CMT 13 P Computer simulation of charge transport in planar P-N junctions
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KLYUKANOV, Alexandr, GASHIN, Peter A., SCURTU, Roman. CMT 13 P Computer simulation of charge transport in planar P-N junctions. In: Materials Science and Condensed Matter Physics, 13-17 septembrie 2010, Chișinău. Chișinău, Republica Moldova: Institutul de Fizică Aplicată, 2010, Editia 5, p. 64.
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Materials Science and Condensed Matter Physics
Editia 5, 2010
Conferința "Materials Science and Condensed Matter Physics"
Chișinău, Moldova, 13-17 septembrie 2010

CMT 13 P Computer simulation of charge transport in planar P-N junctions


Pag. 64-64

Klyukanov Alexandr, Gashin Peter A., Scurtu Roman
 
Moldova State University
 
 
Disponibil în IBN: 14 aprilie 2021


Rezumat

Shockley equation describes the current density in the so-called “ideal “ p-n junctions. To agree a theory and actual experiment it is customary sufficient to use the approximative expression. formula where n is the ideality factor laid in the range 1 to 2. To derive the Eq.(1) theoretically one has to use a number of simplifying assumptions. Nevertheless approximation (1) does not cover the experimental variety of I-V characteristics of the solar cells. Hence dependence of I-V characteristics on the impurities concentration, resistivity, carrier’s lifetime and layer’s thickness is actual problem still now. Experimental determination of optimum parameters of p-n junction requires the fabrication of lots of samples and a number of I-V characteristics measurements. A preliminary computer simulation could simplify and reduce the cost of it. The following scheme of the computer experiment may be offered for the numerical solution. The equations for hole jp (x) and electron jn (x) density currents with account of drift and diffusion of the carriers can be studied as a first-order non-homogeneous linear differential equations regarding to the unknown concentrations of electron n(x) and hole p(x) , which exact formal solution have the form: formula Upper sign “+” is refers to the electron density n(x), the lower “-” -to the hole p(x). Electrostatic potential j(x) is determined by the distribution of impurities, electrons and holes according to the Poisson equation. formula Here formula  is the electric field intensity, ND , NA -impurity concentrations. The value of the E(0)can be determined from the boundary conditionformula, whereV is the applied voltage,Vbi is the built-in potential. To close the system of equations, current densities jn (x) and jp (x) have to be expressed in terms of carrier concentrations n(x) and p(x) . In accordance with the Shockley-Read-Hall theory we have formula Equations obtained (2-4) constitute a self-consistent set of charge transport equations, which can be resolved by successive iterations up to the complete self-consistency. To start the computer simulation process it is necessary to get initial functions n0 (x) and p0 (x) in zero approximation (it can be classical Shockley solution). Using functions n0 (x) , p0 (x) and defining electrostatic potential j0 (x) (3), generation – recombination rate U0 (x) (4) and density currents, jn0 (x) , j p0 (x) (4), we obtain new functions n1 (x) and p1 (x) evaluated in first approximation from the equations(2). In its turn functions n1 (x) and p1 (x) define newj1 (x) , U1 (x) and jn1, p1 (x) . If this process converges, then it can be continued up to a complete self-consistency, until electrostatic potentialj(x) , rate U(x) and density currents jn, p (x) , which appears in equations (2) will lead to the same carrier’s distribution n(x) and p(x) by whomj(x) , U(x) and jn, p (x) were calculated. Thus successive process of iterations should be continued to get the required accuracy of calculation.