201131841 六、發明說明： 【發明所屬之技術領域】 真空流器’特別是關於-種具有 【先前技術】 仆铜Ϊ整流的文獻記载始於1935 _ C.恤宣稱在銅/氧 克萊大2觀測到相依之熱流特性。最近(2°°6年)美國柏 僅处、#干在奈米碳管接面量㈣熱整流的特性。但其效能 勒!! β 到 6%，且操作溫度低[Science，314, 1121 (2006)],其 二Γ由孤立子(S°htGn)來傳輸。除上述兩實驗之文獻外， 冓想包括利用聲子及光子來實踐熱整流元件。利用聲 子在奈米接面的傳導來製作熱整流器，其困難源自接 面的邊界條件，在真實的材料中很難達成，因此利用聲子 載子來建構熱整流是非常困難地[physical201131841 VI. Description of the invention: [Technical field to which the invention pertains] Vacuum flow device 'especially with regard to the type of prior art 仆 Ϊ Ϊ rectification of the literature began in 1935 _ C. shirt declared in copper / oxygen Clay 2 Observed the dependent heat flow characteristics. Recently (2 ° ° 6 years) US cypress only, # dry in the carbon nanotube junction amount (four) thermal rectification characteristics. But its performance is!! β to 6%, and the operating temperature is low [Science, 314, 1121 (2006)], and its second is transmitted by the soliton (S°htGn). In addition to the literature of the above two experiments, delusions include the use of phonons and photons to practice thermal rectifying elements. The use of phonon conduction at the junction of the nanometer to make a thermal rectifier is difficult due to the boundary conditions of the junction, which is difficult to achieve in real materials, so it is very difficult to construct thermal rectification using phonon carriers [physical]
Review Letters, 97, 124302 (2006)]。光子載子熱整流器是由兩個異質材料， 中間隔着真空層所構成[PhySicai Review Letters, 104, 154301 (2010)]。此兩種材料有不同的放射光子頻率。在順 向温差時可以達到光子共振特性而將光子從A材料傳送到 B材料使熱流透過光子傳遞。在逆向温差時，系統失去光 子共振特性’使得熱流無法從B傳送到A材料。因光子放 射不具持定方向，使得多數光子都無法從材料A傳送到 B。因此利用光子來建構熱整流器，其熱整流效率低。本 發明利用電子為熱能的載子，並利用量子點接面來建構高 效率之熱整流器。 201131841 【發明内容】 本發明提供一種熱整流器’包含：一第一電極；一第 二電極；一絕緣層，設置於該第一電極與該第二電極之間； 複數個量子點，設置於該絕緣層内；以及一真空層，設置 於該絕緣層與該第一電極之間。 較佳地，該真空層的厚度係被選擇使得當該第二電極 的溫度比該弟·一電極的溫度南時'一熱流從該弟·一電極流至 該第一電極，且當該第一電極的溫度比該第二電極的溫度 高時基本上無熱流從該第一電極流至該第二電極。 較佳地，該第一電極與該複數個量子點之間的一電子 交互作用係以一第一耦合參數表示，且該第二電極與該複 數個量子點之間的一電子交互作用係以一第二耦合參數表 示。 較佳地，該複數個量子點彼此之間的一電子交互作用 係以一第三耦合參數表示，且該第三耦合參數係大於該第 一耦合參數及該第二耦合參數。 較佳地，該第一耦合參數、該第二耦合參數及該第二 耦合參數係被選擇使得當該第二電極的溫度比該第一電極 的溫度南時·—熱流從該弟二電極流至該弟·—電極，且當該 第·—電極的溫度比s亥弟二電極的溫度南時基本上無熱流從 該第一電極流至該第二電極。 較佳地，該第一電極的溫度與該第二電極的溫度基本 上與室溫相近。 較佳地，每一該複數個量子點的基態與第一激發態之 201131841 間的能距係大於該第一電極與該第二電極的熱能。 較佳地，該量子點係由半導體材料或是絕緣材料形成。 較佳地，每一該複數個量子點的直徑係大約1奈米。 較佳地，該複數個量子點中量子點間的間距係大約3 奈米。 本發明另提供一種熱整流方法，包含：提供一絕緣層， 該絕緣層具有複數個量子點設置於其中；提供一第一電 極，該第一電極與該絕緣層接觸；以及提供一第二電極， 該第二電極藉由一真空層與該第二絕緣層分開。 較佳地，本發明之熱整流方法進一步提供該真空層包 含選擇該真空層的厚度使得當該第二電極的溫度比該第一 電極的溫度高時一熱流從該第二電極流至該第一電極，且 當該弟' —電極的溫度比έ亥弟二電極的溫度而時基本上無熱 流從該第一電極流至該第二電極。 較佳地，本發明之熱整流方法鐘，該第一電極與該複 數個量子點之間的一電子交互作用係以一第一耦合參數表 示，且該第二電極與該複數個量子點之間的電子交互作用 係以一第二搞合參數表示。 較佳地，本發明之熱整流方法中，提供該複數個量子 點包含選擇該量子點的平均尺寸及間距，使得該量子點彼 此之間的一電子交互作用係以一第三耦合參數表示，且該 第三耦合參數係大於該第一耦合參數及該第二耦合參數。 較佳地，本發明之熱整流方法中，該複數個量子點進 一步包含選擇該第一耦合參數、該第二耦合參數及該第二 耦合參數，使得當該第二電極的溫度比該第一電極的溫度 201131841 高時一熱流從該第二電極流至該第一電極，且當該第一電 極的溫度比該第二電極的溫度高時基本上無熱流從該第一 電極流至該第二電極。 較佳地，本發明之熱整流方法中，該複數個量子點包 含選擇該量子點的組成及尺寸，使得該每一量子點的基態 與第一激發態之間的能距係大於該第一電極與該第二電極 的熱能。 綜上所述，本發明熱整流器及熱整流方法利用選擇真 空層的厚度及各項耦合參數，達到熱流僅能以單一方向流 動的效果。 【實施方式】 請參考第一圖，係例示說明本發明熱整流器之基本結 構。如第一圖所示，熱整流器100包含：一第一電極101、 一第二電極102、一絕緣層103、複數個量子點104以及一 真空層105。一般而言，第一電極101的溫度與第二電極 102的溫度基本上與室溫相近。如圖所示，絕緣層103係設 置於第一電極101與第二電極102之間，且第一電極101 與絕緣層103接觸。 量子點104係設置於絕緣層103内。量子點104的組 成及尺寸係被選擇，使每一量子點104的基態與第一激發 態之間的能距係大於第一電極101與第二電極102的熱 能。一般而言，每一量子點104的基態與第一激發態的能 距係比kBT大，其中kB為波滋曼常數，T為熱整流器100 之溫度。因此，每一量子點104只具有一個能階，且量子 201131841 點104係可由半導體材料形成。較佳地，每一量子點ι〇4 的直從係大約為1奈米，且量子點1 〇4間的間距係大約為3 奈米。 、〆 真空層105設置於絕緣層1〇3與第一電極1〇丨之間， 第一電極101藉由真空層1〇5與絕緣層103分開。因為聲 子(phonon)在真空中無法傳輸，真空層ι〇5阻隔聲 .埶 能。此外，真空層105允許電子通過。真空層1〇5的厚^ 係可被選擇使得當第二電極1〇2的溫度比第一電極1〇1 = 溫度而時熱流從第二電極1〇2流至第一電極1〇1，且當第一 電極101的溫度比第二電極1〇2的溫度高時，基本I無熱 流從第一電極101流至第二電極102。 本發明一種實施例中，第一電極1〇1與量子點1〇4之 間的電子父互作用以第一輕合參數表示，且第二電極 ，里子點104之間的電子交互作用以第二耦合參數表示。 1子點104的平均尺寸及間距係被選擇，使量子點1〇4彼 $之間的電子交互作用以第三耦合參數表示，且第三耦合 人，係大於該第一耦合參數及該第二耦合參數。該第一耦 二多數、該第二耦合參數及該第二耦合參數係被選擇使得 田第〜電極104的溫度比該第一電極1〇1的溫度高時熱流 從第二電極102流至第一電極1〇1，且當第一電極1〇1的溫 度比第二電極102的溫度高時基本上無熱流從第一電極1〇1 流至第二電極102。 沾進一步說明本發明之熱整流器’通過熱整流器1〇〇 電與熱流分別以下列方程式表示： 一 2已Review Letters, 97, 124302 (2006)]. The photon carrier thermal rectifier consists of two heterogeneous materials sandwiched by a vacuum layer [PhySicai 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 the photon resonance characteristic' so that heat flow cannot be transferred from B to the A material. 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 for thermal energy and utilizes quantum dot junctions to construct high efficiency thermal rectifiers. The present invention provides a thermal rectifier 'including: a first electrode; a second electrode; an insulating layer disposed between the first electrode and the second electrode; a plurality of quantum dots disposed on the a vacuum layer 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 lower than the temperature of the electrode, a heat flow flows from the electrode to the first electrode, and when the first When the temperature of an electrode 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 lower than the temperature of the first electrode, the heat flow flows from the second electrode To the younger electrode, and substantially no heat flow from the first electrode to the second electrode when the temperature of the first electrode is souther than the temperature of the second electrode. Preferably, the temperature of the first electrode and the temperature of the second electrode are substantially similar to room temperature. Preferably, the energy distance between the ground state of each of the plurality of quantum dots and the first excited state of 201131841 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 when the temperature of the electrode is substantially no heat flow from the first electrode to 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 fit 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 The temperature of the electrode 201131841 is high when 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 first electrode Two electrodes. 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 vacuum layer and the coupling parameters to achieve the effect that the heat flow can only flow in a single direction. [Embodiment] 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 of each quantum dot 104 and the first excited state is greater than the thermal energy of the first electrode 101 and the second electrode 102. In general, the ground state of each quantum dot 104 is greater than the kBT of the first excited state, where kB 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 201131841 point 104 can be formed from a semiconductor material. Preferably, the straight line of each quantum dot ι 4 is about 1 nm, and the spacing between quantum dots 1 〇 4 is about 3 nm. The vacuum layer 105 is disposed between the insulating layer 1〇3 and the first electrode 1〇丨, and the first electrode 101 is separated from the insulating layer 103 by the vacuum layer 1〇5. Because the phonon cannot be transported in a vacuum, the vacuum layer ι〇5 blocks the sound. In addition, the vacuum layer 105 allows electrons to pass. The thickness of the vacuum layer 1〇5 can be selected such that when the temperature of the second electrode 1〇2 is higher than the temperature of the first electrode 1〇1 = 2, the heat flow flows from the second electrode 1〇2 to the first electrode 1〇1, And when the temperature of the first electrode 101 is higher than the temperature of the second electrode 1〇2, substantially no heat flow flows from the first electrode 101 to the second electrode 102. In an embodiment of the invention, the electronic parent interaction between the first electrode 1〇1 and the quantum dot 1〇4 is represented by a first light-synchronization parameter, and the electronic interaction between the second electrode and the neutron point 104 is Two coupled parameter representations. The average size and spacing of the 1 sub-point 104 are selected such that the electronic interaction between the quantum dots 1 〇 4 and the other is represented by a third coupling parameter, and the third coupling person is greater than the first coupling parameter and the first Two coupling parameters. The first coupling two, the second coupling parameter, and the second coupling parameter are selected such that the temperature of the field-electrode 104 is higher than the temperature of the first electrode 1〇1, and the heat flow flows from the second electrode 102 to The first electrode 1〇1, and substantially no heat flow flows from the first electrode 1〇1 to the second electrode 102 when the temperature of the first electrode 1〇1 is higher than the temperature of the second electrode 102. Further, the thermal rectifier of the present invention is shown by the thermal rectifier 1 and the heat flow is represented by the following equation:
Je=~Y Σί^/ι WmGrl(T (ε)/21 (ε) ⑴ 201131841 一 2 Q = 咖-ef -咖认如) (2) 其中以幻為傳輸係數，其關係式為h(g)=J[i，2(g)r以幻 「/,2(^0+^^(5) “ ·Λΐ(匀=/2(幻—乂化)且 乂⑴(^) = 1/(6邓(卜巧⑴V(V2(1)) + 1)為第一 電極1〇1與第一電極1〇2的費米分佈函數(Fermi distribution f:neti〇n)。Τι(Τ2)係分別為第一電極101與第二電極102的 /皿度EF為兩電極的平均費米能量（permi energy) 〇 一第一電極101與第二電極102的化學能差係等於 第一電極101與第二電極102間的偏壓eAV，其中第一電 極yn與第二電極102間的電位勢差eAV係由第一電極1〇1 與第二電極102間的溫度梯度所造成的。]^ι(4&γ/2(4分 別ί表電子從量子點104到第一電極101與第二電極102 的牙遂率。e為電子基本電量，h為普朗克常數。 曰I子點104基態能階與激發態能階的能階分離遠大於 置子點104内電子交互作用能階认，和熱擾動能量匕丁，τ 為系統溫度。因為於量子點1〇4間有很高的位障，量子點 間彈碰項（interdot hopping term)係被忽略。 第一電極101之溫度T〗以Τ〇-ΔΤ/2表示，且第二電極 1〇2之溫度丁2以Τ0+ΔΤ/2表示。Τ〇為第一電極101與第二 電極102達平衡的溫度，ΔΤ為第一電極1〇1與第二電極1〇2 的溫度差。因為電化能差的關係，由第一電極101與第二 電極102間的溫度梯度所造成的eAv將會非常明顯，並維 持每一量子點104能階的偏移。本發明之熱整流器1〇〇在 第一電極1〇2溫度大於第一電極1〇1時具有良好的熱傳 導，而在第二電極102溫度小於第二電極iOi時不具良好Je=~Y Σί^/ι WmGrl(T (ε)/21 (ε) (1) 201131841 a 2 Q = coffee-ef - coffee recognition as (2) where the illusion is the transmission coefficient, the relationship is h (g )=J[i,2(g)r with illusion "/,2(^0+^^(5)" ·Λΐ(even=/2(幻乂化乂) and 乂(1)(^) = 1/( 6 Deng (Bu Q(1)V(V2(1)) + 1) is the Fermi distribution function of the first electrode 1〇1 and the first electrode 1〇2 (Fermi distribution f:neti〇n). Τι(Τ2) is respectively The average EF of the first electrode 101 and the second electrode 102 is the average permi energy of the two electrodes. The chemical energy difference between the first electrode 101 and the second electrode 102 is equal to the first electrode 101 and the first electrode 101 The bias voltage eAV between the two electrodes 102, wherein the potential difference eAV between the first electrode yn and the second electrode 102 is caused by a temperature gradient between the first electrode 1〇1 and the second electrode 102.]^( 4& γ/2 (4 respectively 表 indicates the gingival rate of electrons from the quantum dot 104 to the first electrode 101 and the second electrode 102. e is the basic electric quantity of electricity, h is the Planck constant. 基I sub-point 104 ground state energy The energy level separation of the order and the excited energy level is much larger than the electron interaction energy level in the set point 104, and the thermal perturbation energy, τ It is the system temperature. Because there is a high barrier between the quantum dots 1〇4, the interdot hopping term is ignored. The temperature T of the first electrode 101 is expressed by Τ〇-ΔΤ/2. And the temperature of the second electrode 1〇2 is represented by Τ0+ΔΤ/2. Τ〇 is the temperature at which the first electrode 101 and the second electrode 102 reach equilibrium, and ΔΤ is the first electrode 1〇1 and the second electrode 1 The temperature difference of 〇2. Because of the difference in electrochemical energy, the eAv caused by the temperature gradient between the first electrode 101 and the second electrode 102 will be very significant, and the energy level shift of each quantum dot 104 is maintained. The inventive thermal rectifier 1〇〇 has good heat conduction when the temperature of the first electrode 1〇2 is greater than the first electrode 1〇1, and does not have good when the temperature of the second electrode 102 is smaller than the second electrode iOi.
S 9 201131841 的熱傳導。參考第（1)式及第（2)式，可知影響熱流的不對稱 之因素不只有量子點104與電極101、102間耦合的不對 稱，還有量子點104間電子的庫倫交互作用。一般而言， 可假設並無任何外加迴路施加於於兩端金屬電極101、 102，因此對電子而言，熱整流器100視同開路。同時，藉 由計算第（1)式及第（2)式，可取得所需的AV及熱流。 第二圖係說明本發明熱整流器包含兩個量子點狀況 下，熱流、平均佔據率及微分熱導。量子點A及量子點B 的基態能階係分別以Ea及Eb表不。Εα=Ερ_ΔΕ/5 ’且 ΕΒ=ΕΡ+αΒΔΕ，其中αΒ係介於0至1 〇熱流的表示係以基本 單位Q〇表示，其中Q〇=r2/(2h)。量子點内部的庫倫交互作 用為U尸30kBT〇，且量子點間的庫倫交互作用為 UAB=15kBT〇。量子點A至第一電極101的穿遂率為ΓΑ1=0， 量子點Α至第二電極102的穿遂率為ΓΑ2=2Γ。量子點Β至 第一電極101的穿遂率為ΓΒ1=Γ，量子點Β至第二電極102 的穿遂率為ΓΒ2=Γ。kBT〇等於25Γ。Γ為每一單元的平均穿 遂率，以Γ=(ΓΑ2+Γαι)/2表示。一般而言Γ係介於0.1至 0.5meV。 當假設量子點内的庫倫交互作用力很大，量子點A及B 中的平均佔據率將為0時，可得出下式： Q/yB^( 1 -Nb) [(1 -2NA)(EB-EF)f21 (Eb) +2NA(EB+UAB-EF)f21(EB+UAB)] (3) 其中，NA及NB分別係量子點A及B的平均佔據率，γΒ為 為量子點Β的傳導因子(transmission factor)，f21為第一電極 費米分布函數減去第二電極的費米分布函數。 201131841 第二A圖顯示出熱流與溫差的關係圖，當量子點的基 態能階分別為ΕΡ+2ΔΕ/5及4ΔΕ/5，可以發現到當EB越接近 EF的時候，利用第（3)式與實際計算出來的熱流差距越大， 簡化算出來的效果越不好，但它所呈現的熱流行為仍有一 定程度上的準確性。因此，使用第（3)式對於了解熱整流行 為相當方便。如第二圖B所示，量子點A的電子占據率Na 對於ΔΤ產生不對稱的行為，這是由於量子點左右穿隧率 ΓΑ1=0及ΓΑ2=2Γ非常不對稱。 φ 第二C圖說明微分熱導，其基本單位為Q〇kB/r。由圖 中可看出，EB之變化對於熱整流器100之整流效果的改變 並不明顯。微分熱導在-20Γ<1ίΒΔΤ<20Γ間係大約正比於ΔΤ。 熱整流的機制與電整流類似，然而熱流是靠溫度差以 及化學位勢所產生。比較特別的是，當在線性區域中，由 於兩端電極溫差沒那麼大，熱流對於所產生化學電位勢差 造成的影響為一線性函數，反之在非線性區域下，由於兩 端電極溫差比較大，熱流對於兩端電極化學位勢差的影響 就不是線性關係而是一個非線性的函數。 • 需特別注意的是，因為能量為ΕΒ+υΑΒ的共振通道其能 量相較EF係太高的，因此係能量為EB共振通道產生熱流。 熱流Q的正負號係由f21(EB)決定，其中f21(EB)與庫倫交互 作用、穿遂率及量子點能階有關。熱流Q的整流效果主要 由1-2Na決定，因此說明了量子點A的能階需小於EF以及 量子點間庫倫交互作用的重要性。當ΔΤ<0時，熱流Q的負 號說明熱流係由第一電極101流向第二電極102。整流效率 以下式表示： 11 201131841 ncr(Q(AT=30T)- I Q (ΔΤ=-30Γ) I )/Q(AT=-3〇r) 當 EB=EF+2AE/5 時整流效率 為 0.86，當 EB=EF+4AE/5 時 整流效率為0.88。 第三圖係說明本發明熱整流器包含三個量子點狀況 下’不同ΓΑ1之熱流、微分熱導及熱功率（Thermal power) 與AT之間的關係。本實施例中，三個量子點分別為量子點 A、量子點B及量子點C，且量子點A位於子點B及量子 點C中間。量子點A的裸能階修正係數ηΑ為丨 Γα2·Γα1)/(2Γ) |，用以反應量子點位置在不對稱穿遂率下 的交互作用。穿隧率分別為量子點Α、量 子點Β及量子點C的基態能階分別為ea=Ef-AE/5、 ΕΒ=ΕΡ+2ΔΕ/5及EB=Ec+4AE/5。量子間彼此的庫倫交互作用 為 UAc=UBA=15kBT〇、UBC=8kBT〇。Uc=30kBT〇，其餘參數與 兩量子點的狀況相同。請參考第四A圖，當ΓΑ1為〇時， 熱整流效應較為顯著。熱流Q在ΑΤ=-30Γ時為〇.〇68Qg係較 小的，但在ΔΤ=30Γ時為0.33 Q〇係大的，並可得出整流係 數ηςί為0.79。然而’ ΓΑ1為0時的熱流太小。當當Γαι為 0.1Γ時，熱流Q在ΔΤ=_30Γ時為i.69Qg，在ΔΤ=30Γ時為 5.69 Q0 ’可得出整流係數％為〇 69。由此可知，當ΔΤ<〇 時，ΓΑ1愈小則熱流愈小。進一步言之，量子點a的阻擋效 果對於整流效應係相當重要的。如第三B圖所示，可以非 常明顯地發現在ΓΑ1=0.1Γ、ΓΑ2=1.9Γ的情況下，看到負微 分熱導的產生。而當ΓΑ1=ΓΑ2=Γ時，微分熱導係對稱的。 熱功率與ΔΤ的如第三圖C所示，圖中除了在穿隧率對 稱條件的曲線以外，熱功率都表現出一個高度不對稱的行 201131841 為。根據熱功率的值，電化能eAV可以是非常大的。因此， 由電化能eAV造成的量子點能階之改變係非常重要的。為 了進一步說明，請參考第四圖。第四圖係說明具有不同能 階之量子點C的熱流、微分熱導及熱功率與ΔΤ之間的關 係。第四圖所中’ Γαι=〇、、UBc=8kBT〇、ηΑ=〇·3。其他參數 與第三圖之實施例相同。實線代表所產生的化學電位勢eAV 造成量子點A能階的偏移，而虛線則代表沒將此效率考慮 進去的情況，其中能量偏移的大小為ηΑΔν/2。可明顯得知， 因為AV造成的量子點能階偏移造成熱流的減少。雖然在 Ec=EF+AE/5及Ec=EF+3AE/5的狀況下，熱流皆顯示出整流 效應，但熱功率卻顯示出不同的結果。請同時參考第三圖C 及第四圖C，可得知熱流與電化能AV並非成一線性函數。 由上述說明可知，三量子點系統的整流效率，其效率隨著 溫差越高而整流效率越好。然而，整流效率tIq與量子點C 的基態能階的影響差異並不大。 綜上討論，比較具有兩量子點與三量子點之熱整流 器，可得知熱整流效率在兩種狀況下係幾乎相同的。然而， 在具有三量子點之熱整流器中，熱流的強度係明顯增加 的。同時，可得知本發明熱整流器之整流效應係與量子點 及電極間的耦合、電子庫倫交互作用及不同量子點能階的 差異有關。 由上述敘述可知，本發明實為一新穎、進步且具產業 實用性之發明。雖然本發明已以較佳實施例揭露如上，然 其並非用以限定本發明，任何熟悉此技藝者，在不脫離本 發明之精神和範圍内，當可作各種之更動與潤飾。 13 201131841 【圖式簡單說明】 第一圖係例示說明本發明熱整流器之基本結構。 第二圖係說明本發明熱整流器包含兩個量子點狀況 下，熱流、平均佔據率及微分熱導。 第三圖係說明本發明熱整流器包含三個量子點狀況 下，不同ΓΑ1之熱流、微分熱導及熱功率與ΔΤ之間的關係。 第四圖係說明具有不同能階之量子點的熱流、微分熱 導及熱功率與AT之間的關係。 【主要元件符號說明】 100 熱整流器 101 第一電極板 102 第二電極板 103 絕緣層 104 量子點 105 真空層Heat transfer at S 9 201131841. 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 electronics, the thermal rectifier 100 is considered to be open. At the same time, by calculating equations (1) and (2), the required AV and heat flow can be obtained. The second figure illustrates the heat flow, average occupancy, and differential thermal conductance of a 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 Ea and Eb, respectively. Εα=Ερ_ΔΕ/5 ′ and ΕΒ=ΕΡ+αΒΔΕ, where the expression of the α Β system between 0 and 1 〇 is expressed in the basic unit Q〇, where Q〇=r2/(2h). The Coulomb interaction inside the quantum dot is U corpus 30kBT〇, and the Coulomb interaction between quantum dots is UAB=15kBT〇. The piercing rate of the quantum dot A to the first electrode 101 is ΓΑ1=0, and the piercing rate of the quantum dot Α to the second electrode 102 is ΓΑ2=2Γ. The piercing rate of the quantum dot Β to the first electrode 101 is ΓΒ1 = Γ, and the yield of the quantum dot Β to the second electrode 102 is ΓΒ2 = Γ. kBT〇 is equal to 25Γ. Γ is the average wear rate of each unit, expressed as Γ=(ΓΑ2+Γαι)/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 equation can be derived: Q/yB^( 1 -Nb) [(1 -2NA)( EB-EF)f21 (Eb) +2NA(EB+UAB-EF)f21(EB+UAB)] (3) where NA and NB are the average occupancy of quantum dots A and B, respectively, and γΒ is the quantum dot The transmission factor, f21 is the first electrode Fermi distribution function minus the Fermi distribution function of the second electrode. 201131841 The second A graph shows the relationship between the heat flow and the temperature difference. The ground state energy levels of the equivalence sub-points are ΕΡ+2ΔΕ/5 and 4ΔΕ/5, respectively. It can be found that when the EB is closer to the EF, the equation (3) is used. The greater the difference from the actual calculated heat flow, the less effective the simplified calculation is, but the heat popularity it presents is still somewhat accurate. Therefore, the use of the equation (3) is quite convenient for understanding the thermal rectification behavior. As shown in the second graph B, the electron occupancy rate Na of the quantum dot A produces an asymmetrical behavior for ΔΤ, which is due to the fact that the quantum dot left and right tunneling rates ΓΑ1=0 and ΓΑ2=2Γ are very asymmetrical. φ The second C diagram illustrates the differential thermal conductance, the basic unit of which is Q〇kB/r. As can be seen from the figure, the change in EB is not significant for the rectification effect of the thermal rectifier 100. The differential thermal conductance is approximately proportional to ΔΤ at -20Γ<1ίΒΔΤ<20Γ. 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 ΕΒ+υΑΒ resonant channel is too high compared to the EF system, the energy is generated by the EB resonant channel. The sign of heat flow Q is determined by f21 (EB), where f21 (EB) is related to Coulomb interaction, penetration rate and quantum dot energy level. The rectification effect of heat flow Q is mainly determined by 1-2Na, thus indicating that the energy level of quantum dot A needs to be smaller than that of EF and the coulomb interaction between quantum dots. When ΔΤ < 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 equation: 11 201131841 ncr(Q(AT=30T)- IQ (ΔΤ=-30Γ) I )/Q(AT=-3〇r) When EB=EF+2AE/5, the rectification efficiency is 0.86. The rectification efficiency is 0.88 when EB = EF + 4AE/5. The third figure illustrates the relationship between the heat flow, the differential thermal conductivity, and the thermal power of the thermal rectifier of the present invention containing three quantum dots in different states. 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 ηΑ of quantum dot A is 丨 Γα2·Γα1)/(2Γ) |, which is used to reflect the interaction of quantum dot positions at asymmetric cross-penetration rates. The ground state energy levels of the quantum dot 量, the quantum point Β, and the quantum dot C are ea=Ef-AE/5, ΕΒ=ΕΡ+2ΔΕ/5, and EB=Ec+4AE/5, respectively. The Coulomb interaction between the quantum is UAc=UBA=15kBT〇, UBC=8kBT〇. Uc=30kBT〇, the remaining parameters are the same as those of the two quantum dots. Please refer to the fourth A picture. When ΓΑ1 is 〇, the thermal rectification effect is more significant. When the heat flow Q is ΑΤ=-30Γ, it is 〇.〇68Qg is small, but when ΔΤ=30Γ, it is 0.33 Q〇, and the rectification coefficient ηςί is 0.79. However, the heat flow when ΓΑ1 is 0 is too small. When Γαι is 0.1Γ, the heat flow Q is i.69Qg at ΔΤ=_30Γ, and 5.69 Q0 ’ at ΔΤ=30Γ, and the rectification coefficient % is 〇69. From this, it can be seen that when ΔΤ < ΓΑ, the smaller the ΓΑ1 is, the smaller the heat flow is. Further, 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 ΓΑ1 = 0.1 Γ, ΓΑ 2 = 1.9 ,, the generation of negative differential heat conduction is seen. When ΓΑ1=ΓΑ2=Γ, the differential thermal conductivity is symmetrical. The thermal power and ΔΤ are shown in Figure C. In the figure, except for the curve of the tunneling rate symmetry condition, the thermal power shows a highly asymmetric line 201131841. The electrochemical energy eAV 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 eAV is very important. For further explanation, please refer to the fourth figure. The fourth figure illustrates the relationship between heat flow, differential thermal conductivity, and thermal power and ΔΤ for quantum dots C of different energy levels. In the fourth figure, ' Γαι=〇, UBc=8kBT〇, ηΑ=〇·3. Other parameters are the same as in the embodiment of the third figure. The solid line represents the chemical potential potential eAV 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 Α Δν/2. It is apparent that the quantum dot energy level shift caused by AV causes a decrease in heat flow. Although the heat flow shows a rectifying effect under the conditions of Ec=EF+AE/5 and Ec=EF+3AE/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 AV 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 tIq and the ground state energy level of the quantum dot C is not large. In summary, comparing thermal rectifiers 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 rectification 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, progressive, 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. 13 201131841 [Simple description of the drawings] 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 a 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 of Δ1 in the thermal rectifier of the present invention containing three quantum dots. The fourth figure illustrates the relationship between heat flow, differential thermal conductivity, and thermal power and AT with quantum dots of different energy levels. [Main component symbol description] 100 thermal rectifier 101 first electrode plate 102 second electrode plate 103 insulating layer 104 quantum dot 105 vacuum layer