Theoretical study of the depletion-layer capacitance in abrupt p–n semiconductor junctions

The impedance associated with recombination of free electrons and free holes in the space charge layer has been calculated. It has been shown that this impedance corresponds to a parallel-equivalent circuit of a capacitance and a resistance in parallel with the space charge layer capacitance. It has been calculated that the recombination capacitance has almost the same voltage dependence as the space charge layer capacitance, and that the recombination resistance is inversely proportional to the recombination rate in the space charge layer. The impedance associated with recombination in the space charge layer has been compared with the surface recombination impedance and with experimental results obtained at illuminated GaAs electrodes.

The five longest tune-out wavelengths for the rubidium atom are predicted from existing experimental and theoretical information by using an approximation formula. The formula is derived from the analysis of a non-relativistic configuration-interaction plus core polarization (CICP) calculation of the tune-out wavelengths for rubidium. The differences between the wavelengths predicted from the approximation formula and the exact CICP calculation are at the 10−3 nm level. The predicted five longest tune-out wavelengths are 790.115 nm, 423.155 nm, 421.111 nm, 359.429 nm, and 359.022 nm, respectively.

Molecular energy calculations employing actual and approximate multicenter angular dependent integral evaluations are compared. Individual integral values for three-center integrals used in calculations for the triangular H3+ ion as computed by exact methods and by the approximate formulas of Mulliken and of Rudenberg are given. The results indicate that angular and distance relations of the nuclear skeleton of this polyatomic ion are determinable at almost the identical ``best'' value found using the much more laborious exact integral calculations. The energies of the approximate evaluations, however, indicate that once these ``best'' parametric values are determined the more exact calculations must be used. The approximate evaluations of second angular derivatives of integrals that are dependent on the angular and distance relations of component molecular nuclei are also computed and compared. Use of such derivatives in determination of approximate zero point energies, vibrational frequencies, and force constants is indicated.

Utilizing 3D circuits may reduce components cost significantly. An essential configuration to consider is the embedded transmission line (ETL), an offset stripline with two dielectrics. There is no closed-form solution for the effective dielectric constant. This paper provides an accurate (1% maximum error) approximate formula, and compares it with full wave simulations.

Junctions formed at semiconductor interfaces generate space–charge regions. This can result in diode behavior, a prerequisite for efficient electronic charge separation and photoconversion. Space–charge regions also form at ion-exchange-membrane interfaces, which we are leveraging to demonstrate protonic charge separation from our new light-driven proton-pump platform.Recently, we discovered that an ion-exchange membrane can be diffusion doped to form covalent bonds with dopants of opposite charge to that of the native backbone, thus converting it into a monolithic bipolar membrane. We confirmed this modification using our newly developed membrane-electric-potential sensing procedure. These results are important because diffusion doping is the state-of-the-art means to generate an abrupt buried junction in semiconductors, resulting in high-quality diodes and efficient charge separation. By fabricating our buried-junction bipolar membranes into membrane–electrode assemblies, analogous to fuel cells but instead driving reversible H2 redox, we were able to measure their electrochemical properties. Results suggest that these junctions are more abrupt than those formed by drop-casting or hot-pressing bipolar membranes. Mott–Schottky analysis of potential-dependent capacitance data provides additional insight into junction properties, including potential of zero net charge, electroactive dopant density, and permittivity.Collectively, our discoveries form the foundational framework for new devices and functions that benefit from purely protonic transport and reactivity, such as direct oceanic capture of CO2 from HCO3 –. We are hopeful that they motivate researchers to help us expand our platform to protonic versions of other condensed matter physics phenomena, such as 2D gases, spintronic devices, topological insulators, and chiral semiconductors.

The characteristic equations for bilateral, unilateral and antipodal fin lines are formulated in a convenient form for an approximate evaluation. It is shown that the eigenvalues for all higher-order modes can be calculated from closed-form expressions provided that the two lowest eigenvalues are known. Dispersion relations are developed which are equivalent to those for rectangular waveguides. The analysis also comprehends a simple evaluation of the field configurations of all hybrid eigenmodes. The approximate formulas are checked against exact numerical calculations, the agreement being excellent.

The characteristic equations for bilateral, unilateral and antipodal fin lines are formulated in a convenient form for an approximate evaluation. It is shown that the eigenvalues for all higher-order modes can be calculated from closed-form expressions provided that the two lowest eigenvalues are known. Dispersion relations are developed which are equivalent to those for rectangular waveguides. The analysis also comprehends a simple evaluation of the field configurations of all hybrid eigenmodes. The approximate formulas are checked against exact numerical calculations, the agreement being excellent.

Постановка задачi. З розвитком технологiй радiозв’язку, особливо, мобiльного, усе бiльш важливу
\nроль вiдiграє розробка моделей радiоканалiв. У данiй
\nстаттi розглядається одна з популярних нинi моделей,
\nа саме, двопроменевий радiоканал з розсiюванням потужностi сигналу, яку в лiтературi прийнято позначати
\nабревiатурою TWDP (вiд Two-Wave with Diffuse Power).
\nДля цiєї моделi вiдомi як точнi, так i наближенi вирази
\nдля густини розподiлу iмовiрностей (ГРI) i кумулятивної функцiї розподiлу (КФР) обвiдної сигналу. Однак,
\nзагальним їх недолiком є висока складнiсть з точки зору практичного застосування. У зв’язку iз цим у данiй
\nроботi розглядається можливiсть значно бiльш простої
\nапроксимацiї ГРI та КФР обвiдної сигналу на основi
\nметоду Накагами.
\nРозробка методу. Апроксимацiя розподiлiв по методу Накагами зводиться до обчислення другого та
\nчетвертого початкових моментiв обвiдної сигналу на
\nвиходi каналу. Такi обчислення й виконанi в роботi,
\nщо дозволяє представити зазначенi моменти у виглядi
\nфункцiй вiд двох загальноприйнятих параметрiв каналу
\nTWDP: К-фактора та параметра Д, який визначається
\nспiввiдношенням амплiтуд радiо променiв.
\nАналiз похибок апроксимацiї. Похибки оцiнювалися шляхом зiставлення розрахункiв ГРI i КФР за
\nточними формулами та розрахункiв iз використанням
\nапроксимацiї Накагами. Паралельно також проводилися розрахунки вiдповiдно до формул апроксимацiї, що
\nвiдомi у лiтературi. Аналiз показав, що похибка методу
\nНакагами при обчисленнi КФР є цiлком задовiльною
\nдля практичних потреб майже у всьому дiапазонi змiн
\nпараметрiв каналу. У той же час точнiсть апроксимацiї
\nГРI у порiвняннi з iншими вiдомими методами апроксимацiї виявилася не дуже задовiльна.
\nВисновки. Проведенi дослiдження пiдтвердили можливiсть апроксимацiї КФР обвiдної сигналу в каналi TWDP розподiлом Накагами. Результати такої ж
\nапроксимацiї для ГРI виявилися менш задовiльними.
\nТакож вiдзначається кориснiсть отриманих результатiв
\nдля трактування даних натурних експериментiв.

We study a two-dimensional electron gas in a perpendicular magnetic field in the presence of both Rashba and Dresselhaus spin-orbit interactions. Using a Bogoliubov transformation we are able to write an approximate formula for the Landau levels, thanks to the simpler form of the resulting Hamiltonian. The exact numerical calculation of the energy levels, is also made simpler by our formulation. The approximate formula and the exact numerical results show excellent agreement for typical semiconductors, especially at high magnetic fields. We also show how effective Zeeman coupling is modified by spin-orbit interactions.

An advantageous variant of the Ozawa-Flynn-Wall analysis

Consider $n$ boxes, each box having an associated probability, $p_i, \big(\sigma_i p_i = 1\big)$, and an associated integer, $k_i$. If balls are thrown one by one into these boxes, the probability being $p_i$ that any one ball falls into the $i$th box, then the number of balls which must be thrown in order to obtain, for the first time, at least $k_{i_1}$ balls in the $i_1$th box, at least $k_{i_2}$ balls in the $i_2$th box, $\cdots$, and at least $k_{i_s}$ balls in the $i_s$th box, is a random variable, $N_s\lbrack k_1(p_1), k_2(p_2), \cdots, k_n(p_n)\rbrack$. Here $i_1, i_2, \cdots, i_s$ represent the numbers of that set of $s$ boxes, $(1 \leq s \leq n)$, which first satisfies the stated condition. The distribution of $N_s\lbrack k_1(p_1), k_2(p_2), \cdots, k_n(p_n)\rbrack$ can be written down for any set of values assigned to $n, s$, the $p_i$'s and the $k_i$'s. However, for $n$ greater than 2 the distribution assumes such an extremely complicated multinomial form that except for certain special cases even the mean of the distribution cannot be numerically evaluated without a prohibitive amount of labor. This paper presents the exact moments of $N_1\lbrack k_1(p_1), k_2(p_2)\rbrack$ and $N_2\lbrack k_1(p_1), k_2(p_2)\rbrack$ in forms that readily lend themselves to computation and shows how these moments can be used to obtain approximate values for the mean and variance for certain situations where $n$ is greater than two. These approximation formulae are given for 1. The mean and variance, for any $n$ and any set of $k_i$'s and $p_i$'s when $s = 1$ or $n$. 2. The mean, for any $n$ and $2 \leq s \leq n - 1$, when $p_i = 1/n, k_i = k, (i = 1, 2, \cdots, n)$. Some indications are given concerning the error of the approximations, and the circumstances which lead to a minimum (and maximum) error. Curves have been prepared to show the mean for the two box case, the primary function of these curves being to assist in the application of the approximation formulae. Some problems where the results of this paper might be applicable are suggested in the Introduction.

In the design of radio frequency (RF) microelectronic integrated circuits (IC’s) and of antennas for short-wave radio frequency identification (RFID) and telemetry systems, planar spiral coils are important components. Many approximate analytical formulae for calculating the inductance of such coils can be found in the literature. They can simplify the problem of designing inductors to a predefined inductance considerably. But the error statistics given by different authors cannot be compared because they are based on different or unknown domains of definition. Hence, it is not possible to decide which formula is best in a given case by merely studying the literature. This paper compares the maximum relative errors of six of some of the most cited formulae in the literature. To all formulae, the same domains of definition are applied. Each of them spans all four dimensions of the parameter space. Precise inductances are obtained numerically with the help of the free scientific and industrial standard software FastHenry2 and used as reference values to calculate the errors of the formulae. It has been found that the alleged maximum errors reported by some authors are far too optimistic. Only two formulae feature small enough errors to be useful in circuit design. The method and the domains of definition applied in the present study may also prove useful for the assessment of future formulae.

In this investigation, the nonplanar (spherical and cylindrical) modified fifth-order Korteweg–de Vries (nmKdV5) equation, otherwise known as the nonplanar modified Kawahara equation (nmKE), is solved using the ansatz approach. Two general formulas for the semi-analytical symmetric approximations are derived using the recommended methodology. Using the obtained approximations, the nonplanar modified Kawahara (mK) symmetric solitary waves (SWs) and cnoidal waves (CWs) are obtained. The fluid equations for the electronegative plasmas are reduced to the nmKE as a practical application for the obtained solutions. Using the obtained solutions, the characteristic features of both the cylindrical and spherical mK-SWs and -CWs are studied. All obtained solutions are compared with each other, and the maximum residual errors for these approximations are estimated. Numerous researchers that are interested in studying the complicated nonlinear phenomena in plasma physics can use the obtained approximations to interpret their experimental and observational findings.

Photoelectrochemical characterization of electrodeposited polyaniline

In this work we use Secondary Ion Mass Spectrometry (SIMS), Spreading Resistance Analysis (SRA), Stripping Hall (SH) and Electrochemical Capacitance Voltage (ECV) measurements to analyse different phosphorus-diffused emitters. Such data permit the detailed characterisation of the emitter and facilitate an optimisation of the diffusion process. The measurement techniques provide depth resolved information about the phosphorus concentration and the conductivity as well as the electron concentration and mobility. We include an overview of the different measurement techniques. A comparison of the obtained profiles confirms the presence of electrically inactive phosphorus and demonstrates differences in the surface concentration and the p-n-junction depth, which can be mainly attributed to measurement artefacts. However, a good agreement of all techniques is found.