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.
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To calculate the minority carrier lifetime (τ), we can use the equation:
τ = Ld^2 / 2D
where:
- Ld is the diffusion length of the minority carrier
- D is the minority carrier diffusivity
In this case, Ld = 200 μm and D = 27 cm²/s. However, we need to make sure the units are consistent before using the equation.
First, let's convert Ld from micrometers (μm) to centimeters (cm):
Ld = 200 μm = 200 × 10^(-4) cm = 0.02 cm
Next, let's convert D from cm²/s to μm²/s:
D = 27 cm²/s = 27 × 10^(-4) μm²/s = 0.0027 μm²/s
Now we can substitute these values into the equation to find the minority carrier lifetime:
τ = (0.02 cm)^2 / (2 × 0.0027 μm²/s)
Simplifying the equation:
τ = (0.0004 cm²) / (0.0054 μm²/s)
To divide these values, we need to convert both values to the same unit. Let's convert them both to centimeters:
τ = (0.0004 cm²) / (0.000054 cm²/s)
We can cancel out the square centimeters and calculate the result:
τ = 0.0004 cm² / 0.000054 cm²/s ≈ 7.4 s
Therefore, the minority carrier lifetime is approximately 7.4 seconds (s).