Absorption Depth Calculator
Absorption depth δ = 1/α, the depth for 90 % absorption and the fraction absorbed in a layer, from measured α(λ) of silicon (Green 2008) and water (Pope & Fry, Segelstein) or your own α.
Absorption Coefficient α
6390 cm⁻¹
at 550.0 nm; Green 2008, band-to-band
Absorption Depth δ = 1/α
1.565 µm
intensity falls to 1/e (36.8 %)
Depth for 90 % Absorbed
3.603 µm
ln 10 · δ = 2.303 δ
Absorbed within d
99.83 %
1 − e^(−αd), of the light that enters
I(z) = I₀ · exp(−αz), δ = 1/α, α = 4πk/λ₀
Decadic absorbance of a layer: A = αd / ln 10. Surface reflection is not included: the percentages refer to the light that enters.
Intrinsic silicon at 300 K, band-to-band absorption only. Free-carrier absorption in doped silicon adds to α beyond about 1.1 µm.
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Exact Beer–Lambert decay on measured absorption data, interpolated log-linearly between tabulated points: intrinsic silicon at 300 K (band-to-band only) and pure water at room temperature; surface reflection excluded.
- Green M. A. (2008). Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients. Sol. Energy Mater. Sol. Cells 92, 1305–1310. doi:10.1016/j.solmat.2008.06.009
- Pope R. M., Fry E. S. (1997). Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements. Appl. Opt. 36, 8710–8723. doi:10.1364/AO.36.008710
- Segelstein D. J. (1981). The complex refractive index of water. M.S. thesis, University of Missouri–Kansas City; tabulated at omlc.org/spectra/water. omlc.org
- Hale G. M., Querry M. R. (1973). Optical constants of water in the 200-nm to 200-μm wavelength region. Appl. Opt. 12, 555–563. doi:10.1364/AO.12.000555