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Auger Suppression in n-Type HgSe Colloidal Quantum Dots Christopher Melnychuk, and Philippe Guyot-Sionnest ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.9b04608 • Publication Date (Web): 22 Aug 2019 Downloaded from pubs.acs.org on August 23, 2019
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Auger Suppression in n-Type HgSe Colloidal Quantum Dots Christopher Melnychuk and Philippe Guyot-Sionnest* James Franck Institute, The University of Chicago, 929 East 57th St., Chicago, IL 60615 USA *
[email protected] ABSTRACT Transient infrared photoluminescence upconversion is used to study the exciton dynamics in small-gap HgSe colloidal quantum dots in the 2000 Ð 6500 cm-1 (0.25 Ð 0.80 eV) range. The intraband mid-infrared photoluminescence decays show absent or greatly reduced Auger relaxation of biexcitons, proposed as a generic feature of weakly n-type quantum dots due to the sparse density of states in the conduction band. The nonradiative relaxation of the intraband carriers is instead consistent with near-field energy transfer to molecular vibrations of the surface ligands. In contrast, the interband near-infrared photoluminescence decays exhibit the typical distinct exciton and biexciton lifetimes with Auger coefficients comparable to other similarly-sized quantum dots. Also observed are spectral and dynamical evidence of fine structure in the intraband transitions consistent with spin-orbit splitting of the electron P levels, and the emergence of plasmonic resonances in large particles.
KEYWORDS Auger, doping, infrared, intraband, phonon bottleneck, plasmon, photoluminescence
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Nonradiative multicarrier relaxation is a limitation for many semiconductor technologies. Specific effects of such carrier losses include reduced lasing efficiencies,1 lowered specific detectivity in photodetectors,2,3 and efficiency droop in high-power LEDs.4 At high carrier densities the dominant mode of nonradiative relaxation is typically a carrier-carrier scattering such as Auger relaxation, a process by which an exciton transfers its gap energy to a nearby electron or hole. The Auger mechanism is relatively well-understood in bulk semiconductors. It is often calculated by application of perturbation theory, considering the screened Coulomb interactions between carriers under energy and momentum conservation.5Ð7 For small-gap materials it is a direct process,5,6,8 while phonons are required at larger energies.4,5,8,9 Due to the increasing ease of momentum conservation, the Auger rate grows rapidly in bulk materials as the energy gap decreases. In contrast to the developed understanding of Auger relaxation in bulk materials, its mechanism in colloidal quantum dots (CQDs) is less clear. Following the first observations of fluence-dependent exciton lifetimes in nanocrystal-doped glasses,10,11 this dynamical signature was attributed to the Auger ionization of a trion.12 The majority of CQDs have displayed R-3 scaling of the Auger rate and a strong similarity between the Auger rates for very different materials of the same particle size.13,14 The scaling has been attributed to the combined effects of the density of states and modified Coulomb couplings for hot carriers,15 but there has been no theoretical explanation for the similarity of observed Auger rates in vastly different materials. This motivates further study of the Auger relaxation in strongly-confined systems, especially for small- and negative-gap materials where the dissimilarity between bulk and nanoparticle rates should be greatest. HgSe CQDs are an attractive system for the study of nonradiative processes in confined semiconductors. A negative-gap semimetal in the bulk, quantum confinement in HgSe
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nanoparticles opens a size-tunable gap in the near-infrared. The low energy of the conduction band with respect to typical environmental Fermi levels renders HgSe quantum dots naturally n-doped,16 inducing an additional mid-infrared transition as observed in HgS,17,18 HgTe,19 and Ag2Te CQDs.20 This allows interband and intraband transitions to be easily investigated in the same material. The carrier dynamics in HgSe nanocrystals are also of practical interest for this materialÕs applications in mid-infrared photodetection3,21,22 and light emission.23 Prior spectroscopic studies on HgSe CQDs were limited to static measurements focusing on the spectral response of particles to alterations of their electrochemical environment16 and surface chemistry.3,23Ð26 Here we investigate the carrier dynamics in HgSe by transient photoluminescence upconversion, a nonlinear optical technique that circumvents the lack of fast and sensitive infrared detectors.
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electron dispersion within the two-band ! " # approximation for a particle of radius R, given by ) ,- . -
$ %& ' ( + *
/0
,- . -
1 $2 3 45 65 */ $7 4 $2* 98 with &):; = ; = 8?8@9=, and an intraband 0
exciton binding energy of A?BC * 9D) = (CGS units). Material constants are given in the supporting information. Theory and measurement agree for small particles, but at large sizes the intraband frequencies are significantly blueshifted from the ! " # prediction and saturate at a value around 1900 cm-1. The fluorescence also weakens and is not detected in the largest particles. The blueshift from the single-electron calculation, saturation at a finite energy, narrowing absorption, and quenching of fluorescence are all consistent with the emergence of surface plasmon transitions at large sizes due to further conduction band filling. Such behavior has previously been observed in ZnO27Ð29 and HgS quantum dots.18 These effects arise as the local fields produced by carriers blueshift the collective resonance to the quadratic mean of the one-electron and surface plasmon resonance frequencies.18,30 These frequencies are close for the 9.1 nm particles in Figure 1, and that size therefore lies between the two regimes. The carrier density extracted from the surface plasmon frequency is E?F G AH)I 5JKLM for the 9.1 nm particles and corresponds to 15 electrons, indicating doping through the 1De states. The remainder of this work focuses exclusively on the dynamics in smaller particles where plasmonic effects on the 1Se Ð 1Pe transition should be negligible. For these sizes, notable features in Figure 1 are the spectral narrowing and Stokes shift of the emission with respect to the absorption. These arise in part from the level splitting of 1Pe due to spin-orbit coupling and aspheric particle shape, as in HgTe CQDs.31 Electron-phonon coupling and surface effects may also play a role. The intraband lineshapes are discussed further in a dedicated section.
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Figure 2 (a) absorption and emission spectra of ~ 5 nm diameter HgSe CQDs in arbitrary units; (b) interband fluorescence decay at 5600 cm-1; (c) intraband fluorescence decay at 2100 cm-1 in the same sample. The C-H stretch resonances have been removed from the absorption spectrum for clarity. As shown in Figure 2b, at a low pump fluence of BB NO9JK* we observe a single decay for the interband photoluminescence. As the pump fluence increases, an additional fast decay becomes apparent. The decay dynamics in Figure 2 are accurately described by functions of the form P) C LQRST 54 P* C LQRS- . For the data in Figure 2b, fitting gives U) ( VBHH W XYH ps and U* ( VH W E ps. We assign the slow decay component to the exciton lifetime. Prior work has shown the interband quantum yield to strongly increase with decreasing temperature; along with the beneficial effect of shell growth, this suggested the presence of surface traps.24,25 Based on a calculated radiative lifetime, the exciton lifetime observed here is consistent with measured quantum yields on the order of 10-2.25 The relative amplitude of the short lifetime component increases with fluence, and this behavior is assigned to the Auger relaxation of biexcitons.11,14,32Ð 34
Further support for this assignment, including analysis of the excitation densities and absolute
photoluminescence magnitudes, may be found in the supporting information. In quantum dots, the Auger relaxation can be characterized by an Auger coefficient CA, defined as Z[ ( \ * RFU]] for the Auger decay of a biexciton with a lifetime U]] in a particle of volume V.35 This allows direct comparisons between nanoparticle and bulk Auger relaxation rates. The interband Auger coefficients are V?B G AHL*I 5JK^ R_5at 5 nm diameter and B?A5 G AHL*I 5JK^ R _ at 6 nm diameter. The Auger coefficient for bulk HgSe is not known, but these values are more consistent with a larger gap bulk semiconductor.5 This corroborates our previous observation of slower Auger relaxation in small-gap CQDs versus the corresponding bulk materials.14
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Figure 2c shows the fluorescence decay for the intraband transition under similar pumping conditions. The difference is striking, as there is no longer any substantial fluence-dependence. The data exhibit two decay constants of 35 ± 5 ps and 210 ± 40 ps that are nearly unchanged over the range of pump fluences, and the slow decay always constitutes approximately 60 % of the time-integrated fluorescence. This indicates that Auger relaxation is very strongly suppressed in HgSe quantum dots doped with one or two electrons. The different carrier dynamics in intrinsic and weakly n-type HgSe may be understood by considering that the Auger relaxation rate is affected by the density of states, as determined by FermiÕs golden rule:
`abc ( 5
V< * dc efge\h eije ,5
%A'
` is the Auger transition rate, kgl is an exciton final state, lim is the initial biexciton or trion at the
band edge, \h is a screened Coulomb interaction, and dc is the density of resonant final states. In HgSe, the density of valence states is far greater than the density of conduction states because the hole is much heavier than the electron.36 For interband Auger relaxation, the final state is a valenceconduction exciton and there is a large density of these states resonant with the biexciton. In contrast, Auger relaxation in n-type quantum dots involves conduction states exclusively and the density of exciton states resonant with a 1Se Ð 1Pe biexciton is very low. This situation is summarized in Figure 3. We note that if the lifetime under strong pumping was due to Auger relaxation, a ~ 200 ps Auger lifetime for a particle of ~ 2.5 nm radius gives Z[ ( V?B G AHLMn 5JK^ R_. This upper bound on Z[ is already a factor of 103 Ð 104 smaller than for bulk materials of similar gap,5 and similar to Auger coefficients in CQD systems of o5AH G greater gap.13,33 The suppression of Auger relaxation should be a general phenomenon in weakly n-type
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quantum dots with light electron effective masses, but does not necessarily hold at higher doping levels. The absence of photoluminescence for the larger and more heavily-doped HgSe may indeed be attributed to a very fast relaxation arising from electron-electron scattering across a large number of electron configurations.
a
b
E1Pe-1De
E1Pe-1De
E1Pe-1De
c
E1Se-1Pe
E1Se-1Pe
E1Se-1Pe
E1Sh-1Se
E1Sh-1Se
E1Sh-1Se
Figure 3 Schematics for Auger relaxation in HgSe quantum dots. Blue circles are electrons and red circles are holes. (a) intrinsic particle, hot Auger hole; (b) intrinsic particle, hot Auger electron; (c) n-type particle, hot Auger electron with no hot hole pathway. The dashed lines give the position of the Fermi level.
Nonradiative processes Although intraband Auger relaxation in weakly n-type HgSe CQDs is absent or slow, the intraband fluorescence decay is still fast. A prior study on the intraband photoluminescence from HgSe CQDs showed the quantum yield to be independent of temperature. This indicated that trapping is unlikely and instead suggested an activation-less process.24 Near-field energy transfer via dipolar coupling between the exciton and ligand molecular vibrations is one such mechanism.37Ð40 The nonradiative relaxation rate `pq for this process is derived by considering the energy dissipated by
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a spherical dipole of radius R into an absorbing coating of thickness r= and imaginary dielectric function5Dss. It is given by
`pq
r= u* ( 5Dss t 5 = ,
%V'5
where u is the transition dipole moment. We use this formula to quantitatively model the dynamics. The electric field within a spherical dipole of dielectric constant D) embedded in a host of dielectric constant D* is screened such that u ( un %ED* 'R%D) 4 VD* '. For the 1Se Ð 1Pe transition, un ( CkAvw lxlAyw m and is calculated from the Bessel solutions to an infinite spherical potential well.41 The transition dipole moment is calculated for a given transition energy from the electron dispersion including exciton binding, and a size-dependent emission redshift is taken from an empirical fit to the data in Figure 1a. Dss is determined from the measured absorption spectrum of the aliphatic ligands through the relation z ( V
