TWI420715B - Thermal rectifier and method for enabling thermal rectification - Google Patents

Description

Thermal rectifier and thermal rectification method

This invention relates to a thermal rectifier, and more particularly to a thermal rectifier having a vacuum layer.

The literature on thermal rectification began in 1935 when C. Starr declared that the direction of heat flow was observed at the copper/copper oxide junction. Recently (2006), the University of Berkeley in the United States measured the characteristics of thermal rectification at the carbon nanotube junction. However, its performance is only 6%, and the operating temperature is low [Science, 314, 1121 (2006)], and its heat flow is transmitted by soliton. In addition to the literature from the two experiments above, the theoretical concept involves the use of phonons and photons to practice thermal rectification elements. The use of phonon carriers to conduct thermal rectifiers at the junction of the nano-surfaces is difficult to derive from the boundary conditions of the junction, which is difficult to achieve in real materials. Therefore, it is very difficult to construct thermal rectification using phonon carriers. [Physical Review Letters, 97, 124302 (2006)]. The photon carrier thermal rectifier consists of two heterogeneous materials sandwiched by a vacuum layer [Physical Review Letters, 104, 154301 (2010)]. These two materials have different emission photon frequencies. Photon resonance characteristics can be achieved in the forward temperature difference to transfer photons from the A material to the B material to allow heat flow to pass through the photons. In the case of a reverse temperature difference, the system loses photon resonance characteristics, so that heat flow cannot be transferred from B to material A. Since photon emission does not have a fixed orientation, most photons cannot be transferred from material A to B. Therefore, the use of photons to construct a thermal rectifier has low thermal rectification efficiency. The present invention utilizes electrons as carriers of thermal energy and utilizes quantum dot junctions to construct high efficiency thermal rectifiers.

The present invention provides a thermal rectifier comprising: a first electrode; a second electrode; an insulating layer disposed between the first electrode and the second electrode; a plurality of quantum dots disposed in the insulating layer; A vacuum layer is disposed between the insulating layer and the first electrode.

Preferably, the thickness of the vacuum layer is selected such that when the temperature of the second electrode is higher than the temperature of the first electrode, a heat flow flows from the second electrode to the first electrode, and when the first electrode When the temperature is higher than the temperature of the second electrode, substantially no heat flow flows from the first electrode to the second electrode.

Preferably, an electronic interaction between the first electrode and the plurality of quantum dots is represented by a first coupling parameter, and an electronic interaction between the second electrode and the plurality of quantum dots is A second coupling parameter representation.

Preferably, an electronic interaction between the plurality of quantum dots is represented by a third coupling parameter, and the third coupling parameter is greater than the first coupling parameter and the second coupling parameter.

Preferably, the first coupling parameter, the second coupling parameter and the second coupling parameter are selected such that when the temperature of the second electrode is higher than the temperature of the first electrode, a heat flow flows from the second electrode to The first electrode, and when the temperature of the first electrode is higher than the temperature of the second electrode, substantially no heat flow flows from the first electrode to the second electrode.

Preferably, the temperature of the first electrode and the temperature of the second electrode are substantially close to room temperature.

Preferably, the energy distance between the ground state and the first excited state of each of the plurality of quantum dots is greater than the thermal energy of the first electrode and the second electrode.

Preferably, the quantum dots are formed of a semiconductor material or an insulating material.

Preferably, each of the plurality of quantum dots has a diameter of about 1 nm.

Preferably, the spacing between the quantum dots in the plurality of quantum dots is about 3 nm.

The present invention further provides a thermal rectification method comprising: providing an insulating layer having a plurality of quantum dots disposed therein; providing a first electrode, the first electrode is in contact with the insulating layer; and providing a second electrode The second electrode is separated from the second insulating layer by a vacuum layer.

Preferably, the thermal rectification method of the present invention further provides that the vacuum layer comprises selecting a thickness of the vacuum layer such that when the temperature of the second electrode is higher than the temperature of the first electrode, a heat flow flows from the second electrode to the first An electrode, and substantially no heat flow from the first electrode to the second electrode when the temperature of the first electrode is higher than the temperature of the second electrode.

Preferably, in the thermal rectification method of the present invention, an electronic interaction between the first electrode and the plurality of quantum dots is represented by a first coupling parameter, and the second electrode and the plurality of quantum dots are The electronic interaction between the two is represented by a second coupling parameter.

Preferably, in the thermal rectification method of the present invention, providing the plurality of quantum dots comprises selecting an average size and a spacing of the quantum dots such that an electronic interaction between the quantum dots is represented by a third coupling parameter. And the third coupling parameter is greater than the first coupling parameter and the second coupling parameter.

Preferably, in the thermal rectification method of the present invention, the plurality of quantum dots further includes selecting the first coupling parameter, the second coupling parameter, and the second coupling parameter such that when the temperature of the second electrode is greater than the first a heat flow from the second electrode to the first electrode when the temperature of the electrode is high, and substantially no heat flow from the first electrode to the second when the temperature of the first electrode is higher than the temperature of the second electrode electrode.

Preferably, in the thermal rectification method of the present invention, the plurality of quantum dots comprise a composition and a size of the quantum dots, such that an energy distance between the ground state and the first excited state of each quantum dot is greater than the first Thermal energy of the electrode and the second electrode.

In summary, the thermal rectifier and the thermal rectification method of the present invention utilize the thickness of the selected vacuum layer and various coupling parameters to achieve the effect that the heat flow can only flow in a single direction.

Please refer to the first figure for illustrating the basic structure of the thermal rectifier of the present invention. As shown in the first figure, the thermal rectifier 100 includes a first electrode 101, a second electrode 102, an insulating layer 103, a plurality of quantum dots 104, and a vacuum layer 105. In general, the temperature of the first electrode 101 and the temperature of the second electrode 102 are substantially similar to room temperature. As shown, the insulating layer 103 is disposed between the first electrode 101 and the second electrode 102, and the first electrode 101 is in contact with the insulating layer 103.

The quantum dots 104 are disposed in the insulating layer 103. The composition and size of the quantum dots 104 are selected such that the energy distance between the ground state and the first excited state of each quantum dot 104 is greater than the thermal energy of the first electrode 101 and the second electrode 102. In general, the energy state of the ground state of each quantum dot 104 and the first excited state is greater than k _B T , where k _B is the Boziman constant and T is the temperature of the thermal rectifier 100. Thus, each quantum dot 104 has only one energy level and the quantum dots 104 can be formed from a semiconductor material. Preferably, each quantum dot 104 has a diameter of about 1 nanometer and the quantum dots 104 have a spacing of about 3 nanometers.

The vacuum layer 105 is disposed between the insulating layer 103 and the first electrode 101, and the first electrode 101 is separated from the insulating layer 103 by the vacuum layer 105. Since the phonon cannot be transported in a vacuum, the vacuum layer 105 blocks the phonons from transferring thermal energy. In addition, the vacuum layer 105 allows electrons to pass. The thickness of the vacuum layer 105 may be selected such that when the temperature of the second electrode 102 is higher than the temperature of the first electrode 101, heat flows from the second electrode 102 to the first electrode 101, and when the temperature of the first electrode 101 is lower than the second When the temperature of the electrode 102 is high, substantially no heat flows from the first electrode 101 to the second electrode 102.

In one embodiment of the invention, the electronic interaction between the first electrode 101 and the quantum dot 104 is represented by a first coupling parameter, and the electronic interaction between the second electrode 102 and the quantum dot 104 is represented by a second coupling parameter. The average size and spacing of the quantum dots 104 are selected such that the electronic interaction between the quantum dots 104 is represented by a third coupling parameter, and the third coupling parameter is greater than the first coupling parameter and the second coupling parameter. The first coupling parameter, the second coupling parameter, and the second coupling parameter are selected such that heat flow flows from the second electrode 102 to the first electrode 101 when the temperature of the second electrode 104 is higher than the temperature of the first electrode 101 And substantially no heat flow flows from the first electrode 101 to the second electrode 102 when the temperature of the first electrode 101 is higher than the temperature of the second electrode 102.

To further illustrate the thermal rectifier of the present invention, the current through the thermal rectifier 100 and the heat flow are represented by the following equations, respectively:

Where γ _l ( ε ) is the transmission coefficient and its relation is

f ₂₁ ( ε )= f ₂ ( ε )- f ₁ ( ε ) and f ₂₍₁₎ ( ε )=1( +1) is a Fermi distribution function of the first electrode 101 and the second electrode 102. T ₁ (T ₂ ) is the temperature of the first electrode 101 and the second electrode 102, respectively. E _F is the average Fermi energy of the two electrodes.

The chemical energy difference μ ₂ - μ ₁ of the first electrode 101 and the second electrode 102 is equal to the bias voltage eΔV between the first electrode 101 and the second electrode 102, wherein the potential difference between the first electrode 101 and the second electrode 102 The eΔV is caused by a temperature gradient between the first electrode 101 and the second electrode 102. Γ _{l , 1} ( ε ) and Γ _{l , 2} ( ε ) represent the transmittance of electrons from the quantum dot 104 to the first electrode 101 and the second electrode 102, respectively. e is the basic electrical quantity of electricity, and h is the Planck constant.

The energy level separation of the ground state energy level and the excited state energy level of the quantum dot 104 is much larger than the electron interaction energy level U _{1 in the} quantum dot 104, and the thermal perturbation energy k _B T, T is the system temperature. Because of the high barrier between quantum dots 104, the interdot hopping term is ignored.

The temperature T _{1 of the} first electrode 101 is represented by T ₀ -ΔT/2, and the temperature T _{2 of the} second electrode 102 is represented by T ₀ +ΔT/2. T ₀ is a temperature at which the first electrode 101 and the second electrode 102 are in equilibrium, and ΔT is a temperature difference between the first electrode 101 and the second electrode 102. Because of the difference in electrochemical energy, the eΔV caused by the temperature gradient between the first electrode 101 and the second electrode 102 will be very significant and maintain the energy level shift of each quantum dot 104. The thermal rectifier 100 of the present invention has good heat conduction when the temperature of the second electrode 102 is greater than that of the first electrode 101, and does not have good heat conduction when the temperature of the second electrode 102 is smaller than that of the second electrode 101. Referring to equations (1) and (2), it can be seen that the factors affecting the asymmetry of heat flow are not only the asymmetry of coupling between quantum dots 104 and electrodes 101, 102, but also the coulomb interaction of electrons between quantum dots 104. In general, it can be assumed that no additional loop is applied to the metal electrodes 101, 102 at both ends, so that for the electrons, the thermal rectifier 100 is considered to be open. At the same time, by calculating the equations (1) and (2), the required ΔV and heat flow can be obtained.

The second figure illustrates the heat flow, average occupancy, and differential thermal conductance of the thermal rectifier of the present invention comprising two quantum dots. The ground state energy systems of quantum dot A and quantum dot B are represented by E _A and E _B , respectively. E _A = E _{F -} ΔE/5, and E _B = E _F + α _B ΔE, where α _B is between 0 and 1. The representation of the heat flow is expressed in terms of the basic unit Q ₀ , where Q ₀ = Γ ² / (2h). The Coulomb interaction inside the quantum dot is U ₁ =30k _B T ₀ , and the Coulomb interaction between the quantum dots is U _AB =15k _B T ₀ . The piercing rate of the quantum dot A to the first electrode 101 is Γ _A1 =0, and the piercing rate of the quantum dot A to the second electrode 102 is Γ _A2 = 2 Γ. The penetration rate of the quantum dot B to the first electrode 101 is Γ _B1 = Γ, and the transmittance of the quantum dot B to the second electrode 102 is Γ _B2 = Γ. k _B T ₀ is equal to 25 Γ. Γ is the average wear rate of each unit, expressed as Γ=(Γ _A2 +Γ _A1 )/2. In general, the lanthanide is between 0.1 and 0.5 meV.

When it is assumed that the Coulomb interaction in a quantum dot is large, and the average occupancy in quantum dots A and B will be zero, the following formula can be derived:

Q/γ _B = π(1-N _B )[(1-2N _A )(E _B -E _F )f ₂₁ (E _B )+2N _A (E _B +U _AB -E _F )f ₂₁ (E _B +U _AB )] (3)

Wherein, N _A and N _B are the average occupancy of quantum dots A and B, respectively, γ _B is the transmission factor of quantum dot B, and f ₂₁ is the first electrode Fermi distribution function minus the second electrode Fermi distribution function.

The second graph A shows the relationship between the heat flow and the temperature difference. The ground state energy levels of the equivalence sub-points are E _F +2 ΔE/5 and 4 ΔE/5, respectively. It can be found that when E _{B is} closer to E _F , the third (3) is utilized. The larger the difference between the heat flow and the actual calculated heat flow, the worse the effect of simplifying the calculation, but the heat popularity it presents is still somewhat accurate. Therefore, using equation (3) is quite convenient for understanding the thermal rectification behavior. As shown in the second graph B, the electron occupancy rate N _{A of the} quantum dot A produces an asymmetrical behavior for ΔT, which is due to the fact that the quantum dot left and right tunneling rates Γ _A1 =0 and Γ _A2 = 2 Γ are very asymmetrical.

The second C diagram illustrates the differential thermal conductance, the basic unit of which is Q ₀ k _B /Γ. As can be seen from the figure, the change in E _B is not significant for the rectification effect of the thermal rectifier 100. The differential thermal conductance is approximately proportional to ΔT between -20 Γ < k _B ΔT < 20 Γ.

The mechanism of thermal rectification is similar to that of electrical rectification, however heat flow is generated by temperature difference and chemical potential. More specifically, when in the linear region, because the temperature difference between the electrodes at both ends is not so large, the influence of heat flow on the potential difference of the generated chemical potential is a linear function, whereas in the nonlinear region, the temperature difference between the electrodes at both ends is relatively large. The effect of heat flow on the chemical potential difference between the electrodes at both ends is not a linear relationship but a nonlinear function.

It is important to note that because the energy of the resonant channel of E _B +U _AB is too high compared to the E _F system, the energy is the heat flow of the E _B resonant channel. The sign of heat flow Q is determined by f ₂₁ (E _B ), where f ₂₁ (E _B ) is related to Coulomb interaction, penetration rate and quantum dot energy level. The rectification effect of heat flow Q is mainly determined by 1-2N _A , thus indicating that the energy level of quantum dot A needs to be smaller than E _F and the importance of Coulomb interaction between quantum dots. When ΔT < 0, the negative sign of the heat flow Q indicates that the heat flow system flows from the first electrode 101 to the second electrode 102. The rectification efficiency is expressed by the following formula:

η _Q =(Q(ΔT=30T)-|Q(ΔT=-30Γ)|)/Q(ΔT=-30Γ)

When E _B = E _F + when 2ΔE / 5 rectification efficiency η _Q is 0.86, when the E _B = E _F + when 4ΔE / 5 rectification efficiency η _Q 0.88.

The third figure illustrates the relationship between the heat flow, the differential thermal conductivity, and the thermal power and ΔT of the different Γ _{A1 in} the case where the thermal rectifier of the present invention comprises three quantum dots. In this embodiment, the three quantum dots are quantum dot A, quantum dot B, and quantum dot C, respectively, and quantum dot A is located between sub-point B and quantum dot C. The bare-order correction coefficient η _A of quantum dot A is |Γ _A2 -Γ _A1 )/(2Γ)|, which is used to reflect the interaction of quantum dot positions at asymmetric cross-ratio. The tunneling rates are Γ _{B(C), 1} = Γ _{B(C), 2} = Γ. The ground state energy levels of quantum dot A, quantum dot B, and quantum dot C are E _A =E _F -ΔE/5, E _B =E _F +2ΔE/5, and E _B =E _C +4ΔE/5, respectively. The Coulomb interaction between the quantums is U _AC =U _BA =15k _B T ₀ , U _BC =8k _B T ₀ . U _C = 30k _B T ₀ , and the remaining parameters are the same as those of the two quantum dots. Please refer to the fourth A picture. When Γ _A1 is 0, the thermal rectification effect is more significant. The heat flow Q is 0.068Q ₀ when ΔT=-30Γ, but is 0.33 Q ₀ when ΔT=30Γ, and the rectification coefficient η _Q is 0.79. However, the heat flow when Γ _A1 is 0 is too small. Coupons Γ _A1 is 0.1Γ, the heat flow Q when ΔT = -30Γ 1.69Q _0, at ΔT = time 30Γ is 5.69 Q _{0, Q} [eta] can be derived rectification coefficient is 0.69. From this, it can be seen that when ΔT < 0, the smaller the Γ _{A1 is, the} smaller the heat flow is. Furthermore, the blocking effect of quantum dot A is quite important for the rectification effect system. As shown in the third panel B, it can be very clearly found that in the case of Γ _A1 = 0.1 Γ and Γ _A2 = 1.9 ,, the generation of negative differential thermal conductance is seen. When Γ _A1 = Γ _A2 = Γ, the differential thermal conductance is symmetrical.

The thermal power and ΔT are shown in Figure C. In the figure, except for the curve of the tunneling rate symmetry condition, the thermal power exhibits a highly asymmetric behavior. The electrochemical energy eΔV can be very large depending on the value of the thermal power. Therefore, the change of the quantum dot energy level caused by the electrochemical energy eΔV is very important. For further explanation, please refer to the fourth picture. The fourth graph illustrates the relationship between heat flow, differential thermal conductivity, and thermal power and ΔT for quantum dots C having different energy levels. In the fourth figure, Γ _A1 =0, U _BC = 8k _B T ₀ , η _A = 0.3. Other parameters are the same as in the embodiment of the third figure. The solid line represents the chemical potential potential eΔV generated to cause the shift of the quantum dot A energy level, and the broken line represents the case where the efficiency is not taken into account, wherein the magnitude of the energy offset is η _A ΔV/2. It is apparent that the quantum dot energy level shift caused by ΔV causes a decrease in heat flow. Although the heat flow shows a rectifying effect under the condition of E _C =E _F +ΔE/5 and E _C =E _F +3ΔE/5, the thermal power shows different results. Please refer to the third figure C and the fourth figure C at the same time, it can be seen that the heat flow and the electrochemical energy ΔV are not a linear function. As can be seen from the above description, the rectification efficiency of the three-quantum dot system has a higher rectification efficiency as the temperature difference is higher. However, the difference between the rectification efficiency η _Q and the ground state energy level of the quantum dot C is not large.

In summary, comparing a thermal rectifier with two quantum dots and three quantum dots, it can be seen that the thermal rectification efficiency is almost the same under two conditions. However, in a thermal rectifier with three quantum dots, the intensity of the heat flow is significantly increased. At the same time, it can be known that the rectifying effect system of the thermal rectifier of the present invention is related to the coupling between quantum dots and electrodes, the interaction of electron coulombs and the difference of energy levels of different quantum dots.

As apparent from the above description, the present invention is a novel, advanced and industrially useful invention. While the invention has been described above in terms of the preferred embodiments thereof, it is not intended to limit the invention, and various modifications and changes can be made without departing from the spirit and scope of the invention.

100. . . Thermal rectifier

101. . . First electrode plate

102. . . Second electrode plate

103. . . Insulation

104. . . Quantum dot

105. . . Vacuum layer

The first figure illustrates the basic structure of the thermal rectifier of the present invention.

The second figure illustrates the heat flow, average occupancy, and differential thermal conductance of the thermal rectifier of the present invention comprising two quantum dots.

The third figure illustrates the relationship between the heat flow, the differential thermal conductivity, and the thermal power and ΔT of the different Γ _{A1 in} the case where the thermal rectifier of the present invention comprises three quantum dots.

The fourth graph illustrates the relationship between heat flow, differential thermal conductivity, and thermal power and ΔT for quantum dots with different energy levels.

100. . . Thermal rectifier

101. . . First electrode plate

102. . . Second electrode plate

103. . . Insulation

104. . . Quantum dot

105. . . Vacuum layer

Claims (16)

A unidirectional thermal rectifier comprising: a first electrode; a second electrode; an insulating layer disposed between the first electrode and the second electrode; a plurality of quantum dots disposed in the insulating layer; A vacuum layer is disposed between the insulating layer and the first electrode. The thermal rectifier of claim 1, wherein the thickness of the vacuum layer is selected such that when the temperature of the second electrode is higher than the temperature of the first electrode, a heat flow system flows from the second electrode to The first electrode, and when the temperature of the first electrode is higher than the temperature of the second electrode, substantially no heat flow flows from the first electrode to the second electrode. The thermal rectifier of claim 1, wherein the electronic interaction between the first electrode and the quantum dots is represented by a first coupling parameter, and the second electrode and the plurality of quantum dots are The electronic interaction between the two is represented by a second coupling parameter. The thermal rectifier of claim 3, wherein an electronic interaction between the plurality of quantum dots is represented by a third coupling parameter, and the third coupling parameter is greater than the first coupling parameter and The second coupling parameter. The thermal rectifier of claim 4, wherein the first coupling parameter, the second coupling parameter, and the second coupling parameter are selected such that when the temperature of the second electrode is higher than the temperature of the first electrode A heat flow stream flows from the second electrode to the first electrode, and substantially no heat flow flows from the first electrode to the second electrode when a temperature of the first electrode is higher than a temperature of the second electrode. The thermal rectifier of claim 5, wherein the temperature of the first electrode and the temperature of the second electrode are substantially similar to room temperature. The thermal rectifier of claim 1, wherein an energy distance between a ground state and a first excited state of each of the quantum dots is greater than a thermal energy of the first electrode and the second electrode. The thermal rectifier of claim 1, wherein the quantum dots are formed of a semiconductor material or an insulating material. The thermal rectifier of claim 1, wherein each of the quantum dots has a diameter of about 1 nm. The thermal rectifier of claim 1, wherein the spacing between each of the quantum dots is about 3 nm. A unidirectional thermal rectification method comprising: providing an insulating layer having a plurality of quantum dots; providing a first electrode, the first electrode is in contact with the insulating layer; and providing a second electrode, the second The electrode is separated from the insulating layer by a vacuum layer. The thermal rectification method of claim 11, further comprising: selecting a thickness of the vacuum layer such that when the temperature of the second electrode is higher than a temperature of the first electrode, a heat flow system is from the second electrode Flowing to the first electrode, and when the temperature of the first electrode is higher than the temperature of the second electrode, substantially no heat flow flows from the first electrode to the second electrode. The thermal rectification method of claim 11, wherein the electronic interaction between the first electrode and the quantum dots is represented by a first coupling parameter, and the second electrode and the quantum dots are The electronic interaction between the two is represented by a second coupling parameter. The thermal rectification method of claim 13, further comprising: selecting an average size and a spacing of the quantum dots such that the electronic interaction between the quantum dots is represented by a third coupling parameter, and The third coupling parameter is greater than the first coupling parameter and the second coupling parameter. The thermal rectification method of claim 14, further comprising: selecting the first coupling parameter, the second coupling parameter, and the second coupling parameter such that when the temperature of the second electrode is greater than the temperature of the first electrode When the temperature is high, a heat flow system flows from the second electrode to the first electrode, and when the temperature of the first electrode is higher than the temperature of the second electrode, substantially no heat flow flows from the first electrode to the first electrode Two electrodes. The thermal rectification method of claim 11, further comprising: selecting a composition and a size of the quantum dots such that an energy distance between a ground state and a first excited state of each of the quantum dots is greater than Thermal energy of the first electrode and the second electrode.