Field-dependent THz transport nonlinearities in semiconductor nano structures.

Charge transport nonlinearities in semiconductor quantum dots and nanorods are studied. Using a density matrix formalism, we retrieve the field-dependent nonlinear mobility and show the possibility of intra-pulse gain. We further demonstrate that the dynamics of master equations can be captured in an analytical formula for the field-dependent charge carrier mobility, e.g. for two-level systems. This equation extends the linear response theory based Kubo-Greenwood result to nonlinear processes at elevated field strength, easily reached in THz transport spectroscopy. With these tools we analyze the field strength, chirp, temperature and dephasing dependence of the charge carrier mobility in the model system of CdSe quantum dots and wires. Stark broadening and Rabi splitting result in strong alterations of the mobility spectra, pronounced at low temperatures. The mobility spectra are strongly temperature and pulse shape dependent in the nonlinear regime. The findings are of immediate interest e.g. for nonlinear THz generation, conversion and amplification in 6G technology and nano electronics. Our results further enable experimentalists to fit and understand measured charge transport nonlinearities with analytical expressions and to design nanosystems with engineered material properties.

THz mobility and polarizability: impact of transformation and dephasing on the spectral response of excitons in a 2D semiconductor.

We introduce a response theory based transformation for excitonic polarizability into mobility, which allows an in-depth analysis of optical pump-THz probe conductivity experiments, and compare the results with those of a conventional oscillator model. THz spectroscopy is of high interest e.g. for investigations in high bandwidth and low noise nanoelectronics or solar energy harvesting nanomaterials. In contrast to simple ω scaling of estimated static polarizability, suggested in the literature, an appropriate transformation of the spectral response into mobility can be achieved in principle forward and backward due to the presence of dephasing, as we show for the exemplary system of CdSe nanoplatelets. Common analysis approaches capture the excitonic properties only under specific conditions, and do not apply in many cases. We demonstrate that a thermal distribution of excitons and transitions between higher states in general have to be considered and that dephasing has to be taken into account for a proper transformation at all temperatures. The presented in-depth understanding of the exciton mobility in nanoparticles can help improve e.g. solar hydrogen generation, charge extraction efficiencies of solar cells, or light emission performance of LEDs.

Zeta Potential-Based Control of CdSe/ZnS Quantum Dot Photoluminescence.

The ζ-potential of a colloidal quantum dot (QD) in solution has a strong impact on its photoluminescence emission quantum yield as well as the population lifetime. In this study we show that varying the surface charged groups on CdSe/ZnS QDs allows one to tune the ζ-potential and, with it, to control the quantum yield of emission as well as the recombination dynamics. We infer that the net charge density within the slipping plane around the QD in the solution strongly affects the nonradiative recombination processes, depending on the surface charge sign and value. For zwitterionic surface groups it is possible to tune the ζ-potential and the quantum yield by pH. As a general trend, QDs with zwitterionic surface groups produce a low (absolute) ζ-potential value and exhibit the highest quantum yield. Our results pave the way to, for example, future intracellular, time-resolved pH sensing applications with similar systems.

Population dependence of THz charge carrier mobility and non-Drude-like behavior in short semiconductor nanowires.

We investigate THz radiation absorption by charge carriers, focusing on the mobility in nanorods and wires. We show that for short rods the mobility is limited by the high spacing of the charge carrier energy levels, while for longer wires (greater 25 nm) finite dephasing results in considerably higher low frequency mobility. Analyzing the length, temperature and population dependence, we demonstrate that, apart from the temperature dependent dephasing, the mobility becomes strongly charge carrier population dependent. The latter results in no simple linear relationship between carrier density and conductivity. Additionally their thermal distribution determines the mobility, measured in experiments. We further show that Drude or Plasmon models apply only for long wires at elevated temperatures, while for short length quantization results in considerable alterations. In contrast to those phenomenological models, i.e. a negative imaginary part of the frequency-dependent conductivity in a nanosystem can be understood microscopically. Based on the results, we develop guidelines to analyze 1D terahertz conductivity spectra. Our approach provides also a new tool to optimize the mobility by nanowire length as well as to analyze the dephasing, not by conventional wave mixing techniques, but by coherent optical pump-THz probe spectroscopy.

Terahertz Charge Carrier Mobility in 1D and 2D Semiconductor Nanoparticles.

We investigate the charge carrier mobility in 1D and 2D semiconductor nanoparticle domains with a focus on the interpretation of THz mobility measurements. We provide a microscopic understanding of the frequency-dependent charge carrier transport in these structures of finite lateral size. Yet unexplored oscillations in the frequency-dependent complex conductivity and a strong size dependence of the mobility are observed. The quantum nature of the charge carrier states results in oscillations in the frequency-dependent mobility for subresonant THz probing, seen in experiments. The effect is based on the lack of an energy continuum for the charge motion. In 2D systems the mobility is further governed by transitions in the two orthogonal x- and y-directions and depends nontrivially on the THz polarization, as well as the quantum well lateral aspect ratio, defining the energetic detuning of the lowest THz-photon transitions in both directions. We analyze the frequency, length, and effective mass dependencies.

Correction: Tuning trion binding energy and oscillator strength in a laterally finite 2D system: CdSe nanoplatelets as a model system for trion properties.

Correction for 'Tuning trion binding energy and oscillator strength in a laterally finite 2D system: CdSe nanoplatelets as a model system for trion properties' by Sabrine Ayari et al., Nanoscale, 2020, 12, 14448-14458, DOI: .

Tuning exciton diffusion, mobility and emission line width in CdSe nanoplatelets via lateral size.

We investigate the lateral size tunability of the exciton diffusion coefficient and mobility in colloidal quantum wells by means of line width analysis and theoretical modeling. We show that the exciton diffusion coefficient and mobility in laterally finite 2D systems like CdSe nanoplatelets can be tuned via the lateral size and aspect ratio. The coupling to acoustic and optical phonons can be altered via the lateral size and aspect ratio of the platelets. Subsequently the exciton diffusion and mobility become tunable since these phonon scattering processes determine and limit the mobility. At 4 K the exciton mobility increases from ∼ 4 × 103 cm2 V-1 s-1 to more than 1.4 × 104 cm2 V-1 s-1 for large platelets, while there are weaker changes with size and the mobility is around 8 × 101 cm2 V-1 s-1 for large platelets at room temperature. In turn at 4 K the exciton diffusion coefficient increases with the lateral size from ∼ 1.3 cm2 s-1 to ∼ 5 cm2 s-1, while it is around half the value for large platelets at room temperature. Our experimental results are in good agreement with theoretical modeling, showing a lateral size and aspect ratio dependence. The findings open up the possibility for materials with tunable exciton mobility, diffusion or emission line width, but quasi constant transition energy. High exciton mobility is desirable e.g. for solar cells and allows efficient excitation harvesting and extraction.

Tuning trion binding energy and oscillator strength in a laterally finite 2D system: CdSe nanoplatelets as a model system for trion properties.

We present a theoretical study combined with experimental validations demonstrating that CdSe nanoplatelets are a model system to investigate the tunability of trions and excitons in laterally finite 2D semiconductors. Our results show that the trion binding energy can be tuned from 36 meV to 18 meV with the lateral size and decreasing aspect ratio, while the oscillator strength ratio of trions to excitons decreases. In contrast to conventional quantum dots, the trion oscillator strength in a nanoplatelet at low temperature is smaller than that of the exciton. The trion and exciton Bohr radii become lateral size tunable, e.g. from ∼3.5 to 4.8 nm for the trion. We show that dielectric screening has strong impact on these properties. By theoretical modeling of transition energies, binding energies and oscillator strength of trions and excitons and comparison with experimental findings, we demonstrate that these properties are lateral size and aspect ratio tunable and can be engineered by dielectric confinement, allowing to suppress e.g. detrimental trion emission in devices. Our results strongly impact further in-depth studies, as the demonstrated lateral size tunable trion and exciton manifold is expected to influence properties like gain mechanisms, lasing, quantum efficiency and transport even at room temperature due to the high and tunable trion binding energies.

Two-photon based pulse autocorrelation with CdSe nanoplatelets.

We investigate broadband two-photon absorption autocorrelators based on II-VI semiconductor nanoplatelets as an alternative to common second harmonic generation based techniques. As compared to bulk materials the exceptionally high enhancement of two-photon absorption in these 2D structures results in very efficient two-photon absorption based autocorrelation detected via PL emission. We compare the results with TPA autocorrelation in CdS bulk as well as SHG based autocorrelation in ß-barium borate. We show that CdSe nanoplatelet based autocorrelation can exceed the efficiency of conventional methods by two orders in magnitude, especially for short interaction length, and allows a precise pulse-width determination. We demonstrate that very high two-photon absorption cross sections of the nanoplatelets are the basis for this effective TPA autocorrelation. Based on our results with II-VI nanoplatelets efficient broadband autocorrelation with more than ∼100 nm bandwidth and very high sensitivity seems feasible.

Size-dependent exciton substructure in CdSe nanoplatelets and its relation to photoluminescence dynamics.

CdSe nanoplatelets can be synthesized with different lateral sizes; very small nanoplatelets have almost quantum dot like features (almost discrete exciton states), while very large ones are expected to have properties of colloidal quantum wells (exciton continuum). However, nanoplatelets can be in an intermediate confinement regime with a rich substructure of excitons, which is neither quantum dot like nor an ideal 2D exciton. In this manuscript, we discuss the experimental transition energies and relaxation dynamics of exciton states in CdSe platelets with varying lateral dimensions and compare them with a microscopic theoretical model including exciton-phonon scattering. The model takes special care of the interplay of confinement and Coulomb coupling in the intermediate regime showing strong changes with respect to simple weak or strong confinement models by solving the full four dimensional lateral factorization free exciton wavefunction. Depending on the platelet size broad resonances previously attributed to just ground and excited states are actually composed of a rich substructure of several exciton states in their temporal dynamics. We show that these factorization free exciton states can explain the spectral features observed in photoluminescence experiments. Furthermore we demonstrate that the interplay of exciton bright and dark states provides principle insights into the overall temporal relaxation dynamics, and allows tuning of the exciton cooling via lateral platelet size. Our results and theoretical approach are directly relevant for understanding e.g. the size tuneability of lasing, excitonic cooling dynamics or light harvesting applications in these and similar 2D systems of finite lateral size.

Charge Mobility and Recombination Mechanisms in Tellurium van der Waals Solid.

Trigonal tellurium is a small band gap elemental semiconductor consisting of van der Waals bound one-dimensional helical chains of tellurium atoms. We study the temperature dependence of the charge carrier mobility and recombination pathways in bulk tellurium. Electrons and holes are generated by irradiation of the sample with 3 MeV electrons and detected by time-resolved microwave conductivity measurements. A theoretical model is used to explain the experimental observations for different charge densities and temperatures. Our analysis reveals a high room temperature mobility of 190 ± 20 cm2 V-1 s-1. The mobility is thermally deactivated, suggesting a band-like transport mechanism. According to our analysis, the charges predominantly recombine via radiative recombination with a radiative yield close to 98%, even at room temperature. The remaining charges recombine by either trap-assisted (Shockley-Read-Hall) recombination or undergo trapping to deep traps. The high mobility, near-unity radiative yield, and possibility of large-scale production of atomic wires by liquid exfoliation make Te of high potential for next-generation nanoelectronic and optoelectronic applications, including far-infrared detectors and lasers.

A comparative study demonstrates strong size tunability of carrier-phonon coupling in CdSe-based 2D and 0D nanocrystals.

In a comparative study we investigate the carrier-phonon coupling in CdSe based core-only and hetero 2D as well as 0D nanoparticles. We demonstrate that the coupling can be strongly tuned by the lateral size of nanoplatelets, while, due to the weak lateral confinement, the transition energies are only altered by tens of meV. Our analysis shows that an increase in the lateral platelet area results in a strong decrease in the phonon coupling to acoustic modes due to deformation potential interaction, yielding an exciton deformation potential of 3.0 eV in line with theory. In contrast, coupling to optical modes tends to increase with the platelet area. This cannot be explained by Fröhlich interaction, which is generally dominant in II-VI materials. We compare CdSe/CdS nanoplatelets with their equivalent, spherical CdSe/CdS nanoparticles. Universally, in both systems the introduction of a CdS shell is shown to result in an increase of the average phonon coupling, mainly related to an increase of the coupling to acoustic modes, while the coupling to optical modes is reduced with increasing CdS layer thickness. The demonstrated size and CdS overgrowth tunability has strong implications for applications like tuning carrier cooling and carrier multiplication - relevant for solar energy harvesting applications. Other implications range from transport in nanosystems e.g. for field effect transistors or dephasing control. Our results open up a new toolbox for the design of photonic materials.

Impact of Shell Growth on Recombination Dynamics and Exciton-Phonon Interaction in CdSe-CdS Core-Shell Nanoplatelets.

We investigate the impact of shell growth on the carrier dynamics and exciton-phonon coupling in CdSe-CdS core-shell nanoplatelets with varying shell thickness. We observe that the recombination dynamics can be prolonged by more than one order of magnitude, and analyze the results in a global rate model as well as with simulations including strain and excitonic effects. We reveal that type I band alignment in the hetero platelets is maintained at least up to three monolayers of CdS, resulting in approximately constant radiative rates. Hence, observed changes of decay dynamics are not the result of an increasingly different electron and hole exciton wave function delocalization as often assumed, but an increasingly better passivation of nonradiative surface defects by the shell. Based on a global analysis of time-resolved and time-integrated data, we recover and model the temperature dependent quantum yield of these nanostructures and show that CdS shell growth leads to a strong enhancement of the photoluminescence quantum yield. Our results explain, for example, the very high lasing gain observed in CdSe-CdS nanoplatelets due to the type I band alignment that also makes them interesting as solar energy concentrators. Further, we reveal that the exciton-LO-phonon coupling is strongly tunable by the CdS shell thickness, enabling emission line width and coherence length control.

Directed Two-Photon Absorption in CdSe Nanoplatelets Revealed by k-Space Spectroscopy.

We show that two-photon absorption (TPA) is highly anisotropic in CdSe nanoplatelets, thus promoting them as a new class of directional two-photon absorbers with large cross sections. Comparing two-dimensional k-space spectroscopic measurements of the one-photon and two-photon excitation of an oriented monolayer of platelets, it is revealed that TPA into the continuum is a directional phenomenon. This is in contrast to one-photon absorption. The observed directional TPA is shown to be related to fundamental band anisotropies of zincblende CdSe and the ultrastrong anisotropic confinement. We recover the internal transition dipole distribution and find that this directionality arises from the intrinsic directionality of the underlying Bloch and envelope functions of the states involved. We note that the photoemission from the CdSe platelets is highly anisotropic following either one- or two-photon excitation. Given the directionality and high TPA cross-section of these platelets, they may, for example, find employment as efficient logic AND elements in integrated photonic devices, or directional photon converters.

Directed emission of CdSe nanoplatelets originating from strongly anisotropic 2D electronic structure.

Intrinsically directional light emitters are potentially important for applications in photonics including lasing and energy-efficient display technology. Here, we propose a new route to overcome intrinsic efficiency limitations in light-emitting devices by studying a CdSe nanoplatelets monolayer that exhibits strongly anisotropic, directed photoluminescence. Analysis of the two-dimensional k-space distribution reveals the underlying internal transition dipole distribution. The observed directed emission is related to the anisotropy of the electronic Bloch states governing the exciton transition dipole moment and forming a bright plane. The strongly directed emission perpendicular to the platelet is further enhanced by the optical local density of states and local fields. In contrast to the emission directionality, the off-resonant absorption into the energetically higher 2D-continuum of states is isotropic. These contrasting optical properties make the oriented CdSe nanoplatelets, or superstructures of parallel-oriented platelets, an interesting and potentially useful class of semiconductor-based emitters.

Mobility and Decay Dynamics of Charge Carriers in One-Dimensional Selenium van der Waals Solid.

Trigonal selenium is a semiconducting van der Waals solid that consists of helical atomic chains. We studied the mobility and decay dynamics of excess electrons and holes moving along the selenium chains. Excess charge carriers were generated by irradiation of powdered selenium with 3 MeV electron pulses. Their mobility and decay via trapping or recombination was studied by time-resolved microwave conductivity measurements as a function of temperature. The mobility of charge carriers along the Se chains is at least ca. 0.5 cm2·V-1·s-1 at room temperature. Charges decay predominantly by trapping at defects. The appreciable mobility, together with the potential for large-scale production of Se wires by liquid exfoliation, makes this material of great interest for use in nanoelectronics.

Time-Resolved Stark Spectroscopy in CdSe Nanoplatelets: Exciton Binding Energy, Polarizability, and Field-Dependent Radiative Rates.

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.

p-State Luminescence in CdSe Nanoplatelets: Role of Lateral Confinement and a Longitudinal Optical Phonon Bottleneck.

We evidence excited state emission from p states well below ground state saturation in CdSe nanoplatelets. Size-dependent exciton ground and excited state energies and population dynamics are determined by four independent methods: time-resolved PL, time-integrated PL, rate equation modeling, and Hartree renormalized k·p calculations-all in very good agreement. The ground state-excited state energy spacing strongly increases with the lateral platelet quantization. Depending on its detuning to the LO phonon energy, the PL decay of CdSe platelets is governed by a size tunable LO phonon bottleneck, related to the low exciton-phonon coupling, very large oscillator strength, and energy spacing of both states. This is, for instance, ideal to tune lasing properties. CdSe platelets are perfectly suited to control the exciton-phonon interaction by changing their lateral size while the optical transition energy is determined by their thickness.

Temperature dependent radiative and non-radiative recombination dynamics in CdSe-CdTe and CdTe-CdSe type II hetero nanoplatelets.

We investigate the temperature-dependent decay kinetics of type II CdSe-CdTe and CdTe-CdSe core-lateral shell nanoplatelets. From a kinetic analysis of the photoluminescence (PL) decay and a measurement of the temperature dependent quantum yield we deduce the temperature dependence of the non-radiative and radiative lifetimes of hetero nanoplates. In line with the predictions of the giant oscillator strength effect in 2D we observe a strong increase of the radiative lifetime with temperature. This is attributed to an increase of the homogeneous transition linewidth with temperature. Comparing core only and hetero platelets we observe a significant prolongation of the radiative lifetime in type II platelets by two orders in magnitude while the quantum yield is barely affected. In a careful analysis of the PL decay transients we compare different recombination models, including electron hole pairs and exciton decay, being relevant for the applicability of those structures in photonic applications like solar cells or lasers. We conclude that the observed biexponential PL decay behavior in hetero platelets is predominately due to spatially indirect excitons being present at the hetero junction and not ionized e-h pair recombination.

Two Photon Absorption in II-VI Semiconductors: The Influence of Dimensionality and Size.

We report a comprehensive study on the two-photon absorption cross sections of colloidal CdSe nanoplatelets, -rods, and -dots of different sizes by the means of z-scan and two-photon excitation spectroscopy. Platelets combine large particle volumes with ultra strong confinement. In contrast to weakly confined nanocrystals, the TPA cross sections of CdSe nanoplatelets scale superlinearly with volume (V(∼2)) and show ten times more efficient two-photon absorption than nanorods or dots. This unexpectedly strong shape dependence goes well beyond the effect of local fields. The larger the particles' aspect ratio, the greater is the confinement related electronic contribution to the increased two-photon absorption. Both electronic confinement and local field effects favor the platelets and make them unique two-photon absorbers with outstanding cross sections of up to 10(7) GM, the largest ever reported for (colloidal) semiconductor nanocrystals and ideally suited for two-photon imaging and nonlinear optoelectronics. The obtained results are confirmed by two independent techniques as well as a new self-referencing method.