Defect-Mediated CdS Nanobelt Photoluminescence Up-Conversion

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Defect-Mediated CdS Nanobelt Photoluminescence Up-Conversion Yurii V. Morozov, Sergiu Draguta, Shubin Zhang, Alejandro Cadranel, Yuanxing Wang, Boldizsar Janko, and Masaru Kuno J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05095 • Publication Date (Web): 12 Jul 2017 Downloaded from http://pubs.acs.org on July 12, 2017

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The Journal of Physical Chemistry

Defect-Mediated CdS Nanobelt Photoluminescence Up-Conversion Yurii V. Morozov1, Sergiu Draguta1, Shubin Zhang2, Alejandro Cadranel3, Yuanxing Wang1, Boldizsar Janko2, Masaru Kuno1,* 1

Department of Chemistry and Biochemistry, University of Notre Dame, 251 Nieuwland Science

Hall, Notre Dame, Indiana 46556, United States 2

Department of Physics, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame,

Indiana 46556, United States 3

Departamento de Química Analítica, Inorgánica y Química Física, INQUIMAE, Facultad de

Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 2, Ciudad Universitaria, C1428EHA, Buenos Aires, Argentina. * Corresponding author: [email protected]

Abstract

Laser cooling in semiconductors has recently been demonstrated in cadmium sulfide nanobelts (NBs) as well as in organic-inorganic lead halide perovskites. Cooling by as much as 40 K has been shown in CdS nanobelts and by as much as 58 K in hybrid perovskite films. This suggests that further progress in semiconductor-based optical refrigeration can ultimately lead to

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solid state cryocoolers capable of achieving sub 10 K temperatures. In CdS, highly efficient photoluminescence (PL) up-conversion has been attributed to efficient exciton–longitudinal optical (LO) phonon coupling. However, the nature of its efficient anti-Stokes emission has not been established. Consequently, establishing a detailed understanding about the mechanism leading to efficient PL up-conversion in CdS NBs is essential to furthering the nascent field of semiconductor laser cooling. In this study, we describe a detailed investigation of anti-Stokes photoluminescence (ASPL) in CdS nanobelts. Temperature- and frequency-dependent band edge emission and ASPL spectroscopies conducted on individual belts as well as ensembles suggest that CdS ASPL is defect-mediated via the involvement of donor-acceptor states.

Introduction Advances in refrigeration have been responsible for significant progress in science and technology. The discovery of Bose-Einstein condensation,1 superconductivity,2 superfluidity,3 and the fractional quantum Hall effect4 all result from the ability to reach low temperatures using gases of trapped ions and atoms. It is also essential to numerous modern technologies such as visible and infrared photodetectors, which require low temperatures for efficient operation.5 At present, minimum temperatures for Peltier-based solid state cryocoolers are limited to ~170 K.6 Consequently, a pressing need exists to develop new solid state cooling technologies suitable for future optoelectronic applications. The concept of condensed phase optical refrigeration has existed for nearly 90 years since Pringsheim first proposed cooling through phonon-assisted PL up-conversion.

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In

semiconductors, this entails first creating a cold population of free electrons and holes using a laser tuned to the semiconductor band edge. Subsequent phonon coupling results in carrier


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excitation and leads to emission with energies greater than those of the incident laser. This removes thermal energy from the system and sets the basis for optical cooling.8 Despite the conceptual simplicity of the process, realizing optical refrigeration requires exacting parameters from the condensed phase medium. This includes near unity external quantum efficiencies (EQEs) and corresponding up-conversion efficiencies, both aimed at suppressing unwanted background heating.8 Even with these stringent constraints, significant progress has been made in cooling rare earth doped solids over the last two decades.8,9,10,11 Cooling by as much as 176 K has been achieved in Yb-doped yttrium lithium fluoride crystals.11 Unfortunately, further lowering of the cooling floor, is hampered by atomic ground state depopulation with decreasing temperature. Consequently, solid state cooling below 100 K becomes problematic using existing rare-earth doped systems.8,12 Semiconductors circumvent this problem because their Fermi statistics guarantee populated valence bands at low temperatures. As a result, sub 10 K temperatures are possible.8,12 Apart from dramatically lowering the cooling floor, realizing semiconductor-based laser cooling has the added advantage of involving processing technologies compatible with those of existing semiconductor optoelectronics. Prior attempts at optically cooling semiconductors have predominantly involved metalorganic chemical-vapor deposition (MOCVD)-grown GaAs-based heterostructures.

Internal

quantum efficiencies (QEs) as high as 99.7% have been achieved (corresponding EQEs of ~72%) by carefully minimizing growth defects.13 Further work has enabled EQEs as high as 99.5% to be realized by accounting for reflection losses. 14

Despite these near optimal

parameters, laser cooling has not been achieved with these materials due to the existence of


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unwanted parasitic background absorption, which competes with ASPL-induced laser cooling.8,14 Up-conversion in alternate systems such as MOCVD-grown GaN15 and colloidal CdTe quantum dots16 has also been explored. However, their EQEs are presently too small (GaN: 93%, CdTe QDs: 50-85%) to be used for optical refrigeration. Recently, a major breakthrough has been realized with the demonstrated 40 K laser cooling of chemical vapor deposition (CVD)-grown CdS nanobelts (NBs).17 Their large internal QEs along with sub-wavelength thicknesses, which decrease light trapping, make near unity EQEs possible (estimated EQE > 0.99).17

Although strong exciton-phonon coupling has been invoked to

explain efficient ASPL in CdS NBs, the phenomenon is not well understood.17 Consequently, there is a pressing need to better understand the origin of efficient ASPL in CdS NBs, the first semiconductor to demonstrate optical cooling. Here, we show that phonon-assisted ASPL in CdS NBs is defect-mediated via temperature- and wavelength-dependent ASPL intensity measurements.

Methods Structural characterization Low and high magnification transmission electron microscopy (TEM) micrographs as well as selected area electron diffraction (SAED) patterns were taken with a FEI Titan 80-300 microscope operating at 300 kV. Atomic force microscopy (AFM) images of individual CdS NBs were obtained in noncontact mode using a commercial AFM system (Park Systems, XE70). Samples were prepared in the same manner as for single NB optical measurements. Single NB optical measurements


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All optical measurements on individual CdS NBs were performed using a Nikon inverted microscope with a long working distance, 0.45 numerical aperture (NA) objective (Nikon). Samples were mounted inside a microscope cryostat (Cryo Industries of America) with temperatures controlled by a commercial temperature controller (Lakeshore). For excitation intensity (Iexc)-dependent ASPL intensity (IASPL), band edge emission intensity (Iem) measurements, IASPL detuning measurements, and optical absorption measurements, a supercontinuum laser (Fianium) equipped with an acousto optical tunable filter provided tunable excitation in the range 450 – 780 nm (1.6 - 2.76 eV, 40 MHz repetition rate, 12 ps pulses). For temperature-dependent ASPL/band edge emission measurements, both a 405 nm diode laser (Coherent) and a 532 nm diode-pumped solid state laser (Melles Griot) were used. The 532 nm laser was subsequently rejected using a Bragg grating bandpass filter (Optigrate). Emission spectra were collected using a spectrometer (Acton, 150 groove/mm, 800 nm blaze and 1200 groove/mm, 500 nm blaze) coupled to an electron multiplying CCD camera (Andor). IASPL detuning measurements For these measurements, excitation wavelengths were scanned in the range 538-775 nm (2.30 – 1.6 eV). This provided a ∆E=0.15 - 0.86 eV detuning from the CdS band edge into the gap. At every excitation wavelength, the resulting ASPL spectrum was recorded and its integrated intensity was extracted and normalized by the excitation power at the sample. The incident laser power was simultaneously monitored using a reference photodiode to account for any fluctuations. Iexc-dependent IASPL and Iem measurement For these studies, Iexc was variably attenuated using a Glan-Thompson polarizer mounted to a computer-controlled rotation stage (1000:1 extinction ratio). At each intensity, emission spectra


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were recorded and the emission intensity obtained by integration. The laser intensity was simultaneously measured using a reference photodiode. Single NB absorptance measurement In this study, the excitation was split prior to the microscope with a fraction of the light sent to a reference photodiode.

The remainder was focused onto individual CdS NBs using a

microscope objective (NA=0.45, Nikon). The typical diameter of the focused spot was 1.5 µm. Transmitted light was collected with a second objective (NA = 0.75, Nikon) and was focused onto a photodetector. To obtain an absorptance spectrum at given temperature, the transmitted light intensity at every wavelength was measured with the light first focused onto the bare substrate and then over an individual NB. The associated transmittance (T) was obtained by taking the ratio of the two signals, yielding an absorptance (A) value as A = 1-T. Laser power fluctuations were accounted for by normalizing the transmission photodiode signal to that from the reference photodiode. Ensemble/single NB emission lifetime measurements Ensemble time correlated single photon counting (TCSPC) kinetics were acquired with a Jobin Yvon Fluorocube using 371 nm pulsed light-emitting diode illumination (200 ps pulse width, 1 MHz repetition rate).

The NB emission was detected at 520 nm using a fast

photomultiplier tube. The overall instrument response is ∼1 ns. Single CdS NB band edge PL decay curves were taken on a home-built microscope using a pulsed 405 nm diode laser to excite samples. The excitation pulse width was 70 ps at a repetition rate of 2.5 MHz (PicoQuant). The resulting emission was passed through a barrier filter (Semrock) and was detected with a single photon counting avalanche photodiode (APD, PerkinElmer).

The output of the APD was

subsequently fed into a time-correlated single-photon counter (PicoQuant, PicoHarp 300) to generate decay traces.


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Results and Discussion CdS NBs, prepared in the same manner as those employed in the original semiconductor laser cooling study, were studied.17 Figures 1 (a,b) show corresponding low- and high-magnification TEM images of a typical CdS NB. From these and other micrographs, we establish that typical NB widths range from 1-8 µm with corresponding lengths between 4 - 20 µm. NB thicknesses have been independently estimated using AFM and yield values between 14 and 350 nm. An average thickness is 142±110 nm (sample size = 13 NBs). A representative AFM image as well as a sizing histogram can be found in the SI (Figures S1, S2). Associated high magnification images reveal lattice fringes with d-spacings of 0.207 nm (1120) and 0.334 nm (0002). These values are consistent with those reported for bulk wurtzite CdS. 18 The assignment is corroborated by complementary SAED patterns with an example shown in the inset of Figure 1b. Additional TEM images can be found in the SI (Figures S3, S4). Figure 1c shows both the room temperature absorption and corresponding emission spectrum [λexc=405 nm (3.06 eV)] of a single, representative CdS NB, mechanically extracted from the grown ensemble. The absorption spectrum exhibits a steep step-like feature at ~505 nm (2.46 eV), which is consistent with the 2.42 eV bulk bandgap of CdS.19 Clear band edge emission is also apparent at ~505 nm. Additional deep trap emission is present near 730 nm (1.70 eV) with its relative strength varying from belt to belt and sometimes within a given belt.

These

heterogeneities likely arise from inhomogeneities in NB deep trap densities. Figure 1c reveals that sub-gap excitation of the NB at 532 nm (2.33 eV) results in upconverted emission at 505 nm (2.46 eV). The near identical ASPL spectrum to the NB band


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edge emission strongly suggests that sub-gap photogenerated carriers eventually find their way to corresponding band edges before undergoing radiative, interband recombination. Figure 1d shows additional ASPL spectra acquired from multiple individual NBs. In each case, ASPL peak energies coincide with the band edge emission energy.

Instances also exist where

longitudinal optical (LO) phonon replicas are seen on the red edge of ASPL spectra. Such replicas are denoted 1LO/2LO in Figure 1d and have previously17 been suggested to indicate strong LO phonon couplings in CdS NBs.

Figure 1. (a) Representative low-magnification TEM image of an individual CdS NB. (b) Representative highmagnification TEM image of a CdS NB. Inset: associated SAED pattern. (c) Absorption (dashed green line) and band edge emission (solid blue line) spectra of a single CdS NB when excited at λexc=405 nm. Corresponding ASPL (open red circles) when excited at λexc=532 nm. All spectra acquired at 298 K. Inset: Optical image of individual CdS NBs. (d) Room temperature ASPL spectra from different individual CdS NBs (λexc=532 nm).


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Figure 2. Illustration of possible ASPL mechanisms. (a) ASPL through virtual state-mediated TPA. (b) ASPL through sequential TPA involving a real intermediate state. (c) Phonon-assisted up-conversion through a virtual level. (d) Phonon-assisted up-conversion through a real intermediate level and illustration of possible defect emission.

To begin rationalizing the origin of efficient ASPL in CdS NBs, Figure 2 summarizes known one-

and

two-photon

mechanisms

for

photoluminescence

up-conversion

in

semiconductors.17,20, 21 In particular Figure 2a shows two-photon absorption (TPA)-induced ASPL where the mechanism entails the virtual state-mediated absorption of two sub-gap photons having the same energy. This process is universal and has been observed in a number of different systems.20, 22 , 23 A characteristic feature of TPA-induced ASPL is a quadratic Iexc dependence of IASPL. This has previously been used to rationalize superliner IASPL growth in these CdS NBs at large Iexc-values (Iexc>2.5×105 W/cm2).17


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Figure 2b shows alternate up-conversion through sequential, two-photon absorption. This mechanism has previously been observed in rare earth-doped materials24 and at semiconductor interfaces. In contrast to TPA-induced ASPL, sequential two-photon absorption involves a real, intermediate state within the bandgap. This enhances its likelihood over TPA due to the finite lifetime of the intermediate state. In either case, two-photon processes are not central to laser cooling since they do not involve phonons.

Hence, they cannot remove thermal energy from the system.

Consequently,

complementary processes, which involve phonons, must be invoked. At this point, Figures 2 (c,d) illustrate possible one-photon/phonon-mediated up-conversion mechanisms. As with Figures 2 (a,b), these processes involve virtual (Figure 2c) or real (Figure 2d) intermediate states with probabilities directly proportional to the phonon population ℏ at a given temperature. Of note is that the former one-photon/virtual state process has previously been invoked to rationalize CdS NB laser cooling at low Iexc-values (Iexc 0.210 eV) IASPL arises from a two photon processes with the kinetic data in Figures 3 (c,d) implicating sequential two photon absorption via deep gap states likely responsible for the deep trap emission seen in Figure 1c. It is the room temperature, small detuning scenario that is most relevant to laser cooling. Although the kinetics of Figure 3b suggest the involvement of real intermediate states (i.e. a one-photon/real state mechanism), the assignment is not definitive.

We have therefore

conducted additional experiments to more conclusively establish the involvement of a real state. We first carry out temperature-dependent absorptance (A) measurements on individual CdS NBs, as illustrated in Figure S9.

The data shows that the sub-gap (532 nm) absorption of an

individual NB remains essentially constant over a wide range of temperatures (150-400 K). This


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is consistent with the presence of absorbing gap states with a corresponding absorption coefficient of α532

nm~376

cm-1. Unfortunately, single NB absorptance spectra exhibit only

featureless tails which extend into the gap (Figure S9).

This prevents a more definitive

identification of these intermediate states. Additional details of the single NB absorptance measurements can be found in the SI. We consequently turn to temperature-dependent emission measurements and compare the band edge emission and ASPL spectra of individual CdS NBs. To start, Figure 1c shows little to no difference between the two at room temperature. At low temperatures, however, differences emerge. This is illustrated in Figures 4 (a,b) where at both 190 K and 80 K spectral differences emerge on the lower energy side of ASPL spectra relative to corresponding band edge emission spectra. These differences are shaded to make the distinction apparent. The full data set of temperature-dependent ASPL/band edge emission spectra is shown in Figure 4c. Analogous data for another individual NB can be found in the SI (Figure S10). To identify the origin of these spectral differences, a literature survey reveals that CdS possesses a number of donor-acceptor as well as bound exciton transitions at low temperature. 27 , 28 , 29 Donors (acceptors) are attributed to singly ionized sulfur (cadmium) vacancies.29 In CdS NBs, donor/acceptor transitions are reported to lie between 2.414-2.416 eV for temperatures in the range 2-200 K.29,30 Bound exciton [i.e. neutral acceptor/bound exciton (A0X) and neutral donor/bound exciton (D0X)] transitions reside closer to the band edge. For reference purposes, these literature transitions at ~80 K, including donor acceptor pair (DAP) longitudinal optical phonon replicas are shown at the bottom of Figure 4b.

This enables

subsequent assignment of ASPL features in the current experiment. Specifically, the excellent


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agreement between the literature transitions and data in Figure 4 strongly suggests that the subgap states involved in CdS NB ASPL are DAP-related.

Figure 4. Comparison of band edge emission (solid blue line) and ASPL spectra (open red circles) at (a) 190 K and (b) 80 K. The green arrow denotes the excitation energy (λexc =532 nm) used for the ASPL measurement. Literature energies for CdS free exciton (FX), neutral donor/bound exciton (D0X), neutral acceptor/bound exciton (A0X), donor bound hole (D-h), and DAP transitions denoted along with DAP LO phonon replicas. (c) Full ASPL/band edge emission spectral dataset between 80 and 380 K (λexc=532 nm).

All of the above results thus suggest the direct involvement of real intermediate states specifically DAP states- in yielding efficient CdS NB ASPL. This represents a conundrum since the existence of such real sub-gap levels would suggest that these states potentially act as carrier traps during the normal, above-gap photoexcitation of CdS. Consequently, one would expect


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EQE values to be suppressed from near unity due to the presence of additional non-radiative recombination channels for photogenerated carriers. Since EQE is a critical parameter, which dictates whether laser cooling can be achieved,8 we have conducted individual CdS NB EQE measurements (λexc = 470 nm) through Iexc-dependent Iem (Iem –to be distinguished from IASPL seen earlier which is induced by exciting NBs at 532 nm) measurements. In this regard, it has previously been demonstrated that absolute EQEs of a material can be estimated through appropriate modeling of concentration-dependent carrier recombination processes.31,32 This includes bimolecular (radiative), bimolecular (non-radiative) trapping, and third-order Auger (non-radiative) recombination. Figure 5 summarizes these processes. Parameterized kinetic modeling, in turn, yields corresponding free carrier densities, which enable EQE values to be determined using the fraction of photogenerated electron-hole pairs undergoing radiative, as opposed to non-radiative, recombination.

Figure 5. Illustration of the model used to simulate CdS NB emission efficiencies.

Specific rate expressions for the kinetic model shown in Figure 5 are33 !

# $ %& ∙ ( ∙ ) %" ∙ *" (" ∙ ( %+,- ∙ (. ∙ )

(1)

/

# $ %& ∙ ( ∙ ) %0 ∙ (" ∙ ) %+,- ∙ (. ∙ )

(2)

"

"

!1 "

# %" ∙ *" (" ∙ ( %0 ∙ (" ∙ )

(3)


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where n, p, and (" are the electron, hole and occupied trap concentrations respectively. is the electron/hole generation rate and is linked to experimental excitation intensities through # 2 × with α the NB absorption coefficient 34 ( 2456 78 ≈ 8 × 10< cm-1), %& the bimolecular (radiative) recombination rate constant34 (kb = 9.55×10-12 cm3/s), $ a dimensionless photon extraction efficiency31 (assumed to be unity due to the subwavelength thicknesses of the investigated NBs, Figures S1, S2), %" a bimolecular (non-radiative) electron trapping rate constant32, 35 , 36 , 37 (kt =6.31×10-11 cm3/s), %0 a trapped electron, bimolecular (non-radiative) recombination rate constant32,35, 38 (kh=1.0×10-11 cm3/s), %+,- the third order (nonradiative) Auger recombination rate constant39 (kAuger = 1.0×10-30 cm6/s), and *" the concentration of carrier traps27 (Nt = 3.24×1017 cm-3, assumed to predominantly consist of electron acceptor states). Deep traps suggested by Figure 3c are excluded for simplicity. Specified kb, kt, kh, kAuger, and Nt values above are final fit parameters using initial values from the cited References. Additional details can be found in the SI. By numerically solving Equations 1-3 for the case of pulsed excitation, time-dependent concentrations for n, p and nt are obtained. The ratio of electron-hole pairs undergoing radiative recombination to the initially photogenerated electron-hole pair concentration then yields an expression for Iexc-dependent EQEs.

This equation can be used to fit experimental Iexc-

normalized Iem data, as described below. Additional details regarding the kinetic model can be found in the SI.


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Figure 6. (a) Power law Iexc-dependence (open red circles) of Iem at 298 K. The orange line indicates superliner Iem growth with a power law growth exponent of b=1.56. The green line shows near linear growth at higher Iexc with a corresponding power law coefficient of b=1.02. The blue line shows a region of sublinear growth beyond a critical Iexc, where the corresponding power law growth exponent is b=0.35. (b) Single NB EQE values and corresponding model fit (solid blue line) yielding ηopt = 0.64 (λexc=470 nm).

Figure 6a now plots Iem from a single CdS NB as a function of Iexc. At low Iexc-values (Iexc~ & 104 W/cm2), Iem increases in a power law fashion (i.e. ∝ ) with a corresponding growth

exponent of b≈1.5. Further increasing Iexc causes b to decrease towards b≈1.0 (Iexc=1×105 - 4×105 W/cm2).

Beyond this (i.e. Iexc > 4×105 W/cm2), Iem grows sublinearly with a power law

coefficient of b? @A !BC @D E1

, where F is the laser repetition rate and n0 is the initial photogenerated

. electron concentration, which is proportional to Iexc. Consequently, ∝ . A derivation of

this analytical limit can be found in the SI. Increasing Iexc progressively saturates trap-related recombination channels, which, in turn, gradually increases EQE. This simultaneously causes the power law coefficient to decrease towards a limiting value of b=1.0. Trap saturation leads to electron-hole pairs predominantly recombining radiatively. The expected growth exponent in this regime therefore becomes b=1.0 (i.e. ∝ ). A derivation of this analytical limit can be found in the SI. In between, power law coefficients span the range b=2.0 to b=1.0. Note that excluding trap states yields exclusive, b=1.0 Iem growth over the entire range of Iexc values. This contradicts the data. Carrier traps are therefore essential in modeling the optical response of CdS NBs, again supporting the participation of real intermediate states in inducing CdS NB ASPL. Finally, at the very largest excitation intensities, nonradiative Auger recombination dominates all other kinetic processes.

This stems from its cubic dependence with carrier density.

Consequently, Iem grows to a maximum and plateaus. Further increasing Iexc causes Iem to respond sublinearly since non-radiative recombination dominates photogenerated carrier recovery. All of these model predictions qualitatively agree with the experimental data shown in Figure 6a. Numerical results of the kinetic model over the full range of Iexc values are shown in Figure S11. The observed non-linear Iem growth in Figure 6a means that NB EQEs are Iexc-dependent. Consequently, to obtain the associated EQE at a given Iexc, the Iem/Iexc ratio in Figure 6b is fit using numerical results of the kinetic model (solid blue line). From the fitting, we find that at


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low carrier generation rates, EQE values are on the order of 0.2.

With increasing Iexc,

corresponding EQE values increase to ~0.6. At the highest carrier generation rates, Auger recombination dominates, causing EQEs to plateau and to eventually decrease. The particular NB measured in Figure 6 shows an optimal EQE value (ηopt) of ηopt=0.64. Analogous fitting of data from other NBs yields ηopt-values ranging from 0.1-0.64 for Iexc~105106 W/cm2 (Figures S12 and S13). This illustrates that significant sample heterogeneities exist in the CVD-grown CdS NBs. More relevantly, all measured ηopt-values are smaller than the near unity values required for laser cooling.8 Thus, beyond corroborating our earlier temperature and frequency-dependent results, which suggest the existence of real intermediate states and their direct involvement in ASPL (Figure 3), the EQE data indicates that significant growth optimization is needed if practical laser cooling is to be realized with these materials. To put the above EQE requirement into better context, a simple energy balance estimate for CdS shows that EQEs must satisfy F > HI

IJ

J K ∆I

LM

NN>OPQR K>OPQR >OPQR

S

(4)

if net cooling is to outweigh heating from non-radiative recombination. In Equation 4, $ is an up-conversion efficiency10 [( 1 $ ) is the fraction of sub-gap excitations not upconverted] and f is the fraction of sub-gap excitations not up-converted resulting in non-radiative heating. Consequently, 1 $ T of the total sub-gap excitations lead to heating with the remaining 1 $ 1 T recombining as trap-related emission. A derivation of Equation 4 can be found in the SI. If parameters for CdS are assumed (Eg=2.42eV19 and ∆E ≈ 0.09 eV) the following constraints arise: Namely, the minimum EQE required for cooling is 0.964 along with up-conversion efficiencies ranging from $ =0.211 (f = 0.01) to $ =0.964 (f=1.0). In


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effect, up-conversion efficiencies must exceed $ ~0.2. Figure S14 of the SI shows the relationship between ASPL and f. We now estimate an experimental value for $ . This is done by establishing excitation conditions -whether above gap at λexc = 470 nm in a band edge emission measurement or below gap at λexc = 532 nm in an ASPL measurement- leading to the same Iem or IASPL value at 505 nm. An expression for the resulting up-conversion efficiency is then U

$ ≈ H ?VW,XYB Z[L ^ U?VW,\]C Z[

XYB Z[ \]C Z[

_

(5)

where Iexc, 470 nm (Iexc, 532 nm) is the above (below) gap excitation intensity and A470 nm (A532 nm) is the corresponding NB absorptance at that wavelength. A derivation of Equation 5 can be found in the SI. Using parameters from the experiment and from Figure 1c, we find a nominal upconversion efficiency of $ =0.1. Details of the estimate can be found in the SI. The above modeling therefore suggests that $ is marginal for cooling purposes. Given that the lifetime of the intermediate state directly influences the probability of both single- and multi-phonon interactions, it is evident that DAP lifetimes dictate ηASPL.40 Here a literature survey reveals that semiconductor DAP lifetimes are highly variable, ranging from ns to µs.28,29,41,42,43 This variability stems from the DAP lifetime dependence with spatial separation of constituent electrons and holes. In CdS an explicit expression for the DAP lifetime is τ =τ0 exp (2r/aD)27,28 where τ0 ~ 2 ns27,28, aD=2.5 nm28 is the CdS donor Bohr radius, and r is the nominal donor-electron/acceptor-hole separation. In turn, the electron/hole separation depends upon relevant donor and acceptor concentrations (ND, NA) and decreases with increasing ND or NA.42 Closely separated donor-electron/acceptor-hole pairs in CdS therefore yield DAP emission lifetimes ranging from 2.2-2.5 ns.27,28 Below a critical Mott concentration of ~5×1018 cm-3,41


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DAP lifetimes increase to 100 ns - µs.27,41 The same is true of other semiconductors such as ZnSe (~100 ns43) and GaP (~ms44). Of note then is that prior, low temperature measurements have shown CdS NB DAP lifetimes of ~300 ns [estimated donor-acceptor pair concentration NDAP~1.1×1018 cm-3].29 To estimate the corresponding room temperature DAP lifetime, we have performed both ensemble and single NB TCSPC measurements. Figure S15a shows a representative TCSPC trace acquired by exciting a CdS NB ensemble at λexc=371 nm and monitoring the resulting emission dynamics at 520 nm. Subsequent biexponential fits to the data reveal a short time component of 1.43 ns (39%) along with a substantially longer 239 ns (61%) component. Figure S15b shows results of an analogous single CdS NB measurement (λexc=470 nm) using the integrated emission between 490-530 nm. Obtained time constants are 0.218 ns (24%) and 4.28 ns (76%). These single NB values likely differ from the ensemble result due to the heterogeneous nature of the CVD-grown sample. In either case, the fast decay component is assigned to carrier loss through bimolecular, band edge recombination. The slow component is assigned to DAP-related emission. This suggests that DAP lifetimes are relatively long even at room temperature.

The assignments are

corroborated by the kinetic model outlined in Figure 5 wherein defining an effective, first order band edge decay lifetime as `NN #

a a K bA b1cde

, with `& # >

? @A

and `"-f/ # @ /

1 E1

and assuming n=p

gives τeff~49 ns for a carrier concentration of n=2.3×109 cm-3 (equivalent to Iexc=10-4 W/cm2, an intensity where trap saturation has not occurred and which is identical to that used in the ensemble lifetime measurement). Similarly, defining an effective DAP time constant under the same conditions as `g # @

D E1

gives τDAP=308 ns.

These short and long timescale decay


23


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constants are in qualitative agreement with the slow and fast TCSPC components seen experimentally The TCSPC results, in turn, suggest that ηASPL can be enhanced by increasing DAP lifetimes. In this regard, DAP lifetimes can be tuned by varying relevant donor/acceptor concentrations (i.e. r). Proof-of-concept has already been demonstrated through tuning of bulk CdS and ZnSe DAP lifetimes.41,43

Furthermore, DAP lifetimes have been enhanced using external

perturbations. As an example, an external magnetic field has been used to increase GaP DAP lifetimes twofold.41 Altering/controlling NB production to achieve variable donor/acceptor densities either during or after43 NB growth therefore represents an important next step towards fully understanding as well as controlling CdS NB ASPL. We now address the obvious conundrum posed by the involvement of real intermediate states in ASPL. Recall that identifying defects as the origin of efficient up-conversion is problematic since, from the standpoint of microscopic reversibility, such sub-gap states act as carrier traps. Consequently, NB EQE values are negatively influenced by the existence of an additional recombination channel for photogenerated carriers. This is readily seen by expressing EQE in terms of effective first order rate constants (i.e. kr, knr and kDAP) for the various radiative, nonradiative, and DAP-related processes in the NB, i.e. F ~ @

@c

c K@iOQ K∑ @Zc

.

Assuming that NB EQEs are near unity and that donor-acceptor recombination represents the only other recombination pathway for carriers, i.e. F ~ @

@c

c K@iOQ

, we ask whether it is possible

to maintain a critical EQE of 0.964 (or higher) when NBs possesses realistic donor-acceptor concentrations. To this end, we first find a critical DAP rate constant, expressed in terms of kr, which maintains EQE=0.964. This yields kDAP=0.037kr. Then for the purpose of an order of magnitude estimate, we assume kr=108 s-1. What results is a critical DAP lifetime of τDAP ~270


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ns with an associated DAP concentration of NDAP = 9.3×1017 cm-3.

The analysis therefore

suggests that DAP concentrations at or below ~1018 cm-3 are compatible with near unity NB EQEs. Additional details of this analysis can be found in the SI. The data in Figure S15 suggests that the current NBs possess a corresponding DAP concentration of NDAP~4.68×1018 cm-3.

This is similar to the NDAP~1.1×1018 cm-3 estimate

obtained from prior CdS NB data.29 Together, the analysis suggests that the primary limitation hindering these CdS NBs within the context of laser cooling is their suboptimal EQEs (Figures 6b, S12 and S13). In this regard, none of the CdS NBs studied exhibit cooling. Their low EQEs all result in heating following excitation. An illustration is shown in Figure S16a where PL emission spectra from a single NB have been acquired using both low and high excitation intensities (Ιexc= 4.3×104 W/cm2 and Ιexc= 1.2×106 W/cm2; λexc= 480 nm). The data shows a slight ~1.8 meV redshift of the higher Iexc spectrum relative to the lower Iexc spectrum, as highlighted by the difference spectrum in Figure S16a. This redshift corresponds to a 4.3 K temperature rise and is consistent with the greater excess energy involved in non-radiative relaxation in the high intensity case. Figure S16b shows that the temperature increase depends linearly with Iexc and confirms that that the observed redshift directly stems from the laserinduced heating of the NB. Conclusion In summary, we have demonstrated the use of single NB temperature-, excitation wavelength, and intensity-dependent emission spectroscopies to link the origin of efficient ASPL in CVDgrown CdS NBs to the presence of defect states, which enable one-photon/real intermediate state up-conversion.

An estimated ASPL up-conversion efficiency is $ =0.1.

We have

additionally established that the long lifetime of these states is critical to achieving efficient


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ASPL. For donor-acceptor states, these lifetimes can be tuned by varying corresponding donor and acceptor concentrations. In tandem, optimum single CdS NB EQE values span the range

ηopt=0.10-0.64. These EQE values lie below the estimated critical 0.964 EQE needed to achieve laser cooling in CdS and stem from the existence of efficient non-radiative relaxation pathways for excitations through both donor/acceptor and other sub-gap defect states. Consequently, further growth optimization is needed to increase EQEs by suppressing these undesired recombination pathways.

Finally, ASPL has been observed in a number of other

semiconductors14,15, 45 and semiconductor nanostructures.16

It thus stands to reason that the

conclusions from this study are applicable to these other systems, opening the door to future demonstrations of semiconductor-based laser cooling.

AUTHOR INFORMATION Corresponding Author *M. K.: E-mail: [email protected] Author Contributions Experimental data were collected and analyzed by Y.M., A.C., Y.W., S.D., S.Z., and B.J.. The manuscript was co-written by Y.M., S.D. and M.K. All authors have given approval to the final version of the manuscript. Supporting Information Representative AFM image. AFM sizing histogram. Additional TEM images of CdS NBs. Comparison of the up-conversion probability involving multiple phonons to ∆ , . IASPL comparison to Bose-Einstein statistics. Low temperature ASPL power dependence. Additional


26

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IASPL detuning spectra of CdS NBs.

Additional large detuning IASPL versus Iexc traces and

relationship to NB EQEs. Temperature-dependent absorptance spectrum of a CdS NB along with associated A532 values. Temperature-dependent band edge emission and ASPL for another CdS NB. Details of the kinetic modeling of EQE values. Analytical low and higher power limits of Iem Iexc-dependence. Numerical results of the EQE model. EQE fits for other CdS NBs. Derivation of Equation 4. Plot of ηASPL versus f. Derivation of Equation 5. Ensemble and single NB time-resolved PL decays. Derivation of a critical DAP concentration. Example of NB heating under above gap excitation. The Supporting Information is available free of charge on the ACS Publications website at DOI:

Acknowledgement M. K. thanks the Army Research Office (Award No. W911NF-12-1-0578) and the MURI:MARBLe project under the auspices of the Air Force Office of Scientific Research (Award No. FA9550-16-1-0362) for financial support. CONICET for a postdoctoral fellowship.

A. C. acknowledges support from

We thank Xingzhi Wang and Qihua Xiong for

providing us the CdS NB ensembles used in the study. We also thank the Notre Dame Integrated Imaging Facility (NDIIF), the ND Energy Materials Characterization Facility as well as the Center for Sustainable Energy at Notre Dame (cSEND) for use of their equipment and for partial financial support. Finally, we thank Peter Pauzauskie and Jacob Khurgin for fruitful discussions during the course of this work.

REFERENCES


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TOC Garphic


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Figure 1. (a) Representative low-magnification TEM image of an individual CdS NB. (b) Representative highmagnification TEM image of a CdS NB. Inset: associated SAED pattern. (c) Absorption (dashed green line) and band edge emission (solid blue line) spectra of a single CdS NB when excited at λexc=405 nm. Corresponding ASPL (open red circles) when excited at λexc=532 nm. All spectra acquired at 298 K. Inset: Optical image of individual CdS NBs. (d) Room temperature ASPL spectra from different individual CdS NBs (λexc=532 nm). 205x171mm (300 x 300 DPI)


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Figure 2. Illustration of possible ASPL mechanisms. (a) ASPL through virtual state-mediated TPA. (b) ASPL through sequential TPA involving a real intermediate state. (c) Phonon-assisted up-conversion through a virtual level. (d) Phonon-assisted up-conversion through a real intermediate level and illustration of possible defect emission. 171x158mm (300 x 300 DPI)



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Figure 3. (a) Integrated ASPL temperature dependence of an individual CdS NB (Iexc=105 W/cm2, λexc=532 nm). The shaded red region indicates a temperature range where IASPL follows Bose–Einstein statistics (solid green line). Average m-values at 100 K (sample size 11 NBs), 200 K (sample size 21 NBs), and 298 K (sample size 25 NB) also indicated. (b) Iexc dependence of IASPL (open red circles) and corresponding fit (dashed blue line) at 298 K (λexc=532 nm) under small detuning (∆E=0.124 eV) conditions. An average mvalue for 25 NBs is =1.31±0.10. (c) CdS NB ASPL detuning (open red circles) and representative deep trap emission (solid blue line) spectra at 298 K. The shaded yellow region denotes an energy range where IASPL tracks G(∆E,T) (solid green line). The star denotes an energy where IASPL peaks deep within the gap. (d) Iexc dependence of IASPL (open red circles) and corresponding fit (dashed blue line) at 298 K (λexc=680 nm) under large detuning (∆E=0.632 eV) conditions. An average m-value for 11 NBs is =1.57±0.11. 237x198mm (300 x 300 DPI)


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Figure 4. Comparison of band edge emission (solid blue line) and ASPL spectra (open red circles) at (a) 190 K and (b) 80 K. The green arrow denotes the excitation energy (λexc =532 nm) used for the ASPL measurement. Literature energies for CdS free exciton (FX), neutral donor/bound exciton (D0X), neutral acceptor/bound exciton (A0X), donor bound hole (D-h), and DAP transitions denoted along with DAP LO phonon replicas. (c) Full ASPL/band edge emission spectral dataset between 80 and 380 K (λexc=532 nm). 189x156mm (300 x 300 DPI)



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Figure 5. Illustration of the model used to simulate CdS NB emission efficiencies. 242x147mm (300 x 300 DPI)


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Figure 6. (a) Power law Iexc-dependence (open red circles) of Iem at 298 K. The orange line indicates superliner Iem growth with a power law growth exponent of b=1.56. The green line shows near linear growth at higher Iexc with a corresponding power law coefficient of b=1.02. The blue line shows a region of sublinear growth beyond a critical Iexc, where the corresponding power law growth exponent is b=0.35. (b) Single NB EQE values and corresponding model fit (solid blue line) yielding ηopt = 0.64 (λexc=470 nm). 198x270mm (300 x 300 DPI)



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Defect-Mediated CdS Nanobelt Photoluminescence Up-Conversion

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