For more than three decades, NRL has monitored PV cell efficiencies for the various semiconductor technologies. The thin-film technologies (e. g., copper indium gallium diselenide [CIGS], amorphous silicon [a-Si], and cadmium
telluride [CdTe]) generally have the lowest efficiencies. Crystalline silicon PV cells have efficiencies slightly higher than thin-film technologies but use between 20 and 100 times more semiconductor material. These two classifications dominated the industry in the mid-1980s. At that time, theoretical physicists predicted PV cells would not exceed 22% efficiency. However, with the discovery of multijunction PV cells, efficiencies have now exceeded 40%. Due to the emergence of this new technology, theorist predictions have increased to a maximum efficiency of 58% to 70% [10].
Regardless of chemistry, the entire industry has seen more than an order of magnitude improvement in PV cell efficiency between 1976 (~2%) and 2010 (~41.6%) [11]. When each PV cell chemistry is viewed independently, the improvements are not as startling. Taking amorphous silicon PV cells as an example, the efficiency improved from ~2% reported by RCA in 1976 to ~12% reported by United Solar in 2009 (Figure 5.4). Economists use technology development theory to explain the disparity between the growth of the entire industry and these individual technological innovations.
Economists describe technology development as a sigmoid curve, sometimes referred to as an S-curve. The S-curve is formed from graphing technological advancements as a function of time. Economists have assigned significance to each portion of the curve. First the technology goes through a new invention stage. During this time, there is slow growth with extensive funding and little performance gain (Figure 5.5). This is followed by an exponential growth phase known as technology improvement. During this phase, fewer resources are required because scientists now understand the underlying physical phenomena required for advancement. Finally, the growth levels off when the technology reaches a physical limit preventing further development. The technology has reached maturity and enters an aging phase [12].
These advancements in PV cell efficiency can be described by sigmoidal expressions. Gompertz and logistic curves are the most popular in economic theory. First published in 1825 and used by economists since 1903, the equations describe rising exponential growth with log linearity at the beginning and end of the curve. Taking the Gompertz expression as an example, the highest and lowest plateaus are described as L + x and x, respectively (Equation 5.1):
-e -4t-tc)
У = * + Le (5.1)
The rate of rise is dictated by the variable b found with the goodness of fit to the technology performance data (y) graphed as a function of time (t) [13,14]. The inflection point for growth occurs at a specific time interval (tc) in the technology improvement phase. When applied to advancements in PV cell efficiency over the past four decades, the saturation limit is projected to be 48.5% with an inflection point in 1984 (Table 5.1, Figure 5.6). The poor fit
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Maturity Aging
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FIGURE 5.5
Explanation of the sigmoid technology curve.
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TABLE 5.1 Fitting Coefficients for a Gompertz Curve of Photovoltaic (PV) Cell Efficiencies from 1975 to 2010
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suggests PV cell technology has not completely matured, meaning more technological advancements could theoretically occur.
Often a single sigmoidal curve does not accurately describe industrial performance. Instead, a technology curve is composed of a number of smaller sigmoidal curves with each curve describing a new innovation [12]. There are two possible growth paths defined by the time between innovations. One scenario is that a number of ideas are created during the invention stage and simultaneously pursued. This leads to a series of overlapping S-curves for each innovation (Figure 5.7[I]). A second scenario occurs when there are fewer resources devoted to technology development. In this instance, one idea is pursued until it reaches maturity. Consumer demand starts to decrease, and the industry responds with a slightly new innovation described by a new growth curve (Figure 5.7[II]).
When PV cell efficiency is used as the technology performance metric, the advancements over the recent decades can be visualized as a series of sigmoidal curves. The NREL plot can be reinterpreted to identify the three
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FIGURE 5.7
(I) A number of innovations are simultaneously pursued, leading to simultaneous growth.
(II) Ideas are pursued one at a time, leading to a series of end-to-end growth curves.
changes in material innovations that have led to today’s highest single cell efficiencies of 41.6% (Figure 5.8).
Thin-film, crystalline, and multijunction cells are three overlapping technologies describing the industrial innovation in PV (Figure 5.8). However, based on the statistical values of R-squared and chi-squared, single crystalline silicon cells and thin-film technologies are the only good fits to the
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FIGURE 5.8
Fitted Gompertz curves to thin-film, crystalline silicon, and multiple junction solar cell technology between 1975 and 2010.
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TABLE 5.2 Fitting Coefficients for the Gompertz Curves for Individual PV Cell Technologies from 1975 to 2010
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Gompertz prediction (Table 5.2). Upper limits of 10.1% efficiency for thin-film and 21.2% efficiency for crystalline silicon appear to have been reached, and the majority of technological advancements for both occurred prior to the mid-1990s. The poor fit of multijunction technologies suggests these innovations have not reached their full maturity. This possibility is mirrored in the abundant academic literature focused on continued efficiency improvements for this technology.
Note these efficiencies are of a single PV cell and not the packaged module. NREL’s plot contains individual cell efficiencies demonstrated on
a few test substrates synthesized in controlled academic or industrial laboratories. For instance, thin film single cell efficiencies (19.5%) are approximately two times higher than a packaged module (10%) containing the same CIGS chemistry [15]. This is not necessarily a comment on packaging integrity, but it is a demonstration of the current limitations in scalability of PV cell synthesis. The single cell efficiencies are ideal substrates, termed champion cells by the industry. PV manufacturers currently strive to develop processing equipment to consistently duplicate these efficiencies in high volumes.
The semiconductor chemistry has evolved, and so, too, have encapsu – lant formulations and processes. The principal requirement of the encap – sulant material is to provide an environmental barrier and enable reliable performance of the PV cells. Technological advancements in PV cell stability and packaging integrity contribute to the warranty offered by PV manufacturers.
In 1979, when the first terrestrial PV modules were sold, they were offered with a 5-year warranty. Warranty periods have increased, and by 2010 the lower limit of the industrial norm is 25 years (Figure 5.9). A Gompertz curve fits this historical data (Table 5.3). Based on this theory, the technology has plateaued in the recent years. Therefore, a new innovation must occur for PV packaging to undergo future technological improvement. Unlike PV cell development, there is little literature on the pursuit of packaging material improvements for PV manufacturing.
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FIGURE 5.9 Fitted Gompertz curve to power warranty for solar modules between 1979 and 2010. |
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TABLE 5.3 Fitting Coefficients for a Gompertz Curve to Photovoltaic (PV) Packaging Warranties
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