Electronic, Optoelectronic, and Thermoelectric Single‐Molecule Devices with Different Molecular Unit‐Length

Molecular devices have given impetus to the development of new electronic components. The transport process of organic molecules has a significant impact on device performance. Diketopyrrolopyrrole (DPPn, n = 1,2,3,4.) and derivative molecules have been widely explored due to their long‐range and efficient transport properties. In this paper, the electronic, optoelectronic, and thermoelectric properties of single diketopyrrolopyrrole molecular devices with different molecular units are investigated. By adjusting the bias voltage, the single molecular devices show a negative differential resistance effect, for which the reasons are given. Molecular orbital energy levels are regulated by gate voltages to enable conversion of conductivity. The transformation of molecular device functions in time‐varying alternating current transport is discussed in detail. Bias voltage regulation is performed for the molecular device optical response to produce better photocurrent, and finally the thermoelectric current of the device is also analyzed. This results reveal that single molecular electronic, optoelectronic, and thermoelectric properties are highly correlated with molecular unit‐length, which provides guidance for the development of molecular devices with different unit lengths.


Introduction
Molecular electronics is the product of the increasing demand for electronic components. Molecular electronics is the study of electrical properties at the atomic and molecular scales, using single or multiple molecules to build functional circuits or www.advelectronicmat.de possible. Reed [19] discovered the negative differential resistance (NDR) effect of a single molecule on a gold electrode at 60 K by substituting groups, which was the most representative molecular junction NDR experiment. Since the concept of molecular rectification was proposed, Metzager [20] and Ashwell [21] et al. have achieved single-molecule rectification effects in the laboratory, which is attributed to the asymmetric molecular structure. In addition to the discovery of the molecular transport phenomenon, researchers have also investigated the transport mechanism [22] and selected appropriate methods to regulate the transport process. Hong [23] reported the control of destructive and constructive quantum interference transport in molecular junctions by electrochemical gating. Tao [24] modulated the antiresonance of the molecule in the same way, achieving an increase in conductance by two orders of magnitude. Several research works have also demonstrated that gating control is an effective strategy to regulate the conductance of molecular junctions. [25] The effect of vibration is indispensable in the process of electron transport. [26] Gaudioso [27] discovered the vibration-mediated NDR effect. Guo [28] et al. reported the vibration-assisted electron tunneling for the supramolecular dimer. Thoss [29] studied electron vibrations in molecular junction transport theoretically. Ho reported single-molecule chemistry. [30] Molecular electronics have been booming in recent years because of the researchers' efforts. Molecular electronics is the basis for research at the molecular level, but it should not be limited to pure electronics. [31] The molecular optoelectronic devices that use the interaction between molecules and light are functional devices, such as photovoltaics, optical switching, photodetectors, field-effect transistor, etc. Under the 520 nm irradiation, ITO-Au device with molecules consisting of a porphyrin chromophore and a C 60 electron acceptor can realize long lived charge separation state. [32] In 2005, the results of the changing conductance of dithiophene molecules in the presence of a UV light source were considered useful for the preparation of photosensitive molecular switches. [33] Other optoelectronic phenomena have been extensively studied at the single-molecule level include photoconductivity, [34] electroluminescence, [35] etc. In addition to the field of optoelectronics, the field of thermoelectricity at the single molecule level has been extensively studied. Reddy [36] et al. measured the thermal voltages at the ends of single-molecule junctions and calculated the Seebeck coefficients. Later, Venkataraman's group [37] proposed to measure the thermoelectric current to obtain the Seebeck coefficient of the molecular junction. The improvements in the measurement of Seebeck coefficients are of particular interest in the study of thermoelectric effects at the molecular level. Molecular devices, like other electronic components, will be used in a variety of situations in the future.
To achieve efficient transport of molecular junctions, molecules with repeating conjugated units are a better choice. Diketopyrrolopyrrole [38] (DPP n , n = 1,2,3,4.) oligomers are characterized by a small band gap and high conductivity, which have been synthesized and proved by Zhang [39] et al. to have highly efficient long-range charge transfer properties on the DPP backbone. The significant repetitive NDR effects of DPP and its derivatives have been reported. [40] In this paper, we investigate the electronic, optoelectronic, and thermoelectric properties of unit-length dependent DPP n molecules theoretically. First, electrical properties such as current-voltage (I-V) characteristic curves, conductance, transmission coefficient, the projected density of states (PDOS), etc. The equilibrium and non-equilibrium states are explained separately, and the transport of alternating current (AC) is discussed in this paper. Second, the optical properties such as absorption spectra, dielectric functions, optical response, etc are also studied. Finally, the thermoelectric current of molecular devices is discussed. Our results are instructive for the research of the DPP n derivatives transport properties, demonstrating the excellent optoelectronic and thermoelectric properties of these molecules and establishing a theoretical platform for the design and manufacture of molecular devices.

Method
The Au is a reliable metal electrode material for which high chemical stability and electrical conductivity as well as its high anchoring rate with molecular groups. The model of the twoprobe device is based on experimental work, [39] and is constructed by Device Studio software, where probes were formed by Au atoms. DPP n of different unit-length were connected by the sulfhydryl group in the middle of the Au electrode, as shown in Figure 1. In density functional theory (DFT) studies of molecular devices, both end electrodes are treated as semiinfinite length periodic structures, in this case of 1D gold nanowire electrodes. In order to isolate the interactions between the electrodes, a buffer layer between the two electrodes is required. We have tested the structure and achieved a reasonable buffer layer for DPP 4 (the maximum number of units in calculations) and have applied this specification to smaller unit molecules to ensure consistency of variables in the theoretical calculations.
The geometric structure of all molecules was optimized by Gaussian16 [41] software with B3LYP functional. [42] The properties of the device were calculated by first-principles quantumtransport software Nanodcal, [43] where DFT was applied within the non-equilibrium Green's function (NEGF) method. [44] The GGA_PBE96 electron exchange-correlation was used in the self-consistent process, and the cut-off energy was set to 100 Hartree. Based on the self-consistent calculation, the device properties were studied.

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The electric current (I) and conductance (G) are calculated by Landauer formula, [45] which are expressed as, where V β is the bias voltage applied on lead β.
Linearly polarized photocurrents with or without bias voltage state are calculated respectively. Photocurrent of photon polarization type is determined by the following formula, where θ is polarized angle, e 1 and e 2 denote unit vector. The photocurrent moving into a lead (e.g., lead L) is calculated as [46] Γ ( ) where Γ L denotes interaction between the central scattering region and the left lead. Finally, the photocurrent calculated by Nanodcal is defined as [47] = ω ( ) ( ) In addition to the above case of direct current (DC) circuit, conductance under AC voltage is also studied. The AC conductance  G G formed by dynamic conductance and displacement current, which can be written as [48] where the subscripts α, β denote the leads, and ω denotes the AC frequency. The Fermi Dirac temperature is involved the DFT calculations. The thermoelectric current is calculated by Landauer formula. The thermoelectric current is driven by the difference in the Fermi distribution due to the electrode temperature difference. [45] For the case of temperature difference ΔT = T L − T R , the molecular device thermoelectric current formula is also derived from the Landauer formula [44] and is shown below, where τ σ (ε) is the transmission coefficient, f is the Fermi distribution function at T temperature.

Figure 2a
demonstrates the molecular unit-length dependent I-V curves. It is found the distribution of I-V curves at positive and negative bias voltage is generally symmetric. With the increase of bias voltage, the current of all molecules increases linearly and then decreases after reaching the first peak, NDR effect is manifested. Figure 2b shows the zoom of Figure 2a, i.e., the I-V curves from −0.5 to 0.5 V. Given the general symmetry of current values at positive and negative bias voltage, only the currents at the positive bias voltage are analyzed. It is found that the currents decreased with the increase of molecular units, and from 0 to 0.2 V, the current and voltage are positively correlated, while from 0.25 to 0.5 V, the NDR effect can be obtained, and the peak value decreases with the increase of unit-length, which indicates the NDR effect is getting weak. Figure 2c is bias voltage-dependent conductance, which reflects the ability of electron transport, and the tendency of I = σV in the DC circuit. In the case of small molecular unitlength (n ≤ 2), the largest conductance is within −0.5 to 0.5 V, while in the case of large molecular unit-length (n ≥ 3), the conductance within −0.5 to 0.5 V is smaller than those at large bias voltages. Also, around ± 0.5 V, there is the smallest conductance, which reflects the change in transport mode from small to large unit-length. Detailed molecular unit-length dependent conductance within −0.5 to 0.5 V can be seen in Figure 2d. The conductance value of the molecule decreases as the unit-length increases. Especially for the case of four units, it is an almost broken circuit.
In addition to the case of the non-equilibrium state, the case of the equilibrium state is also described in detail. The equilibrium state can be interpreted by molecular unit-length dependent density of states (DOS), PDOS, and transmission spectrum, see Figure 3. PDOS is the projection of DOS onto the atom, and the size of the color bar represents the number of states, which is the same as the X-axis expression of DOS. The X-axis of the transmission spectrum is the transmission coefficient, which represents the probability that an electron will travel through the molecule to the drain. DOS can provide the probability of electron transport. For all unit-length molecule devices, there are transmission peaks at the Fermi level, and with the increase of unit-length, the number of transmission peaks increased, but the peaks are narrow and sharp. The uniform distribution of PDOS on the atoms can determine the ballistic transport from 0 to 2 eV in Figure 3. Transmission spectra in Figure 3 demonstrate that the resonant transmission peak values increase with the increased unit-length from 0 to 2 eV, and the peaks become narrow, and the area of transmission peaks become narrow simultaneously; which reveals the channel of electrons transportation is increased, but need more kinetic energy, and the current of transport is decreased and difficult. The numbers of transmission peaks are significantly changed from 0 to 2 eV in Figure 3, which reveals that transmission spectral properties are determined by the properties of inter-unit, not by that of intra-unit. The physical mechanism for the increase in unit-length is to increase the width of www.advelectronicmat.de the effective potential, see Figure 4. The number of transmission peaks is little changed from −2 to 0 eV in Figure 3, and PDOS demonstrates that DOS is localized in this region, which depresses the ballistic transport, revealing that transmission spectral properties are determined by the properties of intraunit, not by that of inter-unit in the region from −2 to 0 eV. Thus, the DPP n are the semiconductor with electron transport.
It is found that with the increase of unit-length, the width of effective potential is increasing, see Figure 4. Figure 4a demonstrates that the potential of thiophene at the outer part of the molecule is larger than that of pyridopyrazine at the inner part of a molecule. There is a peak at the central in Figure 4b, resulting from the single bond between two adjacent thiophenes, while the number of such peaks increases to two and three as the units of the DPP n increase to three and four, respectively, which reveals that this single bond decreases the ability of the electron transport. Since dV = W · dE = W · dQ/ε, where ε is the dielectric constant, one can get the barrier capacitance according to , thus, with the increase of unit-length, the width of potential (W) is increased, and then the barrier capacitance C n is decreased. Also, when the molecular unit-length is increased, one can consider the series capacitance of each unit, where C 1 denotes the molecular capacitance with one unit. Molecular charge distribution in electron transport in real space can be seen in Figure 5, which manifests the charge distribution in unit-length dependent characteristics. There is no charge on the single bond connecting two adjacent thiophenes. Within each unit, the charge is not uniformly distributed, and there is more charge accumulated on pyridopyrazine than on thiophene. The charge distribution in electron transport in real space supports the above conclusions of barrier capacitance. The barrier is around U≈ 2.0 eV, which can be seen in Figure 4. The accumulated charge in one unit is 84e/Bohr 3 , thus the barrier capacitance = =1.78 fF, where C denotes capacitance of monomer unit. The capacitance with a unit number (n) can be estimated with The charge distribution in transport in real space reveals that this unit-length dependent single molecule may be considered as capacitance, inductance or resistance in AC circuit.
The AC conductance is the complex function with σ = σ 1 + iσ 2 , which can describe the transport properties in AC circuit. Since the direction of current in an AC circuit varies with time, the conductance value of varies with the frequency (ω) of AC. The AC conductance of molecular unit-length with varying frequencies can be seen in Figure 6. σ 1 describes energy dissipation in the transport process. The value of σ 2 can reveal the electrical properties of resistance (σ 2 = 0), capacitance (σ 2 < 0) and inductance (σ 2 > 0), and when ω → 0, the displacement current will have no contribution, i.e., DC limit. When ω = 2.9 × 10 8 MHz, σ 2 = 0, it is a resistance device; when 0 < ω < 2.9 × 10 8 MHz, it is a inductance device; and 2.9 × 10 8 < ω  Figure 6e, while the region of inductance is slightly decreased from 0 < ω < 2.9 × 10 8 MHz to 0 < ω < 2.4 × 10 8 MHz; and there is also a resistance region around 6.0 × 10 8 MHz for molecule with 4 units. This shows that the conversion between capacitance and inductance can be achieved by changing the molecular unit-length in the low frequency range.
The molecular unit-length dependent currents and conductance in Figure 2 are significantly decreased when the bias voltages are −0.5 and 0.5 V, which can be interpreted by the bias-voltage dependent transmission spectra of one unit (DPP 1 ) molecule, see Figure 7a. For simplicity, only positive bias voltage is discussed. With the increase of bias voltages, the integration area of transmission spectra is gradually increased when the bias voltages are increased from 0 to 0.25 V, therefore the current is gradually increased. When the bias voltage is 0.25 V, the peak area reaches the maximum in the bias window, which is corresponding to the maximum current value; and then the integration area of transmission spectra gradually decreases in the region of bias voltages from 0.25 to 0.5 V, and thus current is gradually decreased. At the bias voltage of 0.5 V, it is found that the integration area of the transmission spectrum is significantly decreased, which results in a decrease in current. Figure 7b shows the molecular unit-length dependent transmission spectra at a bias voltage of 0.5 V, which demonstrates that as the increase of unit-length, the transmission peaks are narrower and sharper, and the integration area of the transmission spectrum is gradually decreased, so the current is gradually decreased. The bias voltage-dependent transmission spectra in Figure 7a can also be used to analyze the physical mechanism of the NDR effect. All the unit-length molecules are of NDR effect in Figure 2a,b. With the increase of bias voltages from 0.25 to 0.5 V, the integration area of transmission spectra is gradually decreased, which is the cause of the NDR effect.
In the bias voltage region in Figure 7, one can consider DPP 3 and DPP 4 as quantum electric capacity, due to the coulomb  Figure 7d. It is found that the gate from 5 to 10 V is a better choice; when the gate voltage is increased to 15 V, the current is significantly decreased for the case of large unit length, due to the mismatch between molecular energy level and metal Fermi level. The negative gate voltage is added, and the energy level of the molecule decreases and repels electrons. When the gate voltage is −5 V for the molecules with 2-4 units, the energy level of molecules is matching the metal Fermi level. In the case of a molecule with one unit, it is found that the current is not increased, because electrons are missing. The transmission and DOS spectra can be used to interpret the current changes caused by gate modulation. The molecular state can be modulated by the gate voltage, thus, the transmission coefficient and DOS of DPP n (n = 1,2,3,4.) were analyzed at different gate voltages. The transmission coefficient curves and DOS curves at different gate voltages show a similar behavior.
The magnitude of the currents at different gate voltages in Figure 7d is determined by the integration area within the same bias window, see Figure 8, where the bias voltage is 0.5 V. It can be seen that there is different trend between DPP 1 and the other unit-length molecules in Figure 7d and Figure 8. For DPP 1 , a gate voltage of 0 V is used as a reference. By increasing the positive gate voltage, the transmission coefficient curves and DOS curves move to the negative direction along the X-axis, with the positive correlation between moving distance and the magnitude of the gate voltage. Thus, the net charge can be increased by positive gate voltages in the device, and energy levels of molecular orbital decrease. There is opposite tendency by increasing negative gate voltages. For the other DPP n with larger unit-length, the transmission coefficient curves and the DOS curves move toward the negative direction along X-axis by increasing the gate voltage, obtaining the maximum value of current. By further increasing the gate voltages, in contrast, the current gradually decreases.

Optoelectronic Single-Molecule Devices with Different Molecular Unit-Length
The σ is relative to the dielectric function (ε ε ε = + i )  Table S1 (Supporting Information). The ε 1 and ε 2 stand for permittivity (ability to store energy) and electroconductivity, respectively. The ε 1 also describes the contribution of displacement current to the magnetic field, and ε 2 stands for the contribution of conducting current to the magnetic field. Also, ε , the real part is phase modulation (dispersion), and the imaginary part is amplitude modulation (loss or gain), and δ is the loss angle. On the electronic resonant transition (Figure 9a), ε 1 is firstly suddenly increased and then dropped; meanwhile, the peak of ε 2 occurs, see Figure 9b,c. On the optical resonant absorption, σ 1 is increased, and thus ε 2 is also increased, which results in strong optical absorption, see Figure 9a. The calculation of optical properties is based on the frequency-dependent dielectric function ε (ω) = ε 1 (ω) + iε 2 (ω), and the absorption coefficient can be calculated by, The dark current is relative to the σ 1 and ε 2 , and the photocurrent is relative to the σ 2 and ε 1 , see Table S1 (Supporting Information). The relationship between photocurrent and dielectric function can be seen from Equation (10), where R is the normalized photocurrent, F ph is the photon stream, ε πσ ω = − 1 4 1 2 , a 0 is the Bohr radius, and more detailed interpretation can be seen from supporting information. The photocurrent is generated by the photogalvanic effect (PGE) [49] and the microscopic mechanism of PGE is the directed movement of free charges resulting from photogenerated exciton relaxation. A non-centrosymmetric structure irradiated by polarized light can produce a constant photocurrent. For the different unit-length molecules at resonant optical absorption peak, ε 1 is decreased, thus J ph is increased, according to Equation (10). Figure 10a demonstrates the polarization-angle dependent photocurrent with or without bias voltages and molecular resonant optical absorption. It is found that resonant absorption at 571 nm can increase the intensity of photocurrent, compared with non-resonant absorption at 650 nm. The photocurrent can obtain the largest value when 40 θ =°, which is determined by molecular dielectric function. Therefore, both dielectric and conductance are relative to the polarization-angle of light, determinated by the angle of pyridopyrazine in the molecule. To increase the photocurrent, small bias voltages of 0.1 and 0.5 V are added. It is found that at resonant optical absorption, the photocurrent in Figure 10b can be significantly increased by 10 3 times compared with that in Figure 10a without the bias voltage. Note that the bias voltage of 0.5 V is suitable, since the dark current and conductance are very small in Figure 2b and Figure 2d, respectively. On the non-resonant optical absorption, the photocurrent cannot be manipulated well by bias voltage (see Figure 10c), since the increase of photocurrent intensity is very small compared to resonant optical absorption. The reason

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is that on the non-resonant optical absorption, ε 1 is large; and thus, the photocurrent is small, according to Equation (9,10). For the molecule with a monomer unit, it is found that there is no photocurrent when adding bias voltage or considering optical resonant absorption, see Figure 10d,e. The reason can be interpreted by: For the molecule with one unit, C 1 is too large to occurrence of photocurrent, while for the molecule with more units, C n is significantly decreased, according to Equation (8), and photocurrent can be detected. The electrostatic energy ε ≡ and with the increase of molecular unit-length, the capacitance is decreased, and thus ε c(n) can be accordingly increased, and much larger than k B T, the larger photocurrent can be produced. When molecular vibrations are considered in I-V curves or conductance, there is also inelastic electron tunneling, except for elastic resonant electron tunneling. The inelastic electron tunneling can provide an additional tunneling channel, which can lead to a slight change in current. The two symmetric peaks around the two sides of the Fermi surface can be used to detect the single molecular structure. The vibration coupling (Raman scattering) can be observed by quadratic differential conductance (d 2 I/dV 2 ). Molecular vibration-resolved current has been successfully observed experimentally. [26e,50] Figure 11a shows the d 2 I/dV 2 , which demonstrates that there are large variations in the region from 0.25 to 0.4 V, and in the region, there are several stretching vibrations of H (within 3000 to 3300 cm −1 ), see Figure 11b, which can provide inelastic electron tunneling for current, and molecular vibration-resolved current can be observed. The Raman spectra of neutral and negative charged (−1 e) can be seen in Figure 11c. The electron can result in large changes in Raman spectroscopy, for example, the Raman peak disappears at 1572 cm −1 , several other peaks disappear, and several Raman peaks occur.

Thermoelectric Single-Molecule Devices with different Molecular Unit-Length
The thermoelectric effect is more sensitive to change in unitlength when the tunneling transport of electrons occurs. [51] In addition, a linear increase in thermal power with increasing molecular unit length was reported by Pauly. [52] The thermoelectric effect of a molecular device can be controlled according to the unit-length. The Seebeck coefficients of molecular device with different unit-length are shown in Figure 12. The X and Y axes are chemical potential and temperature, respectively. It can be seen from the Figure 12, the Seebeck coefficient of molecular devices of different unit-length gradually achieve extreme

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values with the decrease of temperature in the range of −2 to -1.7 eV. The Seebeck coefficient is an indicator of the thermoelectric ability of a device, and the thermoelectric current of the device is further studied.
The temperature difference between two electrodes allows the circuit to form a thermoelectric potential, which drives the thermoelectric current. Figure 13 shows the thermoelectric current for the molecules with different molecular unit-length at  www.advelectronicmat.de different temperature differences (ΔT), where the room temperature at one electrode is fixed at 300 K, (ΔT(K) = T (Fixed) -T (Changed), T (Fixed) = 300 K) and the temperature is changed at another electrode. The thermoelectric current value of the molecular device varies approximately linearly with the temperature difference. It is found that the case of a molecule with two units is of maximum thermoelectric current, and the molecular with four units is of minimum thermoelectric current. When the ΔT between the two electrodes is 250 K, that is, 50 K for the other electrode, the molecular devices with different unit-length obtain the maximum thermoelectric current. The DPP n (2,3,4.) molecular device exhibit a certain quantum coherence in the transport, and with the increase of the unitlength, the thermoelectric current decreased. For DPP 1 , the finiteness of the molecular unit-length affects the conduction in the transport process, so it is a better choice to use the DPP 2 molecule to prepare molecular thermoelectric devices.

Conclusions
DPP n molecules and their derivatives are of properties due to their repeating conjugated units. The unit-length dependent electronic, optoelectronic, and thermoelectric properties of DPP n molecules are discussed in detail. The transport of molecular devices in DC and AC circuits are discussed separately; the DPP n have NDR effect in multiple bias voltage regions. The bias voltage can achieve the regulation of photocurrent value; in addition to this, gate voltage control is an effective strategy in the regulation of molecular devices, and the performance of device thermoelectric currents shows excellent thermoelectric properties, etc. The results show the DPP n molecular properties are greatly dependent on the unit-length.
In our calculations, we have made a more ideal molecular device without considering other background effects such as substrate, electrode material defects and impurities. The substrate configuration on the gate voltage effect in gate voltage modulation, the surface plasmons effect produced by the metal electrode during molecular optical response, the strength of the electrode and molecular coupling, etc., which are beyond the reach of our current theoretical calculations and are subject to experimental verification. However, our theoretical work is a necessary supplement to the existing DPP n derivatives characteristics and provides insights into their application in NDR effect molecular devices, optical detectors, AC circuit molecular devices and thermoelectric devices, etc., offering directional guidance for the development and preparation of DPP n molecular devices.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.