absorption profile of photons in semiconductor devices is by using Lambert-Beer’s law
that we introduced in Eq. (4.25), where it was formulated for the decay of intensity. Here
we formulate it with the photon flux Φ ph,λ (x), which decreases exponentially with the
distance x travelled through the absorber,
where
is the incident photon flux and α(λ) is the absorption coefficient. The photon
flux is defined as the number of photons per unit area, unit time and unit wavelength. As
we have seen in Chapter 5, it is related to the spectral irradiance I eλ of the solar radiation
via
The spectral generation rate G L,λ (x), which is the number of electron-hole pairs
generated at a depth x in the film per second unit volume and unit wavelength, by photons
of wavelength λ, is calculated according to
where we assume zero reflection. η g is the generation quantum efficiency, usually assumed
equal to unity. This assumption means that every photon generates one and only one
electron-hole pair. The optical generation rate G L (x) is calculated from the spectral
generation rate by integrating over the desired wavelength range,
It has the unit [G L ] = cm
−3 s
−1 . The optical generation rate is related to the absorption
profile A(x) in the film via
Hence,
Because of the photogeneration, excess electrons and holes will be created. The rate
of the generated excess electrons’ concentration is equal to the rate of the generated excess
hole concentration per second; therefore we can write
Example
Let us calculate the total absorption in a d = 300 μm thick c-Si wafer for light with an incident irradiance of
1,000 Wm −2 . For simplicity, we assume that all the light has a wavelength of 500 nm. The optical constants of cSi at this wavelength are: refractive index is n = 4.293, extinction coefficient k = 0.045 and absorption coefficient
that we introduced in Eq. (4.25), where it was formulated for the decay of intensity. Here
we formulate it with the photon flux Φ ph,λ (x), which decreases exponentially with the
distance x travelled through the absorber,
where
is the incident photon flux and α(λ) is the absorption coefficient. The photon
flux is defined as the number of photons per unit area, unit time and unit wavelength. As
we have seen in Chapter 5, it is related to the spectral irradiance I eλ of the solar radiation
via
The spectral generation rate G L,λ (x), which is the number of electron-hole pairs
generated at a depth x in the film per second unit volume and unit wavelength, by photons
of wavelength λ, is calculated according to
where we assume zero reflection. η g is the generation quantum efficiency, usually assumed
equal to unity. This assumption means that every photon generates one and only one
electron-hole pair. The optical generation rate G L (x) is calculated from the spectral
generation rate by integrating over the desired wavelength range,
It has the unit [G L ] = cm
−3 s
−1 . The optical generation rate is related to the absorption
profile A(x) in the film via
Hence,
Because of the photogeneration, excess electrons and holes will be created. The rate
of the generated excess electrons’ concentration is equal to the rate of the generated excess
hole concentration per second; therefore we can write
Example
Let us calculate the total absorption in a d = 300 μm thick c-Si wafer for light with an incident irradiance of
1,000 Wm −2 . For simplicity, we assume that all the light has a wavelength of 500 nm. The optical constants of cSi at this wavelength are: refractive index is n = 4.293, extinction coefficient k = 0.045 and absorption coefficient