What is the penetration depth of light with wavelength λ = 560 nm in c-Si?

The **penetration depth** of light into a material is the distance over which the light intensity drops to 1/e (about 37%) of its initial value. For crystalline silicon (c-Si), the penetration depth depends on the wavelength of light and the material's optical properties (such as absorption coefficient).

For a wavelength \( \lambda = 560 \, \text{nm} \), the penetration depth \( d \) in crystalline silicon is determined using the absorption coefficient \( \alpha(\lambda) \), according to the formula:

\[
d = \frac{1}{\alpha(\lambda)}
\]

At \( \lambda = 560 \, \text{nm} \) (green light), the absorption coefficient \( \alpha \) for crystalline silicon is typically around \( 1.7 \times 10^4 \, \text{cm}^{-1} \).

Thus, the penetration depth \( d \) is calculated as:

\[
d = \frac{1}{1.7 \times 10^4 \, \text{cm}^{-1}} = 5.88 \times 10^{-5} \, \text{cm} = 588 \, \text{nm}
\]

So, the penetration depth of light with wavelength \( \lambda = 560 \, \text{nm} \) in crystalline silicon is approximately **588 nm**.

Would you like further clarification or additional details?

Here are 5 related questions:
1. How does the absorption coefficient vary with wavelength in silicon?
2. What are the typical applications of light penetration depth in photovoltaics?
3. How does the refractive index of silicon affect light interaction at different wavelengths?
4. Can the penetration depth change with temperature in crystalline silicon?
5. What is the penetration depth of infrared light in c-Si?

**Tip:** For better light absorption in photovoltaic cells, thin layers of silicon or anti-reflective coatings are often used to enhance the interaction between light and the material.

Explore the calculation of the penetration depth of light with wavelength 560 nm in crystalline silicon (c-Si). This detailed solution involves optical physics concepts like absorption coefficient and provides the formula for determining the depth where light intensity decreases to 37%. Ideal for undergraduate physics or engineering students.

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