The minority carrier lifetime of a material is the average time which a carrier can spend in an excited state after electron-hole generation before it recombines. Calculate the minority carrier lifetime (in μs ) for a single crystalline solar cell having diffusion length of Ld=200μm and minority carrier diffusivity of D=27cm2/s .
To calculate the minority carrier lifetime, we can use the following formula:
τ = (Ld)^2 / (2D)
where:
τ is the minority carrier lifetime
Ld is the diffusion length
D is the minority carrier diffusivity
Now, let's plug in the given values into the formula:
τ = (200 μm)^2 / (2 * (27 cm^2/s))
First, let's convert the diffusion length from micrometers (μm) to centimeters (cm):
200 μm = 200 * 10^(-4) cm = 0.02 cm
Plugging in the values:
τ = (0.02 cm)^2 / (2 * (27 cm^2/s))
Now, let's calculate it step by step:
τ = (0.02 cm * 0.02 cm) / (2 * 27 cm^2/s)
τ = 0.0004 cm^2 / (54 cm^2/s)
τ = 0.0004 cm^2 * s / 54 cm^2
τ = 0.000007407 s
Finally, let's convert the result from seconds (s) to microseconds (μs):
0.000007407 s = 7.407 μs
Therefore, the minority carrier lifetime for the given single crystalline solar cell is approximately 7.407 μs.