— EDU — p-n junction under illumination
Attention
This tutorial is under construction
Header
- Files for the tutorial located in nextnano++\examples\education
pn-junction-illuminated_GaAs_Nelson_2003_1D_nnp.in
- Main adjustable parameters in the input file:
parameter
$sun
- Relevant output files:
bias_XXXXX\bandedges.dat
bias_XXXXX\density_electon.dat
bias_XXXXX\density_hole.dat
bias_XXXXX\electric_field.dat
bias_XXXXX\potential.dat
IV_characteristics.dat
Introduction
In this tutorial, we introduce simulation of a solar cell with nextnano++.
This tutorial is based on
How to illuminate in nextnano++
To control the concentration of the irradiated light, you have to adjust some variables in nextnano++.
$sun = 10 # concentration of the sun, 10 is used for this tutorial
optics{
irradiation{
min_energy = 0.01
max_energy = 5
energy_resolution = 1e-4
global_illumination{
direction_x = 1
database_spectrum{
name = "Solar-ASTM-G173-global"
concentration = $sun
}
}
global_reflectivity{
database_spectrum{ name = "GaAs" }
}
global_absorption_coeff{
database_spectrum{ name = "GaAs" }
}
}
}
min_energy
and max_energy
correspond to the minimum and maximum energy of irradiated photons.
energy_resolution
is the energy step which is used to calculate optical properties.
$sun
controls the concentration of the incident light as it can be defined at global_illumination{ database_spectrum{ concentration = $sun } }
.
In this tutorial, Solar-ASTM-G173-global
, which is equivalent to the solar spectrum, is also used as in GaAs solar cell.
The data of reflectivity and absorption coefficient of GaAs is written at database{ }
at the end of the input file.
You can refer to GaAs solar cell for further information.
Short circuit
Let us investigate the behavior of p-n junction when it is illuminated by the sun light. First, we consider when the voltage across the diode is zero. We call the condition short circuit. The junction before the illumination is at equilibrium, having the space charge region and the electric field as shown in Figure 2.4.71 (a). The electric field impedes the diffusion of majority carriers as explained in — NEW/EDU — p-n junction in the dark.

Figure 2.4.71 The schematic images showing the principles of a solar cell. (a) is the p-n junction at equilibrium. When it is illuminated, an electron-hole pair is generated at the junction (b). The current runs as long as the diode is illuminated (c). We assume the resistance of the light bulb is zero because of the short circuit.
When the light is illuminated, it excites an electron in the valence band if the energy of the light is bigger than the band gap. The excited electron goes to the conduction band and becomes a conduction electron. On the other hand, a hole is generated at the valence band, instead of the excited electron. The electric field drifts the electron-hole pair and the electron goes to the n-doped GaAs whereas the hole goes to the p-doped GaAs as the result (Figure 2.4.71 (b)). As long as the junction is illuminated, the electron-hole pair is generated and constitutes the current (Figure 2.4.71 (c)).
Figure 2.4.72 shows the band profile and the carrier densities at short circuit. bandedges.dat, density_electon.dat, and density_hole.dat are used to produce this figure.

Figure 2.4.72 The band profiles are plotted in (a). When the light reaches the junction and the energy is bigger than the band gap, the electron-hole pair is generated as shown in (b). The carrier densities are plotted in (c). The hole density is shown in violet, whereas the electron density is in green.
In (a),
As you can see from Figure 2.4.72 (a) and (b), the built-in-potential
In the short circuit, the photocurrent density
The Photovoltatic effect
When the circuit is connected to a resistive load, the negative charges accumulated at n-doped GaAs and the positive charges accumulated at p-doped GaAs form a voltage (photovoltage).
The current flows through the diode due to the voltage and is analogy to the current which flows across the diode under applied bias in the dark.
Therefore, this current is called the dark current.
The dark current density (

Figure 2.4.73 The circuit is connected to a resistive load. Note that
Generally speaking, when the photovoltage
The photovoltage
where
As a result,
Now, let us look into the situation

Figure 2.4.74 The band profiles are plotted in (a). The carrier densities are plotted in (b). The hole density is shown in violet, whereas the electron density is in green.
The results are very similar to Fig. 6.8. in [NelsonPSC2003].
As in the diode with forward bias, the built-in-potential is reduced to
Open circuit
When the circuit is open (open circuit), the photovoltage

Figure 2.4.75 The circuit is open and the voltage
Since
The open-circuit voltage is the maximum voltage that the solar cell can produce.
J-V curve
We look into the output characteristics of the solar cell in this section. Figure 2.4.76 shows J-V curves of the solar cell under the illumination and under the dark condition.

Figure 2.4.76 The J-V curves of the solar cell. The J-V curve under the illumination is shown in violet, whereas the J-V curve under the dark condition is in light-blue. The orange-filled area indicates the output of the maximum power density of the solar cell.
Again, the maximum current density that the solar cell can produce is the short-circuit current density, and the maximum voltage of the cell is the open-circuit voltage.
However, the output of the maximum power density
This arises from the parasitic resistances which are connected in series and parallel to the solar cell. The series resistance consist of the electrical resistance present on the carrier transport path, such as the semiconductors and the contacts of the solar cell. The parallel resistance is attributed to leakage of the current due to defects in the solar cell.
We can derive
First, the power density of the solar cell is given by
The condition for the maximum power density is achieved when
Thus,
where
Therefore,
where
In addition, the energy conversion efficiency of the solar cell (
Effects of irradiation intensity and temperature
So far, the effects of the intensity of the incident light and temperature of the system on the behavior of the solar cell have not been considered. In this section, we briefy investigate the effects on J-V characteristics.

Figure 2.4.77 The J-V curves of the solar cell under incident light of various intensities is shown in (a). The J-V curves of the solar cell under different temperatures are shown in (b). The arrows indicate the direction of increasing intensity of the incident sunlight or the temperature.
Effect of irradiation intensity
Figure 2.4.77 (a) illustrates the effect of the light intensity on the J-V curve.
Since the generation rate for electron-hole pairs is proportional to the light intensity, the photocurrent increases as the light intensity gets bigger.
From (2.4.18),
Effect of temperature
The effect of the temperature on the J-V curve is shown in (b) in Figure 2.4.77.
As the temperature is increased, the intrinsic carrier density
This occurs more noticeably than when the recombination current is dominant (
Actually,
Exercises
under construction
Last update: 16/07/2024