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Bias of PN Junctions

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Overview

  1. Forward bias occurs when a voltage is applied across the the solar cell such that the electric field formed by the P-N junction is decreased. It eases carrier diffusion across the depletion region, and leads to increased diffusion current.
  2. In the presence of an external circuit that continually provides majority carriers, recombination increases which constantly depletes the influx of carriers into the solar cell. This increases diffusion and ultimately increases current across the depletion region.
  3. Reverse bias occurs when a voltage is applied across the solar cell such that the electric field formed by the P-N junction is increased. Diffusion current decreases.

Semiconductor devices have three modes of operation:

1. Thermal Equilibrium

At thermal equilibrium there are no external inputs such as light or applied voltage. The currents balance each other out so there is no net current within the device.

2. Steady State

Under steady state there are external inputs such as light or applied voltage, but the conditions do not change with time. Devices typically operate in steady state and are either in forward or reverse bias.

3. Transient

If the applied voltage changes rapidly, there will be a short delay before the solar cell responds. As solar cells are not used for high speed operation there are few extra transient effects that need to be taken into account.

Diodes under Forward Bias

Forward bias refers to the application of voltage across the device such that the electric field at the junction is reduced. By applying a positive voltage to the p-type material and a negative voltage to the n-type material, an electric field with opposite direction to that in the depletion region is applied across the device. Since the resistivity of the depletion region is much higher than that in the remainder of the device (due to the limited number of carriers in the depletion region), nearly all of the applied electric field is dropped across the depletion region. The net electric field is the difference between the existing field in the depletion region and the applied field (for realistic devices, the built-in field is always larger than the applied field), thus reducing the net electric field in the depletion region. Reducing the electric field disturbs the equilibrium existing at the junction, reducing the barrier to the diffusion of carriers from one side of the junction to the other and increasing the diffusion current. While the diffusion current increases, the drift current remains essentially unchanged since it depends on the number of carriers generated within a diffusion length of the depletion region or in the depletion region itself. Since the depletion region is only reduced in width by a minor amount, the number of minority carriers swept across the junction is essentially unchanged.

Carrier Injection and Forward Bias Current Flow

The increased diffusion from one side of the junction to the other causes minority carrier injection at the edge of the depletion region. These carriers move away from the junction due to diffusion and will eventually recombine with a majority carrier. The majority carrier is supplied from the external circuit and hence a net current flows under forward bias. In the absence of recombination, the minority carrier concentration would reach a new, higher equilibrium concentration and the diffusion of carriers from one side of the junction to the other would cease, much the same as when two different gasses are introduced. Initially, gas molecules have a net movement from the high carrier concentration to the low carrier concentration region, but when a uniform concentration is reached, there is no longer a net gas molecule movement. In a semiconductor however, the injected minority carriers recombine and thus more carriers can diffuse across the junction. Consequently, the diffusion current which flows in forward bias is a recombination current. The higher the rate of recombination events, the greater the current which flows across the junction.

The "dark saturation current" (I0) is an extremely important parameter which differentiates one diode from another. I0 is a measure of the recombination in a device. A diode with a larger recombination will have a larger I0.

Reverse Bias

In reverse bias a voltage is applied across the device such that the electric field at the junction increases. The higher electric field in the depletion region decreases the probability that carriers can diffuse from one side of the junction to the other, hence the diffusion current decreases. As in forward bias, the drift current is limited by the number of minority carriers on either side of the p-n junction and is relatively unchanged by the increased electric field. A small increase in the drift current is experienced due to the small increase in the width of the depletion region, but this is essentially a second-order effect in silicon solar cells. In many thin film solar cells where the depletion region is around half the thickness of the solar cell the change in depletion region width with voltage has a large impact on cell operation.