Silicon-based solar cells Characteristics and production processes ...

Silicon-based solar cells – characteristics and production processes
If the electrodes of the cell are not short-circuited, then the result of the negative
accumulation in the p area and the positive accumulation in the p will be an electric
potential and the resulting photovoltage V, which lowers the energy barrier on the
p-n junction. This causes a density increase of the dark currents up to the value
compensating the density of the reverse current. This state corresponds to the
highest value of the cell’s photovoltage, which is called the open circuit voltage V oc
and which, according to (2), can be calculated from the following equation [17]:
kT ⎛ J ⎞
V = ⎜ + 1
⎟
oc
ln
(5)
q ⎝ J
0 ⎠
With the assumption that all the impurity atoms are ionized and the value of the
charge concentration in the equilibrium state in the semi-conductor equals n p N A =
p n N E , we can prove that [16]:
d
( V )
dT
⎡ E ⎤
oc 1
g
= ⎢Voc
− ⎥
(6)
T ⎣ q ⎦
The formula describes the voltage change of the cells’ open circuit with respect to
temperature. The knowledge of this dependence is highly significant in the
measurements of the cell’s I-V characteristics and its practical exploitation. For
example, for a Si cell, when V oc equals 0,6 V, a temperature rise of one degree Celsius
will cause a 1,7 mV drop of V oc .
2.2 Reflection and absorption of electromagnetic radiation
For the radiation operating on the surface of the solar cell, it is necessary to
minimize the reflection coefficient R ref and the transmission coefficient T in such
a way so as the total radiation can be absorbed within the volume of the cell’s active
material. The absorption coefficient α = 4πνξ/c is equal to the inverse density x of
that material’s layer in which the radiation force P(0) of frequency ν decreases
e times assuming the value P(x) according to the relation P(x) = P(0)e -αx . The quantity
ξ is the extinction coefficient which is connected with the light refractive index n with
the formula n * = n-iξ, where n * designates the complex refractive index. In the case of
oblique transitions, as is the case of silicon, α assumes the value A(ν)[hν-E g ±E p ] 2 /
{±exp(±E p /kT)-(±1)}, where: E p is the photon energy value, A(ν) is the function
of energy and the reduced mass of the charge carriers and ± determines whether the
photon is absorbed (+) or emitted (-) [18]. For the crystalline silicon, R ref has the value
of about 0,35 and thus its reduction is necessary. This is realized by coating the front
surface of the cell with an antireflective layer (ARC) or by texturizing the cell’s
18