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http://hdl.handle.net/2014/41263
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| Title: | Analytical solutions and approximations for the equation ydy/dx=(ay+b) h(x) with applications to drift-diffusion. |
| Authors: | Edmonds, Larry D. |
| Keywords: | ambipolar diffusion
charge collections
charge collections
drift diffusion
funnel
sensitivity volume |
| Issue Date: | 2009 |
| Series/Report no.: | JPL Publication
09-13 |
| Abstract: | The problem considered is y(x)dy(x)/dx=(a y(x)+B)h(x) subject to a point-value condition. In principle, this problem is solvable using elementary textbook methods. In practice, two difficulties are encountered. The first difficulty is associated with existence and uniqueness of solutions. The second difficulty is that exact solutions to the differential equation are expressed as solutions to transcendental algebraic equations that require numerical root-finding algorithms. This paper avoids the first difficulty by confining attention to “uniform solutions,” defined as solutions that do not change sign. The second difficulty is avoided by finding accurate, yet simple, approximations for the exact solutions. These approximations are derived for the physical application of charge-carrier drift-diffusion in a quasi-neutral semiconductor material. Exact results are also given, showing that a sufficiently large carrier generation rate creates a sensitive volume in the quasi-neutral region. However, the sensitive volume is a symbolic model and has limited applicability. An alternate model that is a more literal description of charge-collection physics is ambipolar diffusion with a cutoff. |
| URI: | http://hdl.handle.net/2014/41263 |
| Appears in Collections: | JPL TRS 1992+
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