California Polytechnic State University -- Solid State Physics Laboratory
Experiment 27: Characteristics of Photovoltaic Cells
Scope
The output current-voltage characteristic curve for a photovoltaic cell for different input
intensities and the conditions for optimum power transfer to an external load are determined.
Introduction
see Brown 8.4
If a p-n junction diode is bathed in electromagnetic radiation such that hc/λ>Eg, then
electron-hole pairs will be optically stimulated into the conduction band. If the diode is such that
incident radiation reaches the depletion region, then the photo generated electrons and holes will
be swept by the junction field into the regions in which they are majority carriers. This has the
effect of increasing the generation current. The generation current due to optically stimulated
electron-hole pairs is
therefore proportional to the
intensity of the radiation.
Eg
#$
+
In the absence of any
external connections, no net
current could flow across the
! IIgen
p-type
n-type
junction. So any optically
" diff
stimulated carriers swept
across the junction would
have the effect of forward
biasing the diode. That is,
electrons
the electron-hole pairs
+
within the depletion region
stimulated by the incident
holes
light are swept by the
junction field to the regions
in which they are majority.
(a) Equilibrium diode
(b) Photostimulated diode
The increase in conduction
Figure 1: The energy band diagram and distributions of electrons and holes near
the depletion region of the pn junction diode (a) in equilibrium, and (b) under
band electrons in the nphotostimulation.
region near the junction
makes that region less positive (the same effect as if forward biased). The optically stimulated
generation current thus increases the concentration of conduction band electrons in the n-region
which in turn increases the diffusion of electrons from the n- to the p-region. A new equilibrium
is established when the resulting increase in diffusion current balances the photo generation
current.
EF
%
-
#$
The device becomes useful only when an external path is provided for the flow of
"excess" n-region electrons back to the p-region. That is, if an external path is available, the
diffusion current required to establish thermal equilibrium is divided between flow back across
the junction and through the external circuit. The incident light can thus generate an electric
current in an external circuit - and some of the photo energy absorbed by the diode in stimulating
Characteristics of Photovoltaic Cells
27-1
California Polytechnic State University -- Solid State Physics Laboratory
electrons into the conduction band in the depletion region appears as work done or heat
generated in the external circuit load.
Since the external circuit and the junction itself are alternate paths for diffusion of
electrons from the n to the p regions, the effective junction resistance can be thought of as being
in parallel with the path which includes the n and p regions and the external load resistance. In
open circuit, that is in the absence of an external path (or with an infinite load resistance), the
photo stimulation of the diode promotes an open circuit voltage due to the shift of the energy
bands. With an external load, some of the diffusion current flows in the external circuit.
n
p
I0
RP
I0
RN
IJ
IJ
RJ
IL
IL
RL
RL
Figure 2: The equivalent circuit for a photovoltaic cell.
Letting Io represent the generation current due to photostimulation (which therefore only
changes if the incident flux changes) requires that Io = IL + IJ, where IL is the current through the
load (which is in series with the p and n regions) and IJ is the diffusion current through the
depletion region. Using the equivalent circuit, and letting RJ be the junction resistance, RS the
sum of the resistances of p and n regions, and RL as the external load resistance, the effective
resistance of the equivalent circuit is given by
Reff =
RJ ( RS + RL )
RS + RJ + RL
Since IL (RS+RL) must be equal Io Reff, the current through the load can be written in terms of
the generation current and the diode and load resistances,
!
$
RJ
&& I0
IL = ##
" RS + RJ + RL %
The total power delivered to the load resistance would then be just IL2RL, or
!
$
RJ2 RL
#
&
PL = I #
2&
" (RS + RL + RJ ) %
2
0
27-2
Characteristics of Photovoltaic Cells
California Polytechnic State University -- Solid State Physics Laboratory
The power delivered to the load is, of course, dependent on the load resistance. If the circuit
were open, equivalent to RL = ∞, no current would flow and power delivered would be zero. If
the diode were short circuited, the current would be maximized, but power would again be zero
since there would be no voltage drop. Maximizing the power delivered (with respect to changes
in load resistance) requires that the load resistance equal the sum of the internal diode
resistances: RL (at max. power) = RS+RJ.
The maximum output voltage occurs in the open circuit condition (RL = ∞) and is given
by VL (max) = IoRJ, which must be equal to the shift in the junction potential due to optical
stimulation.
The maximum output current would occur in the short circuit condition (RL = 0), and
would be given by
! R $
J
&& I0
IL ( max ) = ##
" RS + RJ %
It should also be noted that the ratio of the open circuit voltage to the short circuit current
is equal to the sum of the diode resistances, which is also the load resistance required for
maximum power output.
Procedure
Carefully measure the output voltage and output current as functions of load resistance
for three different light intensities.
I
V
Solar
cell
Use the flux meter to determine the input intensities (be sure you understand the scale).
Since the efficiency of a diode is dependent on its temperature, you will want to be careful that
the photocell temperature is kept constant throughout the experiment. Be sure that your data will
allow you to obtain graphs of the I-V characteristic curve for the photovoltaic cell and the output
power as a function of load resistance. In order to determine the efficiency of the photocell, you
will need to know its dimensions.
To see the effect of temperature on the efficiency of a photocell, monitor the output
voltage and current with the load resistance set for maximum power output, but with the cooling
fan turned off.
Report
Characteristics of Photovoltaic Cells
27-3
California Polytechnic State University -- Solid State Physics Laboratory
•
•
•
•
Graph the current through the load as a function of the output voltage for all three input
intensities on a single graph.
Graph the power delivered to the load resistance as a function of the logarithm of the load
resistance. Determine the load resistance at which the output power is a maximum.
Calculate the energy conversion efficiency of the photovoltaic cell for each of the three input
intensities.
Determine if the load resistance at maximum power is equal to the ratio of the open circuit
voltage and closed circuit current to within experimental uncertainty.
Questions and Discussion
•
•
•
•
•
Why should you expect that the output voltage is essentially independent of load resistance
as RL becomes increasingly larger?
Show that the maximum power output occurs when the load resistance equals the resistance
of the diode. (This is called impedance matching.)
Is the load resistance that yields the maximum power output the same for all light intensities?
Explain why you should expect that result.
Identify the main reasons why the photocell is not 100% efficient.
Explain the effect of temperature on the efficiency of the photocell.
27-4
Characteristics of Photovoltaic Cells