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Journal articles on the topic 'Semiconductor equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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1

Buot, F. A. "Generalized Semiconductor Bloch Equations." Journal of Computational and Theoretical Nanoscience 1, no. 2 (September 1, 2004): 144–68. http://dx.doi.org/10.1166/jctn.2004.012.

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2

Pospíšek, Miroslav. "Nonlinear boundary value problems with application to semiconductor device equations." Applications of Mathematics 39, no. 4 (1994): 241–58. http://dx.doi.org/10.21136/am.1994.134255.

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3

TALANINA, I. B. "EXCITONIC SELF-INDUCED TRANSPARENCY IN SEMICONDUCTORS." Journal of Nonlinear Optical Physics & Materials 05, no. 01 (January 1996): 51–57. http://dx.doi.org/10.1142/s0218863596000064.

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The form invariant coherent pulse propagation in semiconductors excited at 1s-exciton resonance is studied analytically using the reduced semiconductor Maxwell-Bloch equations. The sech-shaped pulse solution for excitonic self-induced transparency (SIT) is presented, showing significant difference in comparison with the well known SIT solution for non-interacting two-level systems. In contrast to 2π pulses in atomic systems, the phenomenon of SIT of interacting excitons in semiconductors occurs for the pulses of area 1.07π. Possible applications of the SIT solitons in semiconductor all-optical switching devices are discussed.
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4

Dorey, A. P. "Rate Equations in Semiconductor Electronics." Electronics and Power 32, no. 9 (1986): 680. http://dx.doi.org/10.1049/ep.1986.0400.

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5

Sever, Michael, and Peter A. Markowich. "The Stationary Semiconductor Device Equations." Mathematics of Computation 49, no. 179 (July 1987): 306. http://dx.doi.org/10.2307/2008270.

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6

Markowich, P. A. "The stationary semiconductor device equations." Microelectronics Journal 26, no. 2-3 (March 1995): xxv—xxvi. http://dx.doi.org/10.1016/0026-2692(95)90018-7.

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7

Pospíšek, Miroslav. "Convergent algorithms suitable for the solution of the semiconductor device equations." Applications of Mathematics 40, no. 2 (1995): 107–30. http://dx.doi.org/10.21136/am.1995.134283.

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8

Nikonov, D. E., and G. I. Bourianoff. "Spin Gain Transistor in Ferromagnetic Semiconductors—The Semiconductor Bloch-Equations Approach." IEEE Transactions On Nanotechnology 4, no. 2 (March 2005): 206–14. http://dx.doi.org/10.1109/tnano.2004.837847.

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9

Combescot, M., O. Betbeder-Matibet, and M. N. Leuenberger. "Analytical approach to semiconductor Bloch equations." EPL (Europhysics Letters) 88, no. 5 (December 1, 2009): 57007. http://dx.doi.org/10.1209/0295-5075/88/57007.

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10

Frehse, J., and J. Naumann. "Stationary Semiconductor Equations Modeling Avalanche Generation." Journal of Mathematical Analysis and Applications 198, no. 3 (March 1996): 685–702. http://dx.doi.org/10.1006/jmaa.1996.0108.

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11

Burger, M., H. W. Engl, A. Leitao, and P. A. Markowich. "On Inverse Problems for Semiconductor Equations." Milan Journal of Mathematics 72, no. 1 (October 2004): 273–313. http://dx.doi.org/10.1007/s00032-004-0025-6.

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12

Ma, Xi Ying. "Study of the Electrical Properties of Monolayer MoS2 Semiconductor." Advanced Materials Research 651 (January 2013): 193–97. http://dx.doi.org/10.4028/www.scientific.net/amr.651.193.

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We present the study of the electrical properties of monolayer MoS2 in terms of semiconductor theory. The free electron and hole concentrations formulas in two-dimensional (2D) semiconductors have been developed based on three-dimensional (3D) semiconductors theory, and derived the intrinsic carrier concentration equation of 2D system. Using these equations, we simulated the intrinsic carrier concentration in monolayer MoS2 with temperature. The intrinsic carrier density in monolayer MoS2 increases exponentially with temperature, but it lows a few orders of magnitude than that of 3D semiconductor. It means that monolayer MoS2 based devices can operated at very high temperatures. Accordingly, the conductivity and resistivity were simulated for 2D MoS2, the former increases exponentially while the latter decreases with temperature or carrier concentration.
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13

Tonkoshkur, A. S., A. B. Glot, and A. V. Ivanchenko. "Basic models in dielectric spectroscopy of heterogeneous materials with semiconductor inclusions." Multidiscipline Modeling in Materials and Structures 13, no. 1 (June 12, 2017): 36–57. http://dx.doi.org/10.1108/mmms-08-2016-0037.

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Purpose The purpose of this paper is to develop the models of the dielectric permittivity dispersion of heterogeneous systems based on semiconductors to a level that would allow to apply effectively the method of broadband dielectric spectroscopy for the study of electronic processes in ceramic and composite materials. Design/methodology/approach The new approach for determining the complex dielectric permittivity of heterogeneous systems with semiconductor particles is used. It includes finding the analytical expression of the effective dielectric permittivity of the separate semiconductor particle of spherical shape. This approach takes into account the polarization of the free charge carriers in this particle, including capturing to localized electron states. This enabled the authors to use the known equations for complex dielectric permittivity of two-component matrix systems and statistical mixtures. Findings The presented dispersion equations establish the relationship between the parameters of the dielectric spectrum and electronic processes in the structures like semiconductor particles in a dielectric matrix in a wide frequency range. Conditions of manifestation and location of the different dispersion regions of the complex dielectric heterogeneous systems based on semiconductors in the frequency axis and their features are established. The most high-frequency dispersion region corresponds to the separation of free charge carriers at polarization. After this region in the direction of reducing of the frequency, the dispersion regions caused by recharge bulk and/or surface localized states follow. The most low-frequency dispersion region is caused by recharging electron traps in the boundary layer of the dielectric matrix. Originality/value Dielectric dispersion models are developed that are associated with: electronic processes of separation of free charge carriers in the semiconductor component, recapture of free charge carriers in the localized electronic states in bulk and on the surface of the semiconductor and also boundary layers of the dielectric at the polarization. The authors have analyzed to situations that correspond applicable and promising materials: varistor ceramics and composite structure with conductive and semiconductor fillers. The modelling results correspond to the existing level of understanding of the electron phenomena in matrix systems and statistical mixtures based on semiconductors. It allows to raise efficiency of research and control properties of heterogeneous materials by dielectric spectroscopy.
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14

Rossani, A. "Semiconductor spintronics: The full matrix approach." Modern Physics Letters B 29, no. 35n36 (December 30, 2015): 1550243. http://dx.doi.org/10.1142/s0217984915502437.

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A new model, based on an asymptotic procedure for solving the spinor kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Fermi–Dirac distribution function at the leading order. The balance equations for the electron number, energy density and momentum, plus the Poisson’s equation, constitute now a system of six equations. Moreover, two equations for the evolution of the spin densities are added, which account for a general dispersion relation.
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15

An, Dao Khac. "Important Features of Anomalous Single-Dopant Diffusion and Simultaneous Diffusion of Multi-Dopants and Point Defects in Semiconductors." Defect and Diffusion Forum 268 (November 2007): 15–36. http://dx.doi.org/10.4028/www.scientific.net/ddf.268.15.

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This paper summarizes some of the main results obtained concerning aspects of anomalous single-dopant diffusion and the simultaneous diffusion of multi-diffusion species in semiconductors. Some important explanations of theoretical/practical aspects have been investigated, such as anomalous phenomena, general diffusivity expressions, general non-linear diffusion equations, modified Arrhenius equations and lowered activation energy have been offered in the case of the anomalous fast diffusion for single-dopant diffusion process. Indeed, a single diffusion process is always a complex system involving many interacting factors; conventional diffusion theory could not be applied to its investigation. The author has also investigated a system of multi-diffusion species with mutual interactions between them. More concretely, irreversible thermodynamics theory was used to investigate the simultaneous diffusion of dopants (As, B) and point defects (V, I) in Si semiconductors. Some attempts at theory development were made, such as setting up a system of general diffusion equations for the simultaneous diffusion of multi-diffusion species involving mutual interactions between them, such as the pair association and disassociation mechanisms which predominated during the simultaneous diffusion of dopants and point defects. The paper then gives some primary results of the numerical solution of distributions of dopants (B, As) and point defects (V, I) in Si semiconductor, using irreversible thermodynamics theory. Finally, several applications of simultaneous diffusion to semiconductor technology devices are also offered.
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16

Sieber, J., M. Radžiūnas, and K. R. Schneider. "DYNAMICS OF MULTISECTION SEMICONDUCTOR LASERS." Mathematical Modelling and Analysis 9, no. 1 (March 31, 2005): 51–66. http://dx.doi.org/10.3846/13926292.2004.9637241.

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We investigate the longitudinal dynamics of multisection semiconductor lasers based on a model, where a hyperbolic system of partial differential equations is nonlinearly coupled with a system of ordinary differential equations. We present analytic results for that system: global existence and uniqueness of the initial‐boundary value problem, and existence of attracting invariant manifolds of low dimension. The flow on these manifolds is approximately described by the so‐called mode approximations which are systems of ordinary differential equations. Finally, we present a detailed numerical bifurcation analysis of the two-mode approximation system and compare it with the simulated dynamics of the full PDE model.
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17

Hojatkashani, Leila. "Theoretical Investigation of Application of Combining Pristine C60 and doped C60 with Silicon and Germanium atoms for Solar cells ; A DFT Study." Oriental Journal of Chemistry 35, no. 1 (February 21, 2019): 255–63. http://dx.doi.org/10.13005/ojc/350130.

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Solar energy and its conversion to electricity is an important research in the last decade. Solar cells are consist of a p-type semiconductor as donor and an n-type semiconductor as acceptor. Organic polymers as organic semiconductors are used in an organic solar cell. This research is a theoretical investigation of fullerene C60 as donor and C60 doped derivatives with Silicon and Germanium atoms as acceptors for basic structure of a solar cell. This research is done not only with using related equations but also with investigating theoretical UV-VIS spectrum of the chosen donors-acceptors and their absorption wavelengths, oscillator strength and maximum coefficient absorptions of these solar cells.
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18

Wu, Xiaoqin, and Xiangsheng Xu. "Degenerate semiconductor device equations with temperature effect." Nonlinear Analysis: Theory, Methods & Applications 65, no. 2 (July 2006): 321–37. http://dx.doi.org/10.1016/j.na.2005.06.006.

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19

Meza, Juan C., and Ray S. Tuminaro. "A Multigrid Preconditioner for the Semiconductor Equations." SIAM Journal on Scientific Computing 17, no. 1 (January 1996): 118–32. http://dx.doi.org/10.1137/0917010.

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20

Nizette, Michel, Thomas Erneux, Athanasios Gavrielides, and Vassilios Kovanis. "Averaged equations for injection locked semiconductor lasers." Physica D: Nonlinear Phenomena 161, no. 3-4 (January 2002): 220–36. http://dx.doi.org/10.1016/s0167-2789(01)00375-x.

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21

Hosseini, Seyed Ebrahim, and Rahim Faez. "Novel Quantum Hydrodynamic Equations for Semiconductor Devices." Japanese Journal of Applied Physics 41, Part 1, No. 3A (March 15, 2002): 1300–1304. http://dx.doi.org/10.1143/jjap.41.1300.

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22

Xia, G., Z. Wu, J. Chen, and Y. Lu. "Studying semiconductor lasers with multimode rate equations." Applied Optics 34, no. 9 (March 20, 1995): 1523. http://dx.doi.org/10.1364/ao.34.001523.

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23

Parrott, J. E. "Book review: Rate Equations in Semiconductor Electronics." IEE Proceedings I Solid State and Electron Devices 134, no. 6 (1987): 176. http://dx.doi.org/10.1049/ip-i-1.1987.0037.

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24

SZMOLYAN, Peter. "ASYMPTOTIC METHODS FOR TRANSIENT SEMICONDUCTOR DEVICE EQUATIONS." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 8, no. 2 (February 1989): 113–22. http://dx.doi.org/10.1108/eb010053.

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25

Northrop, D. C. "Book Review: Rate Equations in Semiconductor Electronics." International Journal of Electrical Engineering & Education 23, no. 4 (October 1986): 365. http://dx.doi.org/10.1177/002072098602300413.

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26

White, C. E. "Book Review: Rate Equations in Semiconductor Electronics." International Journal of Electrical Engineering Education 28, no. 1 (January 1991): 94–95. http://dx.doi.org/10.1177/002072099102800122.

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27

Pfleiderer, Hans. "Stepwise continuous solution of the semiconductor equations." Solid-State Electronics 38, no. 5 (May 1995): 1089–95. http://dx.doi.org/10.1016/0038-1101(95)98679-w.

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28

Maldon, B., and N. Thamwattana. "A Fractional Diffusion Model for Dye-Sensitized Solar Cells." Molecules 25, no. 13 (June 28, 2020): 2966. http://dx.doi.org/10.3390/molecules25132966.

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Dye-sensitized solar cells have continued to receive much attention since their introduction by O’Regan and Grätzel in 1991. Modelling charge transfer during the sensitization process is one of several active research areas for the development of dye-sensitized solar cells in order to control and improve their performance and efficiency. Mathematical models for transport of electron density inside nanoporous semiconductors based on diffusion equations have been shown to give good agreement with results observed experimentally. However, the process of charge transfer in dye-sensitized solar cells is complicated and many issues are in need of further investigation, such as the effect of the porous structure of the semiconductor and the recombination of electrons at the interfaces between the semiconductor and electrolyte couple. This paper proposes a new model for electron transport inside the conduction band of a dye-sensitized solar cell comprising of TiO 2 as its nanoporous semiconductor. This model is based on fractional diffusion equations, taking into consideration the random walk network of TiO 2 . Finally, the paper presents numerical solutions of the fractional diffusion model to demonstrate the effect of the fractal geometry of TiO 2 on the fundamental performance parameters of dye-sensitized solar cells, such as the short-circuit current density, open-circuit voltage and efficiency.
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29

Chaw, Chaw Su Nandar Hlaing, and Thiri Nwe. "Analysis on Band Layer Design and J-V characteristics of Zinc Oxide Based Junction Field Effect Transistor." Journal La Multiapp 1, no. 2 (June 21, 2020): 14–21. http://dx.doi.org/10.37899/journallamultiapp.v1i2.108.

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This paper presents the band gap design and J-V characteristic curve of Zinc Oxide (ZnO) based on Junction Field Effect Transistor (JFET). The physical properties for analysis of semiconductor field effect transistor play a vital role in semiconductor measurements to obtain the high-performance devices. The main objective of this research is to design and analyse the band diagram design of semiconductor materials which are used for high performance junction field effect transistor. In this paper, the fundamental theory of semiconductors, the electrical properties analysis and bandgap design of materials for junction field effect transistor are described. Firstly, the energy bandgaps are performed based on the existing mathematical equations and the required parameters depending on the specified semiconductor material. Secondly, the J-V characteristic curves of semiconductor material are discussed in this paper. In order to achieve the current-voltage characteristic for specific junction field effect transistor, numerical values of each parameter which are included in analysis are defined and then these resultant values are predicted for the performance of junction field effect transistors. The computerized analyses have also mentioned in this paper.
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30

Abd-alla, Abo-el-nour N., N. F. Hasbullah, and Hala M. Hossen. "The Frequency Equations for Shear Horizontal Waves in Semiconductor/Piezoelectric Structures Under the Influence of Initial Stress." Journal of Computational and Theoretical Nanoscience 13, no. 10 (October 1, 2016): 6475–81. http://dx.doi.org/10.1166/jctn.2016.5589.

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In this paper, we investigated analytically the frequency equations for shear horizontal wave propagation in a piezoelectric half space covered by a semiconductor film with initial stress effect. The semiconducting layer is influenced by initial stress and the interface between the piezoelectric substrate and the semiconductor layer. The governing equations of the mechanical displacement and electrical potential function under the effect of initial stress are obtained by solving the coupled electromechanical field equations of the piezoelectric half-space and the semiconductor film. Next, the numerical examples are presented to illustrate the influence of initial stress and electromagnetic boundary conditions for the different values of the film thickness and wave number. Furthermore, we studied in more details the effect of initial stress on the frequency equation for piezoelectric Barium Titanate (BaTiO3) and semiconductor silicon. The obtained results provide a predictable and theoretical basis for applications of piezoelectric and semiconductor composites to acoustic wave devices.
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31

SHAN, YUEH. "GENERALIZED SPHEROIDAL WAVE EQUATIONS FOR IMPURITY STATES IN A HETEROSTRUCTURE." Modern Physics Letters B 04, no. 17 (September 20, 1990): 1099–102. http://dx.doi.org/10.1142/s0217984990001380.

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Within the framework of effective mass theory, a set of generalized spheroidal wave equations for the exact treatment of a shallow donor impurity in a semiconductor-semiconductor heterostructure is obtained from the relevant Schrödinger equation by the method of separation of variables in prolate spheroidal coordinates. The way of calculating the eigensolutions of these wave equations is briefly discussed.
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32

Erofeev, Vladimir I., Anna V. Leonteva, Alexey O. Malkhanov, and Ashot V. Shekoyan. "Localized nonlinear waves in a semiconductor with charged dislocations." EPJ Web of Conferences 250 (2021): 03012. http://dx.doi.org/10.1051/epjconf/202125003012.

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To describe a nonlinear ultrasonic wave in a semiconductor with charged dislocations, an evolution equation is obtained that generalizes the well-known equations of wave dynamics: Burgers and Korteweg de Vries. By the method of truncated decompositions, an exact analytical solution of the evolution equation with a kink profile has been found. The kind of kink (increasing, decreasing) and its polarity depend on the values of the parameters and their signs. An ultrasonic wave in a semiconductor containing numerous charged dislocations is considered. It is assumed that there is a constant electric field that creates an electric current. The situation is similar to the case of the propagation of ultrasonic waves in piezoelectric semiconductors, but in the problem under consideration, instead of the electric field due to the piezoelectric properties of the medium, the electric field of dislocations appears.
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33

Wilkey, Andrew, Joseph Suelzer, Yogesh Joglekar, and Gautam Vemuri. "Parity–Time Symmetry in Bidirectionally Coupled Semiconductor Lasers." Photonics 6, no. 4 (November 27, 2019): 122. http://dx.doi.org/10.3390/photonics6040122.

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We report on the numerical analysis of intensity dynamics of a pair of mutually coupled, single-mode semiconductor lasers that are operated in a configuration that leads to features reminiscent of parity–time symmetry. Starting from the rate equations for the intracavity electric fields of the two lasers and the rate equations for carrier inversions, we show how these equations reduce to a simple 2 × 2 effective Hamiltonian that is identical to that of a typical parity–time (PT)-symmetric dimer. After establishing that a pair of coupled semiconductor lasers could be PT-symmetric, we solve the full set of rate equations and show that despite complicating factors like gain saturation and nonlinearities, the rate equation model predicts intensity dynamics that are akin to those in a PT-symmetric system. The article describes some of the advantages of using semiconductor lasers to realize a PT-symmetric system and concludes with some possible directions for future work on this system.
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34

Zhou, Jing-Rong, and David K. Ferry. "2-D Simulation of Quantum Effects in Small Semiconductor Devices Using Quantum Hydrodynamic Equations." VLSI Design 3, no. 2 (January 1, 1995): 159–77. http://dx.doi.org/10.1155/1995/93452.

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We discuss the basis of a set of quantum hydrodynamic equations and the use of this set of equations in the two-dimensional simulation of quantum effects in deep submicron semiconductor devices. The equations are obtained from the Wigner function equation-of-motion. Explicit quantum correction is built into these equations by using the quantum mechanical expression of the moments of the Wigner function, and its physical implication is clearly explained. These equations are then applied to numerical simulation of various small semiconductor devices, which demonstrate expected quantum effects, such as barrier penetration and repulsion. These effects modify the electron density distribution and current density distribution, and consequently cause a change of the total current flow by 10-15 per cent for the simulated HEMT devices. Our work suggests that the inclusion of quantum effects into the simulation of deep submicron and ultra-submicron semiconductor devices is necessary.
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35

BRUNK, MARKUS, and ANSGAR JÜNGEL. "SIMULATION OF THERMAL EFFECTS IN OPTOELECTRONIC DEVICES USING COUPLED ENERGY-TRANSPORT AND CIRCUIT MODELS." Mathematical Models and Methods in Applied Sciences 18, no. 12 (December 2008): 2125–50. http://dx.doi.org/10.1142/s0218202508003315.

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A coupled model with optoelectronic semiconductor devices in electric circuits is proposed. The circuit is modeled by differential-algebraic equations derived from modified nodal analysis. The transport of charge carriers in the semiconductor devices (laser diode and photo diode) is described by the energy-transport equations for the electron density and temperature, the drift-diffusion equations for the hole density, and the Poisson equation for the electric potential. The generation of photons in the laser diode is modeled by spontaneous and stimulated recombination terms appearing in the transport equations. The devices are coupled to the circuit by the semiconductor current entering the circuit and by the applied voltage at the device contacts, coming from the circuit. The resulting time-dependent model is a system of nonlinear partial differential-algebraic equations. The one-dimensional transient transport equations are numerically discretized in time by the backward Euler method and in space by a hybridized mixed finite-element method. Numerical results for a circuit consisting of a single-mode heterostructure laser diode, a silicon photo diode, and a high-pass filter are presented.
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36

Levermore, C. David. "Moment Closure Hierarchies for the Boltzmann-Poisson Equation." VLSI Design 6, no. 1-4 (January 1, 1998): 97–101. http://dx.doi.org/10.1155/1998/39370.

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We outline a systematic nonperturbative derivation of a hierarchy of closed systems of moment equations that can be applied to any kinetic description of electrons in a semiconductor. This entropy based closure procedure extends one that was introduced in the context of gas dynamics. In the context of semiconductors, this procedure yields generalizations of socalled hydrodynamic models. It is illustrated on the semiclassical Boltzmann-Poisson equation for a single conduction band in the parabolic band approximation.
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37

Zhao, Peiji, and H. L. Cui. "Quantum transport equations for two-band semiconductor systems." Physics Letters A 252, no. 5 (March 1999): 243–47. http://dx.doi.org/10.1016/s0375-9601(98)00954-2.

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38

Guo, Xiulan, and Kaitai Li. "ASYMPTOTIC BEHAVIOR OF THE DRIFT-DIFFUSION SEMICONDUCTOR EQUATIONS." Acta Mathematica Scientia 24, no. 3 (July 2004): 385–94. http://dx.doi.org/10.1016/s0252-9602(17)30162-5.

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39

Glutsch, S., and D. S. Chemla. "Semiconductor Bloch equations in a homogeneous magnetic field." Physical Review B 52, no. 11 (September 15, 1995): 8317–22. http://dx.doi.org/10.1103/physrevb.52.8317.

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40

Royo, P., R. Koda, and L. A. Coldren. "Rate equations of vertical-cavity semiconductor optical amplifiers." Applied Physics Letters 80, no. 17 (April 29, 2002): 3057–59. http://dx.doi.org/10.1063/1.1476056.

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41

Bonitz, M., J. W. Dufty, and Cheng Sub Kim. "BBGKY Approach to Non-Markovian Semiconductor Bloch Equations." physica status solidi (b) 206, no. 1 (March 1998): 181–87. http://dx.doi.org/10.1002/(sici)1521-3951(199803)206:1<181::aid-pssb181>3.0.co;2-0.

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42

Shen, Wen-Zhong, and Zhen-Ya Li. "General dispersion equations for diluted magnetic semiconductor superlattices." physica status solidi (b) 174, no. 1 (November 1, 1992): 241–45. http://dx.doi.org/10.1002/pssb.2221740124.

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43

Markowich, P. A., and Ch A. Ringhofer. "Stability of the Linearized Transient Semiconductor Device Equations." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 67, no. 7 (1987): 319–32. http://dx.doi.org/10.1002/zamm.19870670710.

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44

Fang, W. F., and K. Ito. "Asymptotic Behavior of the Drift-Diffusion Semiconductor Equations." Journal of Differential Equations 123, no. 2 (December 1995): 567–87. http://dx.doi.org/10.1006/jdeq.1995.1173.

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45

Pimbley, Joseph M. "The Stationary Semiconductor Device Equations. (Peter A. Markowich)." SIAM Review 29, no. 4 (December 1987): 671–73. http://dx.doi.org/10.1137/1029145.

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46

Kerkhoven, Thomas. "On the One-Dimensional Current Driven Semiconductor Equations." SIAM Journal on Applied Mathematics 51, no. 3 (June 1991): 748–74. http://dx.doi.org/10.1137/0151038.

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47

Vänskä, O., J. Nieminen, M. Kira, S. W. Koch, and I. Tittonen. "Structure-independent semiconductor luminescence equations for quantum rings." Physica Scripta T160 (April 1, 2014): 014044. http://dx.doi.org/10.1088/0031-8949/2014/t160/014044.

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48

Efrat, Ilan, and Moshe Israeli. "A HYBRID SOLUTION OF THE SEMICONDUCTOR DEVICE EQUATIONS." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 10, no. 4 (April 1991): 215–29. http://dx.doi.org/10.1108/eb051700.

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49

Bjork, G., and Y. Yamamoto. "Analysis of semiconductor microcavity lasers using rate equations." IEEE Journal of Quantum Electronics 27, no. 11 (1991): 2386–96. http://dx.doi.org/10.1109/3.100877.

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50

Hui Rong-Qing and Tao Shang-Ping. "Improved rate equations for external cavity semiconductor lasers." IEEE Journal of Quantum Electronics 25, no. 6 (June 1989): 1580–84. http://dx.doi.org/10.1109/3.29296.

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