Heterojunctions can convert heat into electric energy Gerhard Kainz E-Mail: gerhard.ka...@siemens.at This paper shows that a special semiconductor heterojunction acts like a homogenous semiconductors which is illuminated: Both produce additional electron-hole pairs which can be separated and so produce electric energy. However, while a normal solar cell needs light as energy source, a special kind of heterojunctions just absorbs heat energy of the lattice in order to produce electric energy. Most importantly, there is no need to have a temperature difference. This is shown by only using the common drift- diffusion equation. Additionally, this effect can be simulated by "SimWindows", a Semiconductor Device Simulator from the University of Colorado. Fig.1 shows a homogenous semiconductor, which is illuminated only on the left part. Photons generate additional electron-hole pairs. Because of these additional charges, the charge concentration is higher than the intrinsic charge concentration. Therefore these charges diffuse in the right part of the semiconductor, where they recombine after a certain time. . photons . | . ********|******************************************* . * \|/ * . * x ----> e -----> e ------> x * . * ----> h -----> h ------> * . * * . **************************************************** . generation diffusion recombination . Fig. 1: A homogenous semiconductor is illuminated on the left part. Electron-hole pairs are generated and this additional charges diffuse to the right part, there they recombine. This kind of diffusion is the base of the photovoltaic effect. However it is possible to generate such a charge diffusion in an other way. Fig. 2 shows two undoped semiconductor with the same work function and band gap, but medium A has higher effective masses of electrons and holes than medium B. Therefore A has also a higher intrinsic carrier concentration. . semiconductor A semiconductor B . ************************** *************************** . * e h e h e * * e h * . * e h e h h * * h e * . * h e h e h * * e * . * h e h e h e * * h * . * e h e h e h * * h e * . ************************** *************************** . Fig. 2: Both undoped semiconductors have the same work function and band gap, but A has higher effective masses of electrons and holes and therefore a higher intrinsic charge concentration compared to B. What happens if the two semiconductors are brought into contact? Since both media have the same work function and band gap, the charges can cross the junction without any restriction or energy emission or absorption. To be more specific, there will be no depletion zone nor interface spike nor quasi-electric field due to discontinuities in the band-edge energies. However the concentration of electrons and holes are in medium A much higher therefore there is a diffusion of charges from A to B, see Fig. 3. . A B . **************************************************** . * e h e h * e h * . * e h e h e -----> e e * . * h e h e h -----> h e * . * h e h e h * h * . * e h e h e * h e * . **************************************************** . generation diffusion recombination . Fig. 3: The semiconductors are in contact. Both media have the same work function and band gap, but A has a higher charge concentration, therefore charges diffuse into B. Thus in B there are more recombinations than generations and in A there are more generations than recombinations. This diffusion would stop if there were the same charge concentration in both media. However in B there is (because of diffusion) a higher charge concentration than in the intrinsic case, therefore more electron-hole pairs will recombine and so the diffusion will not stop. So there will be a special thermodynamic equilibrium: All the time, electrons and holes which are generated in medium A will diffuse to B and recombine there. Fig. 4 shows this situation in the band diagram. . e -------------------> e . /|\ | . ----------------|----------------------|------------------ Ec . | | . ----------------|----------------------|------------------ Ef . | | . ----------------|----------------------|------------------ Ev . | \|/ . h -------------------> h . generation diffusion recombination Fig. 4: The band diagram shows the generation of electron-hole pairs in medium A, the diffusion and recombination in medium B. The Fermi- level Ef remains flat. So in medium A there are more electron-hole pair generations than recombinations because of the diffusion of charges into medium B. Since every generation absorb heat energy and every recombination emit this energy, medium A will cool down a little bit. In medium B there are more recombinations therefore medium B will heat up. So there will be established a temperature difference between media A and B only because of the flow of charges and without any external force or energy. However this temperature difference will be quite small because of heat transfer from B to A. Please note the difference to a normal p-n junction. At a p-n junction electron and holes diffuse in DIFFERENT directions. Moreover the internal potential prevents a higher rate of diffusion. However in the heterojunctions described in this paper, most importantly the electrons and holes diffuse in the SAME direction. And since they always recombine in semiconductor B, there cannot be an end of the diffusion. Lets make an example: Semiconductor A and B have a bandgap of Bg=0.5 eV Semiconductor A has effective electron and hole masses m*=1 Semiconductor B has effective electron and hole masses m*=0.5 The total carrier concentration of A is therefore 1.6*10^15 The total carrier concentration of B is therefore 5.6*10^14 So in semiconductor A, there 2.9 times more charges than in semiconductor B. On the other hand, the kinetic energy E_kin of an electron must be constant at the same temperature. Since the charges in A have more mass, they are a little bit slower: V_th=(3kT / m*)^0.5 At 300 degree: The carriers in A have a velocity v_th=1.17*10^3 m/s The carriers in B have a velocity v_th=1.65*10^3 m/s So the carriers in A are only 1.4 times slower than in A. So there are in A many more charges which are only a bit slower than in B. The pressure of the electron gas is p= 1/3 n m v^2 Since m v^2 is the kinetic energy and constant, the relevant part is only the number of charges n. Therefore the pressure of the electron gas in material A is 2.9 times higher than in B therefore electrons move into B. Exactly the same happens with the holes. Therefore there is a diffusion of electrons and holes in the same direction, from A into B. Every effect which uses the increased charge concentration because of photon absorption can be also done with this special heterojunction, like the photovoltaic or the photomagnetoelectric effect. A possibility to use this effect is to convert heat into electric energy. Fig. 1 and 3 shows the similarity between an illuminated semiconductor and this special heterojunction: Both produce a higher charge concentration than in the normal case. So it is easy to construct a "heat cell" with such a heterojunction, see Fig. 5. . p-doped undoped semiconductor A undoped n-doped . ***************************************************************** . * * * * * * . * * * * * * . * h <------- h <-------- h e -----------> e --------> e * . * * * * * * . * * * * * * . ***************************************************************** . diffusion generation diffusion . Fig. 5: This arrangement is similar to a PIN solar cell, however in this case additional charges are produced from semiconductor A which have a higher charge concentration. Everything else is like in a PIN solar cell: These charges are separated which produce an electric potential. This arrangement is quite similar to a solar PIN cell: In the middle is an undoped semiconductor. In case of a solar cell, photons produce in the middle of the cell additional charges which are separated. However in this case there is instead a special semiconductor A in the middle. This medium has a higher charge concentration and therefore charges diffuse in both directions out of the medium. Because of the internal electric field of the p and n area, the different charges will diffuse in different directions and the electric potential will be produced. The only difference between a PIN-solar cell and this "heat cell" is in the middle, how additional electron-hole pairs are produced. However the "heat cell" produces electric energy without illumination. It just absorbs heat energy because of the higher number of generations than recombinations of electron-hole pairs. This energy will be used to produce electric energy. This effect can be shown with SimWindows, the Semiconductor Device Simulator from David W. Winston, University of Colorado. http://www-ocs.colorado.edu/SimWindows/simwin.html The following device file is used: grid length=2.1 points=1000 structure material=gaas length=2.1 Band_gap length=2.1 value=0.5 ELECTRON_DOS_MASS length=1.0 Value=0.5 ELECTRON_COND_MASS length=1.0 Value=0.5 HOLE_DOS_MASS length=1.0 Value=0.5 HOLE_COND_MASS length=1.0 Value=0.5 ELECTRON_DOS_MASS length=0.1 Value=1.0 ELECTRON_COND_MASS length=0.1 Value=1.0 HOLE_DOS_MASS length=0.1 Value=1.0 HOLE_COND_MASS length=0.1 Value=1.0 ELECTRON_DOS_MASS length=1.0 Value=0.5 ELECTRON_COND_MASS length=1.0 Value=0.5 HOLE_DOS_MASS length=1.0 Value=0.5 HOLE_COND_MASS length=1.0 Value=0.5 doping length=1.0 Na=5e18 doping length=0.1 doping length=1.0 Nd=5e18 This means that there is a structure of 2.1 micrometer based on GaAs. However the bandgap is reduced to 0.5 eV. There is in the left and right a p and n doped material. In the middle there is a 0.1 micrometer undoped material with the double mass of electrons and holes. The short circuit current is about 1.8 mA. (In this case, SimWindows doesn’t solve the drift-diffusion equation for its own since it supposes an equilibrium case. In this case it helps e.g. to define a VERY small illumination of e.g. only 10^-100 mW/cm^2. For comparison: For solar cells, the often used 1.5AM illumination of the sun is 10^2 mW/cm^2.) The open circuit voltage of this "heat cell” is about 1mV. The maximum power delivered by this circuit is about 0.0005 mW/cm^2. This is not very much, however many of this circuits can be put of one another and put together. Moreover there it is very possible to find semiconductors with much better values for this effect. The "heat cell" will cool down a little bit, if it converts heat energy to electric energy. However from the environment heat will flow to the heat cell. Although this is a theoretical case, it shows that this effect exists, but it is hard to find good semiconductors, and especially all the data needed for a device simulator. This "heat cell" would contradict the 2nd law of thermodynamics. However it does not contradict the 1st law of thermodynamics, since the whole energy will be conserved, only the distribution will be changed.