90
S. Leu and D. Sontag
n i
denotes the intrinsic density of charge carriers
14 and is in Standard SI units
15 :
10
10 cm
−3 for silicon
n, p are the concentrations of electrons and of holes
for electrons: n = n 0 + n
for holes: p = p 0 + p
n 0 , p 0
number of electrons, holes in the unexcited (dark) intrinsic state
n, p excess carriers: electrons, holes
B
is the constant of radiative recombination
B is a temperature-dependent and material-dependent constant and characterizes
radiative recombination. In silicon it has, at room temperature, the value: B Si =
~10
−15 cm
3 s
−1 .
In gallium arsenide, we have, at room temperature B GaAs = ~10
−10 cm
3 s
−1 : this
is, thus, a value that is 100,000 times larger than for silicon. This shows that radiative
recombination occurs less frequently and is not so important for indirect-bandgap
semiconductors such as silicon—when compared to direct-bandgap semiconductors,
such as gallium arsenide. Radiative recombination is a material-inherent type of
recombination and does not depend on impurities or doping. It is present in all
semiconductors.
2. Shockley-Read-Hall (SRH) Recombination
In all semiconductors there are also defects caused by impurities, such as oxygen,
carbon or iron. If these impurities (defects) are located on crystal lattice sites of the
silicon wafer, they lead to additional energy levels within the bandgap. These energy
levels are easier to reach for electrons and holes. They can climb down like on a
staircase, which is easier for them, than crossing the whole bandgap in one step.
They, thus, act on the charge carriers as recombination centres. Iron introduces an
energy state that is located in the middle of the Si bandgap. Iron is, thus, attractive
for both electrons and holes and acts as a strong recombination centre. Ni, Cu, Au
and oxygen precipitates—also promote recombination and are strong lifetime-killers.
SRH recombination is the predominant type of recombination in silicon photovoltaic
solar cells. In particular, it will take place in different steps as shown in Fig. 4.13 [5]:
• An electron can be trapped by the defect, Case I
• A hole can be trapped by the defect, Case III.
On the other hand, electron-hole pairs can also be generated starting from the
defect states:
14 The intrinsic carrier density n i is the density of carriers in an undoped sample of the same material
(here: crystalline silicon), which is not subjected to any external field or other activation (e.g. light).
Its value (for silicon) is at room temperature approximately 1 × 10 10 cm −3 .
15 «SI units» refers to the International System of Units (SI, abbreviated from the French Système
international [d’unités]); it is the modern form of the metric system and is the most widely used
system of measurement.
S. Leu and D. Sontag
n i
denotes the intrinsic density of charge carriers
14 and is in Standard SI units
15 :
10
10 cm
−3 for silicon
n, p are the concentrations of electrons and of holes
for electrons: n = n 0 + n
for holes: p = p 0 + p
n 0 , p 0
number of electrons, holes in the unexcited (dark) intrinsic state
n, p excess carriers: electrons, holes
B
is the constant of radiative recombination
B is a temperature-dependent and material-dependent constant and characterizes
radiative recombination. In silicon it has, at room temperature, the value: B Si =
~10
−15 cm
3 s
−1 .
In gallium arsenide, we have, at room temperature B GaAs = ~10
−10 cm
3 s
−1 : this
is, thus, a value that is 100,000 times larger than for silicon. This shows that radiative
recombination occurs less frequently and is not so important for indirect-bandgap
semiconductors such as silicon—when compared to direct-bandgap semiconductors,
such as gallium arsenide. Radiative recombination is a material-inherent type of
recombination and does not depend on impurities or doping. It is present in all
semiconductors.
2. Shockley-Read-Hall (SRH) Recombination
In all semiconductors there are also defects caused by impurities, such as oxygen,
carbon or iron. If these impurities (defects) are located on crystal lattice sites of the
silicon wafer, they lead to additional energy levels within the bandgap. These energy
levels are easier to reach for electrons and holes. They can climb down like on a
staircase, which is easier for them, than crossing the whole bandgap in one step.
They, thus, act on the charge carriers as recombination centres. Iron introduces an
energy state that is located in the middle of the Si bandgap. Iron is, thus, attractive
for both electrons and holes and acts as a strong recombination centre. Ni, Cu, Au
and oxygen precipitates—also promote recombination and are strong lifetime-killers.
SRH recombination is the predominant type of recombination in silicon photovoltaic
solar cells. In particular, it will take place in different steps as shown in Fig. 4.13 [5]:
• An electron can be trapped by the defect, Case I
• A hole can be trapped by the defect, Case III.
On the other hand, electron-hole pairs can also be generated starting from the
defect states:
14 The intrinsic carrier density n i is the density of carriers in an undoped sample of the same material
(here: crystalline silicon), which is not subjected to any external field or other activation (e.g. light).
Its value (for silicon) is at room temperature approximately 1 × 10 10 cm −3 .
15 «SI units» refers to the International System of Units (SI, abbreviated from the French Système
international [d’unités]); it is the modern form of the metric system and is the most widely used
system of measurement.