurements with our global model. Figure 3 shows time-resolved PL spectra of our field-effect sample for both 0 and 175 kV/cm applied field. Clearly a decrease of the emission can be observed in parts a and b in the field-on case. The recombination dynamics is also altered as expected from the considerations above. The biexponential decay with a fast (λF) and a slow (λS) decay constant reflects the intrinsic two PL emission contributions of GS and ES. As shown in ref 31, the recombination dynamics of CdSe nanoplates is governed by both ES and GS emission and an LO-phonon bottleneck between the two states. Figure 1a displays a level scheme with the occurring parameters of the emission and dynamics of both states, the radiative rates ΓrES/GS, a zero temperature inter level scattering rate γ0, nonradiative rates Γnr ES/GS, and nδ a Bose−Einstein statistics factor for the thermal occupation of LO phonon modes (see SI for details). The dynamics of this system can be modeled by a coupled rate equation system for both the ES and GS excitons following the population model in Figure 1a nES ̇ = −nES(Γ rES + Γ nr ES + γ0(nδ + 1)) + nGSγ0nδ r nr nGS + Γ GS + γ0nδ) + nESγ0(nδ + 1) ̇ = −nGS(Γ GS

(7)

with nES/GS the exciton state population. The radiative rates ΓrES/GS are modeled to exhibit the above-mentioned field dependence of eq 6. As we have seen that ES and GS have a different shift with applied field (Figure 2a), the ES−GS energy spacing δEF = EFES − EFGS is field-dependent and decreases with increasing field. The ES−GS energy spacing is thus changed with respect to the above-mentioned resonance of the LOphonon bottleneck31 in CdSe nanoplatelets. As mentioned before, the energetic spacing between ES and GS for the D

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on the detuning dE of the ES−GS energy spacing with respect to the LO-phonon energy in zinc-blend CdSe nanoplatelets.31 Hence a field-induced change in the ES−GS energy spacing δEF makes γ0(δEF) field-dependent (see SI) and externally controllable by the applied voltage. This field-dependent relaxation rate leads apart from the above-mentioned alterations of the radiative rates to an alteration of the time-integrated ratio R of the ES and GS emission intensities. The differential changes of this ratio with respect to zero-field (ΔR/R)TI are depicted in Figure 4a (green). This quantity can be directly related to the parameters of the rate equation system including field-induced changes of both the ES and GS radiative rates and γ0. It can also be fitted globally together with the field-induced changes of the ES and GS emissions (IFES/GS), shown normalized to the respective zero-field emissions as blue and red dots in Figure 4a. The benefit of including the mentioned ratio, deduced from timeintegrated PL, is that it is very sensitive to field-dependent changes of the ES−GS relaxation rate γF0 and makes our global fit approach sensitive to field-induced changes in all three rates r,F F 0 0 Γr,F ES, ΓGS and γ0 . We also fit the zero-field ratio IES/IGS of the time integrated emissions of ES and GS in the global model. The zero-field ratio is obtained before each measurement with a finite field and shown in Figure 4a. No changes are observed from measurement to measurement, indicating that there is no degradation with time. From biexponential fits to the spectrally binned decay transients (Figure 3b), it is also possible to derive the ratio (Δr/r)TR,F of the time integrated population decay (or emission) through the fast component of the biexponential decay divided by the population decaying through the slow component. This is essentially due to the fact that both ES and GS share the same pair of decay constants (slow λS and fast λF) but have different decay (component) amplitudes. The fast and slow decay constants are the eigenvalues of the coupled rate equation system in eq 7 and contain the radiative and nonradiative rates of both ES and GS as well as the interscattering rate γF0, see also SI for definition. The amplitude of the fast decay component of the GS is negative, as it accounts for the filling of the GS from the ES via γF0. With the mentioned approach it is possible to derive the ratio of the population decay through the fast and slow component from the spectrally binned PL transients. The resulting field-induced relative change (Δr/r)TR,F of the PL decay through the fast decay component to the decay through the slow decay component is depicted in Figure 4 a (black). It should be noted that (Δr/r)TR,F and (ΔR/R)TI,F are different quantities, which in general do not coincide as deduced from the rateequation system (see also SI). Our global fit procedure determines at first the fielddependent ES−GS energy spacing by globally fitting the fielddependent PL spectra and the differential spectra in Figure 1 e with the Voigt emission profiles and eq 2, having a shared set of parameters. Then the algorithm fits the obtained fielddependence of the energy spacing (Figure 2a) with eq 3. From that it infers γF0 using Figure 4b (eq S15 in SI). Using these parameters, the four experimental quantities IFES/I0ES, IFGS/ I0GS, the change (ΔR/R)TI,F of the time-integrated intensity ratio of the ES to GS emission, and (Δr/r)TR,F, the change of the time-resolved component ratio of the fast and slow PL decay components, are fitted globally with a shared set of parameters. This way we take both time integrated and resolved data into account in our global model in Figure 4a. (For details see SI.)

Figure 3. (a) Time-resolved photoluminescence and temporally binned PL (white lines) as well as spectrally binned transients (in b) for 0 kV/cm and 175 kV/cm. The binning ranges are indicated in part a, while the instruments response function used for convolution is displayed in b. Transients in b are fitted with biexponentials consisting of a fast and a slow PL decay component as inferred from our rate equation model due to both the emissive GS and ES.

nanoplatelets that were used here lies nearly directly in resonance to the LO-phonon energy. Figure 4b shows the dependence of the zero temperature ES−GS scattering rate γ0

Figure 4. (a) Field-dependent relative change of the time-integrated ES IFES/I0ES and GS IFGS/I0GS emissions and the differential change (ΔRTI/R)TI,F = (RTI,F − RTI,0)/RTI,0 of the time integrated intensity ratio of the ES to GS emission RTI,F (see SI), upon application of an external field F. (Δr/r)TR,F is the differential change of the ratio of the population decaying through the fast and slow PL decay components (SI). The ratio of the ES and GS emission at zero-field I0ES/I0GS before each measurement at a finite field F is also shown. No change in this ratio indicates the absence of degradation or memory effects. (b) Field-dependent change of the ES−GS scattering rate γ0: At zero-field the ES−GS energy spacing, δE0 = E0ES − E0GS of the measured CdSe nanoplatelet sample is near resonant to the LO-phonon bottleneck at ELO = 25.4 meV in zinc blend CdSe.31 An increasing field leads to an alteration of the energy spacing (Figure 2a), thus to a larger detuning dE = δEF − ELO of the energy spacing from the LO-phonon resonance. This results in a reduction of γ0 with applied field. Our accessible field range is indicated by a gray shaded area. The displayed curve is obtained from a fit to data in ref 31 using a Fermi’s Golden rule model for an LO-phonon mediated transition.42 (See also SI for details.) E

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coupled. Hence the linear and quadratic terms in F do not have independent coefficients. We obtain from our fit model in Figure 4: XGS = −6.9 ± 1.8 × 10−37 Cm2/V and XES = −4.1 ± 1.0 × 10−37 Cm2/V. With the above-mentioned results, our model for the fielddependent PL emission also allows for the first time to discriminate between the effects of transition rate changes and field-induced broadening, which also reduces the radiant flux per unit wavelength, and allows to quantify the contributions. For a narrow band PL detection (e.g., 1 nm, much smaller than the fwhm of the zero-field emission) we find for the GS emission at E = 2.215 eV that 29% of the total emission change from zero to 175 kV/cm are related to broadening and 71% of the total changes are related to transition oscillator strength change. The emission can be lowered by 28% in total for this narrow band detection. For a broad detection (much bigger than the spectral zero-field fwhm) only the change in the transition oscillator strength, i.e., the radiative rates, leads to a field-dependent alteration of ≈22% of the measured total emission. Conclusion. We have shown that CdSe nanosheets are a good model system to study the effect of external fields on colloidal 2D quantum wells with respect to changes in the exciton transition dipole moments and line broadening. From our experimental results we have estimated the exciton binding energy in 5.5 ML CdSe nanoplatelets to be EB = 170 meV, in good agreement with theory. Hence CdSe NPLs exhibit highly robust excitons, which are stable even at room temperature. We demonstrate that the photoluminescence emission of these nanoparticles can be changed by more than 28% upon application of external electrical fields of up to 175 kV/cm and narrow band detection, allowing for highly efficient modulation. To investigate the origin of this high modulation depth for potential applications as field-controlled nanoemitters, we have developed a new global model describing field-dependent intensity changes, broadening, spectral shifts, and recombination dynamics. The presented global analysis allows a quantitative discrimination of the spectral changes in PL intensity related to both changes in the intrinsic radiative rates as well as broadening of the emission line width, which are directly connected to the measured changes in the PL decay dynamics. With this analysis we are able to quantify the ground state exciton transition dipole moment as 3.0 × 10−29 Cm, which determines the radiative rate, and the static exciton polarizability to 8.6 × 10−8 eV cm2/kV2. Our results show that an efficient field control over the exciton recombination dynamics, emission line width, and emission energy in these nanoparticles is feasible and opens up application potential as field-controlled emitters.

Figure 5. Field-dependent ES−GS scattering rate γF0 and intrinsic radiative rates Γr,F ES/GS of ES and GS as inferred from our global fit model. The red dot represents the radiative rate obtained from the transition dipole moment calculated using a k·p based simple approximation.

eq 6, and the ES−GS relaxation rate γF0. We observe both a reduction of the radiative and relaxation rates with increasing field. The decrease of the radiative rates can be understood in the frame of the quantum confined Stark and Franz-Keldysh effect: the electric field polarizes the electron and hole wave functions in the exciton and reduces the spatial overlap integral to which the transition dipole moment, and hence the radiative rate is proportional in an envelope function approximation.43 The reduction of the ES−GS relaxation rate on the other side is a consequence of the decrease of the ES−GS energy spacing with applied field. This detunes the energy spacing from resonance to the LO-phonon energy (the used platelets in zerofield are near resonant to the bottleneck) and hence reduces according to Fermi’s golden rule the transition rate between ES and GS (Figure 4b). It turns out that the ES−GS relaxation rate is strongly field-dependent and varies by a factor of ∼3 in our range of applied fields. The intrinsic radiative transition rates have a weaker field dependence. Both together are the reason for the observed strong alteration of the PL emission under applied field seen in Figures 1 and 2. Our global model directly treats these effects in the rate equation model (eq 7) including field-dependent transition rates (eq 6). As the rate equation model uses eq 6 to parametrize the field-dependent quantities displayed in Figure 4, we obtain the GS and ES transition dipole moments and their polarizability directly from our global fit. This results in |μGS|2 = 9.0 ± 2.3 × 10−58 C2 m2 and |μES|2 = 5.5 ± 1.4 × 10−58 C2 m2 for the zero-field transition dipole moment (squared). The squared ground state exciton transition dipole moment can be compared to an estimate of the transition dipole moment using a k·p based simple approximation44 applied to the CdSe nanoplatelets using their material constants from ref 31. The rough theory estimate |μ|2 ≈ 9.3 × 10−58 C2 m2 is shown as a red dot in Figure 5. This is in excellent agreement with our analysis for the GS. We are also able to obtain from our fitting procedure the transition dipole moment polarizability XES/GS using eq 6 in our fit model. The polarizability of the transition dipole moment leads to a linear and quadratic change of ΓrES/GS with applied field, where the coefficients of the second-order binomial are

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b03244. Details to the field-dependent population model, experimental setup, and the change of laser absorption under applied field (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Fax: +49(0)30 31421079. F

DOI: 10.1021/acs.nanolett.6b03244 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters *E-mail: [email protected].

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Author Contributions ∥

R.S. and A.W.A. contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS R.S., U.W., and A.W.A. acknowledge DFG grants WO477 and AC290. M.A. acknowledges financial support from the CHEMREAGENTS program. A.A. acknowledges support from BRFFI grant No. X16M-020.

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DOI: 10.1021/acs.nanolett.6b03244 Nano Lett. XXXX, XXX, XXX−XXX