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Modeling and simulation of molecular armchair graphene nanoribbons as a gas detector

Alireza Tashakori, Ali Rostami, and Mohammad M. Karkhanehchi

Open Access Open Access

Abstract

Optical detectors are essential for gas detection using optical technology. This study introduces an armchair graphene nanoribbon (AGNR) molecular optical gas detector with two conjugated molecular elements and a non-conjugated interface for gas detection using optical technology. The detector absorbs light and generates peaks in the current-voltage curve that correspond to gas concentration and the Raman frequency spectrum. The detector exhibits negative resistances controlled by input light frequency, suitable for high-frequency oscillators. Multiple gases can be simultaneously identified and monitored using the detector. The detector was analyzed using the non-equilibrium Green function method and offers high-speed, accurate selectivity, precise gas detection, and reproducibility with multiple electrical outputs.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Graphene is a two-dimensional semiconductor with a hexagonal honeycomb structure that has received much attention due to its unique electrical and magnetic properties [1–10]. Graphene nanoribbons (GNRs) are thin strips of graphene widely used in manufacturing electronics and chemical catalysts [11–16]. GNR edge energy band engineering is an area of great interest to researchers [16–20]. The two main groups of nanomaterials, armchair graphene nanoribbons (AGNR) and zigzag graphene nanoribbons (ZGNR), are classified based on the structure of the graphene edges. The ZGNR exhibits metallic properties due to the degeneration of the two-edge modes at the forming surface. At the same time, the AGNR can have both metallic and semiconducting properties depending on their width [21–24].

Advancements in nanotechnology and mechanical engineering of nanoscale materials have led researchers to develop molecular devices such as rectifiers, optical detectors, and single-molecule transistors [25,26]. Aviram and Ratner proposed a molecular ware in which the molecule showed rectification in its voltage-current curve, with much effort being made so far to realize it [27,28]. These wares use asymmetric contact-type structures, asymmetric gates, asymmetric edges, different conjugates at the electrodes, and asymmetry in the core position of the wares at the electrodes of asymmetric molecules to perform a detection operation [29–31].

Raman spectroscopy involves emitting single-mode light into a gas and detecting the scattered light with an optical detector. This scattered light contains several distinct frequencies, with the waves having the same frequency as the input light (known as Rayleigh scattering), which is typically filtered out. The remaining waves are called anti-Stokes and Stokes, corresponding to frequencies higher and lower than the incoming light. Each molecule has a unique Raman spectrum, which serves as a fingerprint that distinguishes it from other molecules. Therefore, the Stokes and anti-Stokes components reveal the type of gas molecule.

This paper presents an optical detector based on resonance tunneling that can regulate the absorption frequency and function as a light switch. The electronic properties of this device are investigated using density functional theory and the non-equilibrium Green process. Electron transmission in the device occurs in both elastic and non-elastic modes. Elastic transmission is based on the resonance of molecule orbitals, while non-elastic transmission is based on photon absorption. The I-V curve of the device contains the Raman optical spectrum information of the incident gas, allowing for a linear mapping between the input light frequency and the applied voltage to the detector. Peaks corresponding to the given incident frequency are observed in the voltage-current curve.

2. Modeling and system description

As shown in Fig. 1, the proposed photodetector comprises two AGNRs with nanoscale dimensions (width and length) connected by a non-conjugated interface [28,32]. This non-conjugated interface causes both sides of the central core of the device to have weak conjugation. The molecular orbitals localized on both sides of the two AGNRs have asymmetric conjugation relative to the electrodes on both sides due to the asymmetry in their edges. In other words, the orbital has a stronger conjugation with the nearest electrode compared to the farthest electrode, such that the conjugation of the farther electrode with the orbital can be considered negligible [33].

 figure: Fig. 1.

Fig. 1. Raman spectrum of a) Ethane, C2H6, and b) Butane, C4H10

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Figure 2 illustrates the molecular and electrochemical orbital energies of the ware electrodes. At zero voltage and in the absence of light, the HOMO orbitals are paired with the left electrode with an energy level of ${\varepsilon _2}$, and the LUMO orbitals are paired with the correct electrode. The HOMO-1 and LUMO + 1 orbitals are also present, with energies ${\varepsilon _3}$, ${\varepsilon _1}$, and ${\varepsilon _4}$, and paired with the left and right electrodes, respectively. Electron transfer occurs only when the energy difference between these molecular orbitals is at its minimum and they are placed in the transition window between the electrochemical energies of the electrodes. Therefore, when a voltage is applied that satisfies the energy conditions shown in Fig. 2(b), an elastic current is generated. However, these two conditions are not the only ones for electron transfer when the device is exposed to light. When light is applied to the wares, non-elastic transitions can also occur, as shown in Fig. 2. For example, in the case of (a), two non-elastic changes from L←LUMO + 1←HOMO–1←R and R←LUMO←HOMO←L, respectively, occur at an energy level of ћω=${\Delta _{i,j}}$. Therefore, these transitions are not elastic and do not fall within the transition window.

 figure: Fig. 2.

Fig. 2. Molecular and electrochemical orbital energies of the device electrodes are shown (a) at zero voltage and in the absence of light, the transition window does not overlap, and there is no electron transmission. (b) at voltages where the energy difference between the nondirected molecular orbitals is at the lowest level and their densities of states (DOS) overlap, the orbitals also overlap in the transition window, leading to elastic electron transfer and the formation of a current peak in the voltage-current curve [4]. (c) No elastic current is formed at other voltages where the transition window exists, but the molecular orbitals do not overlap in their DOS curve.

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In Fig. 2(b), an elastic transition occurs in the dark state from R←LUMO←HOMO←L. A non-elastic change from L←LUMO + 1←HOMO–1←R. Figure 2(c) shows a non-elastic transition from L←LUMO + 1←LUMO←R. This transition is more likely to occur than the inelastic transitions formed in states a and b because both LUMO and LUMO + 1 are within the electron transfer window.

In Fig. 3, molecular orbitals of ideal energy levels in Fig. 2 are demonstrated considering orbitals of AGNRs.

 figure: Fig. 3.

Fig. 3. a) Gas Optical Detector: After placing the gas in the chamber, the optical detector emits single-mode light and illuminates the scattered light. An optical detector detects the types of gases present in the chamber by detecting the frequencies of light corresponding to the voltages of the peak peaks in the current-voltage curve of the device and their intensity corresponding to the size of the peaks of the current. The paper deals only with how the optical detector works and generates the voltage curve corresponding to the Raman spectrum. (The curve matching and subsequently the type of gas are ignored.) b) Molecular Optical Detector: Red: nonconjugated interface, and Green: conjugated sites c) Molecular orbitals: It is observed that each of the four orbitals shown is concentrated on one side of the device, which leads to an asymmetric coupling of the molecular orbitals to the electrodes [4].

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The following Hamiltonian matrix is used to study and describe the electron transfer in this structure [34]:

$$H = {H_ \circ } + {H_{e - ph}}$$
where H is the terminal device single electron Hamiltonian in the absence of light, defined as the following:
$${H_ \circ } = \left[ {\begin{array}{cccc} {{\varepsilon_1} - \frac{1}{2}aeV}&0&\tau &\tau \\ 0&{{\varepsilon_2} - \frac{1}{2}aeV}&\tau &\tau \\ \tau &\tau &{{\varepsilon_3} + \frac{1}{2}aeV}&0\\ \tau &\tau &0&{{\varepsilon_4} + \frac{1}{2}aeV} \end{array}} \right]$$
where a is the percentage of applied voltage changing the energy of receiving and giving sections of the molecule due to the electrostatic phenomenon and shows the effective voltage on the central ware core. The difference in molecular level energy is shown as the following [35,36]:
$$\begin{array}{ll} {\Delta _{i,j}} = \sqrt {{{({aeV} )}^2} + 2aeV({{\varepsilon_i} - {\varepsilon_j}} )+ {{({{\varepsilon_i} - {\varepsilon_j}} )}^2} + {{({2\tau } )}^2}}& i = 1,2\\ \textrm{ }&j = 3,4 \end{array}$$
where τ is the coupling between concentrated orbitals in ware sides, calculated from the FERMI Golden relationship [37]:
$$\begin{array}{ll} {\tau _{i,j}}={({{C^\dagger }} )_{i,p}}{\beta _{p,q}}{C_{q,j}}&{{\rm i} = 1,2; \rm{p},\rm{q} = 1,2,}\ldots \mathrm{,atom^{\prime}s\ number}\\ &\textrm{ j = 3,4; } \end{array}$$
where ${C_{\; q,j}}$ is the atomic orbital is weight j in atom q and ${\beta _{p,q}}$ is the hopping parameter between two molecules. In a relationship (1) is the Hamiltonian of the photon-electron reaction written as follows [34]:
$${H_{e - ph}} = \frac{e}{{{m_0}}}A.\hat{p}$$

To express the momentum operator impulse p^ and the electromagnetic vector potential ${H_{e - ph}}$ in the second-quantized form, we first need to write the magnetic field in its second-quantized form, followed by the complete Hamiltonian. Assuming that the magnetic field of a photon is a single-frequency plane wave with a single mode and is monochromatic, we can express it in terms of creation and destruction operators [34]:

$$A({x,t} )= {A_0}(x )({b{e^{ - i\omega t}} + {b^\dagger }{e^{i\omega t}}} )$$

${A_0}(X )$ is obtained from the following Maxwell equation [34]:

$${\nabla ^2}{A_0}(x )+ \frac{{{\omega ^2}}}{{{c^2}}}{A_0}(x )= 0$$

The solution is as follows [34]:

$${A_0}(x )= {A_0}{e^{ik.x}}$$

In which k is the wave eigenvalue vector dependent on frequency $\omega $ [34]:

$$k = \frac{\omega }{c}\sqrt {{{\tilde{\mu }}_r}{{\tilde{\epsilon }}_r}} $$
where ${\tilde{\mu }_r}$ is the magnetic relative permeability, and ${\tilde{\epsilon }_r}$ is the relative dielectric constant. Assuming the inert conditions, one can show that the potential of the second-order quantized vector A(x,t) is obtained from the following [34]:
$$A({x,t} )= \hat{a}{\left( {\frac{{\hbar \sqrt {{{\tilde{\mu }}_r}{{\tilde{\epsilon }}_r}} }}{{2N\omega \tilde{\epsilon }c}}{I_\omega }} \right)^{1/2}}({b{e^{ - i\omega t}} + {b^\dagger }{e^{i\omega t}}} )$$
where ${I_\omega }$ is the photon flux obtained from the following [34,37,38]:
$${I_\omega } = \frac{{Nc}}{{V\sqrt {{{\tilde{\mu }}_r}{{\tilde{\epsilon }}_r}} }} = \frac{{{P_{op}}}}{{\hbar \omega }}$$
where ${P_{op}}$ is the flux power.

The Hamiltonian of photon-electron interaction is shown as creation and annihilation operators [34,37,38]:

$${H_{e - ph}} = \mathop \sum \limits_{l,m} \langle l\textrm{|}{H_{e - ph}}\textrm{|}m\rangle {a_l}^\dagger {a_m}$$

which we have [34,37,38]:

$$\langle l\textrm{|}{H_{e - ph}}\textrm{|}m\rangle = \frac{e}{{{m_0}}}A\langle l\textrm{|}\hat{p}\textrm{|}m\rangle $$

If the field is supposed to be polarized in the x-direction, the above term can be simplified [34,37,38]:

$$\langle l\textrm{|}{H_{e - ph}}\textrm{|}m\rangle = e{\left( {\frac{{\hbar \sqrt {{{\tilde{\mu }}_r}{{\tilde{\epsilon }}_r}} }}{{2N\omega \tilde{\epsilon }c}}{I_\omega }} \right)^{1/2}}({b{e^{ - i\omega t}} + {b^\dagger }{e^{i\omega t}}} )\times \langle l\textrm{|}\frac{{\hat{p}}}{{{m_0}}}\textrm{|}m\rangle$$

The second part can be written as follows:

$$\langle l\textrm{|}\frac{{\hat{p}}}{{{m_ \circ }}}\textrm{|}m\rangle = \langle l\textrm{|}\frac{{dz}}{{dt}}\textrm{|}m\rangle = \langle l\textrm{|}\frac{i}{\hbar }[{{H_ \circ },x} ]\textrm{|}m\rangle = \frac{i}{\hbar }({{x_m} - {x_l}} )\langle l\textrm{|}{H_ \circ }\textrm{|}m\rangle $$

Since ${z_{m,l}}$ the state place is in the z-direction, replacing Eq. (15) in Eq. (13) gives:

$${H_{e - ph}} = \sum\limits_{l,m} {\frac{{ie}}{\hbar }({{z_m} - {z_l}} ){{\left( {\frac{{\hbar \sqrt {{{\tilde{\mu }}_r}{{\tilde{\epsilon }}_r}} }}{{2N\omega \tilde{\epsilon }c}}{I_\omega }} \right)}^{1/2}}({b{e^{ - i\omega t}} + {b^\dagger }{e^{i\omega t}}} )\times \langle l\textrm{|}{H_ \circ }\textrm{|}m\rangle {a_l}^\dagger {a_m}}$$
$${H_{e - ph}} = \mathop \sum \limits_{l,m} {M_{lm}}({b{e^{ - i\omega t}} + {b^\dagger }{e^{i\omega t}}} ){a_l}^\dagger {a_m}$$

which Mlm is the system light matrix, defined as follows:

$$\begin{aligned} {M_{lm}} &= ({{z_m} - {z_l}} )\frac{{ie}}{\hbar }{\left( {\frac{{\hbar \sqrt {{{\tilde{\mu }}_r}{{\tilde{\epsilon }}_r}} }}{{2N\omega \tilde{\epsilon }c}}{I_\omega }} \right)^{1/2}}{P_{lm}}\\ {P_{lm}} &\equiv \left\{ {\scriptstyle + 1\begin{array}{ll} {}&{m = l + 1} \end{array}\atop {\scriptstyle - 1\begin{array}{{ll}} {}&{m = l - 1} \end{array}\atop \scriptstyle0\begin{array}{{ll}} {}&{} \end{array}else}} \right. \end{aligned}$$

After obtaining the system Hamiltonian, we can calculate the lowest-order self-energies for photon-electron interactions using the theory of coupling fields. For instance, in the case of radiative coupling, the lesser and greater Green's functions contribute to the self-energies ‘<‘ and ‘>,’ respectively. These self-energies can be obtained using the self-energy approximation method, which takes into account the influence of the environment on the photon and electron states:

$$\mathrm{\Sigma }_{lm}^\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel> \over {\smash{\scriptstyle< }\vphantom{_x}}$}}\ }(E )= \mathop \sum \limits_{pq} G_{pq}^\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel> \over {\smash{\scriptstyle< }\vphantom{_x}}$}}\ }({{t_1}{\; },{\; }{t_2}{\; }} )D_{lp;qm}^\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel> \over {\smash{\scriptstyle< }\vphantom{_x}}$}}\ }({{t_1}{\; },{\; }{t_2}{\; }} )$$

$D$ shows the diffusion of the photon, defined in the following:

$$D_{lp;qm}^ > ({{t_1}{\; },{\; }{t_2}{\; }} )\equiv H_{lp}^1({{t_1}} )H_{qm}^1({{t_2}} )$$
$$D_{lp;qm}^ < ({{t_1}{\; },{\; }{t_2}{\; }} )\equiv H_{qm}^1({{t_2}} )H_{lp}^1({{t_1}} )$$

In a one-dimensional effective mass system, $H_{\textrm{lp}}^1$ is defined in the following:

$$H_{lp}^1({{t_1}} )\equiv {M_{lp}}({b{e^{ - i\omega {t_1}}} + {b^\dagger }{e^{i\omega {t_1}}}} )$$

Using the commutation relations for the creation and destruction operators and assuming that the photon population remains in thermal equilibrium, we can write:

$$b({{t_1}} )b({{t_2}} )= 0$$
$$b({{t_1}} ){b^\dagger }({{t_2}} )= ({N + 1} ){e^{ - i\omega ({{t_1} - {t_2}} )}}$$
$$b({{t_1}} ){b^\dagger }({{t_2}} )= N{e^{i\omega ({{t_1} - {t_2}} )}}$$
$$\langle {b^\dagger }({{t_1}} ){b^\dagger }({{t_2}} )\rangle = 0$$

Replacing Eq. (23) to (26) in Eq. (20) and (21), we have:

$$D_{lp;qm}^ > ({{t_1}{\; },{\; }{t_2}{\; }} )= {M_{lp}}{M_{qm}}[{N{e^{i\omega ({{t_1} - {t_2}} )}} + ({N + 1} ){e^{ - i\omega ({{t_1} - {t_2}} )}}} ]$$

Taking Fourier transformation relative to (${t_1} - {t_2}$), we have:

$$D_{lp;qm}^ > (E )= 2\pi {M_{lp}}{M_{qm}}[{N\delta ({E + \hbar \omega } )+ ({N + 1} )\delta ({E - \hbar \omega } )} ]$$
$$D_{lp;qm}^ < (E )= 2\pi {M_{lp}}{M_{qm}}[{N\delta ({E - \hbar \omega } )+ ({N + 1} )\delta ({E + \hbar \omega } )} ]$$

Therefore, inlet action and outlet action are written as follows [37,38]:

$$\mathrm{\Sigma }_{lm}^ > (E )= \mathop \sum \limits_{pq} {M_{lp}}{M_{qm}}[{N{G^ > }_{pq}({E + \hbar \omega } )+ ({N + 1} ){G^ > }_{pq}({E - \hbar \omega } )} ]$$
$$\mathrm{\Sigma }_{lm}^ < (E )= \mathop \sum \limits_{pq} {M_{lp}}{M_{qm}}[{N{G^ < }_{pq}({E - \hbar \omega } )+ ({N + 1} ){G^ < }_{pq}({E + \hbar \omega } )} ]$$
where ${G^ < }$ and ${G^ > }$ are retarded and progressive Green functions as the following:
$${G^ < } = G(E )[{{\mathrm{\Gamma }_L}(E ){f_L}(E )+ {\mathrm{\Gamma }_R}(E ){f_R}(E )+ \mathrm{\Sigma }_{ph}^ < } ]G{(E )^\dagger }$$
$${G^ > } = G(E )[{{\mathrm{\Gamma }_L}(E )({1 - {f_L}(E )} )+ {\mathrm{\Gamma }_R}(E )({1 - {f_R}(E )} )+ \mathrm{\Sigma }_{ph}^ > } ]G{(E )^\dagger }$$
where ${\Gamma _{L,R}}$= i(${\Sigma _{L,R}}\Sigma _{L,R}^{}$) is the widening function from the source and drain (coupling between electrode and orbitals) and ${f_{L,R}}$ is the form function of source and drain:
$$G(E )= {[{({E - {0^ + }} )I - H - {\mathrm{\Sigma }_L} - {\mathrm{\Sigma }_R} - {\mathrm{\Sigma }_{ph}}} ]^{ - 1}}$$
where ${\Sigma _{ph}}$ is the self-energy of photon-electron interaction from the following relationship [34,37,38]:
$${\mathrm{\Sigma }_{ph}} ={-} ({i/2} )({\mathrm{\Sigma }_{ph}^{in} + \mathrm{\Sigma }_{ph}^{out}} )$$

After the self-energy is obtained in the Bern self-adaptation approximation, the current is obtained;

$${I_{L,R}} = Trace[{\mathrm{\Sigma }_{L,R}^{in}A} ]- Trace[{{\mathrm{\Gamma }_{L,R}}{G^ < }} ]$$

in which A = i[$\textrm{G} - {\textrm{G}^{}}$], the relationship (36) can be rewritten as:

$${I_{L,R}} = \frac{{2e}}{\hbar }\int {\frac{{dE}}{{2\pi }}({{f_L}(E) - {f_R}(E)} )T(E )}$$
where T(E) is electron transmission defined as the following:
$$T(E )= Tr\{{{\Gamma _L}{G^ > }(E ){\Gamma _R}{G^ < }(E )} \}$$

3. Results

Figures 4(b) and (c) show the current-voltage curve of the ware with the WBL system assumption in entirely dark conditions at zero Kelvin. It is also assumed that the Fermi balance is located on the HOMO and that the LUMO and LUMO + 1 energy levels are 2.28 and 2.46 eV, respectively, above the Fermi level. In contrast, the HOMO-1 level is 0.27 lower than the Fermi level. The ware is also assumed to be mechanically stable for all applied voltages and fields. The amount of coupling between molecular levels is calculated from the relation (3) to be equal to 0.16 eV. As shown in Fig. 4(b), specific peaks in the current-voltage curve correspond to molecular alignments resonating at specific voltages where ${\Delta _{i,j}}$ is at a minimum value and the orbitals are within the transmission window. At a voltage of −4.56 volts, the peak current is due to the degeneration of the HOMO and LUMO orbitals, while at a voltage of 0.54, it is due to the degeneration of the HOMO and HOMO-1 orbitals. Finally, the maximum at 5.46 V is due to the resonance of the LUMO + 1 and HOMO-1 orbitals. These are all three current peaks, all of the elastic transmission types. Depending on where the Fermi level is located, the size of the recent peak and the voltage corresponding to it can be varied at a voltage of 0.54 V. In Fig. 4(c), the Fermi level shows the voltage curve in the 0 to 2 volts range for different energies. By increasing the Fermi level, approaching the midpoint of the HOMO and LUMO levels, it is observed that the peak current decreases and the peak voltage increases.

 figure: Fig. 4.

Fig. 4. a) ${\Delta _{i.j}}$ curve: The energy difference between the molecular orbitals varies with voltage, and at a specific voltage, the energy difference between the two orbitals reaches its minimum value. b) In the absence of light, when the voltage is such that ${\Delta _{i,j}}$ is at its minimum value and both non-degenerate orbitals are in the transmission window, peaks are formed in the voltage-current curve. These peaks result from elastic electron transfer in the ware. c) The voltage-current curve at different Fermi energy levels: A peak occurs at a voltage of 0.54 when the Fermi level is on the HOMO (red graph). Increasing the Fermi level decreases the peak size, and the corresponding voltage magnitude increases. The peak size decreases with increasing Fermi levels so that it can be neglected compared to other peaks resulting from elastic transport.

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Figures 5(b) and (c) display the current-voltage curve of the ware under 2.5 eV and 3 eV single-mode light, respectively. It is observed that the peak current occurs at voltages where ${\Delta _{i,j}}$ is equal to the energy of the input photon. The curves in Fig. 5(e) and (f) demonstrate that at voltages corresponding to peaks P1 and P2, electron transmission occurs through photon absorption between the HOMO-1 and LUMO + 1 levels. The rate of electron transfer from HOMO-1 to LUMO + 1 equals that from LUMO + 1 to HOMO-1 at N/(N + 1). Thus, the electron transfer path in the ware at voltages corresponding to P1 and P2 can be from L←LUMO + 1←LUMO–1←R, as illustrated in Fig. 5(d).

 figure: Fig. 5.

Fig. 5. a) ${\Delta _{i.j}}$ curve b) Current-voltage curve under 2.5V light exposure, c) Current-voltage curve under 3V light exposure, d) Atomic orbital energies in the presence of different electrode voltages, e) Transmission curve for a voltage of 9.5V and light exposure of 2.5V, f) Transmission curve for a voltage of 10.4V and light exposure of 3V.

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In Fig. 6, the current-voltage curve of the ware is examined within the range of non-elastic transfer for different light voltages of 2.5 eV. It can be observed that the peak size increases as the light input power increases. This property can be utilized in optical gas sensors where concentration measurement is crucial. Increasing the concentration reduces the intensity of the reflected light, thereby reducing the size of the current peaks.

 figure: Fig. 6.

Fig. 6. When examining the non-elastic current peak under varying input light power, it was observed that the size of the peak increases with increasing light power

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The negative resistance effect of AGNRs has been discussed in various Refs. [39], including its switching effect in oscillators and switching devices [40].

A critical parameter in gas sensors is the response speed of the sensor to external factors. In this study, the transient response of the ware was investigated using the method presented in Ware [37]. As shown in Fig. 7, it was observed that the current form in the ware is proportional to the input light and exhibits a rapid temporal response to the input when a polarized light pulse of 400 fs period is applied to the ware.

 figure: Fig. 7.

Fig. 7. Transient response of output current and input light pulse over time.

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4. Conclusion

This paper presents an optical detector with an asymmetric structure consisting of two low-length and width AGNRs with hydrogen and fluorine edges and a non-conjugated interface. Due to the localization of the molecular orbitals on one side of the ware, an asymmetric coupling of the molecular orbitals to the electrodes results in a tunneling transition in the ware. Two molecule orbitals form this transition; each localized on one side of the molecule. The voltage curve of the ware exhibits negative resistance, even in elastic transitions. The frequency of the incoming light determines the voltage range of the current peak and negative resistance presence. The voltage-current curve also contains the Raman optical spectral information of the gas. There is a linear mapping between the input light frequencies to the detector, the applied voltage to the detector, and the voltages corresponding to the incoming light frequencies where the peaks in the current flow curve are observed. This detector's asymmetric structure and the molecular orbitals’ localization on the sides of the ware conjugation make it possible to detect all frequencies in visible light by sweeping the voltage and fully detecting the Raman spectrum of each gas and subsequently identifying the gas. The most important feature of the ware is its capability to detect and identify frequencies in the light emitted by the gas concentration.

Acknowledgments

Authors’ contributions: A. Tashakori wore the original paper and simulated the numerical results. A. Rostami conceptualized the idea, wrote the paper, and supervised the paper. M. Karkhanechi supervised the paper and edited the manuscript.

Disclosures

The authors declare no conflict of interest.

Data availability

There is no data to share with the community. All results appeared in the paper.

References

1. A. C. Neto, F. Guinea, N. M. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009). [CrossRef]  

2. K. S. Novoselov, V. Fal, L. Colombo, P. Gellert, M. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012). [CrossRef]  

3. F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010). [CrossRef]  

4. M. Long, P. Wang, H. Fang, and W. Hu, “Progress, challenges, and opportunities for 2D material-based photodetectors,” Adv. Funct. Mater. 29, 1803807 (2019). [CrossRef]  

5. F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009). [CrossRef]  

6. A. C. Neto, F. Guinea, and N. Peres, “Edge and surface states in the quantum Hall effect in graphene,” Phys. Rev. B 73(20), 205408 (2006). [CrossRef]  

7. G. Fiori, F. Bonaccorso, G. Iannaccone, T. Palacios, D. Neumaier, A. Seabaugh, and Sanjay K. Banerjee6 and Luigi Colombo, “Electronics based on two-dimensional materials,” Nat. Nanotechnol. 9(10), 768–779 (2014). [CrossRef]  

8. C. Liu, Z. Yu, D. Neff, A. Zhamu, and B. Z. Jang, “Graphene-based supercapacitor with an ultrahigh energy density,” Nano Lett. 10(12), 4863–4868 (2010). [CrossRef]  

9. Y.-H. Kim, S. S. Jang, Y. H. Jang, and W. A. Goddard III, “First-principles study of the switching mechanism of 2 catenane molecular electronic devices,” Phys. Rev. Lett. 94(15), 156801 (2005). [CrossRef]  

10. S.-H. Ke, H. U. Baranger, and W. Yang, “Contact atomic structure and electron transport through molecules,” J. Chem. Phys. 122(7), 074704 (2005). [CrossRef]  

11. C.-J. Xia, B.-Q. Zhang, Y.-H. Su, Z.-Y. Tu, and X.-A. Yan, “Electronic transport properties of a single chiroptical molecular switch with graphene nanoribbons electrodes,” Optik 127(11), 4774–4777 (2016). [CrossRef]  

12. I. Maity, K. Ghosh, H. Rahaman, and P. Bhattacharyya, “Spin-dependent electronic transport in edge oxidized zigzag graphene nanoribbon,” Mater. Today: Proc. 5, 9892–9898 (2018). [CrossRef]  

13. S. Fujii, M. Ziatdinov, M. Ohtsuka, K. Kusakabe, M. Kiguchi, and T. Enoki, “Role of edge geometry and chemistry in the electronic properties of graphene nanostructures,” Faraday Discuss. 173, 173–199 (2014). [CrossRef]  

14. X. Jia, J. Campos-Delgado, M. Terrones, V. Meunier, and M. S. Dresselhaus, “Graphene edges: a review of their fabrication and characterization,” Nanoscale 3(1), 86–95 (2011). [CrossRef]  

15. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I V Grigorieva, and A A Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef]  

16. S. Prabhakar and R. Melnik, “Band engineering and elastic properties of strained armchair graphene nanoribbons: semiconductor vs metallic characteristics,” arXiv, arXiv:1901.0-0576, (2019). [CrossRef]  

17. D. J. Rizzo, G. Veber, T. Cao, C. Bronner, T. Chen, F. Zhao, Henry Rodriguez, Steven G. Louie, Michael F. Crommie, and Felix R. Fischer, “Topological band engineering of graphene nanoribbons,” Nature 560(7717), 204–208 (2018). [CrossRef]  

18. X. Su, Z. Xue, G. Li, and P. Yu, “Edge state engineering of graphene nanoribbons,” Nano Lett. 18(9), 5744–5751 (2018). [CrossRef]  

19. Xiaowei Zhang, Oleg V Yazyev, Juanjuan Feng, Liming Xie, Chenggang Tao, Yen-Chia Chen, Liying Jiao, Zahra Pedramrazi, Alex Zettl, Steven G Louie, Hongjie Dai, and Michael F Crommie, “Experimentally engineering the edge termination of graphene nanoribbons,” ACS Nano 7(1), 198–202 (2013). [CrossRef]  

20. M. Y. Han, B. Özyilmaz, Y. Zhang, and P. Kim, “Energy band-gap engineering of graphene nanoribbons,” Phys. Rev. Lett. 98, 206805 (2007). [CrossRef]  

21. M. J. Allen, V. C. Tung, and R. B. Kaner, “Honeycomb carbon: a review of graphene,” Chem. Rev. 110(1), 132–145 (2010). [CrossRef]  

22. T. Wang, D. Huang, Z. Yang, S. Xu, G. He, X. Li, Nantao Hu, Guilin Yin, Dannong He, and Liying Zhang, “A review on graphene-based gas/vapor sensors with unique properties and potential applications,” Nano-Micro Lett. 8(2), 95–119 (2016). [CrossRef]  

23. A. Hazra and S. Basu, “Graphene nanoribbon as potential on-chip interconnect material—a review,” C—Journal of Carbon Research 4, 49 (2018). [CrossRef]  

24. U. Rajaji, R. Arumugam, S.-M. Chen, T.-W. Chen, T.-W. Tseng, and S. Chinnapaiyan, “Graphene nanoribbons in electrochemical sensors and biosensors: a review,” Int. J. Electrochem. Sci. 13, 6643–6654 (2018). [CrossRef]  

25. M. L. Perrin, R. Frisenda, M. Koole, J. S. Seldenthuis, J. A. C. Gil, H. Valkenier, Jan C Hummelen, Nicolas Renaud, Ferdinand C Grozema, Joseph M Thijssen, Diana Dulić, and Herre S J van der Zant, “Large negative differential conductance in single-molecule break junctions,” Nat. Nanotechnol. 9(10), 830–834 (2014). [CrossRef]  

26. B. S. Jessen, L. Gammelgaard, M. R. Thomsen, D. M. Mackenzie, J. D. Thomsen, J. M. Caridad, Emil Duegaard, Kenji Watanabe, Takashi Taniguchi, Timothy J. Booth, Thomas G. Pedersen, Antti-Pekka Jauho, and Peter Bøggild, “Lithographic band structure engineering of graphene,” Nat. Nanotechnol. 14(4), 340–346 (2019). [CrossRef]  

27. A. Aviram and M. A. Ratner, “Molecular rectifiers,” Chem. Phys. Lett. 29(2), 277–283 (1974). [CrossRef]  

28. D. Xiang, X. Wang, C. Jia, T. Lee, and X. Guo, “Molecular-scale electronics: from concept to functioning,” Chem. Rev. 116(7), 4318–4440 (2016). [CrossRef]  

29. J. Kang, F. Wu, and J. Li, “Doping induced spin filtering effect in zigzag graphene nanoribbons with asymmetric edge hydrogenation,” Appl. Phys. Lett. 98(8), 083109 (2011). [CrossRef]  

30. G. Lee and K. Cho, “Electronic structures of zigzag graphene nanoribbons with edge hydrogenation and oxidation,” Phys. Rev. B 79(16), 165440 (2009). [CrossRef]  

31. B. Xu, J. Yin, Y. Xia, X. Wan, K. Jiang, and Z. Liu, “Electronic and magnetic properties of a zigzag graphene nanoribbon with one edge saturated,” Appl. Phys. Lett. 96(16), 163102 (2010). [CrossRef]  

32. M. Kilgour and D. Segal, “Inelastic effects in molecular transport junctions: the probe technique at high bias,” J. Chem. Phys. 144(12), 124107 (2016). [CrossRef]  

33. C. Van Dyck and M. A. Ratner, “Molecular junctions: control of the energy gap achieved by a pinning effect,” J. Phys. Chem. C 121(5), 3013–3024 (2017). [CrossRef]  

34. L. E. Henrickson, “Nonequilibrium photocurrent modeling in resonant tunneling photodetectors,” J. Appl. Phys. 91(10), 6273–6281 (2002). [CrossRef]  

35. M. L. Perrin, E. Galan, R. Eelkema, F. Grozema, J. M. Thijssen, and H. S. van der Zant, “Single-molecule resonant tunneling diode,” J. Phys. Chem. C 119(10), 5697–5702 (2015). [CrossRef]  

36. Y. Li, J. A. Mol, S. C. Benjamin, and G. A. D. Briggs, “Interference-based molecular transistors,” Sci. Rep. 6(1), 33686 (2016). [CrossRef]  

37. L. Chen, T. Hansen, and I. Franco, “Simple and accurate method for time-dependent transport along nanoscale junctions,” J. Phys. Chem. C 118(34), 20009–20017 (2014). [CrossRef]  

38. F. Ostovari and M. K. Moravvej-Farshi, “Photodetectors with armchair graphene nanoribbons and asymmetric source and drain contacts,” Appl. Surf. Sci. 318, 108–112 (2014). [CrossRef]  

39. S. Jamalzadeh, K. R. Ghayour, and M. Sanaee, “Negative differential resistance effect in different structures of armchair graphene nanoribbon,” Diamond Relat. Mater. 108, 107970 (2020). [CrossRef]  

40. S. Samuel, L. Juan-Pablo, B. Jeffrey, and S Sayeef, “Negative differential resistance and steep switching in chevron graphene nanoribbon field–effect transistors,” IEEE Electron Device Lett. 39(1), 143–146 (2018). [CrossRef]  

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Figures (7)
Fig. 1.
Fig. 1. Raman spectrum of a) Ethane, C2H6, and b) Butane, C4H10

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Fig. 2.
Fig. 2. Molecular and electrochemical orbital energies of the device electrodes are shown (a) at zero voltage and in the absence of light, the transition window does not overlap, and there is no electron transmission. (b) at voltages where the energy difference between the nondirected molecular orbitals is at the lowest level and their densities of states (DOS) overlap, the orbitals also overlap in the transition window, leading to elastic electron transfer and the formation of a current peak in the voltage-current curve [4]. (c) No elastic current is formed at other voltages where the transition window exists, but the molecular orbitals do not overlap in their DOS curve.

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Fig. 3.
Fig. 3. a) Gas Optical Detector: After placing the gas in the chamber, the optical detector emits single-mode light and illuminates the scattered light. An optical detector detects the types of gases present in the chamber by detecting the frequencies of light corresponding to the voltages of the peak peaks in the current-voltage curve of the device and their intensity corresponding to the size of the peaks of the current. The paper deals only with how the optical detector works and generates the voltage curve corresponding to the Raman spectrum. (The curve matching and subsequently the type of gas are ignored.) b) Molecular Optical Detector: Red: nonconjugated interface, and Green: conjugated sites c) Molecular orbitals: It is observed that each of the four orbitals shown is concentrated on one side of the device, which leads to an asymmetric coupling of the molecular orbitals to the electrodes [4].

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Fig. 4.
Fig. 4. a) ${\Delta _{i.j}}$ curve: The energy difference between the molecular orbitals varies with voltage, and at a specific voltage, the energy difference between the two orbitals reaches its minimum value. b) In the absence of light, when the voltage is such that ${\Delta _{i,j}}$ is at its minimum value and both non-degenerate orbitals are in the transmission window, peaks are formed in the voltage-current curve. These peaks result from elastic electron transfer in the ware. c) The voltage-current curve at different Fermi energy levels: A peak occurs at a voltage of 0.54 when the Fermi level is on the HOMO (red graph). Increasing the Fermi level decreases the peak size, and the corresponding voltage magnitude increases. The peak size decreases with increasing Fermi levels so that it can be neglected compared to other peaks resulting from elastic transport.

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Fig. 5.
Fig. 5. a) ${\Delta _{i.j}}$ curve b) Current-voltage curve under 2.5V light exposure, c) Current-voltage curve under 3V light exposure, d) Atomic orbital energies in the presence of different electrode voltages, e) Transmission curve for a voltage of 9.5V and light exposure of 2.5V, f) Transmission curve for a voltage of 10.4V and light exposure of 3V.

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Fig. 6.
Fig. 6. When examining the non-elastic current peak under varying input light power, it was observed that the size of the peak increases with increasing light power

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Fig. 7.
Fig. 7. Transient response of output current and input light pulse over time.

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Equations (38)

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H = H ∘ + H e − p h
H ∘ = [ ε 1 − 1 2 a e V 0 τ τ 0 ε 2 − 1 2 a e V τ τ τ τ ε 3 + 1 2 a e V 0 τ τ 0 ε 4 + 1 2 a e V ]
Δ i , j = ( a e V ) 2 + 2 a e V ( ε i − ε j ) + ( ε i − ε j ) 2 + ( 2 τ ) 2 i = 1 , 2   j = 3 , 4
τ i , j = ( C † ) i , p β p , q C q , j i = 1 , 2 ; p , q = 1 , 2 , … , a t o m ′ s   n u m b e r  j = 3,4; 
H e − p h = e m 0 A . p ^
A ( x , t ) = A 0 ( x ) ( b e − i ω t + b † e i ω t )
∇ 2 A 0 ( x ) + ω 2 c 2 A 0 ( x ) = 0
A 0 ( x ) = A 0 e i k . x
k = ω c μ ~ r ϵ ~ r
A ( x , t ) = a ^ ( ℏ μ ~ r ϵ ~ r 2 N ω ϵ ~ c I ω ) 1 / 2 ( b e − i ω t + b † e i ω t )
I ω = N c V μ ~ r ϵ ~ r = P o p ℏ ω
H e − p h = ∑ l , m ⁡ ⟨ l | H e − p h | m ⟩ a l † a m
⟨ l | H e − p h | m ⟩ = e m 0 A ⟨ l | p ^ | m ⟩
⟨ l | H e − p h | m ⟩ = e ( ℏ μ ~ r ϵ ~ r 2 N ω ϵ ~ c I ω ) 1 / 2 ( b e − i ω t + b † e i ω t ) × ⟨ l | p ^ m 0 | m ⟩
⟨ l | p ^ m ∘ | m ⟩ = ⟨ l | d z d t | m ⟩ = ⟨ l | i ℏ [ H ∘ , x ] | m ⟩ = i ℏ ( x m − x l ) ⟨ l | H ∘ | m ⟩
H e − p h = ∑ l , m i e ℏ ( z m − z l ) ( ℏ μ ~ r ϵ ~ r 2 N ω ϵ ~ c I ω ) 1 / 2 ( b e − i ω t + b † e i ω t ) × ⟨ l | H ∘ | m ⟩ a l † a m
H e − p h = ∑ l , m ⁡ M l m ( b e − i ω t + b † e i ω t ) a l † a m
M l m = ( z m − z l ) i e ℏ ( ℏ μ ~ r ϵ ~ r 2 N ω ϵ ~ c I ω ) 1 / 2 P l m P l m ≡ { + 1 m = l + 1 − 1 m = l − 1 0 e l s e
Σ l m   < x >   ( E ) = ∑ p q ⁡ G p q   < x >   ( t 1 , t 2 ) D l p ; q m   < x >   ( t 1 , t 2 )
D l p ; q m > ( t 1 , t 2 ) ≡ H l p 1 ( t 1 ) H q m 1 ( t 2 )
D l p ; q m < ( t 1 , t 2 ) ≡ H q m 1 ( t 2 ) H l p 1 ( t 1 )
H l p 1 ( t 1 ) ≡ M l p ( b e − i ω t 1 + b † e i ω t 1 )
b ( t 1 ) b ( t 2 ) = 0
b ( t 1 ) b † ( t 2 ) = ( N + 1 ) e − i ω ( t 1 − t 2 )
b ( t 1 ) b † ( t 2 ) = N e i ω ( t 1 − t 2 )
⟨ b † ( t 1 ) b † ( t 2 ) ⟩ = 0
D l p ; q m > ( t 1 , t 2 ) = M l p M q m [ N e i ω ( t 1 − t 2 ) + ( N + 1 ) e − i ω ( t 1 − t 2 ) ]
D l p ; q m > ( E ) = 2 π M l p M q m [ N δ ( E + ℏ ω ) + ( N + 1 ) δ ( E − ℏ ω ) ]
D l p ; q m < ( E ) = 2 π M l p M q m [ N δ ( E − ℏ ω ) + ( N + 1 ) δ ( E + ℏ ω ) ]
Σ l m > ( E ) = ∑ p q ⁡ M l p M q m [ N G > p q ( E + ℏ ω ) + ( N + 1 ) G > p q ( E − ℏ ω ) ]
Σ l m < ( E ) = ∑ p q ⁡ M l p M q m [ N G < p q ( E − ℏ ω ) + ( N + 1 ) G < p q ( E + ℏ ω ) ]
G < = G ( E ) [ Γ L ( E ) f L ( E ) + Γ R ( E ) f R ( E ) + Σ p h < ] G ( E ) †
G > = G ( E ) [ Γ L ( E ) ( 1 − f L ( E ) ) + Γ R ( E ) ( 1 − f R ( E ) ) + Σ p h > ] G ( E ) †
G ( E ) = [ ( E − 0 + ) I − H − Σ L − Σ R − Σ p h ] − 1
Σ p h = − ( i / 2 ) ( Σ p h i n + Σ p h o u t )
I L , R = T r a c e [ Σ L , R i n A ] − T r a c e [ Γ L , R G < ]
I L , R = 2 e ℏ ∫ d E 2 π ( f L ( E ) − f R ( E ) ) T ( E )
T ( E ) = T r { Γ L G > ( E ) Γ R G < ( E ) }
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