Numerical study on all-optical modulation characteristics of quantum cascade lasers

• Biao Wei,
• Haijun Zhou,
• Guangxiang Li and
• Bin Tang

Beilstein J. Nanotechnol. 2022, 13, 1011–1019, doi:10.3762/bjnano.13.88

• electrons to the conduction band, and obtain the electron number of each subband of the conduction band by solving the partial rate equations (PRE) [17]. Whether the scattering rate and electron population of each subband can be further calculated by the FRE is judged by whether or not the electrons of each

• from a line through the other five points. This results from the arithmetic we used to solve the rate equations. There are numerous solutions to the rate equations, so we solved them iteratively, and for different initial conditions (electron number in the cavity), the solution may not have always been

• findings provide support for further research on all-optical modulation of QCLs. Results and Discussion Numerical approach To examine the all-optical modulation of QCLs, we must consider the output characteristics of QCLs. In the four-level system, the carrier distribution is described by the full rate

Hexagonal boron nitride: a review of the emerging material platform for single-photon sources and the spin–photon interface

• Stefania Castelletto,
• Faraz A. Inam,
• Shin-ichiro Sato and
• Alberto Boretti

Beilstein J. Nanotechnol. 2020, 11, 740–769, doi:10.3762/bjnano.11.61

• decay rate will be the same as the spontaneous emission rate (SER). As described in [69], neglecting all the atomic coherences, the rate equations for the system are given by: Here ρ1,2 represents the population of states |1⟩ and |2⟩ and should satisfy the completeness condition for the system to be in

• either of the two states ρ1 + ρ2 = 1. The solution of the above rate equations gives, with In the equilibrium condition, the steady-state population of the state |2⟩ is given by As the system is in the ground state initially, To correlate the transition rates with the photon detection events, let us now

• relaxes from state v|2⟩ to state v|1⟩ via spontaneous emission, emitting a photon of energy ℏω0. In the same approximation as the 2-level systems, the rate equations for the 3-level system are: The second order autocorrelation function for the three-level system is given by [67][71]: Here the decay times

Electronic structure, transport, and collective effects in molecular layered systems

• Torsten Hahn,
• Tim Ludwig,
• Carsten Timm and
• Jens Kortus

Beilstein J. Nanotechnol. 2017, 8, 2094–2105, doi:10.3762/bjnano.8.209

• in the eigenbasis of Hmol (i.e., coherences) vanish if the system is non-magnetic or all magnetic axes (applied magnetic field, magnetization, easy anisotropy axis) are parallel. Then one obtains rate equations for the diagonal components, i.e., for the probabilities of molecular states, where m and

The role of morphology and coupling of gold nanoparticles in optical breakdown during picosecond pulse exposures

• Yevgeniy R. Davletshin and
• J. Carl Kumaradas

Beilstein J. Nanotechnol. 2016, 7, 869–880, doi:10.3762/bjnano.7.79

• ] provided a theoretical analysis of short pulse interactions with spherical noble-metal nanoparticles, while Boulais et al. [31] developed a model of plasma-mediated nanocavitation for gold nanospheres and nanorods [31][37]. The model by Bisker and Yelin [42] is based on Mie theory and rate equations for

• free-electron density generation [26][34]. This model does not have a full two-way coupling between the Mie simulations and free-electron plasma rate equations and omits the photo-thermal emission of hot electrons off the nanoparticle surface [30]. In addition the Mie theory is not applicable to

Charge and heat transport in soft nanosystems in the presence of time-dependent perturbations

• Alberto Nocera,
• Carmine Antonio Perroni,
• Vincenzo Marigliano Ramaglia and
• Vittorio Cataudella

Beilstein J. Nanotechnol. 2016, 7, 439–464, doi:10.3762/bjnano.7.39

• our review, it has been studied in a fully out-of-equilibrium response regime with different theoretical tools, ranging from rate equations [62][63][64][65][66] to non-equilibrium Green’s function formalisms [48][55][67][68][69]. The adiabatic approach, which has been applied by some of the present

Continuum models of focused electron beam induced processing

• Milos Toth,
• Charlene Lobo,
• Vinzenz Friedli,
• Aleksandra Szkudlarek and
• Ivo Utke

Beilstein J. Nanotechnol. 2015, 6, 1518–1540, doi:10.3762/bjnano.6.157

• underlying growth mechanisms. Continuum FEBIP models are comprised of differential equations for the rates of change of concentrations of all surface-adsorbed species thought to be involved in the deposition or etch kinetics. The rate equations are functions of time and space, and require specification of

• example, SiF2 can either gain F to form SiF3, dissociate to form SiF and F, or it can desorb (and hence give rise to etching by removing a Si atom): Multi-step FEBIE reactions can be modeled using a set of differential rate equations that account for each molecular species at the substrate surface, which

• using a mixture of two precursor gases [8]: This situation, depicted in Figure 10, can be modeled by solving rate equations for two FEBID precursor adsorbates, denoted by “A” and “B”, that compete for adsorption sites on the surface. The adsorbates are dissociated by electrons, producing non-volatile

Current–voltage characteristics of manganite–titanite perovskite junctions

• Benedikt Ifland,
• Patrick Peretzki,
• Birte Kressdorf,
• Philipp Saring,
• Andreas Kelling,
• Michael Seibt and
• Christian Jooss

Beilstein J. Nanotechnol. 2015, 6, 1467–1484, doi:10.3762/bjnano.6.152

• is performed in the framework of the classical Shockley theory [37]. This theory was originally developed for generation and recombination currents of quasi-free electrons. In more recent works, a Shockley-like equation describing a diode-like rectifying behavior has been derived from rate equations

Electronic interaction in composites of a conjugated polymer and carbon nanotubes: first-principles calculation and photophysical approaches

• Florian Massuyeau,
• Jany Wéry,
• Jean-Luc Duvail,
• Serge Lefrant,
• Abu Yaya,
• Chris Ewels and
• Eric Faulques

Beilstein J. Nanotechnol. 2015, 6, 1138–1144, doi:10.3762/bjnano.6.115

• following rate equations: Here, G(t) is the Gaussian exciton generation function, ni is the total population of photogenerated charges in the excited energy states i = 1 and 2 with initial condition ni(−∞) = 0, ki is the inverse of the decay lifetime τi. We note that these populations include species

Superluminescence from an optically pumped molecular tunneling junction by injection of plasmon induced hot electrons

• Kai Braun,
• Xiao Wang,
• Andreas M. Kern,
• Hilmar Adler,
• Heiko Peisert,
• Thomas Chassé,
• Dai Zhang and
• Alfred J. Meixner

Beilstein J. Nanotechnol. 2015, 6, 1100–1106, doi:10.3762/bjnano.6.111

• emission intensity depends non-linearly on the optical pump power. The enhanced emission can be modelled by rate equations taking into account hole injection from the tip (anode) into the highest occupied orbital of the closest substrate-bound molecule (lower level) and radiative recombination with an

Artificial sunlight and ultraviolet light induced photo-epoxidation of propylene over V-Ti/MCM-41 photocatalyst

• Van-Huy Nguyen,
• Shawn D. Lin,
• Jeffrey Chi-Sheng Wu and
• Hsunling Bai

Beilstein J. Nanotechnol. 2014, 5, 566–576, doi:10.3762/bjnano.5.67

• in Equation 4 and Equation 5. These rates are lower but the PO selectivity is higher than that of using mercury arc lamp. The different dependency on NLU in these rate equations of PO formation and C3H6 consumption between UV and UV–visible/artificial sunlight may be due to the difference in light

Probing the plasmonic near-field by one- and two-photon excited surface enhanced Raman scattering

• Katrin Kneipp and
• Harald Kneipp

Beilstein J. Nanotechnol. 2013, 4, 834–842, doi:10.3762/bjnano.4.94

• is in contrast to the relatively weakly enhanced local fields for isolated silver particles that were used in Figure 2a and Figure 2b. Figure 3 displays the energy level diagram for non-resonant and resonant Stokes and anti-Stokes Raman scattering along with rate equations that describe the

• Chemical Society. Non-resonant (left) and resonant (right) Stokes and anti-Stokes Raman scattering in an energy level diagram. The rate equations describe the population of the first excited vibrational level. N1 and N0 are the numbers of molecules in the excited and ground vibrational state, respectively

Focused electron beam induced deposition: A perspective

• Michael Huth,
• Fabrizio Porrati,
• Christian Schwalb,
• Marcel Winhold,
• Roland Sachser,
• Maja Dukic,
• Jonathan Adams and
• Georg Fantner

Beilstein J. Nanotechnol. 2012, 3, 597–619, doi:10.3762/bjnano.3.70

• independently controlled, is analyzed within a continuum model of FEBID that employs rate equations. Predictions are made for the tunability of the composition of the Co–Pt system by simply changing the dwell time of the electron beam during the writing process. The charge-transport regimes of nanogranular

• discussed with a prospect of directly writing a wider range of magnetic or superconducting structures on the nanometer scale. After a very brief discourse of the FEBID process presented in the next section, the modeling of FEBID on the basis of rate equations is discussed with a view to more than one

• typical hydrocarbon contaminant from the residual gas [26]. For two precursors the rate equations read which we consider in the following in a simplified form without the diffusion term and taking again f(r = 0) = f as electron flux at the beam center This system of coupled equations can be analytically

Formation of SiC nanoparticles in an atmospheric microwave plasma

• Martin Vennekamp,
• Ingolf Bauer,
• Matthias Groh,
• Evgeni Sperling,
• Susanne Ueberlein,
• Maksym Myndyk,
• Gerrit Mäder and
• Stefan Kaskel

Beilstein J. Nanotechnol. 2011, 2, 665–673, doi:10.3762/bjnano.2.71

• sizes ranging from 7 nm to about 20 nm according to BET and XRD measurements are produced. The dependency of the particle size on the process parameters is evaluated statistically and explained with growth-rate equations derived from the theory of Ostwald ripening. The results show that the particle

Charge transfer through single molecule contacts: How reliable are rate descriptions?

• Denis Kast,
• L. Kecke and
• J. Ankerhold

Beilstein J. Nanotechnol. 2011, 2, 416–426, doi:10.3762/bjnano.2.47

• ; molecular contacts; nonequilibrium distributions; numerical simulations; rate equations; Introduction Electrical devices on the nanoscale have received substantial interest in the last decade [1]. Impressive progress has been achieved in contacting single molecules or molecular aggregates with conducting

• powerful of which are nonequilibrium Green’s functions [14][15]. However, conceptually simpler, easier to implement, and often better at revealing the physics, are treatments in terms of master or rate equations. Being approximations to the NEGF frame in certain ranges of parameters space, they sometimes