the Mythical Moore’s Law for Solar Energy

It’s understandable when people without any scientific or industry experience to talk about a Moore’s Law for solar energy, but those who understand the technology should know better.  The reason it’s so easy to fall into the trap of believing this is due to the superficial similarities between solar cells and transistors; they’re both typically made from silicon wafers, and utilize many of the same processes during manufacturing (diffusion furnaces/ion implantation, thin film deposition, etching, plating, etc).

And so when people hear that the prices of solar cells are dropping, and they’re made from silicon, it seems that they readily assume that it’s Moore’s Law at work.  Let’s see what Al Gore said a few years ago, as quoted in Vacliv Smil’s book Energy Myths and Realities:
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[the] price of specialized silicon used to make solar cells was recently as high as $300/kg.  But the newest contracts have prices as low as $50/kg.  You know the same thing happened with computer chips – also made out of silicon.  The price paid for the same performance came down 50% every 18 months – year after year.

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More or less the same argument was made by Paul Krugman in this New York Times op-ed, in a Scientific American article here, and in Kevin Kelly’s book What Technology Wants.

What’s surprising is that you have extremely well-qualified people making similar proclamations, though without the fallacious reasoning.  Steven Chu, for example, is a Nobel laureate in physics and current head of the Department of Energy.  As stated in this 2004 conference paper, he conflates learning curves with Moore’s Law (and also fails to distinguish between windmills – which provide mechanical power, and wind turbines – which provide electrical power):
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Every technology seems to follow a Moore’s Law curve, which means that the cost effectiveness improves exponentially as a function of the overall money invested in the deployment of that technology. Figure 1 shows Moore’s Law curves for photovoltaics, windmills, and gas turbines. As you put more money into a technology, that drives the price down.

”
Next we have two CEOs of solar companies.  Let’s start with this statement from the head of NRG:
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A form of Moore’s law — the doubling every two years of the number of transistors that can be placed on an integrated circuit — applies to photovoltaic technology, according to Crane. In the last two years, the delivered cost of energy from PV was cut in half, he said.  NRG expects the cost to fall in half again in the next two years, which would make solar power less expensive than retail electricity in roughly 20 states, he said.

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A few months ago the founder of Suntech, the world’s largest manufacturer of solar panels, gave a talk at Stanford.  One of his slides compared the falling costs of solar to those of digital cameras, cell phones, and DVD players soon after they were first introduced.  He thankfully didn’t explicitly say anything about Moore’s Law, but the comparison nonetheless is not quite apples-to-apples.

So what’s the issue with all of these kinds of statements?

• Moore’s Law is specific to the number of transistors on an integrated circuit, and is not applicable to other fields just because they bear some superficial resemblance with the chip industry.
• The rate of progress in the solar industry (~30X cost reduction in the past three decades) is orders of magnitude below the ~40,000X increase in the number of transistors of a microprocessor of today compared to ones like the Intel 186 from 1982.
• The physics that limit and constrain solar cells are different from those of processors.  With solar cells, you’re fighting thermodynamics, and you’re never going to win the game.  Although we’ll probably get to a 50% efficient multi-junction solar cell soon, you can’t go past 100% – the ceiling is fixed.  With computation, though, there’s still plenty of room at the bottom.  Whether its single-electron transistors or room temperature quantum computers, we’re still very far away from nearing the ultimate limits of computation.
• The generally accepted formulation of the solar industry’s learning curve, which states that prices of solar modules will fall 19% every time production volumes double, makes no predictions about how quickly volumes will double (it may take one year or a hundred).  In contrast, Moore’s Law has a fixed time frame for each doubling of the number of transistors (18 months in its most recent, amended form).
• The market for solar panels is somewhat elastic; prices for solar panels have dropped recently not because of some major technological or manufacturing advance, but because supply has continued to increase, while demand has decreased (likely due to reductions of feed-in tariffs in Europe).  Solar panels are essentially commodity items (albeit, relatively expensive ones) that produce electrons, and any commodity’s price tends to be dictated by the pull between supply and demand, like a feedback loop. As the industry continues down its learning curve, however, the manufacturing cost/Watt-peak of the panels will decrease, putting downward pressure on the prices, irrespective of supply and demand.  You can think of the learning curve as a trend line with a negative slope, around which the market forces oscillate.  Five years ago, when polysilicon was in short supply, the price shot up above the trend line, and today when demand has dropped, we’re below that trend line. The amplitude of the oscillations tends to be large because while demand can change fairly quickly through changes in legislation (feed-in tariffs, tax incentives) and the economy (financial crises that suck up liquidity), it takes time for supply to adjust (polysilicon plants cost over a billion dollars and take years to build).
• The cost structures of solar cells are very different from those of microelectronics.  Silicon wafers make up about half the cost of solar cells; but when you can fit thousands of microchips onto a single wafer, the costs of silicon raw material per chip are minuscule.  The real costs lie in the $6 billion or so it takes to setup a new fab (expensive UV lithography equipment) and R&D.
• The areas where we have seen really stunning improvements over time have all been able to take advantage of engineering on the micro or nano-scale.  These include CPUs (Moore’s Law), hard disk drives (Kryder’s law), fiber optic communications (Butter’s law), LEDs (Haitz’s law), and DNA sequencing.  Solar cells and LCDs, however, have improved much more slowly, even though they too have borrowed many tricks from the microelectronics/optoelectronics industry.  The underlying reason is that the solar and LCD industries are building on the macro scale.  Their key metric is cost/area, whether it’s a solar module or a television.  Prices for LCDs have certainly come down, but not by the orders of magnitude we’ve come to expect (courtesy Hendy Consulting):

• The fundamental disparity between the technology learning curves can perhaps be understood by characterizing them based on density – of power or information flow.  A modern CPU can easily generate fluxes of over 300 Watts/square centimeter:
• Or consider high-brightness LEDs, dissipating heat at over 100 W/square centimeter.  Single mode fiber optic cables can transmit tens of gigabits per second along a fiber just a few micrometers in diameter.  Fourth generation DNA sequencers will use nanopores to read individual DNA bases much faster and more accurately than current technologies.  Hard drives have reached areal densities which are staggering (courtesy IBM):

• Contrast this with solar cells that receive no more than 1,000 Watts per square meter of area, which amounts to a flux of just 0.1 Watt per square centimeter.  Similarly, battery performance improvements in terms of energy density have been moving at a snail’s pace for the past century (courtesy this paper).  Products made on the micro and nano scale can pack a lot of power and information into a tiny space, allowing millions of units to be mass-produced with negligible raw material costs.  Products engineered on the macro scale have a much harder time improving performance or manufacturing.

In summary:

1. Just because a technology has a learning curve, doesn’t mean it’s Moore’s Law.
2. Not all exponentials are equal.
3. Macro-scale engineered solar panels and batteries improve performance over time, but nowhere near as fast as compared to micro-scale engineered products.

the Diffusion of Innovations, or Lack Thereof

Everett Rogers wrote the classic work on the difficulties of spreading new ideas and solutions, none more elucidating than the case of the British Navy and the cure to scurvy:
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In the early days of long sea voyages, scurvy killed more sailors than did warfare, accidents, and other causes. For instance, of Vasco da Gamma’s crew of 160 men who sailed with him around the Cape of Good Hope in 1497, 100 died of scurvy. In 1601, an English sea captain, James Lancaster, conducted an experiment to evaluate the effectiveness of lemon juice in preventing scurvy. Captain Lancaster commanded four ships that sailed from England on a voyage to India. He served three teaspoonfuls of lemon juice every day to the sailors in one of his four ships. These men stayed healthy. The other three ships constituted Lancaster’s ‘control group,’ and their sailors were not given any lemon juice. On the other three ships, by the halfway point in the journey, 110 of 278 sailors had died from scurvy. So many of these sailors got scurvy that Lancaster had to transfer men from his ‘treatment’ ship in order to staff the three other ships for the remainder of the voyage….
Not until 1747, about 150 years later, did James Lind, a British Navy physician who knew of Lancaster’s results, carry out another experiment…
not until 1795, forty-eight years later… was [scurvy] immediately wiped out…
Why were the authorities so slow to adopt the idea of citrus for scurvy prevention? Other, competing remedies for scurvy were also being proposed, and each such cure had its champions. For example, Captain Cook’s reports from his voyages in the Pacific did not provide support for curing scurvy with citrus fruits. Further, Dr. Lind was not a prominent figure in the field of naval medicine, so his experimental findings did not get much attention.

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There was another unsolved problem Britain was facing during the 1800s in the wake of the Felling mine disaster: how to design a safety lamp that wouldn’t lead to explosions.  The most eminent British chemist at the time was Humprhy Davy at the Royal Society, who had discovered several elements and was a spectacularly popular lecturer.  As Richard Holmes relates in the Age of Wonder, the accidents committee approached Davy to help them understand the problem.  He began analyzing the gas (known as fire-damp at the time) and visiting mines and speaking with miners and overseers.  Upon returning to London, he “summoned Faraday to his assistance” and ordered an “apparatus capable of withstanding an explosion.”  He soon discovered that “explosions only occur[ed] when methane reacted critical ratio of gas to air (1:8 parts),” and eventually realized that a fine gauge iron mesh/gauze surrounding the flame would prevent explosions by providing a high surface area for cooling.  He refused to patent his safety lamp, and having “subdued this monster” and “scourge of humanity” to “much public gratitude,” thank you letters poured in from miners across the country; some of the letters were drafted by mine owners, but “the signatures were genuine… 47 [miners] were illiterate and simply put ‘x’ against their names.”

Problem solved, right?  Fast forward over 200 years.  A coal mine collapse earlier this year in Pakistan killed over 40 people when methane gas in the mine ignited and caused an explosion.  But what’s the root cause?  Methane doesn’t auto-ignite until over 500 degrees Celsius, and neither does coal dust below 425 Celsius.  That kind heat could have been generated through friction during mining activities, or even by but coal dust in a pile that oxidizes, leading to a runaway exothermic reaction.  But I think the picture below (taken recently) gives us a clue.  Some of the miners are still using kerosene lamps when they don’t have access to hard hats with electric lamps.  Why would anyone still be using kerosene lamps, when safe electric lamps have been available for almost a hundred years?  Because the people using the lamps are not the ones buying the lamps – the prototypical agent problem, as this article details:

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a major reason why working conditions are bad at the mines lies in the ownership and operational structure of the mines. The mine owners do not actually own the mines; they are long leased from the government. They are then sublet to contractors, delegating the whole responsibility of operating the mine with all the risks involved…Since the contractors are not the legal operators of the mines, the law cannot hold them responsible for the absence of safety measures and equipment as well as accidents.

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The kerosene lamps have a lower up-front cost than the battery-operated electric lights, so the mine owners/operators would favor buying them for the miners.  Even if the miners themselves know about electric lights, they’re simply too poor to afford them on their own.

A Look Inside a Busted Gas Turbine

I was touring a 300 megawatt natural gas combined-cycle power plant last year, when my friend mentioned that one of the turbines had been replaced due to damage. “Oh – what happened?” As it turns out, the engineer who was testing the turbine began spinning it up without checking the lubrication – which was non-existent. Once the RPMs got high enough, the ball bearings couldn’t take the friction and melted away, leaving the rotor to rattle around on its shaft and the blades to scrape against the casing. Insurance paid for the replacement, while the engineer managed to keep his job – and get schooled.





ouch:



The blades are made from single-crystal nickel superalloys with a thermal barrier coating. Rolls Royce has some interesting exploded diagrams and time-lapse construction videos of their jet engines (which are based on very similar technology) here. Single crystals have found other applications in clean energy – from silicon wafers for solar cells to massive, fast-growing KDP crystals for fusion at the National Ignition Facility.

how the Wright brothers invented the airplane

As author Lester Garber has noted, there were a number of key breakthroughs the brothers had to make:

• recognizing that problems of stability and control must be solved before attacking problem of powered flight;
• recognizing that given adequate aircraft, pilot must still learn how to fly;
• recognizing that to maintain equilibrium, control is more important than inherent stability;
• recognizing that use of aerodynamic forces superior to weight-shifting for maintaining control;
• using of wing warping to vary angles of attack from tip to tip for roll control;
• recognizing that aeroplane must bank its wings in order to turn;
• doing wind tunnel tests to determine lift/drag characteristics of different wings;
• realizing that the real value of Smeaton’s coefficient is really .0033;
• recognizing of the need for 3 dimensional control;
• understanding that the proper function of the vertical rear rudder is yaw control, not turning aeroplane;
• the development of a method to design efficient propellers;
• the development of a lightweight engine with sufficient horsepower.

The only real account from the brothers themselves, however, is in an old Harper’s magazine article, which I’ve scanned and posted below (I believe it’s out of copyright):

a look at the new Mars Rover

I got a glimpse of the new Mars rover, Curiosity, in the clean room while taking a tour of the JPL a few months ago. Unlike the last Mars rover, which landed with the aid of a parachute and air bags, this one is going to be lowered down on a cable from another stage which hovers above. It’ll be powered by radioisotope thermoelectric generators (RTGs) instead of solar panels, so dust getting on the rover shouldn’t be an issue. It’s got a pretty neat and tiny X-ray diffraction instrument on board – if you’ve ever been to a university lab that has one, you’ll know that they’re normally the size of an entire bench. I thought initially that inXitu had used the field emission from carbon nanotubes to produce the X-rays, but it seems like it uses a miniature X-ray tube that consumes just 10 Watts of power.