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Bertrand Yitembe
| Speaker: |
Bertrand Yitembe
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| Date: |
Tuesday August 7, 2007
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| Title: |
Analytical study
of the drift-diffusion problem in organic layers (Master's Thesis
Presentation)
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Abstract
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In this
master thesis, the solution of the drift-diffusion for the
semiconductors is studied. In general, when solving problems in
Space-Charge-Limited-Current (SCLC), the contribution of the diffusion
current D is often assumed to be negligible.
The present work focuses on the role of the diffusion term at low and
high current densities. This role is studied both analytically and
numerically in the case of space charge limited current in organic
layers.
Analytical solutions for Direct Current (DC) in the case of constant
carrier mobility are derived. There are no analytical solutions
available, when the mobility follows an exponential density of states.
In such a case, a numerical approach is used.
The AC model of the drift-diffusion problem for b = 0 does not provide
an analytical solution for the electrical field. A numerical approach
was used to provide solutions taking into account various boundary
conditions. From the results obtained, we can conclude that the
behaviour of the field both in DC and AC model remains the same when
plotted on a logarithmic scale. This is not the case for their
respective voltages.
For further studies, it will be important to operate a change of
variable in the resulting equation of the drift-diffusion problem in
order to obtain an equation that could be solved. If this is done, this
will provide a complete mathematical model of the field, the charge
carrier density and the voltage for all the values of b.
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