THE SCIENCE

ENECO's technology is based on the use of thermal diodes, which have no moving parts and convert heat directly into electricity. The concept is drawn from two established direct energy conversion technologies, thermoelectric energy conversion and thermionic energy conversion.

• Thermoelectric energy conversion is based on Peltier and Seebeck effects, which appear when a thermal gradient is applied across a plate of material. Thermoelectric converters are convenient but inefficient. Thermoelectric activity varies greatly from one material to another, but typical commercial thermoelectric converters operate with efficiencies less than 6%.
• Thermionic energy conversion works in the manner shown schematically in Figure 1.

A thermionic converter consists of a heated plate, Metal 1, a cooled plate, Metal 2, a vacuum gap separating the plates, and an external electric circuit, which is open in the figure.  Electrons in metal have a temperature dependent energy distribution. If the temperature of Metal 1 (the emitter) is increased, eventually some electrons can have sufficient energy to overcome the surface potential barrier called the work function ₁, which ordinarily prevents electrons from leaving the surface.  The work function can be considered to sort electrons according to their energy.  Those with energies less than the potential barrier remain in the metal and those with energies greater than the work function can leave the surface. Free electrons leaving the emitter can be intercepted by Metal 2 (the collector). In this process, shown by solid lines on the energy diagram, electrons accumulate a potential = ₂ – ₁, which can be used to drive electric current through the external load R, when the circuit is closed. There also is a reverse or back current of electrons shown by dashed arrows on the energy diagram, which competes with forward current.  Typically this current is minimized by the larger work function of the Metal 2, ₂, and its lower temperature that produces fewer energetic electrons. The minimum known work function is about 1.1 electron-Volts (eV).  This is such a large potential barrier that only temperatures exceeding 1000°C produce significant currents from such a converter.  In reality, typical work functions are significantly higher, i.e. 1.5 eV or more, requiring even higher temperatures for thermionic emission to occur.  Unlike thermoelectrics, thermionic converters allow high conversion efficiencies but at extreme temperatures.  In laboratory conditions, efficiencies as high as 40% are reported.

Thermal diodes have the same functional components as thermionic converters but with a semiconductor wafer substituted for the vacuum gap.  A layout of an n-type thermal diode is shown in Fig 2.

Manufacturing a thermal diode starts with a thermoelectric semiconductor wafer (gap) on which a thin barrier layer is deposited.  The barrier layer is made of the same semiconductor, but doped differently.  The deposited emitter layer is a heavily doped layer of the same semiconductor or a metal.  The collector structure is basically the same two layers as on the hot side.  Potential barriers at the interfaces between emitter and barrier layers and barrier layer and gap serve the same purpose as the work function in a thermionic converter. By changing dopant concentration these potential barriers can be adjusted and optimized for any temperature.  The first barrier on the emitter layer side sorts electrons by energy and the second barrier on the gap side prevents back flow of electrons from the gap into the emitter layer.  Without potential barriers, the output of this device will be defined by the thermoelectric properties of the gap material.  Barrier action leads to accumulation of electric charge behind the barrier, leading to increased operating voltage.  The electric resistance of the device is dominated by the macroscopic gap with very little change from its thermoelectric value, leading to current increase due to increased voltage compared with the thermoelectric performance of the semiconductor gap.  Voltage multiplied by current gives electric power output and if the heat flow through the device stays the same, the result is increased efficiency, defined as the ratio of electric power delivered to the load to the heat flow through the device. Up to nine times improvement relative to the initial thermoelectric performance has been observed with a single barrier [3].

It is critical to form a correct barrier. Correct means correct height and correct width.  The experimentally defined [1] optimum barrier height is ~5 kBT, where kB is the Boltzmann Constant and T is absolute temperature, or ~125 meV at room temperature.  The optimum barrier width is ~1.5 carrier scattering lengths.  For InSb this is 1.5 microns.  For all other semiconductors it is thinner.  Deviation from the optimum leads to gradual return to thermoelectric performance of the gap.  Boundaries for thermal diode performance are five scattering lengths thickness and +/- 1kBT from the optimum barrier height [1].

For barrier formation we have used magnetron sputtering, ion implantation and thermal diffusion of an impurity. Initial barrier height can be calculated using the dependence of Fermi Level shift on impurity concentration [2]. The difference between Fermi level positions in two adjacent layers gives the effective barrier height. For most common semiconductors these dependencies are known from the literature.

An important attribute of barriers is that the contribution of barriers placed thermally in series is additive [2].  This is unlike thermoelectric behavior, when stacking separate plates made from the same material does not change resulting efficiency unless the hot side and cold temperatures are changed.  This leads to the conclusion that efficiency approaching the theoretical limit can be achieved with a multi-barrier thermal diode with stacked barriers separated by relaxation gaps at least five scattering lengths thick.  In many cases this is not practical, for example a thermal diode made of silicon must have approximately 200 barriers to achieve 80% of theoretical efficiency.  For other substrates, such as HgCdTe, a single barrier is sufficient, or three for PbSnTe or six for InSb.  The absolute efficiency limit in all cases is 50% of ideal Carnot Efficiency, since 50% reduction of the internal conversion efficiency results from the requirement to match the external electric load to the diode’s internal resistance for maximum power transfer to the load. Internal conversion efficiency can be extremely high.  The highest experimentally observed internal efficiency of a thermal diode is 88% of Carnot Efficiency, which is competitive with any existing energy converter.

REFERENCES

1. Y. Kucherov, P. Hagelstein, V. Sevastyanenko, H.L. Brown, S. Guruswamy, W. Wingert, Journal of Applied Physics 97, 094902 (2005).
2. Y. Kucherov, P. Hagelstein, Thermoelectric Handbook, Macro to Nano, Chapter 13, edited by D.M. Rowe, CRC, Taylor and Francis, 2005.
3. P. Hagelstein, Y. Kucherov, Applied Physics Letters, V. 81, No. 3, 2002, pp.559-561.