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Minority carrier lifetime of a Solar Cell and its C - V
characteristics
Aim of the Experiment
To measure the open circuit voltage decay of a crystalline
silicon solar cell and calculate minority carrierlife time.
Part 1 : Relation between minority carrier lifetime and the open
circuit voltage decay
Both these experiments use a PN junction. For simplicity, we
consider a P+N junction. Considering an-doped semiconductor with a
shallow donor concentration given by Nd donors /cm
3 . We focus on theN region. Electrons are the majority carriers
and holes are the minority carriers in the N region. Theequilibrium
minority carrier concentration is given by p0 = (n
2i )/Nd . Since we are dealing with a P
+None sided junction, we will ignore the depletion region in the
P+ region. Fig. 1(a) shows only the Nregion in the dark. The N
region consists of a depletion region of width d0 and a neutral
region of widthW - d0 where W is the thickness of the N region.
W
d0
dL L
(a)
(b)Figure 1: N region (a) in dark (b) under illumination
If light of energy > Eg is incident on the semiconductor,
light is absorbed and increases the carrierconcentration of both
carriers - holes and electrons. We choose the intensity of the
light such that thehole concentration in the N region under
illumination is given by pL so that Nd pL p0.
Under illumination the N type region spontaneously breaks up
into two parts - Fig. 1(b). Minoritycarriers (holes) generated
within a diffusion length (L) of the depletion region (shown as dL
in fig 2) candiffuse to the junction and give rise to a current in
the external circuit. (Current generation region inaddition to the
current generation region of the depletion region). Carriers
generated in the region W -
L - dL are lost by recombination (Recombination region).
Under illumination, the diode develops forward bias. At a given
forward bias, carriers are lost due toextraction and to
recombination. We can assume that the depletion region (dL) is
negligibly small atVOCas the cell is under forward bias.
At VOCcarriers can be lost only by recombination. Hence the
decay of the open circuit voltage whenthe light is turned off is a
measure of the minority carrier lifetime . The minority carrier
lifetime ishence given by,
1
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Figure 2: PN junction. (Source: wikipedia)
where is the relative permittivity and 0 the permittivity of
vacuum. A is the device area and xd thedepletion layer thickness.If
we assume that dV is small, then the donor concentration is
approximately constant for the smallmodulation of the depletion
width.
dQ = q Nd(xd) xd (2)
dV =q Nd xd xd xd
0(3)
C
V = (
C
xd) (
xdV
) (4)
Using equations 1 4, we can write
Nd(xd) = -C3(
1
0A2
) ( C
V )1 (5)
A measurement of C and C / V Vs V will determine the doping
profile.Eq. 5 can also be written as
( Nd(xd) )1 = - 1
2C3( q 0 A
2 ) ( d ( 1 / C2) / dV )
3
