The simulation illustrates how diffusion and drift affect the spatial distribution of charge carriers – two processes fundamental to understanding solar cells.
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Description
In an illuminated semiconductor material, free charge carriers are generated: electrons and holes. Both initially move randomly through the material (diffusion). Holes form when electrons leave their lattice sites – they migrate as neighbouring electrons fill the vacancies. Electron current and hole current flow in opposite directions.
This random motion is directly visible in the animation: the blue particles (electrons) and the red particles (holes) change direction at short intervals and gradually spread out. The “Diffusion (px/s)” slider controls the speed of this random movement. The yellow-highlighted area represents the illuminated zone where new particles are generated – its boundaries can be moved using the grey handles on the right-hand side. The “Show hole current” checkbox toggles the red particles on and off, allowing you to observe the electron current alone. The “Number of particles” slider adjusts the number of simulated charge carriers: with fewer particles, individual trajectories are easy to follow; with more, the statistical behaviour becomes clearer.
At the p-n junction inside a solar cell, an electric field is present – the space charge region (SCR). This field arises from the different doping on each side and deflects charge carriers in a directed way: electrons towards the positive side, holes towards the negative side (drift).
In the animation, the space charge region is shown as a band with a colour gradient from blue (n-side) to red (p-side). As soon as a particle enters this region, it is accelerated by the drift force: blue particles are pushed downward, red particles upward – each away from their respective doping side. The strength of this deflection can be adjusted with the “Drift in PN junction (px/s)” slider. The “PN junction” checkbox can be used to deactivate the region entirely – all particles then move by diffusion only, clearly showing that no directed charge separation occurs without drift.
Charge carriers have a limited lifetime τ between generation and recombination. The longer the lifetime, the greater the diffusion length L – the average distance a carrier travels:
\[ L = \sqrt{D \cdot \tau} \]
With:
- \( L \) – diffusion length
- \( D \) – diffusion coefficient
- \( \tau \) – carrier lifetime
This relationship can be observed directly in the animation: the “Lifetime (s)” slider controls how long a particle exists before it recombines and reappears in the yellow illumination zone. At the lowest setting (0.1 s), particles vanish almost immediately and remain close to their point of origin – the diffusion length is very short. At higher settings (e.g. 3–4 s), particles have considerably more time to spread out, increasing the probability that they reach the blue-red p-n region and are separated there by the drift force.
Note: This is an analogy model. Diffusion is represented as motion in which each particle changes its direction randomly at short intervals. In reality, direction changes are far more frequent and irregular. Further simplifications concern recombination and the exact field distribution within the SCR.
Physical Background
When a semiconductor is illuminated, electrons are excited from the valence band into the conduction band, generating electron-hole pairs. Carriers that diffuse to the space charge region are separated by the built-in electric field and directed towards their respective contacts – producing a usable electric voltage. The lower the recombination rate and the greater the diffusion length, the more efficiently the solar cell operates.
Doping and the P-N Junction
The space charge region shown as the central area in the animation arises from deliberate doping of the semiconductor material. The position and width of the space charge region can be adjusted in the animation using the blue and red handles on the right-hand side. This makes it possible to explore how the position of the p-n junction relative to the illumination zone affects charge separation: when the p-n junction is close to the light zone, more charge carriers are separated; when it is far away, many particles recombine before reaching it.
Pure silicon is a poor electrical conductor. By introducing foreign atoms – a process called doping – its conductivity can be precisely controlled:
- n-type doping: Atoms with five valence electrons (e.g. phosphorus) replace individual silicon atoms. The fifth electron is not bound in a covalent bond and is available as a free charge carrier. This creates an excess of electrons.
- p-type doping: Atoms with three valence electrons (e.g. boron) create a vacancy – a “hole”. Neighbouring electrons can move into this hole, causing the hole to effectively migrate through the material.
When an n-doped and a p-doped layer are brought together, electrons diffuse from the n-side into the p-side and holes in the opposite direction. They leave behind fixed, charged dopant atoms: positive ion cores on the n-side and negative ones on the p-side. This builds up an electric field – the space charge region (SCR).
This built-in field opposes further diffusion and reaches an equilibrium state. Only when light generates electron-hole pairs near the SCR are they separated by the field – the basis of electricity generation in a solar cell.
The Solar Cell Characteristic Curve
Diffusion and drift determine not only the internal charge separation but also the external electrical behaviour of the solar cell – represented in the I-V characteristic curve (current-voltage curve).
The characteristic curve shows three key parameters:
- Short-circuit current \( I_{SC} \): The maximum current when the contacts are short-circuited (voltage = 0). It depends directly on how many light-generated charge carriers reach the space charge region – i.e. on the diffusion length and the illumination intensity.
- Open-circuit voltage \( V_{OC} \): The maximum voltage with an open circuit (current = 0). It is determined by the balance between drift current (driven by the built-in field) and diffusion current (driven by concentration gradients).
- Maximum Power Point (MPP): The operating point at which the solar cell delivers its greatest power \( P = V \cdot I \). Here, the product of current and voltage is at its maximum.
The fill factor (FF) describes how “rectangular” the characteristic curve is, and thus how close the actual maximum power comes to the theoretical product \( I_{SC} \cdot V_{OC} \):
\[ FF = \frac{P_{MPP}}{I_{SC} \cdot V_{OC}} \]
A high fill factor means low losses – for example from low series resistance and low recombination. Typical values for silicon solar cells range from 0.75 to 0.85.
Temperature Effects on Diffusion and Drift
The performance of a solar cell depends not only on illumination but also on temperature – an effect that is often underestimated in practice.
Effect on open-circuit voltage: As temperature increases, the open-circuit voltage \( V_{OC} \) decreases significantly – typically by about 2 mV/K for silicon. The reason: the thermal energy of charge carriers increases, allowing more carriers to overcome the potential barrier of the space charge region without the aid of light. The diffusion current increases and the equilibrium shifts.
Effect on short-circuit current: The short-circuit current \( I_{SC} \) increases slightly with temperature because the semiconductor’s band gap narrows, meaning more photons have sufficient energy to generate electron-hole pairs. However, this effect is small and does not compensate for the voltage loss.
Net effect: Overall, the efficiency of a silicon solar cell drops by approximately 0.3 to 0.5 % per kelvin of temperature increase. On a hot summer day with a module temperature of 60 °C, the output can therefore be 15–20 % below the rated value at standard test conditions (25 °C).
The diffusion length is also influenced by temperature: the diffusion coefficient \( D \) increases with temperature, but at the same time the recombination rate rises and the carrier lifetime \( \tau \) decreases. Which effect dominates depends on the specific semiconductor material.
Ideal vs. Real Solar Cell
The analogy model in the animation simplifies a number of effects that play an important role in real solar cells. The following overview shows where the differences lie.
Recombination losses: In the model, charge carriers recombine after a fixed lifetime. In reality, several recombination mechanisms exist:
- Radiative recombination – an electron falls back into the valence band and emits a photon. This process is rare in silicon but plays a larger role in direct-bandgap semiconductors such as GaAs.
- Auger recombination – the energy is transferred to a third charge carrier. This mechanism limits efficiency under high doping or strong illumination.
- Shockley-Read-Hall recombination – impurities and crystal defects create energy levels within the band gap that act as “traps” for charge carriers. In practice, this is often the dominant loss mechanism.
Surface recombination: At the surfaces and interfaces of the semiconductor, the crystal structure is disrupted. The recombination rate there is particularly high. Modern solar cells therefore use passivation layers (e.g. SiN or Al₂O₃) to reduce this loss.
Resistive losses: Real solar cells have a series resistance (contacts, busbars, bulk resistance) and a shunt resistance (leakage currents through defects). Both degrade the fill factor of the characteristic curve and thus the usable power output.
Optical losses: Not all incident light is absorbed. Reflection at the surface, shading by contact fingers, and limited absorption of long-wavelength photons reduce the short-circuit current. Anti-reflection coatings and surface texturing minimise these losses.
Shockley-Queisser limit: Even an ideal solar cell with only one p-n junction has a theoretical maximum efficiency of about 33 % (for a band gap of approximately 1.34 eV). Photons with less energy than the band gap are not absorbed, and excess energy above the band gap is lost as heat (thermalisation). This fundamental limit motivates the development of tandem and multi-junction solar cells.
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Overview
| Title | Solar Cell – Diffusion and Drift |
| Target audience | Teachers and lecturers |
| Features | Full-screen mode Lossless scaling Large screens and projectors supported |
| License | MIT |