Abstract
Open circuit conditions are discussed first. A thin symmetric Si diode with abrupt junction is used first. The current distribution in a symmetric pn junction is computed. Solution curves for symmetric pn junctions are given. A recombination overshoot is identified that influences V oc. The influence of device thickness, of recombination center density, of generation rate, energy of the recombination centers and of doping density is discussed. The parameter dependence of V oc for insufficient minority carrier supply is discussed. Thin asymmetric Si diodes with abrupt junctions are then analyzed. The recombination through charged recombination centers is discussed. Inhomogeneous optical excitation is discussed. Optical excitation only in a thin front layer of the device is computed as example. A thin asymmetric junction design is introduced. Asymmetric bulk thickness, asymmetric recombination rate, and asymmetric generation is discussed. A thick asymmetric Si solar cell is introduced. Non-vanishing bias is discussed. Thin symmetric pn junction devices with bias are analyzed. A Si solar cell with bias is analyzed.
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Notes
- 1.
This comparison is easiest seen for curve pair 7.
- 2.
It is important for the understanding of this critical relation of a net junction recombination and the depletion of minority carriers from the adjacent bulk regions, to focus on current continuity that forces the transport of minority carriers to the recombination sink near the center of the junction, and results in a lemniscate shape of j n (x) and j p (x), as shown in Fig. 32.1.
- 3.
The figure shows the tendency to completely eliminate the junction barrier for a flat band connection at sufficiently high optical generation rates. Such flat band connection can be achieved at even lower optical generation rates in devices with lower doping densities and higher minority carrier life times.
- 4.
In contrast to the jumps of the quasi-Fermi levels at the metal interface of a Schottky barrier, the jumps for the majority quasi-Fermi levels are negligible in the pn-junction device when contact is made at each side with an appropriate, neutral (or injecting) contact metal.
- 5.
This no longer holds when d 1 or d 2 become comparable to L p and L n .
- 6.
The selection of E Fp here as the shifted level is due to the chosen boundary condition of keeping E c (x=d 2)=0.
- 7.
The reduction of the recombination of a center lying at a greater distance from the center of the gap is due to the more trap-like behavior by partial carrier emission into the nearest band rather than recombination.
- 8.
Only in a very general approximation one observes the tendency of A→2 with excessive recombination in the space charge region, and of A→1 with dominant recombination in the space charge-free bulk.
- 9.
Relating to a symmetric carrier flow from both sides of the junction.
- 10.
Even though the average increase of the recombination center density is only by a factor of 5.5.
- 11.
This information is complementary to the one given in Sect. 32.2.2; indicating that the solution curves for n and p and the potentials are independent of the distribution of g o (x) in thin devices, provided that the total number of absorbed photons remains the same.
- 12.
- 13.
This is an artificial condition that is caused by the assumed constant optical generation rate. In actuality g o =g o (x) and rapidly decreases from left to right. With d 2≫L n , averaging of g(x) can no longer be applied. Therefore most of the gr-current flows toward the junction and much less is collected at the right electrode (the light enters from the left).
- 14.
From E F −E Fp =kTln[(p 20+Δp)/p 20], one obtains for this adjustment of the majority quasi-Fermi level approximately 10−8 eV.
- 15.
In actuality, the front is covered by a thin grid electrode, rendering this a three-dimensional problem in which most of the minority carriers a generated more than a diffusion length removed from the actual metal.
- 16.
This split is estimated in the lower doped region (see Sect. 32.2.3).
- 17.
The sloping of the density distribution toward the overshoot region is not visible since (d 1,d 2)≪(L p ,L n ).
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Böer, K.W. (2013). The pn-Junction with Light. In: Handbook of the Physics of Thin-Film Solar Cells. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36748-9_32
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