The global production of solar photovoltaics (PV) has increased dramatically in the past decade, averaging an annual rate of growth of 40% between 1992 and 2008  and reaching an installed capacity of over 68 GW in 2011 , up from 40 GW at the end of 2010 [3, 4]. Among the issues of concern during this extensive deployment are the raw material requirements of certain PV technologies. In particular, thin-film PV technologies such as copper indium (gallium) (di)selenide (CIGS) and cadmium telluride (CdTe) utilise materials such as indium and tellurium (Te) for which there may be a supply risk in the future because of the inability of these metals to concentrate into economically viable deposits , their extraction solely as by-products of mining major metals  and, in the case of indium, high demand from competing uses . The implications of indium and Te scarcity for thin-film production costs have been explored in recent research papers [8-10]. In this study, we use the case of Te to examine the effect of material availability and supply on maximum potential CdTe PV growth by mid-century. CdTe PV, further discussed in Section 1.1, occupied the largest part of the thin-film PV market in 2010  and currently has the lowest manufacturing cost, estimated at $0.74/Wp at the end of 2011 . Te is among the metals most commonly cited as subject to supply constraints, having been examined in detail in recent papers [5, 12-19] as well as shortlisted within several scoping studies on so-called ‘critical metals’ [20-27]. This, along with its distinctive supply characteristics explained in Section 1.1, makes it a suitable case study for the model presented here.
This paper and the modelling techniques used herein are a response to recent studies dealing with Te resource assessment and implications for the PV technology relying on it, that is, cadmium telluride (CdTe) thin-film PV. These studies have reviewed approaches and methods used in the existing literature to assess the potential for material-constrained PV technologies  and examined in more detail the assumptions underlying the PV industry's demand for Te as well as the estimation of future Te supply . Both studies have highlighted the following research needs:
greater transparency in modelling assumptions;
systematic evaluation of the sensitivity of Te demand from the PV sector to technological improvements in manufacturing and module performance of CdTe technology;
treatment of future Te supply as a dynamic system rather than a static system based on known available resources; and
better and more structured understanding of future recycling potential.
This study endeavours to address a number of these issues. The model, described in Section 2, uses system dynamics (SD), a method of understanding and modelling complex and non-linear global systems using the concepts of stocks, flows and feedback loops . SD has been frequently used to model resource discovery and depletion [31-33], particularly for petroleum resources [34-36]. In this paper, we model the future supply of Te to the growing PV sector. The use of SD allows for a more dynamic treatment of critical parameters affecting Te supply and demand from the PV sector highlighted in the previous studies [28, 29]. These parameters are reported Te resources, recovery rate of Te from copper resources, PV module efficiency and layer thickness, material utilisation during manufacturing and recycling of spent PV modules.
The following sections (Sections 1.1 and 1.2) provide an introduction to CdTe technology and the Te supply chain. In Section 2, the model and its four main modules are described. In Section 3, the model is run using three sets of input values, representing ‘conservative’, ‘dynamic’ and ‘optimistic’ projections and allowing for comparison with other studies. Section 4 presents a sensitivity analysis, which brings forth interesting and complex features of the Te supply–demand interaction. Finally, in Section 5, we discuss the findings of these analyses and the insights they generate for future expansion of Te supply and growth of the CdTe PV sector.
1.1 Cadmium telluride PV
Today, the principal use of Te is in the metal alloying and chemicals industries, although its use in CdTe thin-film solar cells is growing quickly, with CdTe industry accounting for about 26% of the global demand in 2010 . Future demand for Te from the PV sector will depend on the future expansion of the CdTe industry and its relative positioning within the PV market.
The market share of thin-film PV technologies, led by CdTe PV, grew rapidly between 1999 and 2009 [37-39], but crystalline silicon technologies dominated in 2010–2011 [40, 41]. In 2009, thin-film CdTe modules, produced principally by one company, First Solar Inc. , accounted for 9% of total PV production; this share fell to 5.5% in 2011 . The remainder of thin-film market share is divided between two technologies: amorphous silicon with 3.4% of total 2011 PV production and CIGS with 2.4%. The annual production of CdTe was 1902 MW at the end of 2011 [39, 41]. This figure is forecast to fall in 2012 before increasing again in later years with recovery of the overall PV market .
Among currently commercialised technologies, thin-film technologies are generally deemed to have a major potential for cost reductions and are thus highly competitive in the PV market. Indeed, CdTe modules are currently the least expensive to manufacture  largely because of the cost-reducing efforts of First Solar, whose manufacturing costs were $0.74/Wp  at the end of 2011, and further cost reductions are deemed achievable [8-10, 43, 44]; the company expects manufacturing costs of $0.60–0.64/Wp in 2013 .
The market share of thin-film PV, and that of CdTe within it, are expected to continue increasing: the International Energy Agency estimates that thin-film technologies will represent 40% of the PV market by 2030, without specifying the exact share of CdTe , whereas the European Photovoltaic Industry Association forecast that CdTe will occupy about 12% of the global PV market by 2020 . However, crystalline silicon production costs are also quickly decreasing and are now below the $1/Wp benchmark [47-49]. Such developments erode thin film and CdTe cost competitiveness. In addition, other PV technologies are also emerging and are likely to account for future PV market share, including organic PV, concentrator PV, dye-sensitised solar cells, multi-junction cells and other high-efficiency devices [50, 51].
Thus, CdTe production will certainly continue to grow in the near and medium terms, increasing the future demand of Te, but longer-term CdTe production, market share and relative demand of Te are rather uncertain. These will depend on the relative competitiveness of CdTe versus other currently commercialised technologies and the effectiveness and speed at which other emerging PV technologies will gain market share. Moreover, future demand for Te coming from the CdTe industry is also uncertain as it is dependent on how much material will be used in future CdTe devices, that is, material intensity. This suggests that the relationship between the growth of the CdTe PV market and the growth in demand for Te may not be linear [28, 29]. The change in material intensity as a result of improvements in CdTe device and module manufacturing is further discussed in Section 2.4.
Tellurium is one of the nine rarest metals, similar in crustal abundance to gold (Au) and platinum, about one billion times less abundant than the major PV metal, silicon . It is generally found in copper ores at a concentration too low to be profitable for primary mining (1–3 ppm) [16, 53]; as a result, it is extracted as a by-product from the solid slimes, which accumulate at the anodes during copper electrolytic refining (anode slimes) , where it has an average concentration of 105 ppm [5, 17]. Other resources do exist: it can be extracted as a by-product from lead, zinc, silver, gold and bismuth ores [6, 55]; additionally, two mines in China and one in Mexico are listed for direct mining of Te [5, 6, 28]. These other resources, however, still do not contribute significantly to the current supply mix: over 90% of Te comes from copper anode slimes, and the remainder is from skimmings at lead refineries and gases generated during bismuth, copper and lead ore smelting . Ferromanganese ocean crusts also contain large Te deposits—estimated at 9 million tonnes at average concentrations of 50 ppm —but deep ocean metal recovery is not currently practised, so this resource is currently unattractive [5, 13].
Historically, the recovery rate (or extraction efficiency) of Te from copper anode slimes was a relatively poor 33% . Ojebuoboh  claims that low recovery rates for Te are simply due to a historically small market for it and that 80% recovery rates are currently achievable. Fthenakis  adds that extraction efficiencies as high as those for Au (95%) can be achieved as long as Te price is sufficiently high. On the other hand, Green  argues that these estimates incorrectly assume that the 33% historical rate ‘applies to the percentage actually extracted from the total pool of available Te, rather than applying to that extracted from the subset from which extraction was attempted’ and that 80% recovery rates are difficult to achieve. The difficulty can be explained by a number of phenomena likely to occur during the recovery process, notably re-precipitation of Te in the post-filter press as other compounds ; these phenomena are possibly affected by the concentrations of antimony, silver and lead in the anode slimes . Stafiej et al.  hold a patent assigned to Noranda Inc. (a Canadian mining company, now part of Xstrata), which demonstrated up to 93.4% Te recovery rates from the anode slimes. The latter rate may not actually apply universally because of the difference in composition of anode slimes at different refineries; Backström  presents evidence of the difficulty in reaching high Te recovery rates at Boliden's Rönnskärsverken smelter in Sweden.
Additionally, in a potentially lucrative Te market, the willingness to share this technology is yet unclear : Te price has grown almost an order of magnitude in the last decade , reaching highs of $420–440 in 2011 . The maximum Te price to sustain CdTe cost competitiveness is debated in the literature, with estimates between $800/kg  and $2000/kg ; recent modelling by Woodhouse et al.  shows that a Te price up to $3500/kg could be offset by improvements in module efficiency and layer thickness, as well as reductions in the cost of capital, to reach a long-term CdTe manufacturing cost of around $0.60/Wp.
2 MODEL DESCRIPTION
In this section, we describe a system dynamics model constructed to simulate the complex nature of Te supply and demand, to generate estimates for maximum potential CdTe market growth and to examine the effects of changing various dynamic techno-economic parameters—namely, mining and extraction efficiency, reported resource estimates and PV module performance—on the maximum potential growth of the CdTe PV sector by mid-century. The model can then estimate the relative importance of each factor to maximum potential CdTe PV capacity in 2050 via a sensitivity analysis.
The model simulates the period from 2010–2050 and estimates maximum potential CdTe PV market growth, producing three main outputs:
annual Te available for CdTe PV (estimated by subtracting the amount of Te required for non-energy applications from the total supply);
maximum annual installed capacity in gigawatt-peak per year (GWp/year); and
maximum cumulative installed capacity in GWp.
The latter two outputs are used for the sensitivity analysis. All three model outputs are estimates of the maximum potential expansion of CdTe as constrained by Te future supply. The model does not intend to predict future market share of CdTe technology, which would depend on several conditions as discussed in Section 1.2. In this model, the maximum installed capacity for CdTe is a function of available Te supplies and performance improvements that reduce material intensity and demand, as shown in Figures 1 and 2.
The model is represented in a causal loop diagram (CLD) in Figure 1. The CLD allows visualisation of the direct effect of parameters on one another via causal linkages as well as the indirect effects via reinforcing (R) or balancing (B) feedback loops. Reinforcing loops indicate that the system output—in this case, maximum installed CdTe PV capacity (‘installed capacity’)—tends to grow exponentially over time, whereas balancing loops indicate a self-correcting or goal-seeking behaviour that results in stabilisation around a desired value . In Loop R1, Te supply from copper and direct mining increases installed CdTe PV capacity, which in turn, can later become a source of recycled Te—after a delay equal to the PV module lifetime—and recycled Te can contribute to future Te supply. As the CdTe PV market grows, research and development efforts in improving module efficiency and reducing active layer thickness improve the performance of PV modules (Loop R3), resulting in less Te usage per module and thus more installed PV capacity (Loop R2).
The nature of this model, represented with three reinforcing loops, implies that the size of the CdTe sector tends to grow exponentially—with some oscillation due to delays in the system—until 2050, without competing with other PV technologies for market share. This situation may not fully represent the real case, but is sufficient for the model's objective of estimating the maximum growth potential of CdTe technology given the complexities of Te supply, the prospects for technology improvement and demand reduction and the implied time lags of these factors, all of which act as constraints, limiting factors and sources of complex system behaviour.
The complete model is shown in Figure 2. The model is composed of four main ‘modules’, described in the following sections (Sections 2.1). Three of these modules relate to the three sources of Te that contribute to the overall supply mix: Te derived (i) from copper production, (ii) from direct mining and (iii) from end-of-use PV module recycling. The fourth module, for material intensity, includes dynamic assumptions about improvements in PV module technology (module efficiency, layer thickness and utilisation rate) and is used to estimate the amount of PV capacity that can be installed from a given amount of Te and vice-versa (Section 2.4).
2.1 Tellurium from copper production
This module estimates annual and cumulative copper production and its corresponding Te by-product content. About 90% of current Te supply is from anode slimes produced during the electrolytic refining (electrorefining) of smelted copper [6, 54, 55, 57], making an accurate representation of copper production crucial to the analysis of Te availability. However, copper reserves and production form the subject of a wide debate and assumptions on copper production growth—and its relationship to Te supply—are not uniform across the literature. Historically (1910–2002), global copper production has grown at 3.3% per annum . More recently, the USGS  estimates a 3.1% average rate of growth of world copper production between 2000 and 2020; so far (2000–2010), this forecast has been correct. In his model assumptions, Fthenakis  assigns the same rate to the growth of Te production. On the other hand, Green  explains that an increasing fraction of copper demand is being met by end-of-use copper recycling or solvent-extraction electrowinning production, neither of which produces Te as a by-product and presents estimates that the share of electrolytic copper decreased from 70% to 68% between 2002 and 2007. Bi-annual data published by the International Copper Study Group from 2002 to 2011 captures a decreasing trend but shows that electrolytic refining capacity was 78.8% of total capacity in 2002 and 77.9% in 2011 [65, 66]. This slight decrease rate is used in the model going forward to 2050. It should be noted that a future decrease in electrolytic copper production may be offset by the co-production of Te from lead–zinc ores , which is not included in this model.
Furthermore, there is debate about the concept of ‘peak copper’. Demand is escalating because of emerging economies and increasing electrification of the world energy system. Like any non-renewable resource, copper production may reach a peak at some point in the future and decline thereafter until further resource discovery or until improved technologies for exploiting lower grade deposits are developed and commercialised. Ayres et al.  developed a model in which various peaks in production can be seen between 2050 and 2100, but the authors express the possibility that a peak can occur considerably earlier. Laherrere  argues that Chile and China are the current leaders in global Cu production, but production in the former peaked in 2007, whereas the latter is likely to peak in 2020; he also argues that recycling (secondary production) is negligible. In sharp contrast, the International Copper Association  estimates that current copper recycling rates are at 80–85% and that 80% of all copper ever mined is still in use today, having been recycled several times. Tilton and Lagos  show doubt towards claims of copper scarcity but conclude that it is impossible to accurately forecast future production and price, making it difficult to draw firm conclusions.
This dynamic nature of estimates of Cu resources—exemplified by the USGS revising its estimate of global Cu resources from 1.6 to over 3 billion tonnes in 2006—makes it more difficult to forecast copper production; this particular model is calibrated to represent historical and current production levels as reported by the USGS [55, 70] and an illustrative production peak around 2050 [13, 53]. Using reported mean concentrations of Te in Cu anode slimes and mean recovery rates of Te (Table 1), we found that it is possible to estimate the corresponding annual Te production streams.
Table 1. Inputs and assumptions used to estimate future global copper production.
The copper debate provides the rationale for modelling Cu production using a logistic function for so-called ‘S-shaped growth’; this is commonly used for modelling resource consumption [30, 71, 72], particularly since its use by Hubbert  to predict a peak in US oil production. The cumulative production Q(t) of copper is given by
In this equation, Qinf represents the ultimately recoverable resource (URR) for copper, gmax the maximum growth rate (%) and th the year in which production reaches half of the URR. The initial value of this stock is the total amount of copper ever produced by humanity up to the present day. A range of estimates for this value exist between 360 and 400 million tonnes [63, 67, 74]; the lower estimate is used here for the purpose of calibration to fit historical annual production data.
Annual Cu production is given by
Annual Te production from Cu anode slimes can be estimated using the proportion of copper production that is electrolytic (and thus produces Te as by-product), the concentration of Te in Cu anode slimes and the recovery rate. The Te concentration in Cu anode slimes was for many years estimated by the USGS and US Bureau of Mines as 200 ppm ; however, in a recent paper, Green  presents the weighted average of reported Te concentrations from 67 refineries worldwide accounting for 9.4 Mt (76% of 2005 Cu production) as 105 ppm. As observed in Section 1.1, the recovery rate of Te from copper anode slimes remains a topic of debate, but it is sound to assume that it will rise if Te demand and price remain high. In this model, increasing recovery rates are used (see inputs to the copper model in Table 1). It is by using these values that the model estimates a copper peak around 2050, as shown in Figure 3 and consistent with estimates by Fthenakis [13, 62]. As a result, in this model, copper production does not decline until after the timeframe simulated here, in 2050–2100.
The Te recovery rate is crucial to determining the annual streams of Te available to CdTe PV. To capture the debate about this factor presented in Section 1.2, the model includes a multiplier for the fraction of Te available in the anode slimes, which is subjected to recovery techniques. However, because of the lack of data or estimates in the literature of this Te fraction upon which extraction is attempted, this multiplier is not used in the model, except to produce a sensitivity analysis. The latter indicates that a 10% decrease in the fraction of Te subjected to extraction results in a 12.3% decrease in model output (cumulative installed CdTe capacity in 2050). This significant sensitivity highlights the need for reliable estimates of this factor in future Te availability studies.
2.2 Direct mining of tellurium
Although Te concentrations in ores are generally too low for direct mining, if Te demand and price continue to rise, then it is likely that certain rich ores will be mined directly or primarily for Te and other valuable metals such as Au, which may offset production costs . Two new mines in China began direct mining of Te and selenium in 2010. First Solar confirmed that it is ‘exploring a variety of Te mineral claims in various locations and expect[s] to develop some of these Te resources in the future’ . Nevertheless, there is a paucity of data regarding direct mining of Te; it is excluded from most of the aforementioned modelling studies on Te availability [5, 12-18], as well as USGS reserve estimates .
Green  provides compiled data on the possibility of direct mining of Te, assuming a maximum allowable Te price of $800/kg and concluding that apart for two ‘bonanza’ Te deposits, there is ‘a lack of sufficiently rich ores’ to strongly sustain the direct mining industry. The two exceptional deposits are Dashuigou in China with 1000 tonnes Te at 0.2–25% grade1 and Moctezuma in Mexico with 1700 tonnes at 0.2% grade. The former has commenced mining in 2010 at 12 tonnes/year , whereas the latter is commencing imminently, with news of direct investment by First Solar [76, 77]. Green  estimates that these two mines can support 30 GWp of cumulative installed CdTe at a (static) material intensity of 100 tonne Te/GWp installed capacity. Following that, lower grade resources and Au–Te mines can be exploited, assuming a profitably high Te price.
In this study, a multi-function model is used: direct mining follows a logistic path until the depletion of the two large Te deposits (2700 tonnes total), after which it follows another S-shaped growth profile with moderate annual growth—since most other primary Te deposits (including Au–Te ores and Cu ores) are not viable in the near and medium terms. Moreover, these other deposits include resources with unconfirmed Te concentrations, or the concentration may be disagreed upon. For example, the Emperor mine in Fiji, an important Au–Te mine, has reported Te concentrations ranging from 89.8 ppm  to an estimated maximum of 5796 ppm . Finally, we exclude other potential resources such as ocean crusts  and sour crude oil and gas . Illustrative growth rates for direct mining are shown along with other inputs to this module in Table 2. The output (Figure 4) shows a peak before 2030 for the Dashuigou and Moctezuma (DM) mines and slow but steady growth after their full depletion.
Table 2. Inputs and assumptions used in the direct mining module.
Pre-DM indicates the depletion period of the Dashuigou and Moctezuma mines; post-DM is the post-depletion period of these mines, after which other deposits gradually become viable. Growth rates assumed are conditional on Te prices remaining profitably high.
The figures estimated by the direct mining multi-function model carry considerable uncertainty given the paucity of input data; as a result, this module has been constructed primarily to illustrate the influence of direct mining on the total Te supply mix rather than to forecast exact direct mining production.
2.3 Tellurium from recycling
The third contribution to total Te supply in the model comes from Te recycled from end-of-life PV modules. Although there is very little recycling of Te at present from photoreceptors in old paper copiers in Europe , widespread deployment of CdTe PV modules could, with disposal regulations in place, provide a considerable amount of recycled Te [13, 28, 29].
In this module, we assume the presence of disposal regulations (e.g. [80, 81]) allowing a high recycling efficiency [13, 82]. Stated recycling efficiencies of 90% to 95% can be found in the literature [83, 84], although commercial recycling rates are likely to be less than this unless driven by legislation [28, 29]. The collection of PV panels for recycling is likely to be subject to such legislation given the toxicity concerns of cadmium .
Recycled Te begins to contribute to supply after the CdTe PV modules installed in 2010 reach their end-of-life. The International Energy Agency  estimates current module lifetime at 25 years and estimates that this will grow to 40 years for modules produced in 2040–2050. However, using these increasing values creates remarkable fluctuations in model output for annual installed capacity, for several reasons: feedback loops in the model (Figure 1), the fact that the model runs only to 2050 and the assumption that all modules have an equal lifetime (see inputs to the recycling module in Table 3). As a result, a 30-year lifetime is assumed , and recycled Te makes its largest contribution to supply after 2050.
Table 3. Inputs and assumptions used in the tellurium recycling module.
The material intensity module estimates the amount of Te required for 1 GWp of installed CdTe PV capacity. This estimate is dynamic, and it decreases as a result of technology improvement and maturity modelled endogenously throughout the 2010–2050 period. The material requirement Mr is defined by Equation (3). The variables in this equation are set to change by specified compound annual growth rates in ranges from 2010 to 2020, 2020 to2035 and then constant values from 2035 to 2050. Thus, a core assumption here is full technology maturity by 2035 (Table 4), used principally due to unavailable data on 2035–2050 development. The equation for the material required for 1 GWp of CdTe PV is
where ρ is the density of the active layer material (g/cm3), F is the percentage of Te in CdTe (51%, a fixed stoichiometric relationship), μ is the active layer thickness (µm), U is the utilisation rate indicating how much Te is wasted in the manufacturing process (%), ISTC is solar insolation under standard test conditions (AM1.5 G − 1000 W/m2) and η is the PV module efficiency (%) indicating energy captured per square metre under ISTC conditions.
Table 4. Inputs and assumptions used in the material intensity module.
A core assumption here is full technology maturity by 2035 due to lack of information thereafter.
Layer thickness, utilisation rate and module efficiency are the dynamic quantities of interest, whereas the others—density, stoichiometry and insolation—are constants. We use 2010 figures reported in the literature as initial values for these parameters in the model. In 2010, layer thickness was reported to be approximately 3 µm [4, 10, 13, 62]. The efficiency of First Solar modules was 11.3% in 2010 and rose to 11.9% in 2011 . Utilisation rate, for both 2010 and 2011, is reported from 35% to 90% [10, 14, 43, 87, 88] with an estimate for First Solar's modules reported as 40%  on the basis of manufacturing data between 2003 and 2010. There is no consistent definition of materials utilisation in the literature. We define utilisation as the weight of material (Te) in produced PV modules as a proportion of the weight of material input in a given year. This includes the efficiency of the manufacturing process in depositing material on the cell substrate and the efficiency of recycling materials not deposited on the substrate. Utilisation figures reported in the literature do not specify whether this includes both manufacturing and recycling efficiency. Utilisation also varies greatly by semiconductor deposition technique, as for example indicated by Barrioz et al. . The deposition technique used by First Solar is vapour transport deposition. Prospects for growth of all these variables are shown alongside references cited in Table 4. Figure 5 shows the model output for the behaviour of each of these three variables as well as the sharp reduction in material requirement for CdTe PV from 242 to 18 tonnes/GW in 2050, which allows for significant future growth in installed CdTe capacity.
The values in Table 4 for 2035 are long-term estimates from the sources shown. There are prospects for growth beyond these figures but at extra cost and loss of performance. Zweibel  estimates a layer thickness of 0.67, below the indicated long-term value of 1 µm, and also proposes a scenario for 0.2 µm. But the deposition of thinner films increases manufacturing costs, of which raw material (Te) costs do not represent a majority. Zweibel argues that if Te scarcity and price were to increase significantly, this would justify the deposition of such thin layers. Nevertheless, reducing to 0.2 µm entails significant losses in efficiency using current manufacturing techniques. Processing of cell back contacts and optimisation of cadmium chloride treatment after deposition have yielded laboratory cells of 11.2% efficiency at 0.7 µm thickness . Long-term module efficiencies can be estimated from the efficiency of current best laboratory cells. These are currently reported as 17.3 ± 0.5%  up to 0.6% from the previous record last year . CdTe has a bandgap of 1.44 eV and is therefore near the top of the theoretical efficiency limit of about 33% for a single-junction cell (the Shockley Quiesser limit). Wadia et al.  use theoretical limits to evaluate CdTe PV technology potential, using a cell efficiency of 33% and a layer thickness of 0.436 µm. This is far from achievable on a commercial scale.
Utilisation, as discussed previously, is also an area of confusion within the literature. We use Green's  value of 40% utilisation as an initial value as it is directly estimated from current First Solar modules based on shipment data from the company's Te supplier, 5 N Plus, and also represents a conservative assumption in the range of estimates in the literature. However, there is significant disagreement regarding this variable, with other authors estimating current material utilisation at 86.6%  or 90% . Because we also assume that by 2020, material utilisation will reach 75%, increasing to 100% in 2035, our conservative assumption affects the models outcomes only in the early years of the time horizon and is unlikely to change estimates of cumulative installed capacity by more than 3–4% in 2050.2
2.5 Implied learning rates
Although the evidence used to inform the assumptions of this model are entirely derived from the published literature, it is worth comparing the implied rates of improvement seen in Figure 5 with the literature on learning rates (LRs). This provides a context within which the assumptions drawn from the literature can be examined.
We estimated the implied LRs over the total period of learning assumed (i.e. until 2035) by plotting cumulative GWp of CdTe installed in the dynamic projection against each of the three dynamic parameters of material intensity on a log–log plot. We then applied a trendline with the equation y = axb where .
The layer thickness LR over the period to 2035 is approximately 10.5%. This is comparable to the learning estimated by Green  for First Solar experience between 2004 and 2009 but is possibly slightly optimistic on current evidence given the non-uniform rate of learning over the period and the extended timescale over which this learning must be sustained.
The module efficiency improvements modelled imply a ~4.4% LR over the period to 2035. This can be compared with the efficiency LRs estimated by Green  of 4.2% in First Solar's early production experience and 1.8% in 2007. Again, this makes current assumptions in the literature appear optimistic, and this is amplified by the period of time over which these improvements must be sustained.
Finally, Green  does not estimate an LR for utilisation but suggests a value for utilisation of approximately 40%. Other sources have estimated current utilisation at 86.6%  or up to 90% . As discussed previously, we assume the conservative figure of 40% for initial utilisation but improve this rate to 99% by 2035. This gives an LR for utilisation of 8.9%. If we were to assume an initial utilisation rate of 90%, then implied learning would appear much more conservative. However, this would make the ultimate installed capacity appear only slightly more optimistic.
In aggregate, the assumptions estimated in the literature and used here to inform the model create a slightly optimistic picture for the development of material intensity over the period to 2035, although in all cases, the assumptions are not entirely incongruous with the historical evidence for these parameters. Moreover, although LRs do tend to fall with increasing maturity of an industry, they are average growth values that do not take into account possible breakthroughs that temporarily shift away from the norm of expected technology improvement. For example, First Solar's recent 14.4% module efficiency record is being targeted in commercial modules by 2015 ; this represents a sudden peak in LRs, which may revert to their historical values after 2015.
3 COMPARISON WITH OTHER STUDIES
The purpose of this section is to compare the model's dynamic results with the results of studies using largely static assumptions. The available literature on Te availability for CdTe PV uses a range of assumptions leading to a large degree of uncertainty and justifying the need for systematic comparison [28, 29]. We develop three model projections corresponding to three sets of inputs and compare these with the conclusions of other studies [13-16, 19, 25] that clearly state most of their assumptions; these model projections and other studies are listed in Table 5. The model outputs that are compared are those listed in Section 2: annual Te availability to CdTe PV, annual installed CdTe capacity and cumulative installed CdTe capacity. The model inputs that are compared include recovery rate, module efficiency, layer thickness and material utilisation. These four parameters are specifically chosen as they are the most comparable across studies, because most studies specify values and assumptions for these parameters but not necessarily for others (see Table 1 in Candelise et al. ).
Table 5. Input values for three model projections (‘Business-as-usual’, ‘Dynamic’ and ‘Optimistic’), as well as assumptions for these values used in other studies.
Recovery rate (%)
Cell efficiency (%)
Layer thickness (µm)
Utilisation rate (%)
The outputs of these projections and studies are shown in Figure 6.
Assume that 25% of the global Te reserve base (47 000 tonnes) are available for PV use.
The 100% recovery rate is implicit in the assumption that all Te from anode slimes can be used , or that the global Te reserve base is available for PV use .
The model's baseline projection is named ‘Dynamic’ and uses the input values stated in Tables 1-4. Two other projections, ‘Business-as-usual’ and ‘Optimistic’, represent low and high CdTe PV deployment cases, respectively. The former assumes that the recovery rate of Te from copper, as well as the material intensity of CdTe PV, remains the same as they are today (as discussed in Section 2.4); the latter assumes optimistic values, suggested as achievable by some sources [10, 57], for these throughout the simulation period. The input values for all three projections are shown in Table 5, along with inputs and assumptions used in other studies for comparison.
Figure 6 shows the three different model projections using the input values cited in Table 5, with the conclusions of other studies shown graphically. We begin by discussing the three model projections. The Dynamic projection produces results higher than Business-as-usual estimates and lower than Optimistic ones in all cases. A significant step change can be seen around 2040 due to the combined effect of a peak in direct mining (depletion of the Dashuigou and Moctezuma mines) and recycled Te coming online. The step is distinct due to the assumption that all modules have an equal module lifetime of 30 years; in reality, modules may be decommissioned before their rated lifetime or last longer thereby making the step smoother. There is also a large gap between the conservative projections and the other two estimates, particularly in forecasts of annual and cumulative installed capacity of CdTe PV which depend on material intensity and thus efficiency, thickness and utilisation assumptions.
The model's Dynamic estimate is in all cases higher than a number of studies that are static projections [14-16, 25], indicating that a dynamic treatment of CdTe material constraints intrinsically improves the outlook for future deployment of this technology. The reason for this is the implicit assumption in a dynamic model that technology improvements will occur throughout the simulation period and that these improvements will apply to the supply of Te (e.g. recovery rates) and to the future Te demand for CdTe PV, which depends on material intensity, which in turn depends on layer thickness, module efficiency and utilisation rate (as shown in the CLD, Figure 1). This is confirmed by the results of Fthenakis [13, 62] whose model includes some dynamic behaviour, notably for copper resource availability and Te recovery, module efficiency and layer thickness, and within whose range of 2050 estimates this model's Dynamic estimates fall. By contrast, the most static estimate, produced by Tao et al. , uses 2010 data for annual Te production, reserve base, module efficiency and layer thickness to conclude that under so-called ‘best-scenario assumptions’, CdTe can contribute little to expected PV demand in 2100 and that its market share is likely to decline soon.
The technological improvements implicit in a dynamic model can be counterbalanced by assumptions about non-PV demand growth throughout the simulation period. Fthenakis assumes a static situation for this parameter, and the illustrative growth of 1% per annum used in this model (owing to lack of information) is subject to uncertainty. This is in stark contrast with the assumption made by Feltrin and Freundlich  that non-PV demand occupies 75% of Te consumption. Finally, Wadia et al.  provide a static projection of maximum theoretical potential electricity production, and thus, their results for cumulative installed capacity are the highest. The comparison is not totally transparent because the difference in results is not solely nor fully explained by the values shown in Table 5; for example, different assumptions about resource availability—size of reserves, non-PV demand, growth or peak of copper production and inclusion of end-of-life recycling—account for further divergence.
4 SENSITIVITY ANALYSIS RESULTS
The sensitivity analysis measures the techno-economic parameters endogenous to the model that most affect the growth of the CdTe PV sector, using the Dynamic projection as a baseline. CdTe PV growth is in turn measured using two metrics: the cumulative installed CdTe PV capacity in 2050 (GWp) and the maximum annual installed capacity (GWp/year) in the 2010–2050 simulation period. The sensitivity of these two metrics is evaluated for nine techno-economic parameters. These are grouped as follows:
Mining and supply parameters
Reported resource estimate (RES) for copper and Te resources
Share of global copper supply provided by electrolytic copper production (ECP)
Recovery rate of Te from copper anode slimes
PV module technology parameters
Active layer thickness (μ)
Module efficiency (η)
Utilisation rate (U) of Te in the vapour transport deposition process
PV module lifetime (ML)
Recycling efficiency (RE), in collecting modules and separating elements
Annual Non-PV sector demand (NPVD) for Te
These parameters are shifted by ±10% from their baseline values specified in Tables 1-4 (the lower end value is used where a range is given). The effect on both metrics is shown in Figures 7 and 8. A non-linear relationship between the metrics and certain inputs (μ, ECP, RES, ML) can be seen in the results, which are not symmetric about the vertical axis. On the other hand, an exact linear relationship is seen for the module efficiency and utilisation rate. The ranking and individual effect of each parameter varies, for instance, maximum annual installed capacity is more affected by changes in most factors than cumulative installed capacity. Recovery rate emerges as the most impacting variable in both cases. For annual capacity, the mining and supply parameters rank first, showing the dependence of CdTe PV sector growth on an imminent increase in Te supply. For cumulative installed capacity, recovery rate is followed by PV module manufacturing parameters (μ, η, U) and then ECP and RES, which are seen to be higher-ranked in the case of maximum annual capacity. Recycling parameters have minor effects on cumulative installed capacity, perhaps because of the fact that the model is run only until 2050; notwithstanding, module lifetime has a noticeable but strongly asymmetric effect on maximum annual installed capacity. Demand from the non-PV sector makes little impact on both metrics, although in the case of a sudden surge in demand from an unforeseen new application, this impact may be much larger, but this prospect is not modelled in this study.
The use of system dynamics modelling has helped visualise and quantify some of the complexities of Te supply and PV demand interactions, as presented in Section 2. Recent studies [28, 29] have highlighted the deficiencies and divergence found in existing Te criticality assessment literature. Zweibel  has observed that studies that underestimate CdTe PV assume a static situation for PV supply and use. The model presented in this paper attempts to incorporate the complex dynamics of Te supply and demand arising from the PV sector, providing a dynamic estimation of Te-constrained maximum installed CdTe PV capacity and a clearer framework for comparison of different estimates available (Section 3). The model's estimates of the maximum future potential market size of CdTe PV (Section 3) add to the debate on Te availability for PV, by providing a more transparent account of the effect of assumptions made about critical parameters (recovery rate, module efficiency, layer thickness and utilisation) on the results of this and previous studies. The results of this model thus lie between those studies that are comparatively conservative in their estimate of future CdTe contribution [14-16, 18] and those that provide optimistic scenarios [10, 13, 19, 44]. The latter are usually upper limits using best laboratory cell efficiencies and the global Te reserve base. The former assume a static or quasi-static situation for Te supply and usage, as pointed out by Zweibel . In this study, we attempt to elucidate these issues by assuming a gradually improving situation for Te supply and demand and evaluating sensitivities for the key parameters.
Most importantly, the model provides insight into the immediate sensitivity of maximum potential CdTe market size to identified critical parameters as presented in Section 4. Some of the achieved results may be evident—that is, recovery rates should increase, modules must become thinner and more efficient—but there are further non-linearities in the system revealed in this sensitivity analysis:
Material utilisation needs to be addressed properly in further studies as it has a strong and directly proportional effect, shown in the sensitivity analysis. More efficient use of Te during deposition as well as increased recycling of the material along the production process are important factors affecting Te demand coming from PV sector. The high-speed deposition techniques mainly used in current CdTe manufacturing (i.e. vapour transport deposition used by First Solar) imply reduced control over layer deposition and possibly higher material wastage. Development of deposition methods with greater materials control could improve material utilisation. Moreover, a proper quantification of Te recycling potential, based on existing recycling practice within the CdTe production process, is envisaged to be a useful step forward in the analysis.
Module lifetime has an important and non-linear effect on the future expected contribution of recycled Te. It is worth noting that almost all other uses of Te are dissipative in nature, and thus, little to no recycling currently takes place . PV modules are certainly a prospective future source of recycled Te, but in looking to meet 2050 decarbonisation targets, one should not overestimate the size of this secondary resource. If current designs last 20 years, then they represent a remarkably larger source of supply before 2050 than if they are to last 30 years. The recycling of today's CdTe PV modules will provide much more Te on a per-module basis because of the higher material intensity of modules produced today, compared with those that will be produced in 2020 and beyond. Previous to the end-of-life of today's modules, some recycling may take place using modules that have been decommissioned before end-of-life because of malfunction, although this is still poorly documented and the quantities involved may not be significant.
The efficiency of collecting PV modules for recycling and separating out the Te should be improved as much as possible, although there may be increasing marginal costs of Te recovery because of the relatively small sensitivity of installed CdTe capacity to recycling efficiency presented here.
Finally, reported resource size of Te plays an important role that is usually neglected: reserves are dynamic, and more deposits become economically viable as commodity prices rise because of high demand and depletion of high-grade ores [23, 63, 94]. Moreover, the USGS no longer reports annual production of Te, and its reserves do not include US data, which is kept proprietary, and other resources not associated with copper. As such, little is known about Te supply relative to the supply of major bulk metals, whose availability appears assured in the immediate future . The model developed here shows the potentially large effect of over-estimating and under-estimating the size of the global Te resource on the future development of CdTe PV. This is confirmed by the divergence in the results of other studies reviewed and compared in the works of Candelise et al.  and Speirs et al. . Therefore, estimates of Te-constrained CdTe production based on static production figures are misleading and can send the wrong risk signal, as carried out for example in a recent JRC report , which lists Te as the most critical of 14 energy-related metals and foresees future CdTe expansion as severely constrained by Te availability.
The model boundaries exclude analysis of the relative positioning of CdTe within the PV industry, its future market share and the implications of this relative positioning in terms of future Te demand. The model outputs are estimates of the maximum potential expansion of CdTe as constrained by Te future supply, but CdTe may not grow to its maximum potential. As introduced in Section 1.1, future CdTe market share and relative Te demand are uncertain and dependent on future developments of other existing and emerging PV technologies. Modelling the implications of Te availability and potential expansion of CdTe PV as a function of competition between various PV technologies for market share could be the subject of further research; the effect of competition on growth has already been demonstrated at a simple level in the study by Moss et al. , where the market shares of CdTe and CIGS in 2020 and 2030 are varied to show the impact on the demand for Te and other metals. The latter is a basic sensitivity analysis, and endogenous dynamic modelling of this competition may provide further insights into the potential Te-constrained future growth of CdTe PV.
Moreover, the model does not account for Te price. As estimated in a recent study , an escalation of Te price could threaten CdTe ambitions to reach and maintain low production costs, and weaken their competitiveness in the wider PV market. This has implications for future growth of CdTe industry and the relative demand of Te coming from it. A robust analysis of future Te price scenarios (as dependent on complex supply and demand dynamics of the end use markets as well as economics of extraction and production) has been highlighted in previous research [5, 18, 28, 29]. Endogenous dynamic modelling of the impact of Te price increase on CdTe market share and Te demand would thus also constitute a valuable addition to the model presented here.
A system dynamics model was developed to simulate Te availability for CdTe PV between 2010 and 2050, in response to a number of deficiencies highlighted in recent reviews of the literature [28, 29], notably the lack of transparency in modelling assumptions and the static treatment of Te supply and recycling as well as PV cell and module parameters.
The model's results and sensitivity analysis demonstrate that some factors have complex impacts on the maximum growth potential of CdTe PV by 2050. The changing module lifetime of CdTe PV plays a crucial role in determining the potential size of the recyclable Te resource, whereas the efficiency of recycling has a relatively minor effect. Demand for Te from its current non-PV uses does not have a large impact on future maximum CdTe growth, and the most important parameters remain the recovery rate, module efficiency, active layer thickness and material utilisation.
System dynamics proves a valuable methodology for understanding the real-world complexity of by-product resource availability for a fast-growing clean energy technology and addresses the lack of a dynamic treatment of this system in the literature, improving upon projections made by comparing current supply or global reserves to future demand. The dynamic treatment of this system, while using values and assumptions commensurate with those suggested in previous studies, estimates a growth potential for CdTe PV that is higher than that estimated by conservative studies assuming no supply growth or technology improvement and lower than studies estimating theoretical or maximum achievable limits.
The authors would like to thank colleagues at Imperial Centre for Energy Policy and Technology (ICEPT) and the UK Energy Research Centre (UKERC) for assistance with technical issues and data collection. We would also like to thank Bill Gross, Professor Ned Ekins-Daukes (Imperial College London), Ana Rebelo (International Copper Study Group), Andreas Wade (First Solar) and Professor Martin Green (University of New South Wales) for advice and responses to the authors' questions.
Ore grade or quality is commonly measured in percent (%), grams per tonne (g/t), or parts per million (ppm). 1% = 10 000 g/t = 10 000 ppm.
A sensitivity analysis of this variable indicates that increasing the initial conditions for material utilisation to 86.6% will approximately halve material intensity in the initial years but only increase cumulative installed capacity in 2050 by ~3% over the 40% initial utilisation rate case.