Greeting All, please assist with the below. Thanks.
The spectral power density of a solar simulator is given by:
P(λ)=7.5∗1015λ−2.25∗109 [Wm^-2m^-1] for 300nm<λ<500nm
P(λ)=2.25∗109−1.5∗1015λ [Wm^-2m^-1] for 500nm<λ<1500nm
Where the wavelength λ is expressed in meters.
Calculate the short circuit current density Jsc (in mA/cm2) of a solar cell if the solar cell is measured under the solar simulator under STC.
EQE=0.8 for 300nm<λ<500nm
Look in the related questions below.....
Its the first one there...
To calculate the short circuit current density Jsc of a solar cell under the solar simulator, we need to integrate the spectral power density P(λ) over the wavelength range where EQE (External Quantum Efficiency) is non-zero.
In this case, the EQE is 0.8 for 300nm < λ < 500nm. So, we need to integrate P(λ) over this range. We can use the following formula:
Jsc = ∫ P(λ) * EQE dλ
Let's break down the steps to calculate Jsc:
Step 1: Convert the wavelength range from nm to meters.
300 nm = 300 * 10^-9 m
500 nm = 500 * 10^-9 m
Step 2: Integrate the spectral power density over the wavelength range with the given equations:
Jsc = ∫ [7.5 * 10^15 λ^(-2.25) * 10^-9] * 0.8 dλ + ∫ [(2.25 * 10^9 - 1.5 * 10^15 λ) * 10^-9] * 0.8 dλ
Step 3: Solve the integrals:
The first integral can be solved using the power rule:
∫ x^n dx = (1/(n+1)) * x^(n+1)
∫ [7.5 * 10^15 λ^(-2.25) * 10^-9] * 0.8 dλ = (1/(2.25-1)) * 7.5 * 10^15 * (λ^(-1.25)) * 10^-9
The second integral can be solved as:
∫ [(2.25 * 10^9 - 1.5 * 10^15 λ) * 10^-9] * 0.8 dλ = 0.8 * [(2.25 * 10^9 * λ - (1.5 * 10^15 * λ^2)/2) * 10^-9]
Step 4: Evaluate the integrals at the upper and lower bounds of the wavelength range and subtract them:
Jsc = [(1/(2.25-1)) * 7.5 * 10^15 * (500^(-1.25)) * 10^-9 - (1/(2.25-1)) * 7.5 * 10^15 * (300^(-1.25)) * 10^-9] + [0.8 * [(2.25 * 10^9 * 500 - (1.5 * 10^15 * 500^2)/2) * 10^-9 - (2.25 * 10^9 * 300 - (1.5 * 10^15 * 300^2)/2) * 10^-9]]
Finally, we convert the result from Wm^(-2)m^(-1) to mA/cm^2 by multiplying it by 10^3 (to convert W to mW) and dividing by the solar cell area in cm^2.
Note: Make sure to use proper units (meters for λ, Wm^(-2)m^(-1) for P(λ), and mA/cm^2 for Jsc) in the calculations.