Nanoscale thermoelectric devices may be considered as new types of devices which may be embedded into integrated chip set to assist the stability of devices by converting the accumulated waste heat into useful electric energy.
There has been ever increasing interest in the thermoelectric properties in nanojunctions. In addition, the experimental measurements of Seebeck coefficient in molecular nanojunction are presented recently, that is the principal motive for our theory calculation1,2,3 of molecular nanojunction. Because the Seebeck coefficients are relevant not only to the magnitude but also to the slope of density of states (DOSs), the Seebeck coefficients can reveal more detailed information about the electronic structures of the materials in nanojunctions beyond the conductance measurements can provide. The Seebeck coefficients have been applied to explore the electronic structures of molecular junctions using functional substitutions for the bridging molecules. Theorists have proposed using the gate fields and external biases as a means to modulate the Seebeck coefficient in nanojunctions.
1-1 Thermoelectric effects
1-1-1 Thermoelectric figure of merit
In 1912, Altenkirch4,5 introduced the concept of thermoelectric figure of merit when he showed that good thermoelectric materials should possess large Seebeck coefficients, high electrical conductivity to minimize Joule heating and low thermal conductivity to retain heat at the junctions that will help maintain a large temperature gradient. Ioffe in 19576 described the quality the efficiency of thermoelectric materials using the figure of merit as7
σ
κ κ
where S is Seebeck coefficient3,8, σ is the electrical conductivity, κ is electron thermal conductivity, κ is phonon thermal conductivity and T is average temperature in the source-drain electrodes. The ideal thermoelectric material would have a large S, a large σ and a small κ and κ. Increasing the electrical thermal conductivity usually leads to a simultaneous increase in the electrical heat conductivity. Therefore, how to enhance ZT for thermoelectric materials is a very challenging problem.
1-1-2 History of thermoelectric effects
There are three reversible thermoelectric effects in physics: Seebeck effect, Peltier effect and Thomson effect. The history of them was described respectively as below.
When two ends of a wire are held at different temperatures, a voltage develops across the two sides. This effect is known as the Seebeck effect , which was discovered by Seebeck in 1821 and published in 18229.
The Seebeck coefficient can be defined as the temperature gradient of the current will carry thermal energy so that the temperature of one end of the wire decreases and the other increases. The Peltier coefficient is defined as the heat emitted per unit time per unit current flow from conductor 1 to 2. Therefore, this heat is directly proportional to the current passing through the junction as
below:
where is the heat current carried by current . The Peltier effect is often overwhelmed by irreversible Joule heating, which also originates from electronic current.
The Thomson effect was predicted in 1854 and found experimentally in 185611. The Thomson effect occurs when a current flows across two points of a homogeneous wire having a temperature gradient along its length and heat is emitted or absorbed in addition to the Joule heat. The Thomson coefficient µ is positive if heat is generated when positive current flows from a higher temperature to lower temperature.
µ
The three thermal-electrical properties provide the basis for modern direct energy conversion devices and their exploitation has been the subject of considerable research.
1-2 Experimental findings
Thermoelectric effects were observed long time ago. The macroscopic and microscopic models have been well developed and have been able to successfully explain the thermoelectric properties in the bulk materials. In the past few decades, thermoelectricity has gained renewal interests due to the progress in growing micro and nano structures, such as quantum well, super lattice, and quantum dot. Small structure can significantly alter the features of density of states by changing the dimensionality. Thus, it leads to novel thermoelectric properties beyond the bulk materials. The efficiency of energy
conversion could be enhanced due to the enhancement of the Seebeck coefficient by small structures in materials.
Although extensive researches have been made on electron transport in the nanoscale junctions, the thermoelectricity in molecular junctions has never been measured until very recent. In 2007, Prof. Majumdar’s12,13,14 group at UC, Berkeley has measured the Seebeck coefficients in a single-molecule junction and demonstrated the capability to fabricate the thermoelectric molecular devices. These experiments open a new era to study the thermoelectric effects at atomic level.
Majumdar’s experimental setup is shown schematically in Fig.1 [12].
Fig. 1. Schematic description of the experimental set up based on an STM break junction. Molecules of BDT, DBDT, or TBDT are trapped between the Au STM tip kept at ambient temperature and a heated Au substrate kept at temperature ∆T above the ambient. When the tip approaches the substrate, a voltage bias is applied and the current is monitored to estimate the conductance. When the conductance reaches a threshold of 0.1 G0, the voltage bias and the current amplifier are disconnected. A voltage amplifier is then used to measure the induced thermoelectric voltage, ∆V, and the tip is gradually pulled away from the substrate. [12]
The result they get was: Seebeck coefficients is independent of the number of molecules is shown in Fig.2 [12], the length dependence of molecular junction Seebeck coefficients is shown in Fig.3 [12], and Seebeck coefficients reveal more detailed information about the electronic structures of the molecule sandwiched in the nanojunctions beyond what the conductance measurements can provide is shown in Fig.4 [12].
Fig. 2. (A) A plot of the thermoelectric voltage measured as a function of the tip-sample distance when a temperature differential ∆T= 20 K is applied (Au tip at ambient and substrate at ambient + 20 K). The blue curve is obtained when a Au-BDT-Au junction is broken. The red curve shows a control experiment performed on a clean gold substrate. (B) Typical thermoelectric voltage traces for tip-substrate temperature differentials of 0, 10, 20, and 30 K for Au-BDT-Au junctions. [12]
In Fig.2 [12], blue curve, they observed a constant thermoelectric voltage of about ∆V= -200 µV, which lasted until all of the molecules trapped in the junction broken away, suggesting that the Seebeck coefficient is independent of the number of molecules.
Fig. 3. Plot of measured junction Seebeck coefficient as a function of molecular length for BDT, DBDT, and TBDT. [12]
In Fig.3 [12], the experiment seems to show a linear dependence of the Seebeck coefficient on the molecular length. The Seebeck coefficients increase as the lengths of the molecules increase.
Fig. 4. Relating the measured Seebeck coefficient of Au-BDT-Au junction to the position of Fermi level. (A) theoretical prediction of the transmission function of a Au-BDT-Au junction plotted as a function of the relative position of the Fermi level of the Au electrodes with respect to the HOMO and LUMO levels. (B) The predicted Seebeck coefficient of a Au-BDT-Au junction as a function of the relative position of the Fermi level with respect to the HOMO and LUMO levels.
When the measured value of SAu-BDT-Au = +8.7 2.1 µV/K (blue band) is shown, it is clear that the Fermi level is 1.2 eV above the HOMO level. At this energy level, the transmission function is ! "". [12]
Measurements of the Seebeck coefficient in nanojunctions can provide insight into the electronic structure of the heterojunction. In Fig.4 [12], the Seebeck coefficient can be related to the transmission probability15 according to the following relation:
#$Г&
' ()* !
! +,-,. /
As shown in Fig.4 [12], the positive value of the Seebeck coefficient may imply that the Fermi level of BDT is closer to HOMO.