1. business and industrial
2. manufacturing

A CPV Thesis
David S. Schultz*a, Shondip Ghosha, Christopher S. Grimmera, Hunter Macka
a
Banyan Energy Inc., 950 Gilman Street, Berkeley, CA, USA 94710-1462;
ABSTRACT
The viability of a concentrator technology is determined by five interrelated factors: economic benefit, cell performance
under concentration, thermal management, optical performance and manufacturability. Considering these factors, the 510x concentration range is ideal for silicon-based receivers because this level of concentration captures the bulk of
available economic gains while mitigating technical risk. Significant gains in capital efficiency are forsaken below the
5x concentration level. Above the 10x level of concentration, marginal improvements to economic benefit are achieved,
but threats to reliability emerge and tend to erode the available economic benefit. Furthermore, optic solutions that
provide for concentration above 10x tend to force a departure from low-profile flat-plate designs that are most adoptable.
For silicon based receivers, a 5-10x level of concentration within a traditional module form factor is optimal.
Keywords: Solar, CPV, Concentrator, Optics, Silicon, Solar Cell
INTRODUCTION
An effective concentrator photovoltaic (CPV) solution that leverages the billions of dollars invested in monocrystalline
silicon PV production into more efficient use will deliver the lowest levelized cost of energy (LCOE) in the solar
industry. Such a solution will help silicon PV companies become more capital efficient, increasing production capacity
and reducing costs. This is the story that many CPV companies convey in one form or another and they have been
selling this story for several decades. This story is often substantive and truthful enough to raise investment. However,
the promises made by CPV companies have to date gone largely unfulfilled in the market because of technological
challenges, financing challenges, and an incomplete understanding of CPV tradeoffs. There likely exists a collective
misunderstanding of the constraints and opportunities involved with CPV, particularly as they relate to the level of
concentration. This manuscript does not intend to address the problems that have plagued the CPV industry or offer a
singular solution to a multifaceted problem. Rather, it offers a perspective on the fundamental constraints of a CPV
system that are often overlooked; constraints that, if properly considered in aggregate, indicate a path to realize promised
economic value.
This decade offers the greatest opportunity for CPV solutions because of optic innovations capable of delivering mid
levels of concentration within a compact form factor, increases in mono-silicon cell efficiencies, and the maturation of
vertically integrated solar companies more focused on delivering system oriented solutions that minimize LCOE.
Monocrystalline silicon cells are well suited for concentration because of their high cost structure and relatively high
efficiency. This is in contrast to low efficiency, low cost thin film approaches that are antithetical as CPV receivers.
Multi-junction receivers inherently have much higher cost structures, involve rare materials and require high levels of
concentration (500-1200x) that in turn mandate precise tracking (better than ±1˚) and lead to thermal management
challenges that impact reliability (Figure 1). For high concentration solutions these challenges typically constitute a
“death by a thousand cuts1.” Simplistic idioms leave room for debate; one fact that is incontrovertible is that
considerably higher risk is requisite for a high concentration system to reach an LCOE target comparable to a low
concentration solution. This higher risk is driven by higher cell operating temperatures and the need for precision twoaxis tracking. In this manuscript it is assumed that the lowest risk approach to minimizing cost is advantageous.
Accordingly, monosilicon based low-concentration systems deployed on one-axis trackers have the greatest potential for
manageable risks and substantial economic benefit.
*david.schultz@banyanenergy.com; phone 1 510 280-2925; fax 1 888 862-3156; www.banyanenergy.com
Figure 1. Model of concentration cost reduction indicates the approximate level of concentration required for
monosilicon and triple-junction receivers to achieve cell cost parity with current LCOE thin-film leader2.
The viability of a concentrator technology is determined by five interrelated factors: economic benefit, cell efficiency
under concentration, thermal management, optical performance and manufacturability. These factors are all related to
each other via the level of concentration.
For instance, increasing the level of concentration may improve capital
efficiency but impose impractical optical, thermal, and assembly tolerance constraints. Although the specific
relationship between these factors and the level of concentration is design dependent, certain fundamental relationships
are ubiquitous for concentrator systems. As the level of concentration increases, the following themes emerge:
1.
Capital efficiency and cost reduction improves with diminishing returns.
2.
Relative cell efficiency increases to a point, but thermal constraints mitigate this benefit leading to an optimal
range of concentration for a given cell design.
3.
Acceptance angles and diffuse capture decrease, increasing tracker cost and reducing power output.
4.
Cell size tends to decrease which leads to an increase in part count and tighter manufacturing tolerances.
Opportunities for improved throughput arise.
In the relations listed above the five factors are mentioned: economic benefit, cell efficiency, operating temperature,
acceptance angles and manufacturing tolerances. Each of these factors impacts cost and determines the competitiveness
of the CPV system in question. It is critical to note that each one of these factors has a relationship with the level of
concentration. Most of these relationships are non-linear such that there exists an abrupt transition region that tends to
define a boundary range of concentration between feasible solutions and costly challenges (Table 1).
Table 1. Summary of CPV variables and their qualitative relationship with the level of concentration (x).
Variable
Cell Cost;
Capex
Cell
Efficiency
sym.
Increased Concentration
$
Higher concentration is
better (diminishing)
η
Higher concentration is
better (diminishing)
Decreased
Concentration
reduces
economic
benefit
reduces
efficiency
vs. Conc. (x)
$
x
η
x
Acceptance
Angle
Cell
Temperature
Mfg.
Tolerance
θ
T
λ
reduced power output &
increased tracking
precision
lower
concentration is
better
θ
reduced cell efficiency &
reduced reliability
lower
concentration is
better
T
increased cost
lower
concentration is
better
λ
x
x
x
The fundamental rationale that repeats as a theme throughout the analysis of the CPV variables is the notion of operating
at or “beyond the bend” in the curve. Alternatively expressed, it is desirable to target a range of operation that garners
the most value without taking on undue challenge that has the potential to erode value (Figure 2).
Figure 2. Essential to understanding the tradeoffs involved with CPV is the concept of operating at or beyond the
bend in the curve. This notion emphasizes targeting a range of operation that captures the vast majority of benefit
without taking on too much challenge.
What follows is a composite analysis of the relations of economic benefit, cell efficiency, acceptance angles and
manufacturing tolerance to the level of concentration that indicates that the 5-10x concentration range is ideal for
monosilicon-based receivers. This range of concentration captures the bulk of available economic gains while
mitigating technical risk.
1. ECONOMIC BENEFIT
The benefits of concentration are the reduction in solar cell cost per unit of output power, the related reduction in
effective manufacturing capital required to reach a certain output power capacity, and increased cell efficiency.
Additionally, there are strategic benefits important to solar businesses including reduced sensitivity to cell cost volatility,
pricing power, and improved technology differentiation. These are the reasons why people invest their money and time
on concentration efforts. Without question, the primary motivation of any CPV system is to make the production of
solar energy cheaper and more capital efficient. As the concentration level increases, less cell material is used and the
electrical current is amplified approximately proportional to the level of flux provided by the optic. Given an ideal optic,
cell area can be reduced without reducing power output for a given aperture. Optics are neither ideal nor costless, but
with increased concentration more theoretical economic benefit may be captured and therefore more considerable
expense can be consumed adding optics, module and tracking technologies with real world imperfections. However, as
a simple consequence of geometry, it is critical to observe that the benefits of increased concentration diminish
nonlinearly. Assuming an 85% efficient optic, a cell cost reduction of 76% can be achieved at a concentration of 5x.
Increasing the concentration further from 10x to 20x leads to cell cost reductions from 88% to 94%, respectively.
Regardless of base cell cost, the vast majority of cell cost reduction can be achieved between 5-15x (Figure 3).
Figure 3. Theoretical relationship between cell cost and concentration level for various base cell costs assuming an
optical efficiency of 85%. Regardless of base cell cost, notice a diminishing marginal cost decrement and an
abrupt transition in slope at 5x concentration.
Although reduced cell cost does not form the only basis of economic benefit for a concentrator solution, this simple
metric illustrates the waning economic incentive to drive towards ever higher levels of concentration on silicon-based
cells (the capex benefit follows a similar curve). This waning economic incentive is compounded by increases in cell
operating temperature, optical penalties and manufacturing challenges that serve to erode or even reverse economic
benefit at higher levels of concentration. These practical concerns impact cost directly in manufacturing or indirectly by
constraining cell efficiency and reliability.
2. CELL EFFICIENCY
There exists a substantial efficiency benefit to operating silicon-based solar cells under concentration as well as a
mitigation of defect induced recombination losses. An increase in open circuit voltage (Voc) under concentration leads to
a relative efficiency increase assuming the cell operating temperature is managed appropriately and metallization is
increased to carry elevated current. Results reported in the literature vary widely according to the specific cell
architecture 3-5. Agnostic to cell architecture, the maximum change in open circuit voltage at any given level of optical
concentration, relative to the ideal gain at infinite concentration, (%Δ Voc) can be calculated as follows6:
Voc =
kT  I  x 
ln 
 1
q  I 0

(1)
I 0  1.5 105 e
%Voc 

 Eg / kT

Voc x   Voc x  1
Voc x     Voc x  1
(2)
(3)
where k is boltzman’s constant, T is the operating temperature, q is one electron charge, I is operating current under one
sun and Eg is the band gap energy for Si (~1.12 eV). This approximation assumes a constant cell operating temperature
and that current is proportional to concentration.
Figure 2. Percent of theoretical maximum achievable voltage increase relative to one-sun Voc for silicon solar cells
at various levels of optical concentration [x]. Increases in open circuit voltage for silicon cells lead to sustainable
improvements in efficiency under concentration. The dashed curve illustrates the reduction in this benefit
assuming a modest 1˚C rise in cell operating temperature per unit of concentration.
The vast majority of theoretical benefit due to Voc increase is garnered at the 5x concentration level and above. With
increased concentration, CPV systems will tend towards higher cell temperatures and this will serve to decrement V oc.
The cell temperature of any one particular system will depend on individual material selection and heat sink design. If a
very modest linear thermal penalty of 1˚C for each unit increase in concentration is assumed along with a reasonable
sensitivity of -0.4%/˚C, a broad peak in the potential Voc benefit occurs in the range of 5-15x (Figure 4). At levels of
concentration beyond this range, temperature will not only erode cell efficiency, but also impact reliability and the
assumed degradation rate associate with a particular technology.
In practice, designing a silicon-based solar cell to achieve the maximum Voc benefit towards improving efficiency is an
optimization challenge. Under concentration solar cells produce higher current. This higher current demands increased
metallization to avoid resistance losses. The benefit of increased cell efficiency is thus reduced slightly by shading losses
stemming from increased metallization. Optimization of a metallization pattern to suit the level of concentration is
essential. In addition, dicing technique and potentially doping technique must be optimized in conjunction with the
metallization pattern in order to realize the cell efficiency benefit under concentration.
3. ACCEPTANCE ANGLE
An acceptance angle profile defines the range of misalignment angles over which a module can generate greater than
90% of peak power given a constant resource. The implicit industry threshold of 90% is arbitrary and rather low.
Regardless, acceptance angle profiles define how well a CPV module performs given a range of misalignments. In
addition to defining a misalignment tolerance, acceptance angle profiles correlate well with diffuse light capture.
The étendue limit is a concept from non-imaging optics that defines the theoretical maximum concentration achievable
as a function of acceptance angle. The étendue relation given here is calculated for optics with planar symmetry (linear
concentration)7.
 n final 

n

x
 initial 
 ( x)  sin 1 
(4)
For this relation θ is the acceptance half-angle, x is the level of concentration, ninitial is the refractive index of air (1.0),
and nfinal is the refractive index of optical material at 1.5. This is purely an optical calculation, whereas, practical
acceptance angles are determined by power measurements from a module with an array of optics. Defining the exact
boundary curve and how it relates to practical measurements is not essential to understanding acceptance angle
constraints. However, it is important to note the shape of the étendue boundary. As the level of concentration increases,
acceptance angles tend towards an asymptote at zero. As concentration decreases, acceptance angles widen. Industry
data, although offset from the theoretical limit, fits reasonably well with the shape of this curve (Figure 5).
Technology
Modeled Conc.
CPower
Banyan Energy
SunPower
Entech
WS Energia
Sol3g
SolFocus
Concentrix
Semprius
x
2
4.5
7
7
8.5
20
21.8
22.4
28.6
32
Source
ZEMAX ray trace
Datasheet8
Conference paper9
Conference paper10
Conference paper11
Conference paper12
Datasheet13
Datasheet14
Conference paper15
Conference paper16
Figure 5. CPV industry survey of acceptance angle vs. level of geometric concentration. The table on the right
lists optic technologies corresponding to the data points in order of increasing concentration. The étendue limit is
an estimate of the theoretical boundary for non-imaging optics. The 2x concentrator datapoint is modeled in
ZEMAX raytrace software as no industry data is available at this level of concentration. Axially symmetric
systems are represented here at lower levels of concentration given by their planar symmetric optic equivalent
found by taking the square root of published concentration.
The acceptance angle tradeoff is a microcosm of the larger suite of CPV tradeoffs. Increasing the concentration garners
more economic value, but decreases acceptance angles which, in turn, reduces diffuse energy capture and increases
tracking costs. Selecting a level of concentration that allows for a balance of these considerations is essential. The 510x level of concentration allows for both significant economic gain and acceptance angles in the 2-4˚ range. Achieving
this range of misalignment tolerance is important because it allows modules to be compatible with low-cost single-axis
tracking solutions that are already being deployed at scale and it allows for significant diffuse light capture.
4. MANUFACTURING TOLERANCES
The specific impact of increased concentration on manufacturing and assembly tolerances is entirely design dependent.
However, one trend that is undeniable is that with increased concentration, tolerances tighten and impact cost. In
practice, higher levels of concentration reach physical limits very quickly. There are two options for increasing
geometric concentration: (1) reducing focal area and cell size relative to optic aperture or (2) increasing optic aperture
relative to focal area. For (1), smaller cells require precise positioning tolerances; effective yields may be reduced as the
bus-bar contact area takes up a greater proportion of the active cell. The less effective use of cell area results in
diminished economic benefit. Similarly for (2), increasing optic aperture demands more material usage (assuming
constant optic aspect ratio), modules become heavier and may no longer be deployed on conventional tracker products.
Both approaches will involve greater thermal gradients that tend to decrease reliability. Either approach will tend to
marginalize economic benefit in a slightly different way.
If it is assumed that staying within a module form factor is desirable then a high aspect ratio optic is essential to reducing
focal area relative to aperture while maintaining a low profile. A reduction in focal area implies a reduction in cell
width. A wafer dicing model illustrates that as cell width decreases, part count and wafer utilization are
disproportionately impacted (Figure 6). The decision to reduce cell width should be approached with caution due to kerf
loss and losses that arise from limitations in positional tolerances, both of which impact wafer utilization. This model
indicates that reducing cell width substantially beyond 10mm is likely to require an abandonment of traditional tabbing
and stringing interconnect methods and a significant investment in new processes in order to handle the increased
number of cells cut from each wafer.
Figure 6. Cell width as it relates to cell count per wafer and wafer utilization. This model assumes cells are cut
from a 141 mm square that is trimmed from a 200mm diameter Si wafer. Wafer utilization values assume a 50μm
kerf loss and a 200μm positional tolerance. Data points shown correspond to local maxima in wafer utilization.
At low cell widths, part count and wafer utilization are disproportionately impacted.
5. DISCUSSION
Five variables were identified that ultimately determine the economic viability of a CPV system: economic benefit, cell
efficiency, acceptance angles, cell temperature and manufacturing tolerances. In order to garner the vast majority of
economic benefit from a silicon-based CPV approach, achieving greater than 5x concentration is advisable. Beyond 15x
concentration very little economic benefit is achieved for an incremental increase in concentration. Similarly, for cell
efficiency, in order to achieve the maximum Voc benefit under concentration the 5-15x range is advisable. Beyond 15x,
reductions in cell efficiency due to higher NOCT are likely as are reductions in product life. Below 5x, gains in
efficiency are squandered. Acceptance angles widen considerably at lower levels of concentration. In order to achieve a
viable acceptance angle profile greater than 2˚, an approximate threshold for less expensive tracking, staying below 10x
is advisable. The qualitative assumptions underlying this analysis are that manufacturing and assembly tolerances are
formulated for standard processes and adoptability is maximized by CPV modules that maintain a profile within the
envelope of a traditional module.
If 5-10x defines the sweet spot for concentration on silicon cells, why are so few CPV companies operating in this
region17? A number of companies have focused on 2-3x concentration. The advantage of this approach is that relatively
simple and low-profile optics can be utilized within a standard module form factor. Although cell dicing and stringing
can come under considerable manufacturing pressure, module integration and system integration can be relatively
streamlined, increasing the adoptability of such approaches. In order to go beyond 2-3x concentration, conventional
optics offers parabolic trough and Fresnel lens-based solutions. These optics choices force module and system design to
deviate from industry standards, with bulky modules or mirror collectors, and custom-engineered, precision trackers.
This increased complexity can push designers to reach beyond 10x for maximum economic benefit.
This manuscript suggests designing a system within the 5-10x range of concentration for the optimal balance of
economic value and technical challenge. Optical solutions that can achieve this range while minimizing disruption to
module and system integration will deliver the maximum value to the solar industry.
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