Graphene - gold grating-based structure to achieve enhanced electromagnetic field distribution

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Graphene - gold grating-based structure to achieve enhanced electromagnetic field distribution

R. Kuzyk, O. Ilin, I. Yaremchuk

Lviv Polytechnic National University

In this work, the field distribution in structures such as a gold grating, a graphene layer, and a silicon substrate was studied. The conditions for maximum electromagnetic field distribution (absorption) by this structure to use in photonics and electronics devices were established . The magnitude of the electromagnetic field of a gold diffraction grating with a graphene layer increases with decreasing slit width. At the same time, an increase in the period leads to small changes in the electromagnetic field distribution. The maximum value of the distribution of the electromagnetic field is increased significantly, almost twice reducing the thickness of the graphene layer.

Key words: grapheme; silicon; grating; surface plasmon resonance; field distribution.

СТРУКТУРА ГРАФЕН - ЗОЛОТА ҐРАТКА ДЛЯ ОТРИМАННЯ ПІДСИЛЕНОГО РОЗПОДІЛУ ЕЛЕКТРОМАГНІТНОГО ПОЛЯ

The study and determination of the optimal geometric values of structures such as a gold grating, a graphene layer, and a silicon substrate to obtain the maximum electromagnetic field distribution was carried out by the finite element method. To calculate the field distribution, the initial parameters are set, namely, the thickness of the gold grating is 120 nm, the grating width is 800 nm, the slit width is 100 nm, the grating period is 1000 nm, and the thickness of the graphene layer is 4 nm. The resonant wavelength was 1100 nm. Gold dielectric constants were used from work [15]. Refractive index of silicon from [16]. The dielectric constant of graphene is used from [17].

The electromagnetic field distribution over the initial parameters is presented in Fig. 1, a. It was determined that the maximum electromagnetic field is 1.96-10⁵ V/m. The thickness of the gold grating has been increased to 150 nm, while the other dimensions remain unchanged (Fig. 1, b). The result showed that increasing the grating thickness increases the electromagnetic field, which is now equal to 2.25T0⁵ V/m. Therefore, the grating thickness was increased up to 200 nm. The simulation results are shown in Fig. 1, c. The absorption has increased significantly, and now the maximum value of the electromagnetic field is 2.73T0⁵ V/m. Thus, the grating thickness continued to increase with a step of 50 nm, which means that now it is 250 nm. The simulation results are shown in Fig. 1, d. It should be noted that after increasing the thickness of the grating, the maximum value of the electromagnetic field is 2.74T0⁵ V/m. These are insignificant changes, and therefore, the absorption peak can be obtained when the grating thickness is from 200 nm to 250 nm. In the next step, the grating thickness has been reduced to 225 nm. The simulation results are shown in Fig. 1, e.

The calculated maximum value of the electromagnetic field after reducing the grating thickness to 225 nm increased and is equal to 2.82T0⁵ V/m. Therefore, it can be considered as the optimal grating thickness.

Fig. 1. The electromagnetic field distribution of the grating-based structure, the elements of which have the following dimensions: a - grating thickness is 120 nm, slot width is 200 nm, grating period is 1000 nm, graphene thickness is 4 nm; b - grating thickness is 150 nm, slit width is 200 nm, grating period is 1000 nm, graphene thickness is 4 nm;

c - grating thickness is 200 nm, slit width is 200 nm, grating period is 1000 nm, graphene thickness is 4 nm;

d - grating thickness is 200 nm, slit width is 200 nm, grating period 1000 nm, graphene thickness is 4 nm; e - grating thickness is 225 nm, slit width is 200 nm, grating period is 1000 nm, graphene thickness is 4 nm

Having determined the optimal grating thickness, a study was carried out at different slit widths to obtain the optimal one. It is already known that the maximum value of the electromagnetic field distribution is 2.82T0⁵ V/m with a slit width of 200 nm. The slit width can be changed by changing the grating width or by changing the grating period. The grating period is increased to 1100 nm. Since the grating width is 800 nm, the slit width will be 150 nm. The simulation results are shown in Fig. 2, a. With the increase in the size of the slit, the maximum intensity of the field decreased to 2.74T0⁵ V/m. Therefore, the width of the slit must be reduced. The grating period is changed to 900 nm, hence the slit size is 50 nm. The simulation results are shown in Fig. 2, b. The maximum value of the electromagnetic field has increased significantly and now equals 4.09-10⁵ V/m. If we reduce the period to 850 nm, the slit width will be equal to 25 nm. The simulation results are shown in Fig. 2, c. The maximum value of the electromagnetic field has decreased to 3.84T0⁵ V/m, which means that the slit width is too small. We increase the period to 950 nm, while the slit width increases to 75 nm. The simulation results are shown in Fig. 2, d.

The result has improved relative to the previous slit width and now the maximum value of the electromagnetic field is 4.04T0⁵ V/m, but still less than with a slit width of 50 nm since with this slit width the maximum value of the electromagnetic field was 4.09T0⁵ V/m. Therefore, the value of the slit width of 50 nm will be the most optimal.

It is necessary to find the optimal value of the grating period having determined the optimal grating thickness and slit width. To keep the slit width constant, it needs to proportionally change the grating width and the grating period. Since it is determined that the peak absorption intensity at a slit width is 50 nm, then the grating width should be 100 nm less, per grating period, since the slit should be the same on both sides. We increase the period up to 1400 nm. The grating width is increased to 1300 nm.

Fig. 2. The electromagnetic field distribution of the grating-based structure and, the elements of which have the following dimensions: a - grating thickness is 225 nm, grating width is 800 nm, slit width is 150 nm, grating period is 1100 nm, graphene thickness is 4 nm; b - grating thickness is 225 nm, grating width is 800 nm, slit width is 50 nm, grating period is 900 nm, graphene thickness is 4 nm; c - grating thickness is 225 nm, grating width is 800 nm, slit width is 25 nm, grating period is 850 nm, graphene thickness is 4 nm; d - grating thickness is 225 nm, grating width is 800 nm, slit width is 75 nm, grating period is 950 nm, graphene thickness is 4 nm

The simulation results are shown in Fig. 3, a. The electromagnetic field distribution has slightly decreased from the previous value and is equal to 4.08T0⁵ V/m. Therefore, we can conclude that the grating period is too large. We decrease the grating period to 1200 nm and the grating width to 1100 nm. The simulation results are shown in Fig. 3, b. The value of the highest value of the distribution of the electromagnetic field has increased to 4.15-105 V/m. Next, we decrease the grating period and grating width in increments of 50 nm. The simulation results are shown in Fig. 3, c. Fig. 3, c shows that the distribution of the electromagnetic field has increased significantly and is now equal to 4.35-105 V/m. We reduce the grating period up to 1100 nm and the grating width to 1000 nm, respectively. The simulation results are shown in Fig. 3, d.

As a result of recent geometric changes, the intensity of the distribution of the electromagnetic field slightly decreased from 4.35-105 V/m to 4.28-10⁵ V/m. Hence, we can conclude that the optimal value of the grating period is 1150 nm, and the grating width is 1050 nm, respectively, since it is necessary to provide a slit width of 50 nm.

Fig. 3. The electromagnetic field distribution of the grating-based structure, the elements of which have the following dimensions: a - grating thickness is 225 nm, grating width is 1300 nm, slot width is 50 nm, grating period is 1400 nm, graphene width is 4 nm; b - grating thickness is 225 nm, grating width is 1100 nm, slit width is 50 nm, grating period is 1200 nm, graphene thickness is 4 nm; c - grating thickness is 225 nm, grating width is 1050 nm, slit width is 50 nm, grating period is 1150 nm, graphene thickness is 4 nm; d - grating thickness is 225 nm, grating width is 1000 nm, slit width is 50 nm, grating period is 1100 nm, graphene thickness is 4 nm

After all parameter changes, it was determined that with a graphene thickness of 4 nm, a better electromagnetic field distribution value than 4.35-10⁵ V/m can be achieved. Next, it remains to find the optimal graphene thickness and establish the maximum value of the distribution of the electromagnetic field in the researched structure. Let us increase the graphene thickness to 5 nm. The simulation results are shown in Fig. 4, a. As can be seen from Fig. 4, a, the maximum value of the electromagnetic field distribution has been significantly reduced and is now 3.8-10⁵ V/m. Hence the conclusion is that the thickness of graphene should be reduced. This is good because graphene is a layered material and with too many layers, graphene will already be graphite. Let's take the thickness of graphene at 2 nm. The

simulation results are shown in Fig. 4, b. As a result of these changes, the maximum value of the distribution of the electromagnetic field has increased significantly, almost twice as compared to the last calculation, and is now equal to 6.65-10⁵ V/m. We reduced the graphene thickness to 1 nm. The simulation results are shown in Fig. 4, c.

Therefore, this will be the final result for the research structure, since further reductions in the thickness of graphene will lead to a sharp drop in the intensity of the electromagnetic field distribution of 9.0-10⁵ V/m.

Conclusion

In this work, the study of the electromagnetic field distribution in structures of type the gold grating, the graphene layer, and the silicon substrate at different geometric parameters was carried out.

The most intense electric field is observed when the electric field is concentrated both in the upper and lower corners of the grating.

The strongest electromagnetic field distribution can be obtained when the grating thickness is in the range from 200 nm to 250 nm, the value of the slit width of 50 nm, the grating period is 1150 nm, and the grating width is 1050 nm at the given parameters.

The maximum value of the distribution of the electromagnetic field has increased significantly, almost twice as compared to the last calculation reducing the thickness of the graphene layer. The optimal graphene thickness of 1 nm was determined.

Fig. 4. The electromagnetic field distribution of the grating-based structure, the elements of which have the following dimensions: a - grating thickness is 225 nm, grating width is 1050 nm, slot width is 50 nm, grating period is 1150 nm, graphene thickness is 5 nm; b - grating thickness is 225 nm, grating width is 1050 nm, slit width is 50 nm, grating period is 1150 nm, graphene thickness is 2 nm; c - grating thickness is 225 nm, grating width is 1050 nm, slit width is 50 nm, grating period is 1150 nm, graphene thickness is 1 nm

The magnitude of the electromagnetic field (absorption) of the gold diffraction grating with a graphene layer increases with decreasing slit width. At the same time, an increase in the period leads to small changes in the electromagnetic field distribution. Therefore, the maximum of the electromagnetic field distribution can be tuned by the values of the structures' geometric parameters.

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