If global photovoltaics (PV) deployment grows rapidly, the required input materials need to be supplied at an increasing rate. In this paper, we quantify the effect of PV deployment levels on the scale of metals production. For example, we find that
if cadmium telluride {copper indium gallium diselenide} PV accounts for more than 3% {10%} of electricity generation by 2030, the required growth rates for the production of indium and tellurium would exceed historically-observed production growth rates for a large set of metals. In contrast, even if crystalline silicon PV supplies all electricity in 2030, the required silicon production growth rate would fall within the historical range. More generally, this paper highlights possible constraints to the rate of scaling up metals production for some PV technologies, and outlines an approach to assessing projected metals growth requirements against an ensemble of past growth rates from across the metals production sector. The framework developed in this paper may be useful for evaluating the scalability of a wide range of materials and devices, to inform technology development in the laboratory, as well as public and private research investment.
We study the costs of coal-fired electricity in the United States between 1882 and 2006 by decomposing it in terms of the price of coal, transportation costs, energy density, thermal efficiency, plant construction cost, interest rate, capacity factor
, and operations and maintenance cost. The dominant determinants of costs have been the price of coal and plant construction cost. The price of coal appears to fluctuate more or less randomly while the construction cost follows long-term trends, decreasing from 1902 - 1970, increasing from 1970 - 1990, and leveling off since then. Our analysis emphasizes the importance of using long time series and comparing electricity generation technologies using decomposed total costs, rather than costs of single components like capital. By taking this approach we find that the history of coal-fired electricity costs suggests there is a fluctuating floor to its future costs, which is determined by coal prices. Even if construction costs resumed a decreasing trend, the cost of coal-based electricity would drop for a while but eventually be determined by the price of coal, which fluctuates while showing no long-term trend.
We study a simple model for the evolution of the cost (or more generally the performance) of a technology or production process. The technology can be decomposed into $n$ components, each of which interacts with a cluster of $d-1$ other, dependent co
mponents. Innovation occurs through a series of trial-and-error events, each of which consists of randomly changing the cost of each component in a cluster, and accepting the changes only if the total cost of the entire cluster is lowered. We show that the relationship between the cost of the whole technology and the number of innovation attempts is asymptotically a power law, matching the functional form often observed for empirical data. The exponent $alpha$ of the power law depends on the intrinsic difficulty of finding better components, and on what we term the {it design complexity}: The more complex the design, the slower the rate of improvement. Letting $d$ as defined above be the connectivity, in the special case in which the connectivity is constant, the design complexity is simply the connectivity. When the connectivity varies, bottlenecks can arise in which a few components limit progress. In this case the design complexity is more complicated, depending on the details of the design. The number of bottlenecks also determines whether progress is steady, or whether there are periods of stasis punctuated by occasional large changes. Our model connects the engineering properties of a design to historical studies of technology improvement.
