Abstract
Starting with a simplified pn-junction model, its basic features are related to a step function change in doping from n only to p only. The solutions of the set of transport and Poisson equations of the simplified model is given and discussed, first in steady state. Junction capacitance, that is often used to infer on space charge densities, is analyzed. Current voltage characteristics are calculated. A diode quality factor is introduced. The relevance to actual pn junctions is discussed. The abrupt pn junction in Ge is computed with example parameters listed and the governing set of equations given. The solution curves are first given for the devices. The position of the pn junction. Junction field and potential distribution is computed. Quasi Fermi level and current distribution in a pn junction are given. Identifying the Boltzmann, DO and DRO ranges with a very instructive graph of j n (x)j p (x), E c (x), E v (x), E Fn (x), E Fp (x), j n (x) and j p (x). Carrier heating in a pn junction. GR and divergence free currents are discussed. The current voltage characteristics are computed. Thick pn junction devices in Ge are analyzed. The changes in current contribution with device thickness is discussed. The quasi Fermi levels of thicker devices are given. The Si homojunction is analyzed. Current voltage characteristics are computed. More complex homojunctions are introduced and analyzed. Linearly doped devices are discussed. High minority carrier injection is discussed. Series resistance limitation is identified. Position dependent parameters are given.
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Notes
- 1.
However, the depletion layer approximation becomes inadequate for larger forward bias.
- 2.
Equation (30.14) is identical to the result of the more general expression.
- 3.
This can indeed occur for long devices with narrow band gap.
- 4.
The device extends only slightly beyond the junction region.
- 5.
Such a flat band electrode connection requires a metal/semiconductor work function ψ MS=E 0−E c −E d for the n-type side and ψ MS=E 0−E v +E a for the p-type side (E 0 is the vacuum level).
- 6.
There are two majority quasi-Fermi levels in a pn-junction, E Fp in the p-type region and E Fn in the n-type region.
- 7.
For vanishing current both Boltzmann regions fill the entire device width with s=5⋅106 cm/s, for a total reverse current contribution of 9.8 mA/cm2.
- 8.
A fourth step in the highly doped region is not fully developed because of the triangular steep decline of p(x).
- 9.
The difference between the minority carrier density at the outer surface and the equilibrium density [Eqs. (30.56) and (30.57)] that controls the surface recombination current is proportional to the difference at the bulk/junction interface (at l n or l p ) that controls the diode current [Eq. (30.18)].
- 10.
The divergence-free current is now reduced to below 10−8 A/cm2, i.e., to completely negligible values in reverse bias.
- 11.
Such a scale break results in a break of slopes at the break point. The actual curves, however, have continuous slopes.
- 12.
Consider the scale break of the figure in your comparison between the DRO and DO ranges.
- 13.
Such profile can (rarely) be achieved by cross diffusion of dopands for compensation; even though this is usually not symmetric, we will assume such symmetric compensation here.
Bibliography
K.W. Böer, Ann. Phys. 42, 371 (1985a)
K.W. Böer, Phys. Status Solidi A 87, 719 (1985b)
P.E. Gray, Physics of Electronics and Circuit Models (Wiley, New York, 1967)
G.W. Neudeck, The pn-Junction Diode (Addison–Wesley, Reading, 1983)
S.M. Sze, Semiconductor Devices (Wiley, New York, 1985)
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Böer, K.W. (2013). pn-Homojunctions. In: Handbook of the Physics of Thin-Film Solar Cells. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36748-9_30
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DOI: https://doi.org/10.1007/978-3-642-36748-9_30
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