# Design of Inverted Nano-Cone Arrayed SERS Substrate for Rapid Detection of Pathogens
## 1 Introduction  
Rapid detection of bacterial infection is a very critical and urgent part of infectious disease diagnostics and treatment. Sepsis kills more than 25 percent of its victims and costs hospitals billions of dollars annually. In the U.S. alone, more than a million people become infected each year, resulting in as many as half of all deaths in hospitals [1, 2]. But the diagnosis of sepsis takes possibly up to five days to cultivate and identify bacteria in current clinical standards [3, 4]. This need of novel diagnosis tools pushes forward the development of biosensors. Many biosensors have been developed to detect bacteria in blood, serum, water, foods and biofilms. Several biomaterials (enzymes, antibodies, DNA and lectin) are used to identify a target molecule and produce perceptible signals detectable by a transducer. Surface Enhanced Raman Spectroscopy (SERS) is a label-free-based optical biosensor, utilizing a modified form of Surface Plasmon Resonance (SPR). In Raman spectroscopy, aslaser light interacts with a sample, the light will be scattered inelastically [5; 6; 7]. During this process, the inelastic scattering of incident photons [8; 9] can change wavelength according to the vibrational modes of the molecules. This difference of wavelength between incident and scattered photons provides rich vibrational information about the chemical bonds. Practically, it can also provide a high spatial resolution [10]. To improve and enhance Raman signals, SERS employs metallic nanomaterials, like a SERS tag. A SERS tag consists of modified metallic nanoparticles with specific capturing probes or Raman reporter molecules. This approach provides a high sensitivity approach with multiplexing potentials. The crucial task to employ SERS into low concentration bio-sensing is to increase the intensity of the vibration mode, \(I_{ SERS}\), by enhancing the electric field at the location of the sensing [11]:  
\[I_{ SERS}\propto\left|\frac{E(\lambda)}{E_{0}(\lambda)}\right|^{2}\left|\frac{E (\lambda_{s})}{E_{0}(\lambda_{s})}\right|^{2} \tag{1}\]  
where \(\lambda\) is the incident wavelength and \(\lambda_{s}\) is the Raman scattering wavelength, \(E\) is the local electric field intensity, and \(E_{0}\) is the incident electric field intensity. Since the frequency shift due to Raman scattering is small compared to the incident wavelength, the enhancement factor (EF) can be written as [12]:  
\[EF\ \propto\left|\frac{E(\lambda)}{E_{0}(\lambda)}\right|^{4} \tag{2}\]  
With a given order of magnitude enhancement on light field, the signal output of a substrate is:  
\[I\propto EF\times N_{molecule} \tag{3}\]  
where \(N_{molecule}\) represents the number of molecules in contact with plasmonic \"hot-spots\". The most common way to improve the EF factor of a substrate is to use plasmonic material that supports Localized Surface Plasmon Resonance (LSPR) [7]. In LSPR, the surface plasmon will bond the photon close to the surface of metal, confine the light field in a short range and increase light field intensity. However, the LSPR made by the deposition process has an EF factor far from perfect. In a typical sepsis detection, when the concentration of bacteria in sepsis patients is as low as 1-100 CFU/mL, the pathogen has to be enriched by a factor of \(10^{5}\) to perform Raman measurement [13; 14]. In this situation, the state-of-the-art Raman enhancement approach is to increase the intensity of the local electromagnetic environment. For example, [PERSON] et al. [15] placed gold dimers on a metallic surface. The metallic surface generates plasmon and confined light fields. The dimers take the photons from a concentrated light field and the EF is around \(10^{5}\). [PERSON] et al. [16] use an Au disc array on a dielectric-metal-quartz substrate. The periodic disc array scatters lights into a wave pack whose wavevector matches the plasmon mode between dielectric and metal, and photons are trapped and delivered to the discs. In this work, the EF rises to \(10^{6}\). [PERSON] et al.