51 Trang 8 LIST OF FIGURES Figure 1.1: Lycurgus cup 1 Figure 1.2: Number of papers 2 Figure 1.3: SPPs at single interface 4 Figure 1.4: SPP on Three-layer system 6 Figure 1.5: Sche
FUNDAMENTALS OF PLASMONICS
History of development
Long before the scientific study of plasmonics, ancient artisans harnessed its properties to produce vivid colors in glass artifacts A notable example is the Lycurgus Cup from the 4th century AD Byzantine Empire, which appears green under normal lighting but shifts to red when illuminated from within This color-changing effect is achieved through the incorporation of gold and silver nanoparticles of varying sizes and shapes within the glass, showcasing the remarkable artistry of the time.
Figure 1.1 Lycurgus cup illuminated under normal external lighting (left) and from within (right)
In the early 20 th century, Robert Wood observed a pattern of extraordinary dark mirror with a di raction grating on its surface This is considered as the first observation of plasmon
In 1956, David Pines proposed a theory to explain the energy losses encountered by fast electrons moving through metals, attributing these losses to the collective oscillations of free electrons within the metal These oscillations bear resemblance to plasma oscillations.
In 1957, Rufus Ritchie published a groundbreaking study on electron energy losses in thin films, demonstrating the existence of plasmon modes near metal surfaces This research provided the first theoretical framework for understanding surface plasmons, and in the following year, it also explored the interaction of bound electrons and light within transparent media.
In 1968, Andreas Otto and Erich Kretschmann introduced two innovative methods for exciting surface plasmons on metal films, significantly simplifying experiments for researchers This breakthrough marked a pivotal advancement in the study of surface plasmons.
Figure 1.2 Number of pape rs containing “surface plasmon” in the title [1]
Fig.1.2 shows the growth of the plasmonic field since 1960 to 2008 In middle s on Plasmonic increased rapidly achievements of nanofabrication techniques, physical analysis techniques and simulation codes
Despite its potential, research on plasmonics in Vietnam remains limited, with only a handful of scientists, including Prof Van Hieu Nguyen, Bich Ha Nguyen, and Van Hop Nguyen, actively exploring this area Their work primarily focuses on theoretical calculations related to bulk and localized plasmons.
Fundamentals of Surface Plasmon Polaritons
Surface plasmon polaritons (SPPs) arise from the strong coupling between electromagnetic waves and the collective oscillations of electrons at the interface of metals and dielectrics This phenomenon, characterized as a surface electromagnetic wave, can be effectively described using Maxwell's theory.
Firstly, we detail in SPPs that propagate on single interface of a metal and a dielectric medium For solving this problem, we consider the haft space z < 0 is
2 (Figure 1.3) By choosing the x axis in the direction of wave propagation, we get the dispersion of field at z = 0 plane [25]
In the context of surface plasmon polaritons (SPP), the tangential and normal components of the wave vector, denoted as kx and kz, are crucial for understanding wave behavior at the interface By applying Maxwell's equations alongside the continuous field conditions at this interface, we can derive the tangential component of the wave vector for SPP when z is greater than zero and when z is less than zero.
(1.2) ko function has the form
Figure 1.3 Geometry for SPPs propagation at a single interface between a metal and a dielectric
Typically, and , we get the complex
For real , we need and , this is the condition to occur SPP on the interface of two mediums Cause of the continuity of through the interface, we have
Surface plasmon polaritons (SPPs) are characterized by their p-polarized nature and an imaginary wave vector component (kz), indicating that they exist solely as transverse magnetic (TM) waves Notably, the wave number of SPPs exceeds that of light in a vacuum (ko) The imaginary component of the tangential wave vector is crucial as it defines the attenuation of SPPs, with the propagation length where the intensity decreases to 1/e being a key parameter in understanding their behavior.
In the case of metal with low losses and , propagation length is given approximately by
To achieve the maximum propagation length, it is essential to select a metal with a significantly negative real part and minimal losses For instance, in the case of silver, the propagation length can range around 50 wavelengths at a value of 0.5.
We will calculate the wave number components in the z-direction to assess the penetration depths in both the dielectric and metal Utilizing equations (1.2) and (1.6), we derive the necessary results.
Because both wavenumbers are purely imaginary, the field perpendicular to the interface evanescent and have the property like the near-field The penetration depth is determined from = 1/
In multilayer structures, surface plasmon polaritons (SPP) occur at each individual interface When the separation between adjacent interfaces is similar to or less than the penetration depth of the interface mode, the interactions between SPP lead to the formation of coupled modes This phenomenon can be analyzed using Maxwell's equations and the continuity conditions of the electromagnetic field at each medium interface.
The thickness of the metal layer, denoted as d, plays a crucial role in the behavior of surface plasmon polaritons (SPP) Due to the complexity of the equations involved, our focus is primarily on simpler scenarios, particularly symmetric structures In these cases, the coupling effect separates SPP into symmetric and anti-symmetric modes, highlighting the significance of structural symmetry in their propagation.
Figure 1.4 Geometry of the three layers system symmetric mode reduces the wavenumber while anti-symmetric mode increases the wavenumber of SPP [15]
In the case SPP propagates in a metal wedge, we can approximate to the propagation of SPP in a thin metal film with the thickness d continuously changing to zero.
Wedge surface plasmon polariton waveguides
To achieve high integration density in photonic circuits, the development of miniature optical components for high-speed signal generation, propagation, detection, and processing is essential Recent research focuses on nano-scale optical waveguides that allow strong field confinement, facilitating denser packaging without crosstalk and minimizing bending loss Three primary types of nanophotonic waveguides have emerged: nanophotonic wires, photonic-crystal waveguides, and nanoplasmonic waveguides While the first two types utilize nano-structures with ultra-high index contrast, they are constrained by classical optical diffraction In contrast, nanoplasmonic waveguides surpass the diffraction limit, enabling deep sub-wavelength confinement and efficient light guiding, positioning them as a promising solution for advanced photonic applications.
Nanoplasmonic waveguides are emerging as attractive candidates for achieving ultra-high integration density, enabling the integration of electronics and photonics This technology has the potential to create ultra-small optoelectronic integrated circuits that offer low power consumption and high-speed signal generation, processing, and detection Various types of nanoplasmonic waveguides have been proposed and demonstrated, including metal nano-slot, strip, metal V-groove, wedge, and hybrid waveguides This study focuses on the structures, characteristics, and applications of wedge waveguides.
The wedge waveguide structure is designed to achieve modal sizes smaller than the wavelength while maintaining a high propagation length As illustrated in Figure 1.5, the evolution of wedge waveguide structures can be traced back to initial research efforts The first wedge waveguide, depicted in Fig 1.5 (a), showcases this innovative design.
The wedge waveguide consists of a metal substrate with a surrounding dielectric material, typically air The second type of wedge waveguide, illustrated in Fig 1.5 (b), is created by adding a dielectric layer over the metal wedge Additionally, the third common configuration features a dielectric wedge waveguide that is coated with a metal layer, as depicted in Fig 1.5 (c).
The modal characteristics of wedge plasmonic waveguides (WPPs) are influenced by geometric parameters, particularly the wedge height As the wedge height decreases, the effective modal index (neff) approaches that of a surface plasmon polariton (SPP) on a flat surface, indicating a transition where the mode becomes unguided when h is less than a critical height (hc) A lower effective index corresponds to a more extended field, while increasing the wedge height results in a reduction of both mode size and propagation length Additionally, the modal behavior changes with increasing wedge angle (φ), similar to the effects of decreasing height, but unlike height, there is no critical angle that leads to the mode becoming unguided.
As the angle approaches 180 degrees, the propagation length, effective index (neff), and modal size converge to those of a surface plasmon polariton (SPP) on a flat surface Although the modal size increases significantly with the angle, numerical simulations indicate that wave guiding persists regardless of the angle, as long as the angle remains less than a certain threshold.
Conventional wedge waveguides are illustrated in Figure 1.5, showcasing three distinct configurations: (a) a V-shaped wedge on a metal substrate, typically surrounded by air as the dielectric material; (b) a dielectric wedge waveguide that is overlaid with a metal layer; and (c) a structure akin to (a) but featuring a dielectric layer above the metal wedge, known as a dielectric-loaded wedge waveguide.
In a comparison of the CPP and WPP modes supported by a V groove and a wedge of identical dimensions, it is observed that while their propagation lengths are similar, the WPP mode exhibits a significantly smaller mode size than the CPP mode This difference arises because the CPP mode hybridizes with wedge modes at the groove's edges Additionally, the cutoff groove height for the CPP mode is greater than that of the WPP mode, indicating that when the groove height falls below this threshold, the mode ceases to be guided Consequently, regarding mode confinement and propagation loss, the WPP mode demonstrates superior performance compared to the CPP mode.
The wedge waveguide structure is designed to achieve modal sizes smaller than the wavelength, but conventional designs suffer from Ohmic losses in metal, resulting in short propagation lengths To address this limitation, several hybrid surface plasmon waveguides have been developed, which combine the tight light confinement of metal wedges with improved propagation lengths Recent advancements in hybrid wedge waveguides are illustrated in the dimensional (2D) cross-sectional schematic shown in Figure 1.6.
The waveguide illustrated in Fig 1.6 (a) is an advancement of the design in Fig 1.5 (c), featuring a high-index dielectric layer atop a low-index dielectric layer This configuration enhances the guiding properties of wedge plasmons, allowing modal sizes to be significantly reduced compared to traditional wedge waveguides The hybrid waveguides depicted in Figs 1.6 (b) and (c) consist of a low-index dielectric layer positioned between a high-index dielectric waveguide and a metal layer, resulting in tight confinement of the electromagnetic field within the low-index dielectric gap Research indicates that the electromagnetic field mode can be effectively confined at the nanoscale, with hybrid waveguides demonstrating longer propagation lengths than their conventional counterparts However, these hybrid waveguides face challenges in lateral confinement of the electromagnetic field within the low-index region To leverage the low-loss propagation capabilities of the waveguides in Figs 1.6 (a) and (c), the strong field confinement at the wedge tips is utilized to further minimize the guided mode size Figs 1.6 (d) and (f) present fundamental structures of hybrid waveguides incorporating wedge waveguide designs, while Figs 1.6 (g) and (h) illustrate double hybrid waveguides developed from the single waveguides in Figs 1.6 (e) and (f), respectively, showcasing strong coupling between the dielectric nanowire mode and long-range surface effects.
Figure 1.6 presents a two-dimensional schematic of typical hybrid wedge waveguides, including various configurations such as a hybrid dielectric-loaded wedge waveguide, a silica buffer layer between silver cladding and a triangular silicon wedge, and a triangular semiconductor waveguide surrounded by a metal layer Notably, the waveguide in Fig 1.6 (g) achieves both deep subwavelength mode confinement and low propagation loss, offering significantly longer propagation lengths compared to the waveguide in Fig 1.6 (e) while maintaining similar mode confinement levels Additionally, the waveguide in Fig 1.6 (h) exhibits a remarkable 9-fold enhancement in mode confinement for the same propagation length or a 2.4-fold increase in propagation length for equivalent mode confinement compared to the waveguide in Fig 1.6 (g).
The fabrication of wedge waveguides involves several key steps: first, a silicon wafer is coated with silicon oxide and photoresist; next, the resist is exposed and developed, allowing the pattern to be transferred into the oxide Subsequently, V-grooves are etched into the silicon, followed by the deposition of gold after the oxide removal Nickel is then deposited, and finally, the silicon substrate is dissolved, resulting in gold wedges with an angle of 70.5°.
In recent years, various models of conventional and hybrid wedge waveguides have been theoretically explored, yet experimental demonstrations remain limited, particularly for those with sharp apexes, which are challenging to fabricate Typically, wedge waveguides are not produced through conventional dry-etching methods; instead, they often utilize focused ion beam (FIB) techniques, as evidenced by the successful creation of a 40° silver triangular nano-wedge Furthermore, reports on wedge waveguides fabricated via wet etching are scarce, likely due to the significantly lower undercut etching rate of the (111) plane in single crystal silicon when using hydroxide solutions, complicating the fabrication process.
The hybrid fabrication process, which combines wet etching and the flip technique, enables the creation of wedge waveguide structures with larger dimensions and higher angles, reaching approximately 70 degrees This method involves chemically etching a V groove into a silicon substrate, followed by metal deposition into the groove and subsequent etching of the silicon substrate to achieve the desired wedge angles To obtain sharper wedge angles, an oxidation process for trench modification is recommended prior to metal layer deposition.
The schematic setup for fabricating surface plasmon polariton (SPP) structures is illustrated on the left, while the right side depicts plasmon propagation within a dielectric waveguide created through two-photon polymerization (2PP), with SPP excitation occurring on the right.
DESIGN AND SIMULATION OF WAVEGUIDE
Basic theory for the simulation of waveguides
Maxwell theory describes the expression of SPPs wave on a metal dielectric interface by [24]
[2.1] where kt and kn are tangential and normal component of wave vector k, respectively The wave vector kt is continuous through the interface, so we obtain
[2.2] and the effective refractive index of SPPs
In Eqs (2.2)-(2 d m are electric per tmi tivities of dielectric medium and metal respectively
For k > 0, the wave number k_n is purely imaginary, resulting in an exponential decay of the field This indicates that the wave is confined in the normal direction In a dielectric medium, the mode size, or skin depth, is defined as the distance at which the field intensity decreases to 1/e.
Using parameters in Table 1, we obtain the effective refractive index and mode size of SPPs propagating along the silver air interface being 1.0038 and 2.86 àm, respectively
At a metal tip, the coupling mode known as WPP is created by two surface plasmon polariton (SPP) waves traveling toward the tip from opposite sides of a wedge As these SPPs reach the tip, both their phase and group velocities diminish, with the group velocity approaching zero and the wave vector becoming infinite This phenomenon results in an infinitesimal mode size, enabling nanofocusing, while allowing the wave to propagate over extended distances.
However, this model is applied only to very small wedge angle (7 o ) For the large wedge angle (180 o imulation methods to
By finite element method, we can find the propagation constant of WPP mode, that satisfies eigenvalue equation
The three-dimensional modal analysis is conducted with a calculation size of 4x4x10³ Two boundary port conditions are applied to the front and back faces to examine the modes that can propagate within the structure Additionally, the perfectly matched layer extends five times larger than the calculation domain, with a minimum mesh size of approximately 1 nanometer near the waveguide's wedge.
Triangular Waveguide
Figure 2.1 Scheme of triangular shaped plasmonic waveguide used for simulation (left side) and the cross sectional view (right side) –
Structure of triangular waveguide is shown in figure 2.1 This structure consists of a triangular silicon waveguide, which is fabricated on a Silicon on Insulator
A noble metal layer is deposited onto the surface of a silicon-on-insulator (SOI) wafer to create a metal-dielectric interface This process involves using the silicon waveguide as a mold to shape the metal layer into an inverted V-like configuration The interface formed between the V-shaped metal layer and the surrounding air medium effectively guides surface plasmon waves, facilitating the manipulation of light at the nanoscale.
The propagation of the polariton (WPP) mode occurs on the wedge structure, and we will analyze how transmission characteristics vary with changes in structural parameters, including the metal layer, the shape of the wedge, and the refractive indices of both the silicon waveguide core and the surrounding air cladding.
Figure 2.2 Shape and distribution of meshing elements in the proposed structure
One of the primary challenges in simulation is meshing, particularly when employing the finite element method, as the accuracy of simulation results is heavily influenced by element size As illustrated in Figure 2.2, the shape and distribution of meshing elements within the waveguide structure are crucial Given the prismatic shape of the model, a swept mesh can be utilized along the waveguide's axis The necessary element size is determined by the electromagnetic field gradient; a higher gradient necessitates a finer mesh In the meshing process, we establish two key parameters: the number of swept elements (ns) and the number of elements per wavelength in the cross-section (nm).
In this context, \( l \) represents the length, \( \lambda \) denotes the wavelength in a vacuum, and \( n \) is the refractive index of the medium The wave vector of the WPP mode remains constant in the direction of propagation, allowing us to use a very coarse mesh (with \( ns \) less than ten) to enhance calculation performance.
Figure 2.3 Distribution of electric field in the waveguide at very coarse and very fine meshing (a) and the dependence of maximum electric field on the meshing (b)
Figure 2.3 (a) illustrates the electric field distributions resulting from simulations using very coarse (ns = 1) and very fine (ns = 60) meshing, highlighting a tenfold difference in results that underscores the significant impact of mesh size on accuracy Figure 2.3 (b) shows how the maximum electric field varies with the number of elements per wavelength, indicating that as ns increases, the maximum electric field value rises and approaches its true value as ns approaches infinity Due to computer memory limitations, ns is set to 60, corresponding to a maximum element size of approximately 2.5 nm in the metal layer.
2.2.3 The thickness of metal layer
Surface Plasmon Polariton only exists on the interface of a metal medium and a dielectric medium The metal medium has complex dielectric permittivity with negative real part
Table 2.1 Parameters used for simulating SPP mode
1.55 àm Wavelength in vacuum l 10 àm Length of waveguide h 1 àm Height of waveguide nSi 3.4757 Refractive index of silicon nSiO2 1.4957 Refractive index of silicon dioxide layer nAg 0.15649 11.567i Complex refractive index of Silver nAu 0.23823 11.263i Complex refractive index of Gold n m 60 Number of elements per wavelength ns 9 Number of elements sweep
54.7 o Sidewall angle t (10:10:200) nm Thickness of metal layer
The dielectric function of metals is effectively described by the Drude model, which posits that valence electrons are entirely detached from their ions and move freely within the lattice, resembling a free electron gas This model is particularly applicable to metals with high electron mobility, such as alkali metals, transition metals, and highly doped semiconductors In our study, we focused on gold and silver, both of which are prevalent in plasmonic technology We employed a sputtering technique to deposit a metal layer onto a triangular silicon waveguide, allowing for precise control over the metal thickness, which can be accurately adjusted to several nanometers.
25 metal film is the same throughout the structure, the wedge of metal is fillet with a ed radius equal to the thickness of metal layer
Table 2.1 presents optical parameters and structural parameters us for this ed simulation The thickness is studied in each step of 10 nm in the range from 10 to
The distribution of the normalized electric field across the cross-section of a waveguide varies with different thicknesses of silver and gold layers Specifically, for silver (Ag), the electric field distribution is analyzed at thicknesses of 10 nm and 200 nm, while for gold (Au), the corresponding thicknesses are also 10 nm and 200 nm.
Figure 2.4 (a) illustrates the normalized distributions of the electric field, highlighting that the maximum electric field values for both metals are nearly identical As the thickness of the metal layer increases, the maximum electric field also rises.
The electric field in a waveguide primarily concentrates around the wedge area, reaching its peak at the metal surface before rapidly declining with distance As illustrated in Figure 2.4 (b), this sharp decline is quantitatively represented by the intersection of the curves with the 1/e line, providing an estimation of electromagnetic energy confinement Notably, the mode size remains nearly constant for two different metals For a very thin metal layer of 10nm, the field drops to 1/e within just a few tens of nanometers, while for a thicker metal film of 200nm, the mode size increases to approximately 400nm This indicates that the confinement of waveguide modes is significantly influenced by the thickness of the metal layer rather than the type of metal used.
The transmission characteristics of the waveguide are illustrated in Fig 2.5, highlighting the impact of varying metal thicknesses This evaluation focuses on three key parameters: the effective mode index (n eff), which represents the ratio of the wave number of the WPP mode to that in a vacuum; the propagation length, defined as the distance over which the field intensity diminishes to 1/e; and the mode area, which encompasses the region where the electric field intensity falls off.
As depicted in Figure 2.5(d), the mode area, represented by the red region at the waveguide's wedge, exhibits significant changes with varying metal thickness An increase in metal thickness results in a decrease in the effective mode index and an increase in propagation length, both of which approach a constant value as thickness approaches infinity The mode areas for gold and silver are nearly identical, with a pronounced increase as thickness rises However, gold exhibits approximately double the attenuation compared to silver under similar structural parameters, prompting the selection of silver as the preferred metal medium for further studies.
Figure 2.5 Transmission characteristics of WPP mode at various thicknesses of metal (a-c) and the shape of mode area (d)
At a thickness of 20 nm, the propagation length reaches its minimum, indicating maximum wave attenuation Analysis of the electric field distribution reveals that it concentrates on the metal wedge while also spreading within the silicon waveguide This distribution resembles a high-order mode in the triangular silicon waveguide for both silver and gold cases As the metal thickness varies, the wavenumber of the WPP mode and high-order mode changes at different rates Notably, at 20 nm, the wavenumbers of both modes are equal, resulting in the strongest coupling, which significantly increases the loss of the WPP mode As the metal layer thickness increases, this coupling diminishes due to the divergence of the wavenumbers.
28 reason that the field falls off quickly in metal At the thickness more than 150nm, the coupling is negligible
Figure 2.6 Distribution of electric field of WPP mode at 20nm thickness of
Silver metal (top row) and Gold (bottom row)
2.2.4 The tip angle of triangular waveguide
This section explores the WPP mode in triangular waveguides with various tip configurations, where the wedge angle is defined as the angle between the two sidewalls of the silicon waveguide The wedge angle can be adjusted through different fabrication methods This thesis focuses on the fabrication of waveguides using wet bulk micromachining, specifically examining angles of 0°, 90°, 125.3°, and 135° The optical and structural parameters utilized in this simulation are consistent with those outlined in Table 2.1.
The distribution of the normalized electric field for the wedge-shaped plasmonic (WPP) mode varies with different wedge angles, as illustrated in Figure 2.7 This analysis focuses on silver as the sole metal, with thicknesses of 60 nm and 200 nm, demonstrating a relationship between the wedge angle and the electric field components in the y and z directions.
The distribution of normalized electric field component of the waveguide at variou
10 o , 30 o ), the structures can be fabricated only by dry etching or complicated value of electric field decreases and field is spread over a larger region Figure 2.7
Trapezoidal waveguide
In this section, we explored the properties of guided surface plasmon polariton (SPP) modes in a wedge waveguide with a triangular cross-section Utilizing wet bulk micromachining, we successfully fabricated both triangular and trapezoidal waveguides, allowing for precise control over the top surface dimensions of the trapezoidal design Notably, the wedge-shaped top surfaces support waveguide plasmon polariton (WPP) modes that can couple to create a hybrid WPP mode The characteristics of this hybrid mode will be examined in the subsequent section.
Figure 2.12 Sketch of the simulated structure at various sidewall angles (a) and cross-section of the trapezoidal waveguide (b)
Geometry structure of waveguide is schematically drawn in Fig 2.12 Silicon waveguide is fabricated on SOI wafer which has thickness of device layer h s = 1
The trapezoidal cross-section has an approximate height of 1 m, with a 2 μm thick SiO₂ buffer layer A silver film, applied through sputtering, encases the waveguide, all supported on a silicon substrate and situated in air Surface plasmon polariton (SPP) waves will propagate at the interface between the silver and air, assuming a perfectly smooth boundary This ideal condition is closely attainable through wet bulk micromachining techniques.
The study focuses on the design of crystal planes with a filleted top corner in a metal layer, maintaining consistent thickness at the tip Utilizing a (100) SOI wafer, we can achieve three distinct sidewall corner angles—45°, 54.7°, and 90°—as demonstrated in the accompanying figure The structural parameters for simulation align with those of a triangular waveguide, as outlined in the referenced table A new parameter, the width of the top surface of the trapezoidal silicon waveguide (w), has been introduced, which is marginally smaller than that of the hybrid WPP waveguide Despite this difference, the variability of both parameters is consistent, allowing for their unification in analysis This section will explore the influence of the top surface width and sidewall corner angles on the hybrid WPP mode.
Figure 2.13 Distribution of the normal electric field on waveguide structure of WPP mode at various sidewall angles (45 o , 54.7 o , 90 o ) with top face width of 1àm (a-c) and 100 nm(d- f)
Figure 2.13 shows the distribution of normal electric field on the cross section of waveguides The electric field amplitudes were normalized to the field maximum
As the sidewall angle increases, the electric field strength in the WPP mode also rises, aligning with previous findings Conversely, a decrease in wedge angle leads to an enhancement of the electric field in the WPP mode, resulting in a further increase in the field strength of the hybrid WPP mode.
As seen from the bottom row, it shows that the magnitude of field slightly increases, when the size of top surface is decreased (electric field increases less than
40 percent when top surface size decreases by 10 times) This may be hint that the hybridization of two WPP modes does not depend strongly on the distance
Figure 2.14 Variability of the rmal electric field on the top surface of no waveguide ( along AA’ cutline)
The distribution of the electric field in the hybrid wind power plant (WPP) mode on the top surface is illustrated in Fig 2.14, where the field's magnitude peaks at two wedges and reaches its lowest point at the center of the surface Adjusting the wedge angle leads to greater variability in the maximum field value compared to the minimum Conversely, altering the top surface size causes a rapid change in the minimum field magnitude This behavior can be further understood by examining the different components of the electric field, as shown in Fig 2.15, which depicts the distribution of the y and z components.
The electric field structure with a width of 1 am reveals that the Ey and Ez components exhibit anti-symmetry and symmetry across the y=0 plane, respectively The Ey component is primarily concentrated on two wedges and the side walls, while the Ez component is evenly distributed across the top face At the center of the top plane, Ey reaches zero, resulting in the normal electric field achieving its minimum value, Ez This minimum value is significantly influenced by the characteristics of the top surface, whereas the maximum value is determined by both the wedge angle and the top surface.
Figure 2.15 Distribution of different components of electric field E y (a-c) and E z -f) for the hybrid WPP mode with various sidewall angles (the width (d of top surface is 1 àm)
For estimating the mode size of hybrid WPP mode, we analyze the attenuation of electric field air medium along the norin
The dispersion relation of the electric field is illustrated, normalized to its maximum magnitude, indicating that the field diminishes exponentially The mode size at which the field decreases to 1/e is approximately between 200 nm and 500 nm, significantly smaller than the corresponding mode size.
The effective index and propagation length of the hybrid Waveguide Plasmon Polariton (WPP) mode are shown in Figure 2.16 (b) The WPP mode exhibits a higher effective mode index compared to Surface Plasmon Polaritons (SPPs), indicating that the wave number and field magnitude of the hybrid mode surpass those of SPPs propagating along a surface.
The attenuation of the field in the normal direction at a wedge in an air medium is illustrated in Figure 2.16(a) Additionally, Figure 2.16(b) presents the effective refractive index (blue line) and propagation length (red line) of waveguide structures with widths of 100 nm (solid line) and 1 µm (dashed line).
However, when neff increases, the propagation length decreases and depends quite strongly on the wedge angle
Figure 2.17 illustrates how the transmission properties are affected by the width of the top surface As the width (w) approaches zero, the characteristics approximate to zero Increasing the top surface width leads to a decrease in both the wavenumber and attenuation, approaching a value as w approaches infinity To avoid coupling between the waveguide mode and the wave propagation properties (WPP), we have established a metal layer thickness of 200 nm.
Figure 2.17 The characteristic of WPP mode in trapezoid waveguide when the width of top surface is varied
This section explores the characteristics of hybrid waveguide plasmonic (WPP) modes within various plasmonic waveguide structures that can be fabricated using wet-bulk micromachining The wave exhibits strong localization at both the wedges and the top surface of the waveguide Increasing the sidewall angle or reducing the width of the top surface enhances confinement, but this also leads to increased attenuation, highlighting a trade-off between these two factors.
FABRICATION OF WAVEGUIDE
Process of fabrication
Wet bulk micromachining is a widely utilized technology for fabricating Microelectromechanical systems (MEMS) devices, where micro-structures are created within a substrate through selective material etching This technique offers several advantages, including simplicity, cost-effectiveness, and high productivity, while also enabling the fabrication of atomically smooth surfaces due to its reliance on crystallographic orientations Such smoothness is crucial for the performance of surface plasmonic devices, as rough surfaces can significantly degrade the propagation of surface waves In this chapter, we will fabricate WPP waveguides on (100) SOI wafers using wet bulk micromachining, as designed in chapter 2.
Based on (100) silicon wafer, the anisotropic wet etching is usually uses the alkali solutions such as Tetra Methyl Ammonium Hydroxide (™AH), Ethylene
Diamine Pyrocatechol (EDP), or Potassium Hydroxide (KOH) solution Using lowly anisotropic etchants such as ™AH or EDP, we can fabricate V shape structures with sidewall being (110) or (100) lattice planes The s
45 o or 90 o In the case of highly anisotropic etchant KOH, the sidewall is (100) or
The sidewall angle of a plane can be either 90° or 54.7°, depending on the orientation of the mask line Simulation results from Chapter 2 indicate a significant relationship between the attenuation and the configuration at an angle of 54.7°.
The WPP mode exhibits the lowest etching rate in the direction, measuring only a few dozen nanometers per minute, facilitating precise control over the size of structures Consequently, we will utilize a KOH solution as the etchant to create waveguides with a sidewall angle of 54.7 degrees.
Figure 3.1 Schematic of fabrication process of waveguide
The fabrication process of waveguides, as illustrated in Figure 3.1, involves four key stages: first, traditional photolithography is used to create a photoresist mask line; second, isotropic etching in Buffered Hydrofluoric Acid (BHF) reduces the size of the mask lines and forms a silicon dioxide mask line; third, anisotropic etching in KOH solution defines the triangular or trapezoidal shape of the silicon waveguide; and finally, sputtering is employed to deposit a silver metal film onto the structure Detailed discussions of each fabrication step will follow in the subsequent sections.
We start our fabrication process with a 4-inch SOI wafer, featuring a device layer thickness of 1 µm and a buffered oxide layer thickness of 2 µm The goal is to grow a silicon dioxide layer on the wafer's surface, which will serve as an oxide mask in later steps Initially, we clean the wafer using a Piranha solution, composed of 98% sulfuric acid, 35% hydrogen peroxide, and deionized water in a 1:2:2 volume ratio The heat generated during hydration boils the solution and produces oxygen, effectively removing impurities from the wafer's surface The wafer is immersed in this solution until it reaches room temperature, after which it is thoroughly rinsed.
DI water This process would be used to clean up the sample, interspersed with later steps
Following, the wafer is oxidized in furnace at temperature 1100 o C The dry thermal oxidation occurred in reaction
After a 3-hour oxidation process, a silicon dioxide layer with a thickness of 200nm is achieved According to expression 3.1, producing 1 mole of SiO2 requires the consumption of 1 mole of Si This leads to a relative relationship between the thickness of the growing oxide layer (t_ox) and the thickness of the silicon layer lost (t_si).
Silicon has a density of 2.3209 g/cm³, while silicon dioxide has a density of 2.196 g/cm³ When calculating the thickness of a silicon layer consumed during the oxidation process, we find that for a silicon dioxide layer of 200 nm, 88 nm of silicon is used Consequently, the remaining thickness of the device layer, which serves as the height of the waveguide, is approximately 912 nm To maintain a consistent device layer thickness, alternative methods such as Chemical Vapor Deposition (CVD), Epitaxy, or Sputtering must be employed.
Fig 3.2 Array of designed Cr mask line patterns is used for investigating the fabrication process of WPP waveguides (a) and the arrangement of it on wafer
The next step involves creating a photoresist mask on the surface of an oxidized wafer, where the shapes of the resist mask align with the Chromium mask lines produced through a lift-off process on a glass substrate These metal strips, with widths ranging from 0.8 µm to 2 µm and spaced 5.0 µm apart, measure 2 cm in length, determined by the capabilities of the photolithography machine To achieve the desired (111) plane sidewall for the waveguide, the mask lines are oriented in the directions, either parallel or perpendicular to the wafer's flat Figure 3.2 illustrates the mask line shapes and their arrangement on the silicon wafer.
44 mask size enables the optimization of etching-time in the later stages to become easier
Figure 3.3 Spinner unit (a) and schem atically illustrating the spin coating of photoresist onto the SOI wafer (b)
The process of photolithography involves spin coating a photoresist layer onto a wafer's surface, as illustrated in Figure 3.3 (a), which shows the spinner unit used for applying both primer and photoresist Prior to this, a thin primer layer is applied to improve the adhesion between the resist layer and the substrate The rotation speed and time settings for the spin coating process are depicted in Figure 3.3 (b) Following the application of the photoresist layer, the wafer is baked on a hotplate at 90°C for 90 seconds to evaporate any remaining solvent.
After the spin coating process, the Chromium mask line is transferred to the wafer using the Double Side Align system PEM 800, which employs a 250W mercury vapor lamp to emit ultraviolet radiation at a wavelength of approximately 400nm The UV source radiates power at 12 mW/cm², and the wafer is exposed for 45 seconds in hard contact mode before being soft baked on a hotplate at 90°C for 120 seconds.
Following mask alignment, the photoresist undergoes development for 45 seconds Subsequently, the photoresist mask is hard baked at 120°C for 15 minutes The quality of the mask lines is initially assessed using an optical microscope.
Figure 3.4 Double Side Align System PEM-800 used for photolithography
3.1.3 Isotropic wet–etching in buffered Hydrofluoric acid solution
In this stage, the photoresist mask is utilized to define the oxide mask lines that safeguard silicon in a potassium hydroxide solution Employing photolithography, we can create mask lines at the micro scale; however, this section focuses on refining the oxide mask lines to achieve a sub-micro scale size.
Isotropic etching of silicon dioxide is performed using a Buffered Hydrofluoric (BHF) acid solution at a 1:5 ratio This etching solution consists of a mixture of 40% by weight ammonium fluoride (NH4F) and 49% by weight hydrofluoric acid (HF) in a 5:1 volume ratio The chemical reaction between these components effectively dissolves silicon dioxide.
In the initial phase of isotropic etching, the etchant targets the exposed silicon dioxide surface, creating oxide mask lines that match the width of the photoresist mask At room temperature, a BHF 1:5 solution etches at a rate of approximately 100 nm per minute, requiring roughly two minutes to fully etch the unprotected SiO2 layer.
In the second step of isotropic etching, the etchant targets both side walls of the silicon dioxide strip, leading to undercut etching that reduces the mask line width to sub-microscale This phenomenon occurs because the reaction products hinder the movement of etchant, resulting in a decreased etching rate Consequently, achieving smaller structures becomes challenging due to the accumulation of reaction products and the wet adhesion of photoresist on the buffer layer's surface To further reduce the size of the structures, an additional undercut etching process using KOH solution is required.
3.1.4 Anisotropic etching in Potassium Hydroxide
Results of the fabrication of waveguide
Figure 3.6 Scanning electron microscope image of silicon dioxide mask lines after isotropic etching in 2 min
The scanning electron microscope (SEM) image in Figure 3.6 illustrates the oxide mask lines, revealing that the width of the second mask line measures 1.02 µm, which is slightly narrower than the Chromium mask at 1.1 µm This discrepancy may result from diffraction during photolithography or variations in room temperature affecting the etching rate of BHF However, this level of error is considered acceptable at the microscale.
The SEM image in Figure 3.7 shows the second mask line after an etching time of 8 minutes, indicating an average undercut etching rate of approximately 60 nm per minute, which is lower than the etching rate observed in the first step.
Reducing the size of oxide mask lines to under 100nm is challenging due to the increased under distance, which hinders the movement of reaction products This accumulation makes it difficult for the etchant to effectively reach the sidewalls of the oxide mask lines, resulting in a decreased etch rate over time Additionally, embedding the sample further complicates the etching process.
Figure 3.7 Scanning electron microscope image of dioxide mask lines after isotropic etching in 8 minutes
The BHF solution effectively destroys the photoresist layer, which consequently leads to the rapid degradation of the oxide mask To facilitate the easier movement of reaction products, increasing the thickness of the oxide layer is beneficial However, it's important to note that this may affect the deposited rate of the dry film.
We can use wet oxidation for depositing the thick oxide mask, but the oxide which forms by this technique is porous and low quality
After 2 minutes of etching, the top surface size measures 244nm, decreasing to 91nm after 6 minutes This indicates an etching rate of approximately 16nm per minute on the (111) plane, with an anisotropy ratio of about 90 By continuing the etching process, it is possible to reduce the top surface size to zero, ultimately forming a triangular waveguide.
We introduced a high-throughput top-down fabrication method for creating single-crystal silicon waveguides using standard photolithography and KOH wet-bulk micromachining techniques These single-crystal silicon waveguides serve as molds for the subsequent formation of surface plasmonic waveguides after the deposition of a metal layer.
Figure 3.8 The SEM images of silicon waveguide after anisotropic in 2 min
In this thesis, we have proposed wedge plasmon polariton waveguide structures that are based on the etching properties of single crystal silicon in Potassium Hydroxide solution
The thesis conducts a simulation analysis to examine how structural parameters affect the transmission characteristics of waveguides It reveals that electromagnetic waves are strongly confined at the nanoscale within the wedge and top surfaces of the structures Reducing the wedge corner distance or increasing the refractive index of the surrounding medium enhances confinement, although it also leads to increased attenuation Additionally, in the presence of a very thin metal layer, the waveguide photonic plasmon (WPP) can couple with high-order modes in silicon dielectric waveguides, resulting in changes to the propagation characteristics.
This article presents an innovative and cost-effective technique for fabricating waveguide structures through wet bulk micromachining, enabling precise control at the nanoscale Utilizing this method, we have successfully created various structures based on our simulation results.
- Establish a measurement setup to verified the obtained results from simulation
- Explore a possible solution for integrating the waveguides into optic circuits
- Develop coupling mechanism for the waveguide and optical sensors based on the waveguide
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