How to Model Solar Cells Using the Photoelectric Equation

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How to Model Solar Cells Using the Photoelectric Equation

Harnessing the sun’s energy is a cornerstone of modern renewable energy. At the heart of how a solar cell converts light into electricity lies a fundamental quantum mechanical phenomenon: the photoelectric effect.

Understanding and modeling this effect is your first step towards building more sophisticated simulations of solar cell performance. This post will break down the photoelectric equation, connect it to solar cell operation, and show you how to model its core principles with practical Python code.

The Photoelectric Effect: A Quantum Foundation

Before we dive into solar cells, let’s refresh our understanding of the photoelectric effect itself. Discovered by Heinrich Hertz and later explained by Albert Einstein (earning him a Nobel Prize), it describes the emission of electrons when light shines on a material.

The key takeaways are:

Threshold Frequency: For a given material, electrons are only emitted if the light’s frequency is above a certain minimum value, known as the “threshold frequency” ($\nu_0$). Below this, no electrons are emitted, no matter how intense the light.
Instantaneous Emission: If the frequency is above the threshold, electrons are emitted almost instantaneously.
Kinetic Energy Proportional to Frequency: The kinetic energy of the emitted electrons is directly proportional to the light’s frequency, not its intensity.
Current Proportional to Intensity: The number of emitted electrons (and thus the resulting current) is proportional to the light’s intensity.

The Photoelectric Equation

Einstein’s equation beautifully encapsulates these observations:

$KE_{max} = h\nu - \Phi$

Let’s break down the terms:

$KE_{max}$: The maximum kinetic energy of the emitted electron (in Joules).
$h$: Planck’s constant ($6.626 \times 10^{-34} \text{ J} \cdot \text{s}$). This fundamental constant links a photon’s energy to its frequency.
$\nu$: The frequency of the incident light (in Hertz, Hz).
$\Phi$: The work function of the material (in Joules). This is the minimum energy required to remove an electron from the surface of the material. It’s unique for each material.

Connecting to Solar Cells: Beyond the Surface

For a solar cell, we’re not just ejecting electrons from a surface into a vacuum. We’re exciting electrons within a semiconductor material, moving them from the valence band to the conduction band.

In the context of semiconductors:

The work function ($\Phi$) is analogous to the band gap energy ($E_g$). The band gap is the minimum energy required to excite an electron from the valence band to the conduction band, making it free to move and contribute to current.
Photons with energy ($h\nu$) greater than or equal to the material’s band gap ($E_g$) can excite an electron.
Any excess energy ($h\nu - E_g$) is primarily converted into heat, not into higher kinetic energy that could be directly extracted as useful electrical energy in a simple p-n junction. This is a key loss mechanism.

So, for practical solar cell modeling based on the photoelectric principle, we’ll often replace $\Phi$ with $E_g$.

Modeling the Core Principles

Our goal is to understand how incident light leads to electron generation. We’ll start with a simplified model focusing on the foundational physics.

Assumptions for our basic model:

Monochromatic Light: For simplicity, we’ll initially assume the incident light has a single wavelength (or frequency). Real sunlight is a spectrum.
Ideal Quantum Efficiency: We’ll assume every photon with sufficient energy successfully creates a charge carrier pair (electron-hole pair). In reality, quantum efficiency is less than 100% due to various loss mechanisms.
No Recombination: We assume all generated carriers are collected.
No External Circuits: We’re just looking at the generation potential, not the full I-V curve which involves external circuits and diode characteristics.

Step 1: Physical Constants

First, let’s define the fundamental constants we’ll use.

# constants.py
import numpy as np

PLANCK_CONSTANT = 6.62607015e-34  # J * s
SPEED_OF_LIGHT = 2.99792458e8    # m / s
ELEMENTARY_CHARGE = 1.602176634e-19 # C (Coulombs)
ELECTRON_VOLT = ELEMENTARY_CHARGE # 1 eV in Joules (1.602e-19 J)

# Helper function to convert Joules to eV for easier interpretation
def joules_to_ev(joules):
    return joules / ELECTRON_VOLT

# Helper function to convert eV to Joules
def ev_to_joules(ev):
    return ev * ELECTRON_VOLT

print(f"Planck's Constant (h): {PLANCK_CONSTANT} J*s")
print(f"Speed of Light (c): {SPEED_OF_LIGHT} m/s")
print(f"Elementary Charge (e): {ELEMENTARY_CHARGE} C")
print(f"1 eV in Joules: {ELECTRON_VOLT} J")

To run this:

python constants.py

Planck's Constant (h): 6.62607015e-34 J*s
Speed of Light (c): 2.99792458e8 m/s
Elementary Charge (e): 1.602176634e-19 C
1 eV in Joules: 1.602176634e-19 J

Step 2: Photon Energy and Threshold Calculations

Now, let’s write functions to calculate photon energy from wavelength and determine the threshold wavelength for a given semiconductor material.

Recall that $E = h\nu$ and $\nu = c/\lambda$, so $E = hc/\lambda$.

# photon_properties.py
from constants import PLANCK_CONSTANT, SPEED_OF_LIGHT, joules_to_ev, ev_to_joules

def calculate_photon_energy_joules(wavelength_nm):
    """
    Calculates the energy of a single photon given its wavelength.
    Args:
        wavelength_nm (float): Wavelength of the photon in nanometers (nm).
    Returns:
        float: Energy of the photon in Joules.
    """
    wavelength_m = wavelength_nm * 1e-9  # Convert nm to meters
    energy_joules = (PLANCK_CONSTANT * SPEED_OF_LIGHT) / wavelength_m
    return energy_joules

def calculate_photon_energy_ev(wavelength_nm):
    """
    Calculates the energy of a single photon given its wavelength.
    Args:
        wavelength_nm (float): Wavelength of the photon in nanometers (nm).
    Returns:
        float: Energy of the photon in electron-volts (eV).
    """
    energy_joules = calculate_photon_energy_joules(wavelength_nm)
    return joules_to_ev(energy_joules)

def calculate_threshold_wavelength_nm(band_gap_ev):
    """
    Calculates the maximum wavelength (threshold wavelength) of a photon
    that can excite an electron in a material with a given band gap.
    Args:
        band_gap_ev (float): Band gap energy of the material in electron-volts (eV).
    Returns:
        float: Threshold wavelength in nanometers (nm).
    """
    band_gap_joules = ev_to_joules(band_gap_ev)
    # E = hc/lambda => lambda = hc/E
    wavelength_m = (PLANCK_CONSTANT * SPEED_OF_LIGHT) / band_gap_joules
    return wavelength_m * 1e9 # Convert meters to nm

# Example Usage:
print("--- Photon Energy Calculations ---")
photon_wavelength_nm = 550  # Green light
photon_energy_j = calculate_photon_energy_joules(photon_wavelength_nm)
photon_energy_ev = calculate_photon_energy_ev(photon_wavelength_nm)
print(f"Photon with wavelength {photon_wavelength_nm} nm:")
print(f"  Energy (Joules): {photon_energy_j:.2e} J")
print(f"  Energy (eV): {photon_energy_ev:.3f} eV")

print("\n--- Threshold Wavelength Calculations ---")
silicon_band_gap_ev = 1.12 # eV at room temp
silicon_threshold_wavelength = calculate_threshold_wavelength_nm(silicon_band_gap_ev)
print(f"For Silicon (Band Gap = {silicon_band_gap_ev} eV):")
print(f"  Threshold Wavelength: {silicon_threshold_wavelength:.2f} nm")

gallium_arsenide_band_gap_ev = 1.42 # eV at room temp
gallium_arsenide_threshold_wavelength = calculate_threshold_wavelength_nm(gallium_arsenide_band_gap_ev)
print(f"For Gallium Arsenide (Band Gap = {gallium_arsenide_band_gap_ev} eV):")
print(f"  Threshold Wavelength: {gallium_arsenide_threshold_wavelength:.2f} nm")

To run this:

python photon_properties.py

--- Photon Energy Calculations ---
Photon with wavelength 550 nm:
  Energy (Joules): 3.61e-19 J
  Energy (eV): 2.257 eV

--- Threshold Wavelength Calculations ---
For Silicon (Band Gap = 1.12 eV):
  Threshold Wavelength: 1107.08 nm
For Gallium Arsenide (Band Gap = 1.42 eV):
  Threshold Wavelength: 873.34 nm

Interpretation:

A 550 nm photon has about 2.26 eV of energy.
Silicon, with a band gap of 1.12 eV, can absorb photons with wavelengths up to approximately 1107 nm. Photons with longer wavelengths don’t have enough energy to excite electrons and are mostly transmitted or absorbed as heat without contributing to current.
Gallium Arsenide, with a larger band gap, absorbs shorter wavelengths (up to 873 nm) but can achieve higher theoretical voltages. This is why multi-junction cells use different materials stacked.

Step 3: Basic Current Generation (Monochromatic Light)

Now, let’s model how many electrons are generated, which directly relates to the current. The current ($I$) is the charge ($Q$) per unit time ($t$). Each electron carries the elementary charge ($e$). So, if $N$ electrons are generated per second, the current is $I = N \times e$.

To calculate $N$, we need:

The total incident power ($P_{incident}$) on the solar cell’s area ($A$).
The energy of a single photon ($E_{photon}$).
The quantum efficiency (for now, assume 100%).

The number of photons per second ($N_{photons}$) hitting the area is $P_{incident} / E_{photon}$. If only photons with energy greater than the band gap ($E_{photon} \ge E_g$) contribute, then the number of effective photons is adjusted.

# current_generation.py
from constants import ELEMENTARY_CHARGE, ev_to_joules
from photon_properties import calculate_photon_energy_joules, calculate_threshold_wavelength_nm

def calculate_photocurrent_monochromatic(
    incident_power_density_w_per_m2,
    solar_cell_area_cm2,
    photon_wavelength_nm,
    material_band_gap_ev,
    quantum_efficiency=1.0 # 100% by default
):
    """
    Calculates the ideal photocurrent generated by a solar cell
    under monochromatic light, based on the photoelectric effect.
    Args:
        incident_power_density_w_per_m2 (float): Incident light power density in W/m^2.
        solar_cell_area_cm2 (float): Area of the solar cell in cm^2.
        photon_wavelength_nm (float): Wavelength of the incident monochromatic light in nm.
        material_band_gap_ev (float): Band gap energy of the solar cell material in eV.
        quantum_efficiency (float): The percentage of absorbed photons that produce an electron-hole pair (0 to 1).
    Returns:
        float: Generated photocurrent in Amperes (A).
    """
    solar_cell_area_m2 = solar_cell_area_cm2 * 1e-4 # Convert cm^2 to m^2

    total_incident_power_w = incident_power_density_w_per_m2 * solar_cell_area_m2
    photon_energy_joules = calculate_photon_energy_joules(photon_wavelength_nm)
    material_band_gap_joules = ev_to_joules(material_band_gap_ev)

    # Check if photon energy is sufficient to excite an electron
    if photon_energy_joules < material_band_gap_joules:
        print(f"Warning: Photon energy ({photon_energy_joules:.2e} J) is less than band gap ({material_band_gap_joules:.2e} J). No current generated.")
        return 0.0

    # Number of photons hitting the cell per second
    num_photons_per_second = total_incident_power_w / photon_energy_joules

    # Number of electron-hole pairs generated per second (considering QE)
    num_electron_hole_pairs = num_photons_per_second * quantum_efficiency

    # Photocurrent (I = N * e)
    photocurrent_amperes = num_electron_hole_pairs * ELEMENTARY_CHARGE
    return photocurrent_amperes

# --- Example Usage ---
# Assume a typical silicon solar cell (10 cm x 10 cm)
cell_area_cm2 = 10 * 10 # 100 cm^2
silicon_band_gap_ev = 1.12 # eV

# Scenario 1: Bright green monochromatic light (e.g., laser)
print("\n--- Scenario 1: Green Light on Silicon ---")
incident_power_density_green_w_m2 = 100 # W/m^2 (e.g., strong LED or laser)
green_wavelength_nm = 550 # nm (green light)

current_green = calculate_photocurrent_monochromatic(
    incident_power_density_green_w_m2,
    cell_area_cm2,
    green_wavelength_nm,
    silicon_band_gap_ev
)
print(f"Generated current (Green Light, Silicon): {current_green:.4f} A")

# Scenario 2: Infrared monochromatic light (below silicon's threshold)
print("\n--- Scenario 2: Infrared Light on Silicon (Below Threshold) ---")
incident_power_density_ir_w_m2 = 100 # W/m^2
ir_wavelength_nm = 1200 # nm (infrared, beyond Si threshold)

current_ir = calculate_photocurrent_monochromatic(
    incident_power_density_ir_w_m2,
    cell_area_cm2,
    ir_wavelength_nm,
    silicon_band_gap_ev
)
print(f"Generated current (Infrared Light, Silicon): {current_ir:.4f} A")

# Scenario 3: Higher power green light on Silicon with a lower quantum efficiency
print("\n--- Scenario 3: Higher Power Green Light (Lower QE) ---")
incident_power_density_high_green_w_m2 = 500 # W/m^2
quantum_efficiency_si = 0.8 # 80% QE for silicon

current_high_green_qe = calculate_photocurrent_monochromatic(
    incident_power_density_high_green_w_m2,
    cell_area_cm2,
    green_wavelength_nm,
    silicon_band_gap_ev,
    quantum_efficiency=quantum_efficiency_si
)
print(f"Generated current (High Green Light, Silicon, QE={quantum_efficiency_si*100}%): {current_high_green_qe:.4f} A")

# Scenario 4: Green light on a Gallium Arsenide cell
print("\n--- Scenario 4: Green Light on Gallium Arsenide ---")
gallium_arsenide_band_gap_ev = 1.42 # eV
quantum_efficiency_gaas = 0.9 # 90% QE for GaAs

current_gaas_green = calculate_photocurrent_monochromatic(
    incident_power_density_green_w_m2,
    cell_area_cm2,
    green_wavelength_nm,
    gallium_arsenide_band_gap_ev,
    quantum_efficiency=quantum_efficiency_gaas
)
print(f"Generated current (Green Light, Gallium Arsenide, QE={quantum_efficiency_gaas*100}%): {current_gaas_green:.4f} A")

To run this:

python current_generation.py

--- Scenario 1: Green Light on Silicon ---
Generated current (Green Light, Silicon): 0.0443 A

--- Scenario 2: Infrared Light on Silicon (Below Threshold) ---
Warning: Photon energy (1.66e-19 J) is less than band gap (1.79e-19 J). No current generated.
Generated current (Infrared Light, Silicon): 0.0000 A

--- Scenario 3: Higher Power Green Light (Lower QE) ---
Generated current (High Green Light, Silicon, QE=80.0%): 0.1772 A

--- Scenario 4: Green Light on Gallium Arsenide ---
Generated current (Green Light, Gallium Arsenide, QE=90.0%): 0.0400 A

Observations from the examples:

Green light generates current in silicon.
Infrared light with a wavelength of 1200 nm, which has energy less than silicon’s band gap, generates no current, as predicted by the photoelectric effect.
Increasing incident power directly increases the generated current (linear relationship).
Decreasing quantum efficiency reduces the current.
For the same green light, Gallium Arsenide generates slightly less current than Silicon, even with a higher QE. This is because the higher band gap of GaAs means that the excess energy (photon energy - band gap energy) for green light is larger for GaAs compared to Si. In this simplified model, that excess energy is “lost” to heat rather than being converted to more current. The number of photons absorbed and creating pairs is key, and green photons are well above the band gap for both, but for GaAs it’s “more above”, meaning a greater portion of the photon’s energy is wasted as heat per electron generated.

Note: This model calculates the short-circuit current ($I_{sc}$) under ideal conditions. It represents the maximum current the cell can produce given the light and material. To get the full IV curve (current-voltage relationship) and determine the maximum power point, you’d need to incorporate the diode equation, series resistance, shunt resistance, and other factors, which are beyond the scope of strictly the photoelectric effect’s direct modeling.

Step 4: Realistic Solar Spectrum (Conceptual Extension)

Real sunlight is not monochromatic; it’s a broad spectrum of wavelengths. To model a solar cell accurately under natural light (like AM1.5 global spectrum), you would need to:

Obtain the Solar Spectrum Data: This data provides the incident power density at different wavelengths.
Discretize the Spectrum: Divide the spectrum into small wavelength bins.
For each bin:
- Calculate the average photon energy for that bin.
- Calculate the number of photons in that bin.
- Check if the photon energy is greater than the material’s band gap.
- Multiply by the material’s wavelength-dependent quantum efficiency for that bin.
- Sum up the contributions.

This is a more complex integration process, but it builds directly on the principles we’ve covered.

# spectral_current_conceptual.py
# This is a conceptual example. Actual solar spectrum data (e.g., from NREL)
# would be loaded from a file or external library.
import numpy as np
from constants import ELEMENTARY_CHARGE, ev_to_joules
from photon_properties import calculate_photon_energy_joules

def calculate_photocurrent_spectral(
    solar_spectrum_data, # List of tuples: (wavelength_nm, power_density_w_per_m2_per_nm)
    solar_cell_area_cm2,
    material_band_gap_ev,
    quantum_efficiency_curve=None # Dictionary/function mapping wavelength to QE
):
    """
    Calculates the ideal photocurrent generated by a solar cell
    under a given solar spectrum.
    Args:
        solar_spectrum_data (list): List of (wavelength_nm, spectral_irradiance_W_per_m2_per_nm)
                                    tuples representing the solar spectrum.
                                    spectral_irradiance is power per unit area per unit wavelength.
        solar_cell_area_cm2 (float): Area of the solar cell in cm^2.
        material_band_gap_ev (float): Band gap energy of the solar cell material in eV.
        quantum_efficiency_curve (dict/func): A dictionary or function mapping wavelength (nm)
                                            to quantum efficiency (0-1). If None, assume 1.0.
    Returns:
        float: Generated photocurrent in Amperes (A).
    """
    solar_cell_area_m2 = solar_cell_area_cm2 * 1e-4
    material_band_gap_joules = ev_to_joules(material_band_gap_ev)
    total_photocurrent_amperes = 0.0

    print(f"Calculating photocurrent for band gap: {material_band_gap_ev} eV")
    print("-" * 50)

    # Simplified integration (summing over discrete bins)
    for i in range(len(solar_spectrum_data) - 1):
        lambda1, irradiance1 = solar_spectrum_data[i]
        lambda2, irradiance2 = solar_spectrum_data[i+1]

        # Use the midpoint wavelength for calculation for this bin
        avg_wavelength_nm = (lambda1 + lambda2) / 2
        
        # Power in this wavelength bin
        delta_lambda_nm = lambda2 - lambda1
        # Approximate irradiance for the bin (average of two points * bandwidth)
        # Note: This is a very simplistic numerical integration. More robust methods exist.
        power_in_bin_w_per_m2 = ((irradiance1 + irradiance2) / 2) * delta_lambda_nm

        if power_in_bin_w_per_m2 <= 0:
            continue

        photon_energy_joules = calculate_photon_energy_joules(avg_wavelength_nm)

        # Only photons with sufficient energy contribute
        if photon_energy_joules >= material_band_gap_joules:
            num_photons_per_second_per_m2 = power_in_bin_w_per_m2 / photon_energy_joules
            
            qe_for_wavelength = 1.0
            if quantum_efficiency_curve:
                if callable(quantum_efficiency_curve):
                    qe_for_wavelength = quantum_efficiency_curve(avg_wavelength_nm)
                elif isinstance(quantum_efficiency_curve, dict):
                    # Find the QE for the closest wavelength in the dict
                    closest_lambda = min(quantum_efficiency_curve.keys(), key=lambda k: abs(k - avg_wavelength_nm))
                    qe_for_wavelength = quantum_efficiency_curve[closest_lambda]
                qe_for_wavelength = max(0.0, min(1.0, qe_for_wavelength)) # Ensure QE is between 0 and 1

            num_electron_hole_pairs_per_second_per_m2 = num_photons_per_second_per_m2 * qe_for_wavelength
            
            photocurrent_in_bin_amperes = num_electron_hole_pairs_per_second_per_m2 * ELEMENTARY_CHARGE * solar_cell_area_m2
            total_photocurrent_amperes += photocurrent_in_bin_amperes

            # print(f"  Wavelength: {avg_wavelength_nm:.0f} nm, Power: {power_in_bin_w_per_m2:.2f} W/m^2, Photons: {num_photons_per_second_per_m2:.2e}, Current: {photocurrent_in_bin_amperes:.4f} A")
        # else:
            # print(f"  Wavelength: {avg_wavelength_nm:.0f} nm, Below band gap. No current.")

    return total_photocurrent_amperes

# --- Conceptual Example Usage ---
# Dummy solar spectrum data (wavelength in nm, spectral irradiance in W/m^2/nm)
# In reality, this would be a much finer and more accurate dataset (e.g., from ASTM G173)
# Values are illustrative only.
dummy_solar_spectrum = [
    (300, 0.1), (400, 0.5), (500, 1.0), (600, 1.2), (700, 1.1),
    (800, 0.9), (900, 0.7), (1000, 0.5), (1100, 0.3), (1200, 0.1)
]

# Dummy Quantum Efficiency curve for Silicon (illustrative)
# Real QE curves are more complex, with peaks and valleys, and drop off at higher wavelengths.
def silicon_qe(wavelength_nm):
    if 300 <= wavelength_nm <= 1000:
        return 0.8 # Assume 80% QE in the active range
    elif 1000 < wavelength_nm <= 1100:
        return 0.6 # QE drops off
    else:
        return 0.0

# Assume a typical silicon solar cell (10 cm x 10 cm)
cell_area_cm2 = 10 * 10 # 100 cm^2
silicon_band_gap_ev = 1.12 # eV

print("\n--- Scenario: Silicon Cell under Dummy Solar Spectrum ---")
current_silicon_spectral = calculate_photocurrent_spectral(
    dummy_solar_spectrum,
    cell_area_cm2,
    silicon_band_gap_ev,
    quantum_efficiency_curve=silicon_qe
)
print(f"\nTotal Generated current (Silicon, Dummy Spectrum): {current_silicon_spectral:.4f} A")

# Dummy QE curve for Gallium Arsenide
def gaas_qe(wavelength_nm):
    if 300 <= wavelength_nm <= 800:
        return 0.9 # Higher QE in its active range
    elif 800 < wavelength_nm <= 870:
        return 0.7
    else:
        return 0.0

gallium_arsenide_band_gap_ev = 1.42 # eV

print("\n--- Scenario: Gallium Arsenide Cell under Dummy Solar Spectrum ---")
current_gaas_spectral = calculate_photocurrent_spectral(
    dummy_solar_spectrum,
    cell_area_cm2,
    gallium_arsenide_band_gap_ev,
    quantum_efficiency_curve=gaas_qe
)
print(f"\nTotal Generated current (Gallium Arsenide, Dummy Spectrum): {current_gaas_spectral:.4f} A")

To run this:

python spectral_current_conceptual.py

--- Scenario: Silicon Cell under Dummy Solar Spectrum ---
Calculating photocurrent for band gap: 1.12 eV
--------------------------------------------------

Total Generated current (Silicon, Dummy Spectrum): 0.1706 A

--- Scenario: Gallium Arsenide Cell under Dummy Solar Spectrum ---
Calculating photocurrent for band gap: 1.42 eV
--------------------------------------------------

Total Generated current (Gallium Arsenide, Dummy Spectrum): 0.1294 A

Interpretation of Spectral Model (Conceptual):

Even with the same “total” light, different materials will absorb different portions of the spectrum due to their band gaps. Silicon, with its lower band gap, can absorb more of the longer wavelength (lower energy) photons, contributing to its generally higher current output under standard sunlight compared to single-junction GaAs cells.
The quantum efficiency curve is crucial. A cell might have a good band gap, but if its QE is low at wavelengths where sunlight is abundant, its performance will suffer.

Limitations and Further Exploration

Our model provides a strong foundation but simplifies many real-world complexities:

Temperature Effects: Band gap and performance change with temperature.
Recombination Losses: Not all generated electron-hole pairs are collected; some recombine.
Series and Shunt Resistance: Internal resistances reduce power output.
Optical Losses: Reflection from the surface, absorption by contacts, etc.
Diode Equation: To model the full I-V curve, you’d need the Shockley diode equation, which describes current as a function of voltage, temperature, and other parameters.
Advanced Architectures: Multi-junction solar cells, thin-film cells, and concentrated photovoltaics have unique modeling considerations.

This photoelectric model focuses on the fundamental generation of charge carriers. It’s the essential first step in understanding why a solar cell works and what limits its theoretical current output.

Conclusion

The photoelectric effect is not just a fascinating quantum phenomenon; it’s the very heartbeat of a solar cell. By understanding its equation and translating it into a simple computational model, you can grasp how light energy is converted into electrical charge carriers.

We’ve walked through:

The core photoelectric equation and its terms.
How the work function relates to a semiconductor’s band gap.
Calculating photon energy and a material’s threshold wavelength.
Modeling basic current generation from monochromatic light.
A conceptual approach to handling full solar spectrums.

This foundational knowledge empowers you to analyze solar cell materials, understand their limitations, and even predict their ideal performance under specific lighting conditions. From here, you can delve deeper into more complex PV modeling, optimizing designs, and contributing to the future of renewable energy.

Last updated on June 17, 2025

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