Economically sustainable scaling of photovoltaics to meet climate targets

To meet climate goals, photovoltaics (PV) deployment will have to grow rapidly over the next fifteen years. We identify two barriers to this growth: scale-up of manufacturing capacity and the cost of PV module production. We explore several technoeconomic approaches to overcoming these barriers and identify deep reductions in the capital intensity (capex) of PV module manufacturing and large increases in module efficiency as the most promising routes to rapid deployment. Given the lag inherent in rolling out new technology, we explore an approach where growth is fueled by debt or subsidies in the short-term and technological advances in the medium term. Finally, we analyze the current capex structure of crystalline silicon PV module manufacturing to identify potential savings.

effective and least risky ways to address these barriers to scale. We also assess the effects of variations in demand due to hard-to-predict factors, like public policy, on the necessary reductions in cost. Finally, we review examples of redundant technology pathways for crystalline silicon PV to achieve the necessary innovations in capex, performance, and price.

Broader context
To reduce CO 2 emissions enough over the next fifteen years and avoid the worst effects of climate change will require dramatic increases in the deployment of renewable energy, photovoltaics (PV) in particular. Climate action plans call for 2-10 terawatts (TW) of PV by 2030. Current manufacturing capacity could supply enough for 1 TW of cumulative installations at the end of this period, implying that growth in manufacturing capacity is necessary. Industry roadmaps project up to 2.6 TW but largely fail to assess whether these targets are economically feasible with today's PV module technology. Addressing the question of what technological innovations, if any, would enable rapid manufacturing scale-up requires a conceptual advance in modeling methodology. We address this challenge by coupling three industry-validated models: a bottom-up cost model, an economically sustainable growth-rate calculator, and a constraining demand curve. This approach enables us to determine the sensitivity of PV industry growth to specific technological and economic variables, considering both their effect on the ratio of up-front factory costs to revenue and demand as a function of PV module price. Shifting the demand curve enables us to consider the effects of different policy decisions, like a carbon tax or deployment subsidies.

Climate-driven deployment targets for photovoltaics
Recent studies show that carbon dioxide (CO 2 ) emissions must peak in the next fifteen years to ensure a high probability of limiting average global warming to less than 1.5-2 1C above pre-industrial levels [1][2][3][4][5] and thereby avoid the worst effects of climate change.
As global energy demand is expected to rise significantly over the same period, [1][2]6 achieving this goal will require the deployment of terawatts of new low-carbon energy generation, compared with less than 1 TW of non-hydro renewables today.
Photovoltaics (PV) have several advantages compared with other low-carbon technologies: the vast size of the solar resource, 6,7 the proven track record of reliability 8-10 and bankability 11 of PV installations, the rapidity with which new manufacturing capacity can be brought online and projects developed and built, 12 and their modular nature, which allows deployment in areas that may lack electric grid infrastructure. Concordantly, aggressive PV deployment targets, ranging from 2-10 TW by 2030, are widely viewed as vital to mitigate climate change (Fig. 1, green symbols/line). 1,2,[13][14][15] We consider a range of climate and CO 2 reduction scenarios, which results in a range of PV deployment targets. The high end provides the lowest risk to the climate.
Future deployment of PV depends on a number of factors. We will focus this discussion on the upper bound imposed by one technical constraint, the annual manufacturing capacity for PV modules, and one market constraint, total demand for PV. Manufacturing capacity limits annual installed capacity, which in turn limits cumulative installed capacity each year. Demand for PV modules has a strong dependence on public policy and the cost of competing (e.g., fossil fuel) and supporting (e.g., balanceof-systems, energy storage) technologies. However, under a given set of assumptions about the economic and technology environment, total demand can be given as a function of PV module price. This relationship is called a demand curve.
As shown by the pink curve in Fig. 1, current PV manufacturing capacity 16 is sufficient to produce just under 1 TW in the next 15 years. Thus, growth in manufacturing capacity ‡ is needed to meet climate-driven deployment targets. According to market research, 16 under the current cost structure for PV modules, total demand would be less than 1 TW even if their price was equal to their variable cost of production.
Several PV industry projections 15,[17][18][19][20][21][22][23][24][25][26] (Fig. 1, blue symbols/ lines) predict deployment comparable to some climate-driven targets. The most aggressive projections fall well short of targets that minimize climate risks, but even these projections imply significant growth in manufacturing capacity and easing of demand constraints. However, most publicly available projections do not establish whether current technology can reach these targets and fail to identify effective pathways to achieve the necessary manufacturing capacity and demand.
In this work, we use bottom-up cost modeling to determine (1) if current crystalline silicon PV module technology can achieve growth rates commensurate with climate targets without external financial support and (2) what innovation-driven cost reductions are needed for sufficient demand to achieve these targets. We find that dramatic reductions in the capital intensity and cost of PV module manufacturing are needed. The technology pathways we identify to achieve these goals are also likely to greatly reduce the energy and CO 2 payback times for PV modules. 27

PV manufacturing cost and growth models
Our cost model, § 28,29 presented schematically in Fig. 2, produces a discounted cash flow for a hypothetical PV manufacturer by summing the individual cost components of the manufacturing process and subtracting these from revenues and financing. In simple terms, the ''cash in'' variables are (1) net revenues from PV module sales, expressed per unit as operating margin (margin), and (2) debt financing. Because debt typically leverages equity within the company, we use the variable debt/equity ratio, which we hold constant over time.
The ''cash out'' variables (before taxes and interest on debt are paid) are the fixed costs of new factories and equipment (expressed as capex) and the variable costs of production. Because we are interested in the cost per unit power, not per panel, we divide both fixed and variable costs by the power produced by the module. We use efficiency as a proxy variable for module power, dollars per watt as the unit of cost, and dollars per watt of installed annual capacity as the unit of capex. 28,70 To estimate an upper bound for manufacturing capacity growth rate, we assume that no dividends are paid and all profits (after taxes and interest on debt) are reinvested in expansion. 28 The ratio of ''cash in'' (margin and debt) to capex determines how quickly new factories can be built and therefore how quickly PV manufacturing capacity can grow. Thus, increases in ''cash in'' or decreases in capex increase growth rate. To set an upper bound on cumulative installed capacity, we assume 100% utilization of manufacturing capacity. Because we consider a 15-year time horizon while PV panels typically last at least 20 years, we further assume no replacement. Therefore, cumulative installed capacity is just the sum of the previous year's cumulative capacity and the manufacturing capacity in the current year. Manufacturing capacity in the current year is manufacturing capacity in the previous year times one plus the growth rate.
The growth rate calculator begins by assuming a constant margin. The product of this margin and the sum of fixed and variable costs sets a selling price. If cumulative capacity exceeds If data was represented as lines in the source, it is represented as lines here. If it was reported as individual data points in the source, it is represented by symbols here. Sources for specific data can be found in ESI, † Fig. S1. ‡ The growth rate of cumulative installed capacity is often quoted for the PV industry. In this paper, we will use ''growth'' and ''growth rate'' to refer only to growth of manufacturing capacity (i.e. annual, not cumulative, installations). § The cost model is available for download as an Excel file in the ESI, † as are the Matlab scripts used to calculate manufacturing growth rate and thereby annual and cumulative installations over time.
demand at this price, the calculator takes the price corresponding to this capacity on the demand curve, and uses the (lower) margin implied by this price. This reduced margin limits growth. If price falls below variable cost, production ceases altogether. For this work, we use a power law fit to a demand curve from ref. 16 containing historical data on PV module sales and projected demand as a function of price (see Fig. 2). We fit the data because the historical data is not single-valued. For more details on these variables, calculations, and the demand curve, see ESI † and ref. 29.
We perform a sensitivity analysis on each of the variables in our cash flow to discern which have the greatest potential to increase growth rate and ease the demand constraint. For our baseline calculation, around which we vary these parameters, we use current industry data for variable costs, capex, and efficiency, set margin such that the net profit is equal to the cost of capital, 30 and use a debt/equity ratio of 1 : 1. These baseline parameters are listed in Table S1 in the ESI, † and details of how they were selected are in ESI † and ref. 28 and 29. We model crystalline silicon because it represents over 90% of the PV market, 31 has dominated for decades, 32 has a large existing manufacturing base, is sufficiently abundant to scale to tens of terawatts, 33 and reliable cost data is available. However, our sustainable growth modeling methodology, and therefore the capex and cost implications, could apply to any technology. This includes commercially available thin-film technologies like cadmium telluride and copper (indium, gallium) diselenide, if they are not limited by the availability of Te and In. 14,34,35 Given the aggressive capex, variable cost, and efficiency improvements demanded by the advanced scenario, non-silicon technologies have the challenge of scaling from a lower baseline, but an opportunity to gain market share through significantly higher margins and lower capex; further discussion is provided in ESI. †

Sensitivity analysis of cost and growth model variables
Results from the baseline scenario (the point of intersection of the curves in Fig. 3) show that growth rate must be increased while costs are decreased to reach aggressive deployment targets.
As stated above, the baseline scenario is limited by demand to less than 1 TW in 2030 (Fig. 3a), but even without demand constraints, manufacturing growth would limit cumulative installed capacity to 3.4 TW (Fig. 3b). Fig. 3a shows the demand-constrained cumulative installed capacity in 2030 for a range of values, varying each parameter independently. The left axis in Fig. 3b shows the unconstrained installed PV capacity in 2030, which depends only on the Fig. 2 Schematic of our model to calculate economically sustainable growth rate, constrained by power law fit to a market-driven demand curve, 16 to predict cumulative capacity.  Fig. 3b shows the corresponding growth rates. This sensitivity analysis shows that three of our variables (margin, debt/equity ratio, and capex) can increase growth rate but have little potential to reduce cost and increase demand, while the other two (variable costs and efficiency) can reduce cost but have little potential to increase growth rate.
Increasing margin increases growth rate by increasing revenue from sales (a major component of ''cash in''). However, PV modules have become a commodity with little product differentiation. Module manufacturers are therefore price-takers with little ability to impact margin, 36,37 and we see little practical opportunity to increase growth rate by increasing margins.
Increased debt without significant reductions in cost will increase growth temporarily. Ultimately, however, once the demand ceiling is reached, margin will be eroded, leading to reduced revenue, reduced growth and lower total installed capacity. The increased debt approach is therefore risky for manufacturers. Increased debt is also a weaker lever on growth than reducing capex, which reduces the cost for a new factory. Assuming constant ''cash in,'' reduced capex increases the rate at which new factories can be built and manufacturing capacity added.
In our growth model, the only positive effect reducing variable cost has on installed capacity is triggering a reduction of price due to the assumption of constant margin. We assume margins are constant because technology diffusion and the treatment of PV modules as a commodity by consumers and installers drive down prices in response to reduced variable costs. Lower prices mean lower revenue (''cash in''). At constant capex, that means slower growth. Therefore, while reducing variable costs eases the demand constraint on total installed PV capacity, it reduces growth rate as well. This trade-off leads to the maximum in the variable costs curve in Fig. 3a.
Increasing efficiency, on the other hand, reduces both fixed and variable costs (per unit power). Assuming efficiency increases while capex and variable costs per module remain constant, higher efficiency can ease the demand constraint while maintaining a constant growth rate. This constant growth rate is indicated by the flat efficiency curve in Fig. 3b.
In certain instances, the financial incentives experienced by an individual company can oppose the goal of maximizing PV deployment. For example, to maximize short-term revenue, a company is motivated to reduce costs, striving for first-mover advantage or struggling to keep up with competitors. However, once a cost-reducing innovation spreads throughout the entire industry and prices are reduced across the board, lower prices decrease margins in absolute dollars. 38 Thus, the so-called ''race to the bottom'' generally results in decreased sustainable manufacturing growth rates, except for the first movers. In contrast, acrossthe-board increases in sustainable manufacturing growth rates can be achieved by reducing capex. Note that even if the entire industry lowers capex, the sustainable growth rate will increase for all companies, as new factories cost less money to build. However, the longer-term investment in capex reduction does not have as strong an impact on short-term revenue as other cost-reduction measures; thus, capex reduction is often not prioritized in industry roadmaps. Other trade-offs between the techno-economic inputs shown in Fig. 3 are analyzed in Fig. S3 in the ESI. †

PV deployment scenarios
To quantify the efficacy of various capex-and cost-reduction approaches, Fig. 4 shows the cumulative installed capacity as a function of time ¶ for several representative scenarios: our baseline scenario with today's technology (light blue), line-of-sight technology improvements from industry roadmaps (red), two advanced technology scenarios (dark blue and green), and line-of-sight technology with an increased debt/equity ratio (tan). Key input parameters for each scenario are in the ESI, † Table S1. The colored lines are constrained by our baseline assumptions for demand as a function of module price. The shaded area indicates the range of installed capacity when demand is increased or decreased from this baseline, as described in the ESI. † When the colored line is on the top boundary of the shaded area, it indicates that installed capacity is growth-constrained rather than demand-constrained for that scenario with our baseline demand assumptions. Climate targets are also include for reference (gray).

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Line-of-sight technology reduces wafer thickness from 180 mm with 130 mm of kerf (sawdust) to 120 mm with 130 mm of kerf. Additional modest reductions in capex and variable costs and an increase in efficiency are included as well. In this scenario, a total installed capacity of 3.2 TW is achievable by 2030. Gains in growth rate due to reduced capex are offset by reductions in revenue due to reduced variable costs, so the line-of-sight technology actually has a slightly lower unconstrained growth rate than baseline. Total installed capacity is limited by both price (3.2 TW) and growth rate (3.3 TW) for line-of-sight technology, indicating a need to reduce both capex and cost further.
We therefore consider scenarios for two advanced PV technology concepts. In both scenarios, wafer thickness and kerf are reduced to 20 mm each (the equivalent of 40 mm-thick kerfless wafers), which significantly reduces both capex and variable costs. Further deep reductions in capex are then coupled to either (1) a further large reduction of variable cost and the same increase in efficiency as in the line-of-sight scenario, or (2) a modest further reduction of variable costs and a large increase in efficiency (which further reduces both capex and variable costs). Scenario 1 represents direct reduction of variable costs by reducing the cost of inputs to production like electricity and silver, either through price reductions, quantity reductions, or replacement. This approach results in reduced revenue, which limits growth rate, and a cumulative installed capacity in 2030 of 6.9 TW. Scenario 2, which drives cost reduction primarily by increasing efficiency, results in faster growth and a cumulative installed capacity in 2030 of 11.2 TW.
There are clear and redundant pathways to achieve the reductions in capex and variable costs, as well as the improvements in efficiency described in the advanced scenarios. Over 30% of the capex in PV module manufacturing is in the production of polysilicon. Therefore, reduction of the silicon wafer thickness from its current value of about 180 mm to 10-20 mm (with equivalent reductions in kerf loss, or 30-50 mm with no kerf loss) would eliminate 90% of this capex. Multiple technologies exist, some of which have already demonstrated high efficiency on wafers as thin as 35 mm, including silicon grown epitaxially directly from vapor sources, 39 silicon wafers produced directly from molten silicon without casting and wire-sawing, 40 and thinner wire saws. [41][42][43] Thinner wafers also contribute to higher throughput processing, further reducing capex. Specifically, the throughput of crystal growth, ingot cropping, wire sawing, and wet chemical steps are increased by having thinner wafers.
Czochralski growth of monocrystalline silicon is very capitalintensive, representing over 15% of the capex in a monocrystalline silicon PV module. 29 Directional solidification of multicrystalline silicon is relatively low capex, and recent results on ''highperformance'' multicrystalline silicon offer promising routes to high efficiency. 39,44 The capex associated with multicrystalline silicon could be reduced by planned moves to larger ingots 31,45 (further increasing throughput). Czochralski growth could be replaced by multicrystalline silicon, one of the growth techniques mentioned above, or another technique like kyropolis growth, which has demonstrated good material quality with potentially low capex. 46 Further capex reductions are available through a variety of process modifications. Some examples follow. Replacing slurry wire sawing with structured or diamond wire eliminates equipment for slurry collection and increases throughput. 41 Kerfless wafering would also eliminate this equipment and the equipment used to recondition scrap silicon. The throughput of emitter formation can be increased in the case of batch processing with a gas dopant source (e.g., POCl 3 ) by depositing at lower pressure. 47 This process can also be completely replaced by ion implantation 48,49 or chemical vapor deposition (CVD) either of a dopant source, 50 a doped epitaxial silicon layer, 51 or a polysilicon layer. 52 CVD and implant emitter formation also obviate the need for edge isolation because they are single-sided processes. The capex associated with contact firing can be reduced for a traditional belt furnace process by increasing the throughput of the entire manufacturing process (the throughput of a belt furnace is just determined by the belt length). Belt furnace firing can also be replaced by laser-firing [53][54][55] or another more efficient furnace. 56,57 On the module level, capex can be reduced by eliminating the aluminum frame 27,58,59 and simplified tabbing and stringing of cells together. 60 Combined, the processes mentioned above represent over 75% of the capex of producing a monocrystalline PV module. 29 As discussed in the main text, increasing efficiency also proportionally reduces capex (in dollars per watt). Additionally, the processes mentioned above represent over 70% of the embedded energy and CO 2 of a PV module, 61,62 and efficiency is inversely proportional to energy payback time. Thus, the advanced concepts described would drastically reduce PV systems' embedded CO 2 and energy payback times, 27,63 mitigating the risk of substantial added electrical loads for PV system production at elevated manufacturing capacities; 64 see further discussion in ESI. † Variable cost reductions up to 40% are on industry roadmaps as described in detail in ref. 28 and 31. Multiple technologies, including passivated emitter and rear local contacts, heterojunctions, interdigitated back contact designs, and fully passivated contacts, have demonstrated efficiencies over 25%, 39 and roadmaps exist up to 26-29%. 31,65,66 There is also promising work to reduce cell-to-module losses. [67][68][69] The price constraint on installed capacity depends strongly on the demand curve for PV. The demand curve in turn depends on a multitude of factors unrelated to PV module technology.8 To capture the uncertainty in these factors over a period of decades, we shift the demand curve to simulate increased and decreased demand at a given PV module price (see ESI † for details) and recalculate installations over time for each of our technology scenarios. As stated above, the range of installed capacity with increased and decreased demand is indicated by the shaded 8 Some example of these factors are: grid constraints and electricity markets, including utility tariff structures, ancillary services markets, and electric grid technology; energy and climate policy, including carbon pricing, fossil fuel subsidies, and supply-and demand-side PV subsidies like feed-in-tariffs, investment tax credits, renewable portfolio standards, low/zero-interest loans, subsidized land and equipment and the cost of supporting or competing technologies like fossil fuels, energy storage, PV balance-of-systems, and labor for manufacturing and installation.  Fig. 4. These results show that relatively small changes in demand can have dramatic impacts on installed capacity. For the high-efficiency advanced technology concept, a 25% (rel.) change in the price at which a given capacity is demanded can increase installed capacity to 11.5 TW or reduce it to 8.5 TW. Debt can also be used to increase growth rate. However, it must come with significant reductions in cost to reach high installed capacity. To illustrate this point, a scenario with line-ofsight technology improvements and a debt/equity ratio of 5 : 1 is also shown in Fig. 4. As with the line-of-sight scenario with a debt/equity ratio of 1 : 1, installed capacity is limited to less than 5 TW. In addition, the demand curve has a much stronger effect on this scenario than on technology innovations, with the high demand case yielding 11 TW of PV but the low demand case less than 3 TW. This leads to a large range in the total amount of debt that would have to be sourced in such a scenario, ranging from $0.9 trillion to $3.7 trillion with baseline projected demand requiring $1.6 trillion. Finally, the interest rate on debt also has a significant impact on the installed capacity in the increased debt scenario. An increase from 5% (baseline assumption) to 10% reduces installed capacity in the high-demand case from 11 to 7 TW. This data is shown in Fig. S5 of the ESI. †

Conclusions
In summary, we find that further innovation is necessary to reach cumulative installed PV capacities commensurate with targets for keeping average global temperatures below 1.5-2 1C above pre-industrial levels without external subsidies. Line-ofsight technology improvements are insufficient to reach aggressive targets, which give the highest likelihood of preventing catastrophic climate change. To meet these targets will require dramatic reductions in capex along with significant increases in efficiency and/or hefty reductions in variable costs. Because reductions in variable costs also reduce growth rate under the assumption of fixed operating margins, we find that increased efficiency is preferred.
Finally, demand for PV, which limits total deployment at a given price, is strongly dependent on policy decisions. Installers price PV and consumers demand PV as an alternative to existing electricity options. Many policy decisions affect the relative prices of PV and fossil fuel alternatives, including utility tariff structures, ancillary services markets, electric grid technology, carbon pricing, renewable portfolio standards, fossil fuel subsidies, supply-and demand-side PV subsidies like feed-in-tariffs, investment tax credits, low and zero-interest loans, and subsidized land and equipment. Decisions about these policies will either increase or decrease dramatically the innovation and R&D investment required to achieve climate-driven PV deployment targets.