9.1 Photovoltaic effect and solar cell operation

Solar cells are the heart of photovoltaic systems, converting sunlight into electricity. They work through the photovoltaic effect, where light creates electron-hole pairs in semiconductors. This process happens at the p-n junction, the core of a solar cell.

The built-in electric field at the p-n junction separates these charges, generating current. Key performance factors include open-circuit voltage, short-circuit current, and fill factor. These determine how efficiently a solar cell turns light into usable power.

Photovoltaic Effect and Charge Generation

Photovoltaic Effect and P-N Junction

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• Photovoltaic effect converts light energy into electrical energy using semiconductors
• Occurs in materials that absorb photons and generate electron-hole pairs
• P-N junction forms the basis of a solar cell
  • Created by joining p-type and n-type semiconductors
  • P-type semiconductor doped with elements having fewer valence electrons (boron)
  • N-type semiconductor doped with elements having extra valence electrons (phosphorus)

Charge Generation and Separation

• Electron-hole pair generation occurs when a photon with sufficient energy is absorbed by the semiconductor
  • Photon energy must be greater than or equal to the bandgap energy of the semiconductor
  • Electrons excited from the valence band to the conduction band, leaving behind holes
• Charge separation takes place due to the built-in electric field at the P-N junction
  • Electric field created by the diffusion of electrons and holes across the junction
  • Electrons drift towards the n-type region, while holes drift towards the p-type region
  • Prevents recombination of generated electron-hole pairs

Built-in Electric Field

• Built-in electric field is a key factor in the operation of solar cells
• Formed at the P-N junction due to the difference in work functions of p-type and n-type semiconductors
• Facilitates the separation and collection of photogenerated charge carriers
  • Drives electrons to the n-type region and holes to the p-type region
  • Establishes a potential difference across the junction, known as the built-in potential ($V_{bi}$)

Solar Cell Performance Parameters

Depletion Region and Photocurrent

• Depletion region forms at the P-N junction due to the built-in electric field
  • Region depleted of free charge carriers (electrons and holes)
  • Width of the depletion region depends on the doping concentrations and applied voltage
• Photocurrent ($I_{ph}$) is the current generated by the solar cell under illumination
  • Directly proportional to the number of photogenerated electron-hole pairs
  • Depends on the intensity and wavelength of the incident light
  • Can be expressed as: $I_{ph} = qAG(L_n + L_p + W)$, where $q$ is the elementary charge, $A$ is the cell area, $G$ is the generation rate, $L_n$ and $L_p$ are the electron and hole diffusion lengths, and $W$ is the depletion region width

Open-Circuit Voltage and Short-Circuit Current

• Open-circuit voltage ($V_{oc}$) is the maximum voltage generated by the solar cell when no current flows
  • Occurs when the cell is not connected to an external load
  • Can be expressed as: $V_{oc} = \frac{nkT}{q} \ln(\frac{I_{ph}}{I_0} + 1)$, where $n$ is the ideality factor, $k$ is the Boltzmann constant, $T$ is the temperature, and $I_0$ is the dark saturation current
• Short-circuit current ($I_{sc}$) is the maximum current generated by the solar cell when the voltage across the cell is zero
  • Occurs when the cell is short-circuited
  • Directly proportional to the photocurrent: $I_{sc} = I_{ph}$

Fill Factor

• Fill factor ($FF$) is a measure of the squareness of the solar cell's current-voltage ($I-V$) curve
  • Represents the ratio of the maximum power output to the product of $V_{oc}$ and $I_{sc}$
  • Can be expressed as: $FF = \frac{V_{mp}I_{mp}}{V_{oc}I_{sc}}$, where $V_{mp}$ and $I_{mp}$ are the voltage and current at the maximum power point
• Higher fill factor indicates better solar cell performance and energy conversion efficiency
  • Ideal solar cells have a fill factor close to 1, while practical cells have lower values due to various losses (recombination, series resistance)