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. Our results predict strongly field-dependent nonlinear charge carrier mobility and intra-pulse gain in semiconductor nanostructures using master equations. The size and temperature dependence is analyzed.

Herein, the THz mobility of charge carriers in low‐dimensional semiconductors based on a density matrix approach involving master equations for population and polarization dynamics is modeled. Pulsed THz fields induce intraband transitions between quantized subband states, creating polarization and subsequent charge transport that governs the electron mobility. It is shown that an equilibration current emerges—a purely quantum mechanical contribution understood via the Ehrenfest theorem in 1D—reshaping the low‐frequency mobility. Apart from thermal population, the results further demonstrate that the frequency‐dependent mobility becomes THz field strength and spectrum, as well as pulse width and chirp dependent, already at moderate THz probe fields of 1 kV cm−1, e.g., for 1D CdSe or GaAs nanostructures. The parametric nature of the underlying master differential equations for polarization and population, driving the intraband conductivity, results in a nonlinear, third‐order mobility and susceptibility, causing a nontrivial field dependence as well as power broadening even at moderate field strength. The obtained results are in good agreement with experiments. The observed high nonlinearities strongly impact the design and interpretation of THz charge carrier mobility experiments and further allow applications like coherent control, frequency mixing, or synthesis through a field‐controlled nonlinearity or high harmonics generation, especially interesting for future 6G telecommunication.

Kubo-Greenwood theory of the frequency-dependent conductivity in nanosystems lacks a general treatment of nonunitarian system dynamics, i.e., population decay and dephasing. We show, based on density matrix evolution, that in consequence, the mobility of charge carriers is suppressed in a low-frequency regime up to the GHz or THz range, e.g., for 1D semiconductor nanorods. We demonstrate that the effect is based on a compensation of charge carrier motion introduced by absorption of, for example, THz radiation by means of a counteracting equilibration current. We derive a new formalism, allowing efficient calculation of the charge mobility or exciton polarizability contribution to the conductivity of nanosystems, either as predictive modeling or fitting to experimental results. A calculation of the charge trajectories allows us further to conclude that backscattering at domain ends, like in Drude-Smith models, is insignificant in typical nanorods. To understand both, low-frequency transport properties (e.g., for use in solar cells or for hydrogen generation applications), as well as high-frequency THz generation and detection by nanomaterials in emerging 6G technology are important factors to optimize these functionalities.

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.

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.

As for many technological applications, excitation transport determines their performance, we investigate the THz conductivity of electrons, holes, excitons, and trions in 2D semiconductor nanoparticles. While the non-Drude-like frequency response of charge carriers in these systems has been established recently, the responses of excitons and trions remain not fully understood. We show that the exciton polarizability is related to intraexcitonic transitions between different states of relative motion and independent of the center-of-mass motion of an exciton. In contrast to simplifying models, a thermal distribution among those states leads to a considerable alteration of the resultant polarizability. To understand experimental data, we develop a quantum mechanical model for the mobility of trions and describe a linear-response based formalism for the polarizability of excitons with a thermal distribution. Discussing the size-and aspect ratio dependent mobility of these species, we show that the particle manifold can be tuned. While for small nanoplatelets and a high number of background electrons signatures of negative trions dominate the THz response, in contrast, for extended 2D systems, excitons prevail. Like the conductance for charge carriers, the polarizability of excitons as well as mobility of trions is altered by quantization effects. Our results give basic insights to the understanding of the THz spectra of colloidal, epitaxial, and free-standing 2D semiconductors, for instance, monolayer perovskites and TMDCs, materials of current interest for solar energy harvesting, photocatalysis, or high bandwidth and low-noise nanoelectronics or THz detection in imaging systems for security applications. We provide a toolbox for the analysis of experiments and improved microscopic understanding, which in reverse allows optimization of technological applications.

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: .

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.

Electrophoretically deposited (EPD) quantum dots (QDs) can be charged electrochemically via electron injection from a conducting substrate, leading to pronounced changes in their electrical and optical properties. The 180-550 nm thick EPD films composed of CdSe QDs with different diameters (2.8-6.3 nm) demonstrate a strong and reversible electrochromic response due to bleaching of excitonic transitions. The number of injected electrons was found to increase with QD size from 1.3 (QD diameter of 2.8 nm) to 6 (QD diameter of 6.3 nm) electrons per nanoparticle. As a result for 3.4 nm, 4.5 nm, and 6.3 nm QDs a complete 1Se level filling was observed, while the smallest studied QDs (2.8 nm) exhibited only a partial 1Se level population. In addition, 4.5 and 6.3 nm QDs also showed partial 1P(e) level filling with electrons. The data from both cyclic voltammetry measurements and electrochemically driven spectral bleaching enabled determining the electrochemically derived 1Se level energies. Additionally, we demonstrate fast charging-discharging kinetics for EPD CdSe QD films with complete absorption bleaching and recovery in a sub-100 ms time scale, which opens prospects for utilizing such films in various applications such as electrochromic displays, smart windows or tunable color filters for photography.

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.

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.

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 β-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.