Band gap by technology, given coefficient

Method

The band gap in the saturation-current law (1) is the cell technology's, from the table below. Mermoud and Lejeune give 1.12 eV for silicon and no value for thin films, whose values come from the module model's own documentation. The temperature coefficient of the ideality factor (2) is the value given with the module: the paper's optional correction that gives the module its stated power temperature coefficient. When the module gives none, or gives 0, the coefficient is fitted so that the curve's maximum power at 1000 W/m² falls from 25 °C to 45 °C by the module's power temperature coefficient (3).

Settings

Cell technology	Band gap $E_g$
Cadmium telluride	1.5 eV
Copper indium gallium selenide	1.03 eV
Amorphous silicon	1.7 eV
Crystalline silicon, or no technology given	1.12 eV

The math

1. Saturation current
2. Ideality factor
3. The fitted coefficient

$$I_0 = \max\!\left(2.07 \times 10^{-14}\ \text{A},\ I_{0,ref}\left(\frac{T}{T_{ref}}\right)^3 \exp\!\left[\frac{E_g}{\gamma_d\,k_B}\left(\frac{1}{T_{ref}} - \frac{1}{T}\right)\right]\right) \tag{1}$$ $$\gamma_d = \gamma_{d,ref} + \mu_{\gamma}\,(T - T_{ref}) \tag{2}$$ $$P_{mp}(G_{ref}, T_{45}) = P_{mp}(G_{ref}, T_{ref})\left[1 + \mu_{P}\,(T_{45} - T_{ref})\right] \tag{3}$$

where

Symbol	Meaning	Unit
$I_0$	the diode saturation current	A
$I_{0,ref}$	the saturation current at reference conditions	A
$T$	the cell temperature	K
$T_{ref}$	the cell temperature of standard test conditions, 25 °C	K
$E_g$	the band gap	J
$k_B$	Boltzmann's constant. 1.380649 × 10⁻²³ J/K	J/K
$\gamma_d$	the diode ideality factor	—
$\gamma_{d,ref}$	the ideality factor at standard conditions	—
$\mu_{\gamma}$	the temperature coefficient of the ideality factor	1/K
$P_{mp}(G, T)$	the maximum power of the module curve at irradiance $G$ and cell temperature $T$	W
$G_{ref}$	the irradiance of standard test conditions, 1000 W/m²	W/m²
$T_{45}$	45 °C	K
$\mu_{P}$	the module's power temperature coefficient	1/K

References

1. Mermoud & Lejeune 2010, Performance assessment of a simulation model for PV modules of any available technology, 25th European Photovoltaic Solar Energy Conference

API

options.module_temperature_fit = band_gap_by_technology

Symbols follow the symbol registry.