From Watts Up With That?

Kevin Kilty

Crises produce a lot of dubious effort to supposedly solve them. The long past energy crisis of the 1970s for example, the one that actually started as a utility crisis in the 1960s, caused many completely mad proposals for how to generate useful energy without using petroleum liquids. Limestone caverns filled with air during high pressure, let back out through a turbine when pressure is low; air foils propelled by wind around an elongated railroad track; magnets placed on automobile fuel lines to do something, never clearly explained, with the electrons in gasoline to improve mileage – that sort of stuff.

That 1960s-1970s crisis ended, I would argue, once we began burning coal in great quantities to generate electrical energy. We solved the crisis by simply substituting a plentiful fuel without having to adopt complicated schemes. Yet, those less-than-useful ideas live on and we see some of them today now proposed to solve the alleged CO2 crisis.

Unworkable schemes come in two flavors. The first involves schemes too mad capped to work because they have no principle of operation behind them or they violate how the universe works – they violate one of the laws of thermodynamics, for example. The second includes schemes that could work in principle, but could never be made to operate economically.

When I read this headline in the Cowboy State Daily “Research Shows Solar Panels Can Also Generate Electricity At Night”; I figured this to be a routine bout of physics madness. It turns out, though, that this is a case of saying it’s a solar panel that works at night, when, in fact, it is a totally different device. Let’s figure this out.

How does a solar panel work?

Figure 1 shows the cross section of a crystalline silicon solar cell. There are five layers of material; 1) a conductive surface to make device contact; 2) a thin layer of n-type silicon (silicon doped with a bit of phosphorus); 3) a space charge region created at the interface of p-type and n-type material (a pn junction) by diffusion of charge carriers from concentration gradient; 4) a p-type silicon (silicon doped with a bit of boron); 5) finally a lower layer of conductive material to make device electrical contact.

Reading from left to right, Figure 1 illustrates a minimal explanation of solar cell operation. In its equilibrium state on the left, the space charge region sports an electric field that acts counter to the diffusion of charge carriers to establish equilibrium. A photon of sunlight enters the device, and if absorbed delivers enough energy to lift an electron from the valence (bonding) band into the conduction (mobile) band. Raising this electron into a mobile state leaves behind an empty mobile charge known as a hole. The internal electrical field separates the paired electron and hole to prevent them from recombining (maybe 90% effective at this task). Finally, on the right side of the diagram the electron is able to join a current flow through an external load to recombine with the hole.

Figure 1 shows plainly why solar cells don’t work at night. Photons from sunlight provide the fuel to produce mobile charge pairs. There are none at night.

As an aside, knowing that there is an intense radiative flux from the sky to ground during all hours (the greenhouse flux), why don’t the photons in this flux generate an electrical current?

The answer here lies in how much energy a photon absorbed can deliver in relation to the valence to conduction band gap. In a silicon solar cell this band gap energy is about 1.1 electron volts (eV). The energy a photon carries is E=hc/λ; where h is Planck’s constant, c is the speed of light, and λ is the wavelength of the photon. A photon of 1.0 micrometer wavelength, which is in the near infrared part of the spectrum, carries energy of 1.24eV, enough to create a conduction charge pair. A photon from the peak of the Planck function at a temperature of 288K, on the other hand, has wavelength (per Wien’s law) of 10 micrometers and carries energy of only 0.124eV, far too little to create a pair. No photons coming from terrestrial radiation ever supply 1.1eV. These photons can only interact with lattice vibrations (phonons) in the solid material to maintain temperature equilibrium with its surroundings.

Adding a Completely Different Device to Generate at Night

This should put to rest any notion that the solar panels generate energy at night from, what the article says, and the Stanford PR amplifies, radiation. What our researchers have done is to add a separate device to the solar panel, one that operates with temperature differences, and the journalists call it a solar panel for nighttime operation. It’s a collision of science with journalism.

This device is actually a thermoelectric generator. It produces electrical energy from heat flow, or from a temperature difference. The physical basis of this is the Seebeck effect, a voltage that appears along with a difference in temperature – i.e. V=B(T_h-Tc), where B is the Seebeck coefficient.

The Seebeck coefficient in metals is small, less than a limiting value of 87 microvolts per Kelvin (uV/K). So metal junctions are used only for temperature measurement as the lower part of Figure 2 shows. Some semiconductors, on the other hand, have much larger Seebeck coefficients (300 uV/K), making them useful for energy generation in some situations; mainly where waste heat is available and when no other, less expensive, method of producing a small amount of electrical energy is available.

For example, the Galileo mission to Jupiter in 1989 used a thermoelectric generator powered by the radioactive decay of plutonium 238. The 41 kg system in this case produced 5W per kg and ran flawlessly for 7 years. No other system available from 1980 era technology could have done the same.

The upper part of Figure 2 shows a long series of pn junctions connected in series to produce a voltage large enough to be useful. This is a thermoelectric generator.

Since a thermoelectric generator operates from heat flow, it is subject to a maximum efficiency that includes the Carnot factor. N_eff=K(1-T_c/T_h); where the K factor involves what is known as the figure of merit, ZT, of the thermoelectric materials. Current thermoelectric materials have a poor figure of merit, and then considering the small temperature differences in the Carnot factor on a typical solar panel, almost everything works against this energy scheme.

Although no diagram of the “night-time solar panel” was available in the news article, Stanford PR, or other PR, a person can surmise that the device would resemble Figure 3.  

Figure 3 shows a solar panel. Heat fins on the lower face of the panel maintain a temperature near ambient. Sandwiched in between is a thermoelectric generator like that in Figure 2. The upper surface of the panel might have a temperature 40C above ambient when exposed to the full day sun. Or, it might have a temperature 10C below ambient on a clear night in the arid and elevated portions of the West and Southwest. The temperature difference powers the thermoelectric circuitry.

There is no doubt the additional equipment will produce some power in addition to or in place of the solar generator. But this is not a solar panel that works at night. It doesn’t use starlight or moonlight. It doesn’t even necessarily use radiation as some of its PR claims. It works from a temperature difference.

In what I view as a misleading claim, the press release states this (bold text is mine):

Advantages

• Low cost, off-grid
• Nighttime 2.2 W/m² power density
• Outperforms other ambient energy harvesting techniques like wind or radio frequency
• Daytime performance estimated to be 3-4x higher than nighttime

Wyoming wind plants currently dedicate about 100 acres, or about 40 hectares, to each MW of nameplate wind. Since wind plants have an annual average capacity factor of about one-third, the power density computed from dedicated land area is about 0.7W/m². So, the claim that this 2.2W/m² of thermoelectric power exceeds the power density of wind is true. Yet, then what must also be true is that the panels having  thermoelectric generators must cover the entire 40 hectare area with modified panels to “outperform wind”.

Even though the PR says that the thermoelectric modules need only cover 1% of the solar panel area, many must be connected in series to reach a usable voltage. It seems like a lot of trouble and expense in a weak attempt to address the intermittency of solar energy.