76
S. Leu and D. Sontag
Fig. 4.2 Illustration of the
absorption of light within a
silicon crystal
illustrated in Fig. 4.2, the light intensity I E (x) decreases exponentially within the
material at the position x. One has the following function for the light intensity I E :
I E (x) = I E0 e
−αx
(4.1)
The absorption depth d α indicates how deep light of a specific wavelength λ
penetrates into the material, before its intensity has fallen to 1/e, e.g. ≈ 36% of its
original intensity.
3 In silicon (and in most other semiconductors used for solar cells),
d α increases for increasing wavelengths λ. For light with a wavelength λ = 575 nm,
the absorption depth d α is 1 μm and for λ = 980 nm d α is already 100 μm. At longer
wavelengths there is, thus, the danger that some of the photons leak out from the
back side of the solar cell.
For semiconductors with direct transitions (like GaAs, CdTe, etc.), an electron,
which absorbs the energy of a photon, does not need to change its momentum.
4
The crystal structure is formed in such a way that in the diagram of Energy versus
3 e ≈ 2.71828… is a mathematical constant called “Euler’s number”—it is the base of the natural
logarithm.
4 In contrast to energy, the momentum has an amount and a direction. In quantum physics, light,
electrical current and mechanical vibration are all represented by “quanta” or “elementary particles”.
• for light: photons
• for electrical current: electrons
• for mechanical vibration: phonons.
These particles are not only characterized by their energy E but also by their momentum P.
For a transition, i.e. from valence band to conduction band, it is necessary to consider not only
energy but also momentum. In a rough approximation one can say: electrons have both energy
and momentum; photons have energy but zero momentum; phonons have very little energy, but
considerable momentum.
Since the momentum of a photon is zero it cannot change the momentum of an electron-holepair. This requires the additional vibrational energy of the crystal lattice, which is transmitted by a
phonon.
S. Leu and D. Sontag
Fig. 4.2 Illustration of the
absorption of light within a
silicon crystal
illustrated in Fig. 4.2, the light intensity I E (x) decreases exponentially within the
material at the position x. One has the following function for the light intensity I E :
I E (x) = I E0 e
−αx
(4.1)
The absorption depth d α indicates how deep light of a specific wavelength λ
penetrates into the material, before its intensity has fallen to 1/e, e.g. ≈ 36% of its
original intensity.
3 In silicon (and in most other semiconductors used for solar cells),
d α increases for increasing wavelengths λ. For light with a wavelength λ = 575 nm,
the absorption depth d α is 1 μm and for λ = 980 nm d α is already 100 μm. At longer
wavelengths there is, thus, the danger that some of the photons leak out from the
back side of the solar cell.
For semiconductors with direct transitions (like GaAs, CdTe, etc.), an electron,
which absorbs the energy of a photon, does not need to change its momentum.
4
The crystal structure is formed in such a way that in the diagram of Energy versus
3 e ≈ 2.71828… is a mathematical constant called “Euler’s number”—it is the base of the natural
logarithm.
4 In contrast to energy, the momentum has an amount and a direction. In quantum physics, light,
electrical current and mechanical vibration are all represented by “quanta” or “elementary particles”.
• for light: photons
• for electrical current: electrons
• for mechanical vibration: phonons.
These particles are not only characterized by their energy E but also by their momentum P.
For a transition, i.e. from valence band to conduction band, it is necessary to consider not only
energy but also momentum. In a rough approximation one can say: electrons have both energy
and momentum; photons have energy but zero momentum; phonons have very little energy, but
considerable momentum.
Since the momentum of a photon is zero it cannot change the momentum of an electron-holepair. This requires the additional vibrational energy of the crystal lattice, which is transmitted by a
phonon.