Mobility and Spatial Distribution of Photoexcited Electrons in CdSe

Jan 18, 2013 - Jannika Lauth , Aditya Kulkarni , Frank C. M. Spoor , Nicolas Renaud , Ferdinand C. Grozema , Arjan J. Houtepen , Juleon M. Schins , Sa...
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Mobility and Spatial Distribution of Photoexcited Electrons in CdSe/ CdS Nanorods Lucas T. Kunneman,† Marco Zanella,‡ Liberato Manna,‡ Laurens D. A. Siebbeles,*,† and Juleon M. Schins*,† †

Opto-eletronic Materials Section, Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands ‡ Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy S Supporting Information *

ABSTRACT: The mobility and spatial distribution of photoexcited electrons in CdSe/CdS core/shell nanorods was studied using optical-pump THz-probe spectroscopy. Measurements were conducted on two samples, differing in rod length. After photoexcitation the hole localizes in the CdSe core within a picosecond, while the electron delocalizes around the core. Analysis of the THz mobility with a model of one-dimensional electron diffusion on a finite rod yields an electron delocalization of ∼25% into the CdS shell and a mobility of 700 cm2/ (V s). This is one and a half times the mobility value for bulk CdS, which can be due to quantum confinement effects on electron−phonon scattering and electronic structure.

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INTRODUCTION Colloidal semiconductor nanocrystals are of interest for applications in photovoltaics,1 photodetectors,2 LEDs,3 lasers,4 and single photon sources.5 This interest stems from the possibility to tune the optoelectronic properties of nanocrystals by variation of composition, size, or shape.6,7 It is possible to combine two or more (semi)conductor materials in a heteronanocrystal with a spherical or rod-like shape or an even more complicated geometry.8−10 In this context CdSe/ CdS core/shell heteronanorods (HNRs) receive attention due to prospects for applications in optical biolabeling,11 photocatalytic solar fuel production,12−14 and photoconductive films.15,16 In the above-mentioned applications the HNR absorbs light and the photoexcited electron is bound to its sibling hole to an extent that depends on the combination of the size of the spherical CdSe core and the geometry of the elongated rodshaped CdS shell. The band gap of bulk CdSe falls within that of bulk CdS, and this type-I band alignment favors localization of both electrons and holes in CdSe.8,17 However, in a HNR quantum confinement of electrons and holes causes the band alignment to depend on the size of the CdSe core and the geometry of the CdS shell, as well as on strain induced by the lattice mismatch between the core and shell materials.17−19 As a result the band alignment in a CdSe/CdS HNR may be of quasi-type II character, which facilitates spatial separation of electrons and holes. In the literature, CdSe/CdS HNRs are often regarded as a quasi-type II system, where the hole localizes in the core and the electron partly delocalizes into the CdS shell. A quasi-type II band alignment has been inferred from photoluminescence studies, which show that the radiative decay rate of photo© 2013 American Chemical Society

excited CdSe/CdS HNRs becomes smaller as the aspect ratio of the CdS rod increases.15,20,21 Accordingly, it has been found that photoexcitation not only bleaches the absorption of the CdSe core but also that of the CdS shell.22,23 Furthermore, photoluminescence experiments suggest that electron delocalization in the rod increases for smaller CdSe core size.24−26 In agreement with this, it has been found from scanning probe measurements that the photoexcited electron becomes localized in the CdSe core with a diameter larger than 4 nm.27,28 Results from ultrafast transient grating experiments were found to be insensitive to the length of the CdS rod, from which it has been inferred that the electron is delocalized isotropically around the CdSe core.29 The studies mentioned above have shown that a photoexcited electron in a CdSe/CdS HNR can exhibit spatial extension into the CdS rod, while the hole is localized in the CdSe core. The aim of the present work is to provide information about the spatial distribution and mobility of a photoexcited electron that moves along the CdS rod in the attractive Coulomb potential due to the hole in the CdSe core and undergoes scattering at the rod ends. Studies were carried using optical-pump THz-probe spectroscopy (OPTP). Electron−hole pairs are produced by photoexcitation with an ultrashort laser pulse. Subsequently, charge motion and decay dynamics are probed by a 1 ps single cycle THz pulse. For readers not acquainted with OPTP,30 the following idealization may help. In the case of a monochromatic electric field E(t) = E0 cos(ωt), the velocity of electrons varies in time as v(t) = Received: November 30, 2012 Revised: January 17, 2013 Published: January 18, 2013 3146

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μre(ω)E0 cos(ωt) + μim(ω)E0 sin(ωt), where μre(ω) and μim(ω) are the real and imaginary components of the complex frequency-dependent mobility. The electron velocity in phase with the electric field is determined by μre(ω); the magnitude of the electron velocity out of phase with the electric field is determined by μim(ω). The transmission of the THz probe is modulated in proportion to the electron mobility, thereby revealing the electron motion in a nanorod.

where ε is the molar extinction coefficient, related to the cross section as σ = (3.82 × 10−21 M cm3)ε. From the measured absorption spectrum one can determine the cross section at 400 nm excitation. We found σ(400 nm) ≈ 1 × 10−14 cm2 for the 34 nm rods and σ(400 nm) ≈ 3 × 10−14 cm2 for the 74 nm nanorods. Optical-Pump THz-Probe Measurements. The setup is as described in Figure 2B of the review on THz spectroscopy

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EXPERIMENTAL SECTION Nanorods. The HNRs were synthesized by growing a CdS nanorod along the Wurtzite c-axis from a CdSe quantum dot seed.15 The CdSe core is found at one-quarter to one-third of the length of the rod; the location of the core does not necessarily coincide with the darker regions seen in TEM.15 Nanorods with lengths of 33.5 ± 3.5 and 74.1 ± 6.3 nm were studied, with diameters of 2.5 ± 0.7 and 3.0 ± 0.4 nm, respectively. They were grown from CdSe cores with diameters of 2.1 and 2.6 nm, respectively. Figure 1 shows two

Figure 2. (A) THz probe E0(t) through the unexcited sample (red, scaled) and differential transmission ΔE(t,τ = 4ps)/Emax (blue) as a function of THz time delay for 34 nm HNRs. The THz probe undergoes a phase lag in the excited sample, as ΔE(t)/Emax peaks after the maximum of E0. This indicates a pump-induced change of the imaginary component of the mobility. The real component of mobility is revealed by the negative ΔE(t)/Emax at the delay where E0 peaks. (B) Pump-induced changes in real (solid line) and imaginary conductivity components as a function of pump−probe delay τ for 34 nm HNRs. The real component was measured at the THz time delay marked by the full blue dot in panel A, the imaginary component at the delay marked by the open blue dot.

Figure 1. (A) TEM image of CdSe/CdS HNRs with a length of 74 nm, scale bar 100 nm. (B) Similar for 34 nm rods. (C) Optical absorption spectrum of the colloidal dispersion, used for THz spectroscopy, of the 34 nm rods in toluene. The small absorption peak at 616 nm corresponds to a hole in the CdSe core with the electron delocalized around it, whereas the onset of absorption at 500 nm corresponds to electron−hole pairs in the CdS shell. The inset shows a sketch of the structure of the HNRs and conduction band (CB) and valence band (VB) levels.

by Baxter and Guglietta.34 The laser system consists of a Mira oscillator and a Legend HE-USP regenerative amplifier, both by Coherent Inc. The system yields a 1 kHz pulse train of 800 nm pulses, with an energy per pulse of 2.5 mJ and a pulse duration of ∼60 fs. The 800 nm pulses are used for generation and detection of THz radiation in ⟨110⟩ cut ZnTe crystals, respectively of 1.0 and 0.5 mm thickness. For exciting the nanorods, a BBO-crystal was used to generate 400 nm photons by second harmonic generation. A dichroic mirror separated the remaining 800 nm photons before excitation. The unfocused, optical pump has a diameter of ∼5 mm, whereas the focused THz probe has a diameter of ∼1.5 mm. This ensures a homogeneous illumination over the whole probe. The frequency dependent THz conductivity data was acquired overnight, and measured under N2 atmosphere, as to prevent absorption of THz radiation by water vapor. The data has not been smoothed. Measurements are performed in solution, the cuvettes used are airtight 1 mm thin QS Suprasil from Hellma, and stored under nitrogen atmosphere when not used. The

transmission electron microscope (TEM) images, which display the narrow size dispersion and the high geometric homogeneity of both types of rods. The optical absorption spectrum of the nanorods with a length of 34 nm dissolved in toluene is shown in Figure 1C. The small peak at 616 nm is due to an excited state with a localized hole in the CdSe core and a delocalized electron; the electron delocalization causes a slight red shift.22 The large absorption at 500 nm is due to excitation of electron−hole pairs in the larger CdS shell. At a wavelength of 350 nm, the absorption cross section (σ) depends linearly on volume (V) and not on nanocrystal shape for both CdSe and CdS31−33 εCdSe(350 nm) = 3.8 × 1025 M−1 cm−4 V εCdS(350 nm) = 2.8 ×1025 M−1 cm−4 V

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duration of the measurements may, depending on the signal-tonoise ratio, exceed 14 h. Optical-pump THz-probe spectroscopy has two independent time delays. The “pump−probe delay” time τ determines the arrival of the pump relative to the THz detection. The “THz time delay” t determines the THz generation relative to detection.30,34,35 The THz probe consists of a well-defined electric field waveform E0(t), which can be mapped by scanning the THz time delay. THz differential signals are expressed as the difference between an excited and unexcited sample: ΔE(t,τ) = Eexcited(t,τ) − E0(t). To obtain ΔE, the sample is probed with THz on each laser pulse, while the pump pulse is chopped away every other shot.

where L is the thickness of the excited sample, c is the speed of light in vacuum, ε0 is the vacuum permittivity, and neff is the effective refractive index of the unexcited sample. Equation 2 holds for pump delay times larger than the temporal extent of the THz waveform and therefore applies to our differential transmission taken at a pump delay, τ, of 4 ps. We calculated neff using the Maxwell−Garnett (MG) model for randomly oriented prolate spheroids of CdS dissolved in toluene.39 The complex dielectric function for both materials in the THz frequency range was taken from literature,40,41 and for the low concentration of rods, neff is equal to the refractive index of toluene, ntol. As shown in the Supporting Information, the intrarod mobility μ rod (ω) can be retrieved from the experimental data with eq 2 and the relation

RESULTS AND DISCUSSION Figure 2A shows both the THz probe E0(t) and the pumpinduced differential transmission ΔE(t)/Emax as a function of THz time delay for 34 nm HNRs in solution, where Emax = max(E0(t)). The pump−probe delay was fixed at τ = 4 ps, and ⟨n⟩, the average number of absorbed photons per nanorod at the front of the cuvette, was 1. Figure 2A shows that photoexcitation leads to both an amplitude reduction (i.e., THz absorption) and a phase shift of the THz probe. The absorption implies formation of mobile charges that move along a HNR, with a velocity largely in phase with the THz field. In contrast, excitons in CdSe QDs of similar diameter do not absorb THz radiation, and move with a velocity 90° out of phase with the THz field.36,37 Furthermore, excitons in CdSe QDs of similar diameter yield a ΔE(t)/Emax signal with an amplitude a factor 50 lower than that measured here.36 As the probe is absorbed, and the amplitude of the signal is much larger compared to quantum dots, we conclude that the electron delocalizes into the shell. To study the time evolution of the photoconductivity as a function of pump−probe delay, it is common to probe only two specific THz time delays. The differential trace in Figure 2A is marked with two blue dots: a full dot corresponding to the THz time delay when E0 peaks, and an open dot to mark when E0 goes through zero. The values of ΔE at these two points give the frequency averaged real and imaginary photoconductivity, respectively. Figure 2B displays the differential THz signal obtained in this way as a function of pump delay time, with ⟨n⟩ = 0.1. After the initial picosecond decay, both signals are constant (within noise) for the full range of 500 ps. This indicates that electron trapping at defects does not play a role in the 500 ps time window of the measurement, which is consistent with a photoluminescence quantum yield of around 50% and a lifetime of around 20 ns.15 The initial decay is attributed to relaxation of the initially hot electron−hole pair in the CdS rod and hole transfer to the CdSe core where it becomes localized.22 The long-lived signal, from times later than two picoseconds, results from motion of the electron along the rod. To get more insight into the spatial extent of the electrons moving along the nanorods in the Coulomb potential of the hole in the CdSe core, the THz photoconductivity was analyzed in the frequency domain. The Fourier transform of ΔE(t), with respect to the THz time delay, t, is proportional to the effective change in conductivity, Δσef f(ω), according to30,38

⎛1 ⎞ 8εtol 2(ω) ⎟eNa /L Δσeff (ω) = μrod (ω)⎜ + 2 3(εtol(ω) + εCdS(ω)) ⎠ ⎝3

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ΔE(ω) = −Δσeff (ω)E0(ω)

L 2cε0neff

(3)

where εtol and εCdS are dielectric functions of toluene and CdS in the THz frequency range, e is the elementary charge unit, and Na the number of absorbed photons per unit area. Figure 3 shows the frequency-dependent complex mobility μrod(ω) (to be called AC mobility) and fit for both 34 and 74

Figure 3. AC intrarod mobility data (symbols) and global fit (lines) for CdSe/CdS HNRs with length of 34 nm (blue, circles) and 74 nm (red, squares). Filled symbols represent the real component of the mobility, open symbols the imaginary component. The increase of mobility with rod length indicates that electron motion is hindered by the extremes of the 34 nm HNRs.

nm nanorods. The excited nanorods induce a phase lag in the THz probe, i.e., retarding the waveform with respect to the reference probe. The sign of the corresponding imaginary mobility depends on the Fourier convention used, which is f(ω) = ∫ dt e−iωtf(t) in our case. Higher probing frequencies induce smaller charge displacements during a THz field cycle. The real part of mobility increases with frequency, which indicates that at low frequencies electron movement is hindered by the rod ends. Both the real and imaginary mobility for 74 nm rods are higher than that for 34 nm rods, which implies a larger amplitude of the electron motion in the 74 nm nanorods. This rules out complete electron localization in the CdSe core, in which case nanorod length should not affect the mobility. The imaginary mobility is caused by an electron velocity in quadrature with the THz field (i.e., 90° out of phase), which is due to backscattering on the extremes of the nanorods, and to the restoring force resulting from the attractive electron−hole interaction. The imaginary mobility of the 74 nm rods exhibits a maximum, because the motion amplitude at higher probing frequencies becomes so small compared to the nanorod length,

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magnitude of all four curves. The fit parameters are μin = (700 ± 30) cm2/(V s), U0 = (140 ± 10) meV, z0 = (20 ± 1) nm, and d = (83 ± 4) meV. The uncertainties in the fit parameters correspond to 5% experimental confidence. Previous studies found the core location between 1/4 and 1/3 of the rod length,15 and the fitted intrinsic mobility decreases about 20% over this small range of locations. The reported value of μin = (700 ± 30) cm2/(V s) is the mean value over this range, whereas the other fit parameters do not sensitively depend on the core location in this range. The potential energy well, displayed in Figure 4A, is quite steep near the CdSe core and

that backscattering on the nanorod ends does not contribute to the imaginary mobility any more. Quantitative information on the degree of electron delocalization, the electron mobility, and the Coulomb interaction with the hole was obtained by comparing the experimental findings with a theoretical model. The model describes the one-dimensional diffusion of the electron along a rod in the potential due to a fixed hole, excluding electron inertia. Classically the motion of an electron in a onedimensional rod can be described by the continuity equation for current J and electron density ρ as a function of position along the rod, z, and time, t, according to ∂J(z , t ) ∂ρ(z , t ) =0 + ∂z ∂t

(4)

The current consists of three contributions J = J1 + J2 + J3, given by J1(z , t ) = −D

∂ρ(z , t ) ∂z

J2 (z , t ) = μin ρ(z , t )E0(t ) J3(z , t ) = −

μin e

ρ (z , t )

∂U (z) ∂z

(5)

where μin = eD/kBT is the intrinsic mobility of an electron in an infinite rod, D is the electron diffusion constant, and U(z) is the potential energy due to Coulomb interaction with the hole in the CdSe core. The first current is induced by diffusion, whereas the second contribution to the current results from the force exerted on the charge by the THz electric field. The third represents the current induced by the Coulomb attraction of the hole. In the absence of an external electric field E0, the current J2 vanishes and the electron distribution ρ(z,t) assumes its time-independent equilibrium value ρeq(z) given by

ρeq (z) = ρ ̅ e−U (z)/ kBT

Figure 4. (A) Fitted electron−hole Coulomb interaction U(z) and (B) corresponding electron probability distributions versus distance z (note the vertical log scale). The gray band marks the core size. Although the electron is centered at the hole in the CdSe core, it has a probability of ∼25% to be found in the CdS shell.

(6)

where ρ̅ is obtained by normalization of charge density: ∫ dz ρeq(z) = e. Following a simplified expression valid for equal dielectric constant in the rod and the medium,42 the potential energy is modeled as U (z ) =

⎛ z2 ⎞ −U0z 0 − d exp⎜ − 2 ⎟ |z | + z 0 ⎝ 2w ⎠

has a smaller slope further away in the CdS shell. The potential of a point charge in an infinitely long CdS cylinder embedded in a medium with the dielectric constant of toluene is both steeper and deeper.43 This is even the case when this potential is averaged (in three dimensions) over the localized hole distribution, and (in two dimensions) over the radial electron distribution. However, the potential found from the fit of the classical diffusive motion of an electron includes the high kinetic energy (highly oscillating electron wave function) when the electron is at the potential minimum. The fitted potential can be considered analogous to the pseudopotential used to describe valence electrons in solids.44 The fitted intrinsic electron mobility corresponds to electron motion along the rod axis, which is the c-axis of bulk Wurtzite CdS. The fitted value is approximately one and a half times as large as the literature value of 440 cm2/(V s) for the electron mobility perpendicular to the c-axis of bulk Wurtzite CdS.45 According to calculations the electron effective mass in bulk Wurtzite CdS is similar for different crystallographic directions.46 The difference between the mobility in a nanorod and bulk can be due to the following reasons. First, the rate for

(7)

where U0 is the Coulomb well depth, z0 is the screening length, d is the depth of a Gaussian energy offset at the CdSe core (possibly due to an offset between the CdSe and CdS conduction bands), and w is the width of the Gaussian offset. The diffusion model can also reproduce the right shape of the complex mobility as a function of frequency without this offset, but it is needed to reproduce the magnitude of the mobility. The width of the Gaussian offset was taken w = 1 nm, so that the full width at half-maximum equals the diameter of the CdSe core (2.35 nm). The experimental data for the complex mobility, shown in Figure 3, can be reproduced by the solution of eqs 4 and 5 in the frequency domain (see the Supporting Information) upon using only four fit parameters: the intrinsic electron mobility μin, and the potential parameters U0, z0, and d. As the fit is global, only one set of parameters was used to fit the real and imaginary mobility of the 34 and 74 nm HNRs simultaneously. The fit is very sensitive to the four parameters, as changes affect both the frequency dependence and the 3149

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electron−phonon scattering in a one-dimensional semiconductor wire differs from that for bulk.47,48 Second, quantum confinement of the electron in a nanorod gives rise to mixing of the lowest conduction band states with other electronic states.42 This changes the electronic band dispersion and consequently the electron effective mass as compared to bulk. These effects on the electron scattering rate and effective mass will cause the mobility in a nanorod to differ from that for bulk. In agreement with this, it was recently found that the charge mobility in GaN nanowires differs from the bulk value.49 In addition, HNRs might possess small doping due to either Cd or S vacancies, although the effect on mobility is not a priori clear. Figure 4 shows the fitted potential U(z) and the resulting equilibrium probability distribution of the electron versus z. The electron is weakly delocalized around the CdSe core, i.e. the electron has ∼25% probability to be found in the CdS shell. For HNRs with a larger CdSe core (>4 nm), a type I band offset has been reported,24 in which case we expect the electron to localize even more strongly at the CdSe core, yielding a purely imaginary THz response independent of nanorod length.

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ASSOCIATED CONTENT

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The THz conductivity of photoexcited CdSe/CdS HNRs shows the distinct signature of a mobile electron, moving in the Coulomb field of a localized hole and constrained within the nanorod. The frequency dependence of the real and imaginary mobility was reproduced with a classical model, describing diffusive motion of an electron in the nanorod, while experiencing the Coulomb attraction to the hole in the CdSe core. A total binding energy of the electron to the hole in the core equal to 220 meV was fitted. As a result the electron has ∼25% probability to be found in the CdS shell. The fitted intrinsic electron mobility is 700 cm2/(V s). This is higher than the mobility of electrons in bulk CdS, which can be due to quantum confinement effects on electron−phonon scattering and electronic structure. Further work is needed to quantify the effect of electron inertia on the high-frequency behavior of the AC mobility. Optical-pump THz-probe spectroscopy is shown to be a suitable tool for determining the spatial extent and mobility of electrons and holes in heteronanorods.

S Supporting Information *

Derivation of the diffusion model and of the intrarod mobility. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Dutch Foundation for Fundamental research on Matter (FOM), in the programma “Control over Functional Nanoparticle Solids”, and by the European Union through the FP7 starting ERC grant NANOARCH (Contract No. 240111). 3150

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The Journal of Physical Chemistry C

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dx.doi.org/10.1021/jp3117984 | J. Phys. Chem. C 2013, 117, 3146−3151