7.2.2
α = 1.11 × 10 4 cm −1 .
First we calculate the photon flux at 500 nm corresponding to the irradiance of 1000 Wm −2 .
Using Eq. (7.3) we obtain
Using Eq. (4.15) we calculate how many incident photons are reflected from the surface,
Using Lambert–Beer’s law (Eq. (7.2)) we calculate the photon flux at the backside of the wafer, i.e. at 300 μm
distance from the surface. We take the reflected light into account by adapting Eq. (7.2),
The total absorption in the wafer is the difference between the photon flux at the surface after reflection and the
photon flux at the back of the wafer,
When we assume that all the absorbed photons generate one electron-hole pair (η g = 1), we can calculate the
photocurrent density corresponding to the absorbed photon flux,
J ph = qA = 1.602 × 10 −19 C × 1.55 × 10 21 m −2 s −1 = 248.31 Cm −2 s −1 = 248.31 Am −2 .
Direct recombination
We will now discuss direct recombination which mainly occurs in direct bandgap
semiconductors, such as gallium arsenide. It is illustrated in Figure 7.2 (b). In this section
we roughly follow the derivation by Sze [31].
Let us first look at the situation at thermal equilibrium. If the temperature is higher
than 0 K, the crystal lattice is vibrating. This vibrational energy will be sufficient to break
bonds from time to time, which leads to the generation of electron-hole pairs at a
generation rate G th , where the th stands for thermal. As we are in thermal equilibrium, the
expression
must be valid. Hence, recombination takes place at the same rate as generation,
We may assume that the direct recombination rate is proportional to the concentration of
electrons in the conduction band and to the concentration of the available holes in the
valence band,
α = 1.11 × 10 4 cm −1 .
First we calculate the photon flux at 500 nm corresponding to the irradiance of 1000 Wm −2 .
Using Eq. (7.3) we obtain
Using Eq. (4.15) we calculate how many incident photons are reflected from the surface,
Using Lambert–Beer’s law (Eq. (7.2)) we calculate the photon flux at the backside of the wafer, i.e. at 300 μm
distance from the surface. We take the reflected light into account by adapting Eq. (7.2),
The total absorption in the wafer is the difference between the photon flux at the surface after reflection and the
photon flux at the back of the wafer,
When we assume that all the absorbed photons generate one electron-hole pair (η g = 1), we can calculate the
photocurrent density corresponding to the absorbed photon flux,
J ph = qA = 1.602 × 10 −19 C × 1.55 × 10 21 m −2 s −1 = 248.31 Cm −2 s −1 = 248.31 Am −2 .
Direct recombination
We will now discuss direct recombination which mainly occurs in direct bandgap
semiconductors, such as gallium arsenide. It is illustrated in Figure 7.2 (b). In this section
we roughly follow the derivation by Sze [31].
Let us first look at the situation at thermal equilibrium. If the temperature is higher
than 0 K, the crystal lattice is vibrating. This vibrational energy will be sufficient to break
bonds from time to time, which leads to the generation of electron-hole pairs at a
generation rate G th , where the th stands for thermal. As we are in thermal equilibrium, the
expression
must be valid. Hence, recombination takes place at the same rate as generation,
We may assume that the direct recombination rate is proportional to the concentration of
electrons in the conduction band and to the concentration of the available holes in the
valence band,