Numerical Solution for the Forward Steady-State Behaviour of an Abrupt p+-n Junction

1968 ◽  
Vol 23 (8) ◽  
pp. 1135-1146
Author(s):  
M. Sánchez

The forward steady-state behaviour of a one-dimensional abrupt p+-n junction germanium diode at zero and at low to high injection levels is analysed. For this purpose the numerical integration of the current differential equations, the continuity equations, and Poisson’s differential equation is performed not only inside the space-charge layer but also along the quasineutral regions of the diode satisfying the boundary and continuity conditions. The integration is made on a digital computer without applying the Boltzmann equilibrium approximation in the space-charge layer and the space-charge neutrality approximation in the quasineutral regions. Furthermore, the acoustical and optical mode scattering, the ionized impurity scattering, and the Hall-Shockley-Read and Auger recombination processes are included in the calculation. The method of solution applied differs from those already available in the literature and permits the “exact” computation of the space-charge density inside the relatively long (compared with the Debye length) quasineutral p and n regions of the diode considered. The numerical results for the hole and electron concentration distributions, the electric field distributions, the electron current density distributions, the electrostatic potential distributions and the space-charge density distributions are reported for five values of the total current density across the p-n junction. The comparison of the obtained numerical solutions with the closed analytical solutions for zero bias (as a test of the computer program) on the one side and of the computed current/voltage characteristic of the p-n junction with experimental values on the other side shows satisfactory agreement.

2009 ◽  
Vol 471 (1-3) ◽  
pp. 174-177 ◽  
Author(s):  
S. Jenkins ◽  
P.W. Ayers ◽  
S.R. Kirk ◽  
P. Mori-Sánchez ◽  
A. Martín Pendás

Membranes ◽  
2018 ◽  
Vol 8 (3) ◽  
pp. 84 ◽  
Author(s):  
Aminat Uzdenova ◽  
Anna Kovalenko ◽  
Makhamet Urtenov ◽  
Victor Nikonenko

The use of the Nernst–Planck and Poisson (NPP) equations allows computation of the space charge density near solution/electrode or solution/ion-exchange membrane interface. This is important in modelling ion transfer, especially when taking into account electroconvective transport. The most solutions in literature use the condition setting a potential difference in the system (potentiostatic or potentiodynamic mode). However, very often in practice and experiment (such as chronopotentiometry and voltammetry), the galvanostatic/galvanodynamic mode is applied. In this study, a depleted stagnant diffusion layer adjacent to an ion-exchange membrane is considered. In this article, a new boundary condition is proposed, which sets a total current density, i, via an equation expressing the potential gradient as an explicit function of i. The numerical solution of the problem is compared with an approximate solution, which is obtained by a combination of numerical solution in one part of the diffusion layer (including the electroneutral region and the extended space charge region, zone (I) with an analytical solution in the other part (the quasi-equilibrium electric double layer (EDL), zone (II). It is shown that this approach (called the “zonal” model) allows reducing the computational complexity of the problem tens of times without significant loss of accuracy. An additional simplification is introduced by neglecting the thickness of the quasi-equilibrium EDL in comparison to the diffusion layer thickness (the “simplified” model). For the first time, the distributions of concentrations, space charge density and current density along the distance to an ion-exchange membrane surface are computed as functions of time in galvanostatic mode. The calculation of the transition time, τ, for an ion-exchange membrane agree with an experiment from literature. It is suggested that rapid changes of space charge density, and current density with time and distance, could lead to lateral electroosmotic flows delaying depletion of near-surface solution and increasing τ.


2004 ◽  
Vol 7 (1-2) ◽  
pp. 177-194 ◽  
Author(s):  
Véronique Favier ◽  
Carole Rouff ◽  
Régis Bigot ◽  
Marcel Berveiller ◽  
Marc Robellet

1988 ◽  
Vol 25 (3) ◽  
pp. 251-264
Author(s):  
A. Hughes ◽  
D. W. J. Pulle

Brushless drives are important, but are often thought to be difficult to treat quantitatively at the undergraduate level. The Blondel circle diagram is shown to be ideal for illuminating the steady-state behaviour and limitations of small brushless system, at a level suitable for undergraduate courses.


2013 ◽  
Vol 06 (04) ◽  
pp. 1330004 ◽  
Author(s):  
RÜDIGER-A. EICHEL ◽  
EMRE ERDEM ◽  
PETER JAKES ◽  
ANDREW OZAROWSKI ◽  
JOHAN VAN TOL ◽  
...  

The defect structure of ZnO nanoparticles is characterized by means of high-field electron paramagnetic resonance (EPR) spectroscopy. Different point and complex defects could be identified, located at the "bulk" or the surface region of the nanoparticles. In particular, by exploiting the enhanced g-value resolution at a Larmor frequency of 406.4 GHz, it could be shown that the resonance commonly observed at g = 1.96 is comprised of several overlapping resonances from different defects. Based on the high-field EPR analysis, the development of a space-charge layer could be monitored that consists of (shallow) donor-type [Formula: see text] defects at the "bulk" and acceptor-type [Formula: see text] and complex [Formula: see text] defects at the surface. Application of a core-shell model allows to determine the thickness of the depletion layer to 1.0 nm for the here studied compounds [J.J. Schneider et al., Chem. Mater.22, 2203 (2010)].


1974 ◽  
Vol 3 (12) ◽  
pp. 1459-1462
Author(s):  
Masahiro Kotani ◽  
Yoko Watanabe ◽  
Tomoko Kato

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