Supporting Information for. Materials Availability Drives the Opportunity for Large-Scale Photovoltaics Deployment

Transcription

1 Wadia, Alivisatos & Kammen 1 Supporting Information for Materials Availability Drives the Opportunity for Large-Scale Photovoltaics Deployment Cyrus Wadia*, A. Paul Alivisatos and Dan Kammen* *To whom correspondence should be addressed. s: cyrusw@berkeley.edu, kammen@berkeley.edu November 24, 2008

2 Wadia, Alivisatos & Kammen 2 S1: Abundance and Economics of Mined Elements Geological Abundance Geological data provides estimates for all naturally occurring elements in the earth s crust. Figure S1 shows that 99.99% of the earth s crust by mass is comprised of 32 elements. The five most abundant, in order, are: oxygen, silicon, aluminum, calcium, and iron. F Mn Ba C Sr S Zr V Cl Cr Rb Ni Zn Ce Cu Nd La Y N Li Figure S1: Geological Elemental Abundance 1 Market Price of Mined Minerals Figure S2 is a plot of thirty-two minerals cataloged by the U.S. Geological Survey(USGS). Each mineral will go through price fluctuations over time, but the aggregate view and ordering of minerals relative to each other is extremely stable. The correlation between the natural logarithms of reserve base and mined cost shows a linear relationship.

3 Wadia, Alivisatos & Kammen 3 Figure S2: Abundance versus Market Price 2 Economics of Mineral Extraction The majority of metals occur in the earth s crust in the following chemical states 3 : 1. Oxides (Fe 2 O 3, TiO 2 ) 2. Sulphides (PbS, ZnS) 3. Oxysalts (FeCO 3, ZrSiO 3 ) There are three ways the desired metal can be extracted from the ore: pyrometallurgy where smelting refines through a melt, hydrometallurgy which provides an aqueous solution and subsequent precipitation of the metal, and electrometallurgy that uses electrolysis to extract a metal. The cost of mineral processing is given by C T = C e +C p. The cost of extraction (C e ) is given by C e = a/g and the cost of mineral reining (C p ) is given by Cp = b*δg, where a

4 Wadia, Alivisatos & Kammen 4 and b are constants, g is ore grade or mineral content of the raw ore, and ΔG is the Gibbs free energy of transforming mineral into useable metal 4-7. As an analog to the cost of extraction, fuel costs may be considered in the same form, with: F = F o /g + F s F = fuel requirements per ton of metal F o = fuel used in mining F s = fuel used in smelting and refining Energy input (F) is a good proxy for total extraction cost where values of F are inversely related to ore quality. Ore quality is defined as the percentage by mass a particular ore contains of a specific element. This indirect correlation stems from the idea that more material must be moved to generate the same concentrate that goes into the smelting and refining. For example, for an ore with a grade of 2%, it is necessary to mine, crush, grind, and flotate 50 tons of the ore material to provide enough concentrate to make one ton of metal. For an ore grade of 1%, it would be necessary to process 100 tons of ore. Unique Extraction Attributes of Solar PV We are in an era of declining ore grades and quality 4, 8. Copper ore grade in the early 1900 s was ~2-4%, and now the average grade is 1%. With declining average ore grade, the energy inputs in extraction go up thereby increasing the cost of extraction and ultimately price of these metals in the market. To address these concerns, economists may turn to a Ricardian view that as costs push up against some market limits, new resources may take their place as substitute technologies Solar PV represents a departure from most industrial applications of mined materials. In most industrial applications, another metal may be used as a substitute for any particular material when resource constraints are real. This is not the case for solar PV. Solar PV does not adhere to this because it is the very unique combination of mined materials that is the nature of a PV cell. In a CuInGaS (CIGS) solar cell, you could not arbitrarily replace the expensive indium for nickel and have a working device. You would have to substitute the entire

5 Wadia, Alivisatos & Kammen 5 material system for another. Solar PV is also material intensive. With expectations of large growth in PV, abundance of materials poses a real concern for the long view. S2: Model Calcuation Methods The starting list of compounds to be analyzed was divided into two broad categories: existing technologies (II-VI thin films, silicon based films, and high performance III-V technologies) and emerging materials which are yet to be commercialized 12. Table S1: List of Compounds For Consideration Existing Emerging Materials Technologies x-si ZnTe ZnO a-si ZnSe CuO CIGS PbSe Cu 2 S CdTe PbS FeS 2 CdSe Ag 2 S NiS CdS Bi 2 S 3 CZTS GaAs Zn 3 P 2 Cu 2 O InP WSe 2 To form a proper homojunction each of these compounds must either be doped to form a p-n junction. Alternatively, each material can form a heterojunction, with a second material system. For this analysis, the maximum electricity potential of any pair of semiconductors in a heterojunction is defined as the potential of the limiting compound. For example, in the case of Cu 2 S paired with CdS, the results of the CdS electricity potential calculation are the critical number.

6 Wadia, Alivisatos & Kammen 6 There are 3 generally available numbers that may be important in isolating the effects of material abundance on future PV cell production 1. Geologic Abundance - this is an absolute maximum concentration of every element in the earth s crust. Nine elements make up 99% of the earth s continental crust 1. This upper limit is unattainable and doesn t provide an accurate picture for PV potential. 2. Economic Reserves - the USGS catalogs over 32 mined elements for known reserves that are economic to extract 2. This is an economic term and not a geologic term. Because this number will fluctuate with market supply/ demand dynamics, the number is non transparent and would make it difficult to draw reliable conclusions in this type of analysis. 3. WW Annual Production the USGS details the annual production of all mined elements 2. As an order of magnitude comparison across several minerals, this is the most level number for comparisons. For this analysis we choose the conservative worldwide annual production numbers documented by the USGS. The rationale for this is demonstrated by Figure S3, a plot of the change in economic reserves for copper over the last 70 years. What becomes clear is that economic reserve increase over time is a result of significant shifts in market supply and demand as opposed to new discovery of ores at equal or greater quality.

7 Wadia, Alivisatos & Kammen 7 Figure S3: Copper Economic Reserves 2 Mineral Abundance and Price Data Used in the Model The data for this analysis was taken from the 2007 U.S Geological Survey Mineral Commodity Summaries which report estimates for the year Table S2: Mineral Abundance and Cost Data Mineral Price ($/kg) Annual Production (000 MT) Au $21, Tl $5, Rh $1, Ge $ In $ Ga $ Ag $ Te $ Li $ Se $ Co $ Ni $ , Sn $ Bi $ Cu $ , Sb $ Mg $3.46 4,050.00

8 Wadia, Alivisatos & Kammen 8 Zn $ , Cd $ Al $ , Si $1.70 4, Ti $0.55 5, W $ Cr $ , Sr $ Fe $0.05 1, S $ , Pb $1.69 3, Mn $ P $ , Maximum TWh Potential Calculation Method (Manuscript Figure 1) Maximum electricity potential is calculated based on the available resource of the limiting element. For example, in the case of CdS, the more scarce material is cadmium thus acting as the limiting element for CdS. Whereas in CdSe, it is selenium that acts as the limiting element and therefore determines the results. To calculate the maximum annual power production potential, we assume 100% of the mined limiting element is converted into a solar photovoltaic devices. Equation S1 details the core calculation for energy potential (P) in units of TWh. P = I η A C H β Equation S1: Electricity Potential Calculation Variables Defined

9 Wadia, Alivisatos & Kammen 9 I: Solar spectrum intensity taken as global air mass index (AM1.5G) of 1,000 W/m 213 A: Annual production per mineral (MT) 2 C: Capacity factor for PV applications taken as 20% 13 H: Annual hours in the year taken as 8,760 hours η: Maximum power conversion efficiency of material as calculated in percentage of solar AM1.5 spectrum (see methods below) β: Minimum material intensity as calculated in kg/m 2 and converted to MT/m 2 (see methods below) So that we are calculating the best-case scenario, our calculations assume the theoretical limits in both minimum material intensity (β) and maximum power conversion efficiency (η). Calculating Minimum β Minimum β values in g/m 2 are calculated by multiplying material density by a minimum material thickness (t). Values of t are calculated for each material where full absorption spectra are available, including: Zn 3 P 2, PbSe, CdS, CdSe, CuO, Cu 2 O, FeS 2, x-si, GaAs, InP, PbS, CdTe, a-si, ZnO, ZnTe, ZnSe 14. Minimum t values are calculated by solving the Equation S2 for a fixed I/I o ratio of 0.85 which is qualitatively the thickness t required for the semi-conducting material to absorb 85% of the available energy equal to or larger than the material bandgap. I o is the intensity of the AM1.5G solar dependant on wavelength. α is the material absorption coefficient that varies with energy wavelength.

10 Wadia, Alivisatos & Kammen 10 I I o = λ bg 280nm I o (λ)dλ I o (λ)e α(λ)t dλ λ bg I o (λ)dλ 280nm Equation S2: Calculating t Values For those material systems for which full absorption spectra were not available, we used published values for absorption coefficients integrated over the entire solar spectrum or estimated appropriate thickness based on the absorption coefficient data that was available 12, Calculating η Performance (η) was taken as 100% of each semiconductor s theoretical power conversion efficiency limit, also known as the single junction thermodynamic limit. These values are calculated using a detailed balance model first described by Shockley & Queisser and re-calculated using more accurate solar incidence energy by others We use the calculation describe by Hanna and Nozik where the maximum efficiency is 33.7% at 1.34 ev. Figure S4 charts these values between 0.3eV and 4.5eV 20. Material bandgap values were taken from multiple sources 12, 15, 19, 21, 22.

11 Wadia, Alivisatos & Kammen 11 Figure S4: Maximum Theoretical Efficiency Table S3 details the η, β, and t values calculated for this analysis. It s important to note that these values will differ from industrial state of the art practices. However, these numbers are representative of a theoretical best case scenario and help us in making comparative analyses between materials as opposed to comparing a single compound between this analysis and its current status experimentally. Table S3: Model Results Table Material Bandgap (ev) η (%) t (µm) β (g/m 2 ) x-si % a-si % CIGS %

12 Wadia, Alivisatos & Kammen 12 CdTe % CdSe % GaAs % InP % ZnTe % ZnSe % PbSe % PbS % Ag2S % Bi 2 S % ZnO 3.4 2% CuO % Cu 2 S % FeS % NiS % CZTS % Zn 3 P % Cu2O % CdS % WSe % Total $/W Calculation Method (Manuscript Figure 2) Material extraction costs C e are expressed in $/W for each semiconductor compound with x components and calculated by Equation S3.

13 Wadia, Alivisatos & Kammen 13 C e = β η I x n=1 C n x (x n )(M n ) (x m )(M m ) m=1 Equation S3: $/W Calculation Variables Defined C n : The mined cost per material n given in $/kg 2 x n /x m : molar quantities of an individual species in the semi conducting compound M n /M m : molar masses of an individual species in the semi conducting compound I: Solar spectrum intensity taken as global air mass index (AM1.5G) of 1,000 W/m 2 13 η: Maximum power conversion efficiency of material as calculated in percentage of solar AM1.5 spectrum β: Minimum material intensity as calculated in kg/m 2 C e is taken as raw mineral market price as given by the U.S. Geological Survey production data 2. These values will fluctuate over time based on supply demand dynamics but the order of magnitude difference between any two mined minerals is a relatively stable number. The values for β, I, and η are calculated as described in the preceding section. S3: Additional Calculations Surface Area Requirements

14 Wadia, Alivisatos & Kammen 14 While the analysis addresses material costs as the fundamental building blocks for module price, it doesn t address balance of system (BOS), operation management (OM) or costs associated with land use. Naturally, some lower efficiency technologies are disadvantaged along these cost components. To demonstrate surface area requirements, we graph each compound analyzed as a fraction of the total U.S. land area of 9MM km 2 (Figure S5). Figure S5: Land Use per Material 1. Evolution of Photovoltaic Technology Since the crystalline silicon solar cell was demonstrated at Bell Labs in 1954, there has been over five decades of interest in novel semi conducting materials as photovoltaic replacements for silicon. In the recent past, photovoltaic demand has been tempered by periodic capacity constraints of refined silicon. These are temporary problems in the marketplace but it stands to reason that perhaps other material systems could be employed with a higher resistance to capacity shortfalls while not coming in more expensive. This broad effort has been in mostly thin films like CIGS, CdSe/CdS

15 Wadia, Alivisatos & Kammen 15 technologies. Figure S6 captures how the technologies have advanced both in share of the market and power conversion efficiency. Figure S6: Evolution of Primary PV Technologies Over Time 2. Simon Ehrlich Wager Calculations Table S3 lists the commodity prices for the 5 metals in question for the Simon Ehrilch wager. Each price is given in 1980 dollars. The total wager was for $200 per metal which yielded different wager weights as shown in the table. Table S4: Commodity Price Date for Simon-Ehrlich Debate

16 Wadia, Alivisatos & Kammen 16 Metal Total Wager ($/lb.) ($/lb.)* ($/lb.)* (lbs) Chrome $3.90 $2.34 $ Copper $1.02 $0.83 $ Nickel $3.15 $3.04 $ Tin $0.87 $0.24 $ Tungsten $14.66 $6.30 $ *inflation adjusted for 1980 prices 1. Emsley, J., Nature's building blocks : an A-Z guide to the elements; Oxford University Press: Oxford ; New York, U.S. Geological Survey: Mineral commodity summaries 2007; U.S. Geological Survey: Washington, D.C., Moore, J. J., Chemical metallurgy; Butterworths: London ; Boston, Engh, T. A.; Simensen, C. J.; Wijk, O., Principles of metal refining; Oxford University Press: Oxford ; New York, Chapman, P. F.; Roberts, F., Metal resources and energy; Butterworths: London ; Boston, Bodsworth, C., The extraction and refining of metals; CRC Press: Boca Raton, Fla., Morita, K.; Miki, T., Thermodynamics of solar-grade-silicon refining. Intermetallics 2003, 11, (11-12), Gordon, R. B.; Bertram, M.; Graedel, T. E., Metal stocks and sustainability. Proc Natl Acad Sci U S A 2006, 103, (5),

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