3.1. Thermoelectric effect similar to the Peltier effect.
We assume that this system shown in Fig. 1 is examined at room temperature. The configuration of electrode C, section A2 and the insulating film B is actually a capacitor; therefore, The operation of applying an external electric field to A2 by electrode C is actually to apply a voltage between them to charge the capacitor. For example, if electrode C is negatively charged, that is, a negative electric field is applied to section A2, the free electrons in A2 are repulsed by the external electric field, resulting in a decrease in number density. Therefore, there is a difference in number density of free electrons between section A2 and its adjacent sections of A1 and A3. Any excess charge lies only at the surface of the conductor at electrostatic equilibrium, so the number density of the excess charges decreases with increasing depth. Here it requires the conductive layer A to be sufficiently thin so that the number density of free electron can be assumed to be uniform throughout section A2. Now if a voltage is applied on the two ends of conductive layer A to drive a net current through it, in addition to the Joule heat due to the conductor's resistance, we believe we will also observe a thermal effect–the net current causes a temperature difference between the two junctions of J1 and J2.
From the perspective of potential energy state of free electrons, the two sections of A1 and A3 both are not affected by the external electric field applied by electrode C, so the potential energy state of free electrons in section A1 is equal to that in section A3, i.e. \({\varepsilon _1}\)=\({\varepsilon _3}\). But the free electrons in section A2 are affected by the external electric field [4–6], creating a potential barrier between section A2 and the other two sections. When electrode C is negatively charged, the free electrons in section A1 (or in section A3) have to overcome the repulsion of the external electric field when they move into section A2. Therefore, free electrons in section A2 have a higher potential energy; i.e. \({\varepsilon _2}\)>\({\varepsilon _1}\). That is to say, when free electrons are driven to move from section A1 into section A2, junction J1 of A1 and A2 will cool down, and the heat absorbed by each electron \({Q_1}\) is equivalent to its potential energy gain when it moves across the junction, \({Q_1}\)=\({\varepsilon _2}\)-\({\varepsilon _1}\). Similarly, because \({\varepsilon _2}\)>\({\varepsilon _3}\), junction J2 will heat up when electrons move from section A2 into section A3, the heat each electron releases \({Q_2}\) will be \({\varepsilon _2}\)-\({\varepsilon _3}\). It is similar to the Peltier effect.
Strictly speaking, there is no clear interface between sections of A1 and A2 or between sections of A2 and A3. The so-called "interface" is just a tiny transition region where free electrons transit from one number density to another and also transit from one potential state to another. In practical use, insulating film B should be as thin as possible. The external electric field can change the energy states of electrons in section A2. Naturally, the strength of the external electric field determines the potential energy difference of the electrons (the height of the potential barrier) between section A2 and section A1, so the amount of heat absorbed (or released) can be adjusted by adjusting the strength of the external electric field. It sounds like that we can make a generator with an adjustable thermoelectric conversion efficiency. Changing the polarity of the net charges electrode C carries can also shift the junction from heat absorption to heat release without changing the current direction through conductive layer A. We can also add another insulating film and another electrode on conductive layer A; to enhance the affect of external electric field on section A2, that will help enhance the thermoelectric effect.
3.2. Thermoelectric effect similar to the Seebeck effect.
We also believe that there will be a reverse manifestation of the above effect, which means that the temperature difference between the two junctions of J1 and J2 can generate an electromotive force. Set the temperature at junction J1 \({T_1}\), while the temperature at junction J2 \({T_2}\). When \({T_1}\)≠\({T_2}\), a non-zero thermoelectric electromotive force (V≠ 0) could be detected between the two ends of conductive layer A, which is similar to the Seebeck effect.
Taking the negatively charged electrode C as an example, when \({T_1}\)=\({T_2}\), the distribution transitions of electron density at J1 and J2 are symmetric, and there will be no non-zero potential difference between the two ends of conductive layer A. But when \({T_1}\) is higher, the electron distribution junction at J1 will change. Due to the greater kinetic energy of free electrons, the density of electrons becomes lower, and the electric field induced by Atomic nucleus cannot be fully canceled out, creating a positively charged background. That is to say, the potential energy gain when a free electron move through the higher-temperature junction J1 will be greater than the potential energy gain when it moves through J2. The potential gradient at junction J1 is greater than that at junction J2, \({V_1}\)>\({V_2}\); thus there is a non zero electromotive force between the two ends of conductive layer A. When the two ends of conductive layer A are connected to form a circuit, a net current will be driven by the temperature-difference-induced electromotive force–the free electrons are driven to move from the left to the right (from A1 to A3) in conductive layer A. When they move through J1, they absorb heat and their potential energies become higher; when they move through J2, they release heat there and the potential energies become lower.
Because \({V_1}\)>\({V_2}\), when an electron move cross J1, the potential energy gain \({\varepsilon _{\text{g}}}\) is greater than the potential energy released \({\varepsilon _r}\) when it move across J2. The difference, \({\varepsilon _{\text{g}}}\)-\({\varepsilon _r}\), is the work that drives the current in the circuit, so this model can be developed to be a thermoelectric generator. Similarly, with the polarity of the net charges electrode C carries unchanged, when we switch from \({T_1}\)>\({T_2}\) to \({T_2}\)>\({T_1}\), an electromotive force in the opposite direction will be generated. If \({T_1}\)>\({T_2}\), and but electrode C switches from negatively charged to positively charged, it will also reverse the direction of the electromotive force.
The above analysis about generation of thermoelectric electromotive force can be extended to the Seebeck effect of common thermal couples. At present, the explanations for the Seebeck effect are related to factors such as the Seebeck coefficient of materials, Thomson effect, and thermal diffusion of electrons, but I believe these explanations are not close to the microscopic essence. At the hot junction, the free electrons move faster, causing a greater tendency to expand like a gas; thereby the number density of free electrons decreases, creating a positively charged background. Therefore, there is a greater potential difference (a higher potential barrier) through the hot junction, when the free electrons move through the hot junction it will obtain a larger potential energy gain. This is the fundamental cause of the generation of thermoelectric electromotive force.
3.3. Optoelectronic conversion.
Heating is not the only way to increase the kinetic energy of electrons. Considering the coupling oscillation between phonons and electromagnetic waves, as well as the influence of electron-phonon interaction on electron transitions, if the wavelength of the incident beam is within the appropriate range, the kinetic energy of electrons can also be increased. It can be expected that, in the system shown in Fig. 1, even if the two junctions of J1 and J2 are at the same temperature, a non zero electromotive force, similar to that caused by temperature difference, can be generated by asymmetric lighting on the two junctions. This is another photoelectric effect. Similarly, for common thermocouples made of two materials, if the size of the junction is so small that the light can penetrate through, and the wavelength of the light is within the appropriate range, asymmetric lighting will also generate non zero electromotive force.
In addition, our model can also enhance the thermoelectric effect of typical thermocouples. That is to say, if section A2 is originally a different material, the thermoelectric effect caused by applying the external electric field can be superimposed on its inherent Peltier–Seebeck effect; that could weaken or enhance its original thermoelectric effect.