☀️ Solar Cell I-V Curve

A photovoltaic cell is a large-area p-n junction that converts photons into electricity. The Shockley diode equation gives the current as a function of terminal voltage; the operating point shifts with irradiance and temperature.

Voc: - V
Isc: - A
Pmax: - W
FF: -
PCE: - %
Vmp: - V

How it works

The single-diode model with series resistance gives the implicit I-V equation:

I = Iph − I0 ⋅ [exp(q(V + IRs) / nkT) − 1]

The photocurrent Iph = Iph0 ⋅ G/GSTC scales with irradiance. Increasing temperature reduces Voc (≈ −2 mV/K for silicon) while slightly increasing Isc.

Fill factor FF = Pmax / (Isc ⋅ Voc) measures the "squareness" of the I-V curve. High series resistance degrades FF. Ideal cells have FF ≈ 0.85.

The power conversion efficiency PCE = Pmax / (G ⋅ Acell) where Acell = 0.01 m² (100 cm²).

The left half of the canvas shows a simplified band diagram with the p-n junction, depletion region, photon absorption, and minority carrier drift under the built-in field.

About the Solar Cell I–V Curve

This simulation models a silicon photovoltaic cell using the single-diode equation with series resistance: I = Iph − I0·[exp(q(V + IRs)/nkT) − 1]. Because the current appears on both sides, the page solves it iteratively at 300 voltage points to trace the I–V and P–V curves, then extracts the open-circuit voltage, short-circuit current, maximum power point, fill factor and efficiency.

Five sliders set irradiance G (100–1400 W/m²), temperature T (250–380 K), diode ideality factor n, dark saturation current I0 and series resistance Rs. An accompanying band diagram shows the p–n junction, depletion region and photon absorption. Understanding these curves is central to sizing solar panels, maximum-power-point tracking and predicting yield in real installations.

Frequently Asked Questions

What is a solar cell I–V curve?

It is the relationship between the current a photovoltaic cell delivers and the voltage across its terminals, from short circuit to open circuit. Every point on the curve is a possible operating state; the panel only generates useful power at the maximum power point (MPP) where the V×I product peaks.

What equation does this simulation use?

It uses the single-diode model with series resistance: I = Iph − I0·[exp(q(V + IRs)/nkT) − 1]. The photocurrent Iph scales linearly with irradiance, while the diode term sets the exponential roll-off near the open-circuit voltage.

Why is the equation solved iteratively?

The series resistance Rs makes the current appear on both sides of the equation (inside the exponential as IRs), so it is implicit and cannot be rearranged algebraically. The simulation uses a fixed-point loop of up to 100 iterations per voltage step to converge on the current.

What do the irradiance and temperature sliders do?

Irradiance G scales the photocurrent, so raising it lifts the whole curve and increases the short-circuit current Isc almost proportionally. Temperature mainly lowers the open-circuit voltage by roughly 2 mV per kelvin for silicon, slightly raising Isc, which is why hot panels lose efficiency.

What is the fill factor?

The fill factor FF = Pmax / (Isc·Voc) measures how “square” the I–V curve is. A perfect rectangle would give FF = 1; good silicon cells reach about 0.80–0.85. Increasing the series resistance slider visibly tilts the knee of the curve and drives the fill factor down.

How is power conversion efficiency calculated here?

Efficiency PCE = Pmax / (G·Acell), expressed as a percentage. The model assumes a cell area Acell of 0.01 m² (100 cm²), so it divides the peak electrical power by the optical power landing on that area at the chosen irradiance.

What does the ideality factor n represent?

The ideality factor describes how closely the junction follows ideal diode behaviour. A value of 1 implies recombination is dominated by diffusion in the bulk, while values approaching 2 indicate significant recombination in the depletion region. Raising n softens the exponential and shifts the open-circuit voltage.

What is the dark saturation current I0?

I0 is the tiny leakage current that flows under reverse bias with no light, set by carrier recombination in the cell. A larger I0 lowers the open-circuit voltage, since Voc ≈ nkT/q · ln(Iph/I0 + 1). The slider spans a realistic 10−11 to 10−9 A range.

Is this simulation physically accurate?

It captures the correct qualitative physics and realistic trends for a single silicon cell, including the irradiance, temperature, resistance and ideality dependencies. It is simplified: it omits shunt resistance, spectral effects and partial shading, and uses representative rather than datasheet-exact parameters, so treat the figures as illustrative.

What is the maximum power point and why does it matter?

The MPP is the single voltage where the product of current and voltage is largest, marked on the plot. Real systems use maximum-power-point tracking (MPPT) electronics to hold the panel at this point as sunlight and temperature change, extracting up to 30% more energy than a fixed operating voltage would.

Why does the band diagram split the Fermi level?

Under illumination the single equilibrium Fermi level separates into two quasi-Fermi levels for electrons and holes. The size of this splitting corresponds to the photovoltage the cell can produce; the diagram widens the gap as the open-circuit voltage rises, illustrating how absorbed photons drive charge separation across the junction.