Where are the 70% Efficient Solar Cells?
VernonNemitz asks: "Back in 1984 a patent was granted for silicon chip micro rectennas, which would convert visible photons into electricity in the same way that ordinary rectennas convert microwaves into electricity, at perhaps 70% or greater efficiency. Nobody could make such solar cells back in 1984, but we certainly can today, with sizes of antennas that would capture everything from infrared to the edges of UV -- and the patent has expired. So, where are they?" Currently the most popular type of solar technology is photovoltaics, however PV technology only has an efficiency of about 7-17%. With the potential gains claimed by the technology in the cited patent, has anyone even tried to build one of these units to see if it can live up to the given promise, or at least prove to be a technology than we should be exploring?
Semiconductor photocells can easily be >90% effecient, but over a rather small range of wavelengths. This is due to the bandgap. An electron is freed if the electron gains enough energy from the photon(s) to overcome the bandgap. the energy of several photons can be combined to free and electron, but is lossy. If the photon has more energy than is required to free the electron, the extra will mostly be dumped as heat. The equation governing wavelength, energy, and Boltzmann's constant is
E=hw
Silicon is actually a rather poor photomaterial, being an indirect material, it's limited to about 60% effeciency at any wavelength. The electron must not only gain energy, but also move a slight bit within the crystal in order to reach the conduction band. Direct materials, such GaAs, being direct, can be > 95%
Perhaps the are other techniques??
For simplicity we take the solar energy density falling onto a window to be 1000 kWh/m2 yr. This is regarded as a typical number for a south-facing window, and more correct values for south-facing/north-facing/horizontal surfaces would be 850/350/920, 1400/450/1700, and 1100/560/1800 kWh/m2 yr for Stockholm, Sweden, Denver, USA, and Miami, USA.
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Then there's a wide variety of other radioactive substances that can be burned in reactors. For example, breeder reactors can actually breed plutonium from the very common U-238 (U-238 is one of the most common elements in the Earth's crust), creating an almost infinite supply of fuel. Military breeder reactors work fine for producing lots of plutonium for atomic bombs. Research on commercial breeder reactors (basically the military reactors tied to turbines to power electric generators) was stopped by worries about arms proliferation (it is much easier to seperate Pu-239 from U-238 than it is to seperate U-235 from U-235 in raw uranium ore, thus makes it easier to get enough fissile material to crete atomic bombs), but could be re-started pretty swiftly if necessary. Which would not be for 50 or 100 years, as you mention.
Regarding 100 and 400 years of oil, my own best estimates are somewhat lower than that. My estimates are that we will experience shortages within 20 to 25 years, and that within fifty years we will have basically exhausted all economically accessible oil resources (i.e., there will be oil out there, but it will take more energy to extract it than can be obtained by burning it). However, hopefully by that time the current taboo regarding nuclear power will have eased, and we will be able to replace the lost petrochemical resources with synthetic hydrocarbons or other such creations. (Don't laugh, we use petroleum as feedstock for chemical plants because it's cheap, available, and readily "cracked", but there are certainly other feedstocks that could be "cracked" into various petrochemicals if necessary, including coal, for that matter -- after all, both the Nazis and the South Africans did it).
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I see a serious theoretical difficulty here that may explain why the optical rectenna was never built.
Sunlight at the earth's surface has a power flux density of about 1 kilowatt per square meter. To convert that to an electric field strength, we take the square root of the power flux density times the impedance of free space, 377 ohms. This gives 614 volts/meter.
Yellow light has a wavelength of 570 nm. That means the electric potential over that distance is only about 350 microvolts. This is approximately the voltage you'd see at the terminals of a 50 ohm half wave dipole, and it's far below the voltage needed to switch a rectifier. Silicon rectifiers take about 600-700 millivolts of forward bias to begin conducting, even if one could be constructed to work efficiently at optical frequencies. Germanium takes about 300 mV, and silicon Schottky diodes take about the same.
It is not possible to construct a diode that doesn't require a forward bias, otherwise we could rectify the noise from room-temperature resistors and convert ambient heat to useful work. This is specifically prohibited by the second law of thermodynamics.