We have performed first-principles calculations to investigate the electron transport and the thermoelectric properties in the amino-substituted (-NH2) and nitro-substituted (-NO) 1,4-benzenedithiolates based on the density functional theory (DFT) as described in the previous chapter. In this work, we have applied the source-drain biases and the gate voltages to explore I-V characteristics in the amino-substituted (-NH2) and the nitro-substituted (-NO) 1,4-benzenedithiolates molecular junctions.
Following the study of electronic transport properties, we proceed a step further to investigate the thermoelectric properties in the amino-substituted (-NH2) and the nitro-substituted (-NO) 1,4-benzenedithiolates molecular junctions. We perform comparative study on the Seebeck coefficient as a function of source-drain biases and gate voltages for various temperatures in the amino-substituted and the nitro-substituted 1,4-benzenedithiolates molecular junctions.
We find that the functional substitution of 1,4-benzenedithiolates molecular junctions may donate or retrieve electrons from the -orbital, and thus it may have influence on the conductance. For example, the amino-substituted 1,4-benzenedithiolates molecular junctions withdraw electrons from the -orbital and suppresses the conductance. In contrast to -NH2 substituted 1,4-benzenedithiolates molecule which retrieve electrons, the nitro-substituted 1,4-benzenedithiolates molecular junctions donate electrons to -orbital and create states closer to the current-carrying window such that the conductance is enhanced. Consequently, the I-V characteristics and the Seebeck coefficients in -NO substituted 1,4-benzenedithiolates molecular junctions display richer features in the I-V characteristics and the Seebeck coefficients due to theses -donating states.
We will discuss the electron transport and the Seebeck coefficients in section 3-1 and 3-2, respectively.
3-1 Electronic transport of single-molecule junctions
3-1-1 The effect of finite source-drain biases
Firstly, we investigate the current (I) and the differential conductance (dI/dVSD) as a function of source-drain biases (VSD) for the amino-substituted (-NH2) and the nitro-substituted (-NO) 1,4-benzenedithiolates junctions as shown in Fig.13. As shown in Fig.14, the density of states is very different according to the electron-retrieving and electron-donating natures of the amino-substituted and nitro-substituted systems.
In the -NH2 substituted system, the withdrawal of electrons does not contribute new state around the Fermi levels as shown in the left panel of Fig. 14. The Fermi levels remain sitting between the HOMO-LUMO gap. As a result, the conductance is small in the small bias regime with a value around 0.07 G0 (1 G0 77 S), which is comparable with the case without functional substitution (dI dV/ SD 0.12 G0). The functional substitution breaks the symmetry of the molecular junction and leads to asymmetric I-V curve. We find two peaks (34.7μS and 22.5μS) in the differential conductance at the biases 0.85V and -0.75V, respectively.
In contrast, the -NO substituted system donates electrons to the -orbital and create new states near the current-carrying energy window, formed between the left and the right Fermi levels. Consequently, the differential conductance in the small bias regime is greatly enhanced to 0.71 G0 due to more electrons with the energy within the current-carrying energy window. As shown in the right panel of Fig. 14, there are more electron states created near the current-carrying energy window. As the bias increases, these states may gradually enter the current-carrying energy window and cause richer features in the I-V characteristics. We observe two peaks (63.8μS and 70.2μS) in the differential conductance at the bias 0.05V and 1.0V, respectively.
Fig. 13. The current (left axis) and differential conductance (right) as a function of VSD in amino-substituted (-NH2) and nitro-substituted (-NO) 1,4-benzenedithiolates junctions.
Fig. 14. The density of states for various source-drain biases (VSD=-1.0,-0.4,-0.1, 0.01, 0.1, 0.4, 0.7, and 1.0) in amino-substituted and nitro-substituted junction. The left Fermi level μL (red lines) is set to be the zero of energy, and the right Fermi level μR (blue lines) defines VSD=(μR -μL)/e
The above calculations provide evidence that the resonant tunneling may exist in the nitro-substituted benzenedithiolates junction, in contrast to the non-resonant tunneling in the amino-substituted system. Our calculations show that the substitutions of valence orbital have the influence on the molecular conductance and the I-V characteristics. The conductance ofwithdrawal (-NH2) is lower than the conductance ofdonation (-NO) in the 1,4-benzenedithiolates molecular junctions.
3-1-2 The effect of gate voltages
As three-terminal field-effect transistor like devices are highly desirable, we also investigate source-drain conductance as a function of gate voltage when a small source-drain bias is applied. In Fig. 15, we compare the conductance of the -NH2
substituted and the -NO substituted 1,4-benzenedithiolates molecule junctions. In the -NH2 substituted system, the response of the conductance to the gate voltage is mild.
The small and featureless conductance stems from nonresonant tunneling, realizing that
the Fermi levels lie between the HOMO and LUMO gap. However, in the -NO substituted system, as the gate voltage varies from -1.18 to 1.18 V, the conductance decreases from 1.18 to 0.73 G0.
To explain why gate voltage can significantly modulate the source-drain conductance, we examine the DOSs for the various gate voltages, as shown in the inset of Fig. 16. At zero gate voltage, the energies between two Fermi levels open a current-carrying window. The -NH2 substitution withdraws electrons from-orbital and produces a large HOMO-LUMO gap. Conversely, the -NO substitution donates electrons to the -orbital and create new states around the Fermi levels. When we strengthen the resonant tunneling by shifting the position of the state peak toward the current-carrying window, we find that the change of donating system is obvious.
Considering the density of states for an -NH2 substituted 1,4-benzenedithiolates molecule junctions as shown in Fig.16, we observe that Fermi levels lie between the HOMO-LUMO gap. Thus, the dependence of the conductance on the gate voltage is weak. In contrast, we observe new states introduced by the -NO substitution in the 1,4-benzenedithiolates molecule junction. These states significantly enhance the conductance and improve the ability to modulate the conductance by the gate voltage.
At a gate voltage of −0.57 V, the central peak of state is between the left and right Fermi levels, and the conductance reaches a maximum. Conversely, a positive gate voltage shifts the position of the state peak away from the current-carrying window, and therefore, the source-drain conductance decreases.
Fig. 15. The source-drain conductance as a function of gate voltage in three-terminal geometry for NH2-substituted and NO-substituted 1,4-benzenedithiolates.
Fig. 16. The density of states for NH2-substituted (left) and NO-substituted (right) 1,4-benzenedithiolates in different gate-voltages.
3-2 Seebeck coefficient of single-molecule junctions
3-2-1 The effect of finite source-drain biases
In this subsection, we calculate the Seebeck coefficients as a function of finite biases, VB FR FL
e
. The Seebeck coefficient closely relates to the transmission function in the vicinity of the left and right chemical potential. According to Eq.(2.49), we have shown that the Seebeck coefficients depend on the magnitude and the slope of the transmission function at the left and right Fermi levels.
As shown in Fig.17 and 18, we plot the Seebeck coefficients and transmission functions as a function of biases for -NH2 and -NO systems. To observe these results finds several interesting phenomena that the transmission functions are influenced by the DOSs between the left and right Fermi levels. Especially, when significant states appear around the current-carrying window, the transmission function has significant change. The sign and value of Seebeck coefficients are influenced by the transmission probability around the Fermi levels.
However, the functional substitutions of 1,4-benzenedithiolates may donate or retrieve electrons from the-orbital, and thus have influence on the transmission function of molecular junctions. We explain the Seebeck coefficient of -NH2 and -NO systems as shown in Fig.17 and 18 for TL=TR=T by varying the source-drain biases VSD.
The contribution to the Seebeck coefficient is dominated by the transmission function in the vicinity of both the left and right Fermi levels from Eq. (2.49). In the
We can obtain some special points that for –NH2 system the Seebeck coefficients are close to zero at VSD=0.75V and 1.15V around. For example, at VSD=1.15V the peak position of the transmission function is located in the middle of the left and right Fermi
levels such that ( ) / ( ) /
L R
E E
E E E E
(from Eq.2.49), so the Seebeck coefficients are close to zero. Similarly, for -NO system we find the points such as VSD=0.4V and 0.6V around, and their Seebeck coefficients is close to zero.
Fig. 17. The Seebeck coefficient as a function of source-drain biases for the system of NH2-substituted
1,4-benzenedithiolates. The other graph expresses the probability of transmission under the distinct biases.
Fig. 18. The Seebeck coefficient as a function of source-drain biases for the system of NO-substituted 1,4-benzenedithiolates. The other graphs expresses the probability of transmission under the distinct biases.
3-2-2 The effect of finite gate voltages
Finally, we investigate the Seebeck coefficient as a function of gate voltages at small bias regime (VSD=0.01 V, where L R ). According to Eq.(2.51), we have shown that the Seebeck coefficients depend on the magnitude and the slope of the transmission function at the Fermi levels as shown in Fig 19 and 20.
For the amino-substituted (-NH2) system, the Seebeck coefficients vary in a small range when the gate voltage varies from -1.0 to 1.0 V. The influence of gate voltage on the Seebeck coefficients is weak as shown in Fig. 19. Although the transmission probability (as shown in Fig. 19) is not obviously affected by gate voltage, it can still modulate the Seebeck coefficients. We note the probability of transmission for VG=-0.4V and VG=1.02V. They have the bigger positive slopes ln ( ) / 0
E EF
E E
.
According to the Eq.19, we obtain the smaller negative Seebeck coefficient.
The nitro-substituted system is interesting to compare with the amino-substituted system. In contrast to the amino-substituted system, new states appear near the Fermi levels in the nitro-substituted (-NO) 1,4-benzenedithiolate system. These states can be modulated by the gate voltages, thus the change of Seebeck coefficientsas wshown in Fig. 20. The value of the Seebeck coefficient is determined by the slope and the magnitude of transmission probability. We illustrate this point by the following cases.
In this case there are some special points, and their Seebeck coefficients are close to zero. Such as around VG=0.25 V. At VG=0.25 V, the Fermi level align with the Seebeck coefficient is positive because ln ( ) / 0
E EF
E E
at VG=-0.82V.
Therefore, the Seebeck coefficients of molecular junction could change sign from positive value (p-type) to negative value (n-type) by applying the gate voltages and the source-drain biases. The electric current can carry the thermal energy. The direction of thermal current is opposite (along) the direction of thermal current for n-type (p-type) junction.
Fig. 19. The Seebeck coefficient in a three terminal geometry with VSD=0.01V for the system of molecular junction, NH2-substituted 1,4-benzenedithiolates. The gate field is applied in a direction perpendicular to direction of charge transport. The other graph expresses the probability of transmission under the distinct gate voltages
Fig. 20. The Seebeck coefficient in a three terminal geometry with VSD=0.01V for the system of molecular junction NO-substituted 1,4-benzenedithiolates. The other graph expresses the probability of transmission under the distinct gate voltages