Bandgap Optimizer for Spectral Splitting Multijunction PV Systems (BOSS)
1. Introduction
The choice of individual bandgaps is important for achieving the maximum efficiency of a multijunction
photovoltaic system. BOSS uses a multijunction photovoltaic (PV) model and determines the bandgap
energies, EG, that yield the highest possible system power efficiency for a given number of PV junctions.
This numerical tool can simulate multijunction PV systems with various configurations. These include
combinations of PV junctions that are electrically in series, electrically independent but optically in
series, and optically independent, such as dichroic splitting. It also has the ability to optimize a system
holding one or more PV junctions and/or optical splitting elements constant. For example, if you want to
use silicon as one of your PV junctions, this bandgap energy can be held constant while the other
bandgap energies in the system vary. The figure below shows a variety of elementary PV system
configurations.
Fig. 1: (a) PV junctions electrically in series. (b) Top junction electrically independent from the rest but
optically in series. (c) Top junction optically independent from the remaining junctions.
2. Background
A wide variety of semiconductor materials with different bandgap energies have been investigated by
researchers to develop multiple junction solar cell systems with the highest possible system power
efficiency. While significant improvements have been made to increase the efficiency, these devices are
still below the maximum system conversion efficiency possible for a given number of junctions. As the
number of junctions and the number of optical splits increase, the number of possible system
configurations increase quickly, this makes it more difficult to locate the optimal system design. This is
one case where the optimization tool has proven to be useful.
BOSS simulates the terminal current-voltage characteristics of each individual PV junction. These results
are then used to determine the overall system power efficiency. The short-circuit current density (𝐽𝑠𝑐 ) is
found by assuming a specific collection efficiency above the bandgap energy of each junction. This
allows (𝐽𝑠𝑐 ) to be equal to the collected light current (𝐽𝐿 ) as shown below
EG ,i 1
J SC ,i  J L ,i  q
   E  dE
EG ,i
Where i is the junction number, q is the electron charge, and   E  is the photon flux density per unit
energy of the incident light spectrum. The current-voltage characteristic are simulated using the ideal
diode equation with series resistance as

J i  J SC ,i  J 0,i e
q Vi  RS ,i Ji  ni kT

1
Where V is the voltage, 𝑅𝑆 is the series resistance, n is the ideality factor, k is the boltzmann constant,
and T is the temperature. A bisection method is used to find the maximum output power of each of the
PV junctions. The current at maximum power point is given by


 J SC ,i  J 0,i  J MP ,1 N 
n
kT
ln

R
J
 i

 S ,i MP ,1 N 

J
i 1 
0,
i





N 

ni kT
R




 S ,i J  J  J
j 1 
SC , i
0, i
MP ,1 N 
N
J MP ,1 N
Where N is the number of junctions.
Each individual junction voltage is give as
 J  J 0,i  J MP,1 N
VMP,i  nkT ln  SC ,i

J 0,i


  RS ,i J MP,1 N

Therefore, the total voltage in an ith PV device for a series connected stack is just the sum of these voltages
N
VMP ,1 N  VMP ,i
i 1
Finally we can determine the total instantaneous maximum output power of the system as
Pout 
N
J
i 1
VMP ,i
MP , i
The tool has built-in models for the reverse saturation current density (𝐽0 ). The first model is the
Shockley-Queisser detailed balance radiative limit and the second is a simple empirical expression
obtained from published “state-of-the-art” solar cells performance characteristics. The ShockleyQueisser limit used to estimate the saturation current density is as follows
J 0,i
 2  kT 
 q
 hc
3
2
3
 E
e

G ,i
kT
 EG ,i 2  EG ,i  

  2  kT   2
kT


 

Where h is plank’s constant and c is the speed of light.
The “stat-of-the-art” model used to estimate the saturation current density is
J 0,i  1.14 109 exp(40.5EG,i )
In BOSS, the PV model for each junction is simulated inside of an algorithm for determining the optimal
bandgap energies. This algorithm uses a multidimensional unconstrained nonlinear minimization
method (Nelder-Mead).
When there are optical splits involved in a system, some of the incident light is reflected and some are
transmitted. The figure below shows the general principle of how light is reflected and transmitted in an
optically split system.
Fig. 2: Diagram showing how incident light is reflected and transmitted in an optically split system.
3. Using the tool
Like any other software tool, there are input parameters required in order to get your desired output.
Fig. 3 shows the device input parameters and Fig. 4 shows the global input parameters. As can be seen
at the bottom of the interface screen there is an example tab that has various PV configuration
examples to help first time users get acquainted with the tool.
Fig. 3: Interface showing device input parameters.
Fig. 4: Interface showing global input parameters.
A description of each of the input parameters (both device and global) and their character types are
given in the table below
Table 1: Tool input parameters and descriptions
Device parameters
Type
Default
Units
Number of splits
Integer
0
Number of
junctions
Integer
1
Electrically in series
String
yes
Initial band gap
energy
Integer
1
eV
Series resistance
Collection
efficiency
Initial optical split
cut-off
Optical split
transition width
Integer
0
𝛀/𝑐𝑚2
Integer
1
ratio
Integer
-100
eV
Integer
0
μm
Reflectivity
Integer
1
ratio
Transmission loss
integer
0
ratio
Global parameters
Geometric
concentration
Operating
temperature
Type
Default
Units
Integer
300
suns
Integer
300
kelvin
Solar spectrum file
String
am1.5dc
Junction Jo model
String
s-q
Junction Jo derate
Number of
iterations
Closest Eg spacing
Integer
1
Integer
10
Integer
0.03
ratio
eV
Description
The number of optical splits in the system –
each optical split adds a PV junction stack to
the system
The number of PV junctions contained in each
stack
Choose whether a junction is electrically in
series with the junction above it
Bandgap energy used in the first iteration of
the optimization - negating bandgap will stop
bandgap from changing during optimization.
Series resistance component of this junction
Current collection efficiency ratio
The initial photon energy of the optical
transition of this split
The optical transition width in wavelength of
this split
The efficiency ratio of light transmitted by this
split to a stack , with photon energies above
the optical transition width range of the split
The efficiency ratio of light transmitted by this
split to the next split, with photon energies
below the optical transition width range. If
there is not another split below this in the
system, the light will be directed to last stack
Description
The geometric concentration of the system
The operating temperature of each PV junction
Input solar spectrum file which contains
am1.5dc, am1.5g, am0, and blackbody
Reverse saturation current density model used
to determine the JO of each junction based on
the EG
Coefficient used to adjust the the JO model
Number of iterations attempted to get the
optimum bandgaps
Closest allowable bandgap energy spacing
3.1 Instructions for tool
 When entering the initial bandgap energies for a PV system, it is important to ensure that they
are in descending order from the first junction to the last. The bandgap energies for each
junction should be at least 0.1 eV apart from each other.
 To keep the bandgap energy of a PV junction from optimizing (holding it constant); simply add a
negative sign “-” to the bandgap value.
 The “electrically in series” tab in each junction gives the option for that junction to be
electrically in series or independent to the junction above it. When a junction is electrically
independent from another it creates sub-stacks with in a stack.
 To have a split in a configuration simply click on the “number of splits’’ tab and choose the
number of splits. The number of stacks created by the tool will always be 1 more than the
number of splits chosen.
 The “initial optical split cut-off” is selected based on the configuration of the system. For
example, if the user wants the optical split to be below the junction with bandgap energy of 2
eV, then the “initial optical split cut-off” will be 2 eV.
 The “Junction Jo model” tab allows the user to choose a reverse saturation current density
model. “s-q” is for The Shockley-Queisser limit and “sota” is for the “state of the art” model.
The tool interface has examples of all possible configurations that the program can simulate. These
examples together with the above instructions make it easy for the user to understand this tool.
4. Generated outputs
(I)
The tool generates the optimum band gap for each junction in the system along with the
efficiency associated with that individual band gap as shown below
Fig. 5: Efficiency of each individual band gap in a 5-junction PV system.
(II)
The tool generates other important solar cell parameters that are found in the output log of
the results tab. These parameters are listed in the table below along with their description
Table 2: Output parameters and descriptions
Parameters
Eg
Jsc
Voc
Jmp
Vmp
FF
FFi
Jo
Jo (D)
Power (in)
Power (out)
Total Efficiency
Optical split cut-off
Description
Optimum bandgap energy
Short circuit current
Open circuit voltage
Current at max power point
Voltage at max power point
Fill factor which is the ratio of the maximum power of the
system to the product of Voc and Jsc
Intrinsic fill factor
Reverse saturation current density
Derating coefficient used to adjust the the Jo model
Solar spectrum input power to the PV system
Power generated by the PV system
Efficiency of the PV system which is the ratio of the Power
(in) to the Power (out)
Optimized photon energy of the optical transition of a split
(III)
Plots of the solar spectrum as well as how the solar spectrum is absorbed by each
junction are generated by this tool. The solar spectrum is absorbed by the junctions in a
PV system based on the energy of the photons in the spectrum. Photons with energy less
than the bandgap energy are not absorbed and passed on to the lower energy bandgaps.
Examples of both plots are shown in Fig. 4 and Fig. 5.
Fig. 6: Plot showing am1.5dc spectrum.
Fig. 6: Plot showing the spectral absorption of each bandgap in a 5-junction system
(IV)
A transmission plot is also generated if a split is present in the configuration. This
plot shows how the incident spectrum is reflected and transmitted by the split as
shown in Fig. 7. On the y-axis, 0 represents reflection and 1 represents transmission.
Fig. 7: Plot showing the transmission of a split.
5. Remarks
This tool is capable of simulating various multijunction PV configurations. It is important that the user
follow the instructions in this manual on how to enter the parameters into the tool interface. The tool
allows one to get a better understanding of the various configurations of multijunction solar cells and
the importance of optimum bandgaps for maximum efficiency. Future work for this tool will involve
using more realistic solar cell models and examining a variety of geographic locations.