In summary, DNA patterns have been successfully fabricated on silicon (100) substrates via UV light initiated covalent attachment of the alkene UANHS, modified with functional groups for the conjugation of oligonucleotides. Patterns were designed and masks were pro- duced to meet both the biological and optical requirements for fabrication and functionality. DNA patterns were then successfully created on silicon substrates for use in diffraction ex- periments. The patterns were neat and well-defined, with an absence of non-specific attach- ment and high density of DNA attachment, with a fluorescent probe hybridisation density of 1.2×1013 molecules/cm2 representing a major achievement. Oligonucleotides were attached
to gold nanoparticle labels complementary to sequences immobilised on the silicon surface. The gold nanoparticles were then successfully hybridised to DNA immobilised on the planar silicon substrate for use in diffraction experiments.
Silver enhancement (of gold nanoparticles) enabled the presence of hybridised gold nanopar- ticles to be detected using optical microscope reflection images to observe the change in contrast between silvered-DNA regions and the silicon substrate. The silver enhancement was verified, and individual particles with sizes in the range of 200−700nm were observed, by using SEM. The silver enhancement of gold colloids should increase the sensitivity of the DNA grating sensor compared to using gold alone by increasing the size of particles, causing a larger change in the reflectivity contrast between the DNA and silicon regions and generating more diffraction.
The physical and biochemical fabrication processes have been successfully established and optimised so that biological diffraction gratings could be prepared to enable the sensor performance to be evaluated.
CHAPTER 4: MODELLING 1-D DIFFRACTION GRATINGS 94
Chapter 4
Modelling 1-D Diffraction Gratings
4.1
Principles of Diffraction Analysis
The first DNA analysis sensor investigated in this project was based on a one-dimensional re- flecting diffraction grating. This consists of an array of parallel lines with periodic repetition. This chapter outlines the basic principles of how reflecting diffraction gratings work.
In order to develop the optimum diffraction grating pattern design for a DNA grating on silicon, diffraction theory had to be extended and modelled to cover an interlaced diffraction grating. In this situation both the DNA lines and the silicon substrate between the lines form reflecting diffraction gratings, which combine to contribute to the final diffraction pat- tern. The aim was to develop a grating structure which would maximise the sensitivity of diffraction order intensities to an increase in reflectivity of the DNA region (associated with hybridisation of gold nanoparticle probes).
The results of modelling interlaced reflecting diffraction gratings are used to design the opti- mum grating for fabricating with DNA on silicon. The surface coverage of gold nanoparticles is related to the change in reflectivity of the DNA lines and used to predict the change in diffraction. The effects of variations of diffraction grating parameters are also considered later in the chapter.
4.1.1
The Causes of Diffraction
Diffraction is a wave phenomena property of electromagnetic radiation. Diffraction may be defined as the departure from rectilinear propagation that cannot be interpreted as reflection or refraction. It is an effect resulting from interference of electromagnetic waves encountering obstacles, being scattered off surfaces, or passing through apertures. Diffraction is a useful technique to analyse the spacing between layers or rows of particles. For example, X-ray diffraction has been used to determine the orientation of single crystal grains, to determine the crystalline structure of materials, and to measure the size, shape and internal stress of small crystalline regions.
When light scatters off an atom the photon interacts with the atom and the resultant re- radiated photon has an equal probability of travelling in any direction. In scattering from regular arrays (for example in crystalline materials), constructive interference occurs in cer- tain directions due to the geometry. This occurs when probability density waves of scattered photons interfere in-phase, adding constructively in superposition [218].
Electromagnetic waves may be described by the solution of Maxwell’s wave equation, E =
Eoei(k.r−ωt+φ), where E is the electric field intensity, E
o the maximum intensity, ω is the
angular frequency of propagation andφ is the phase shift,kthe propagation constant and r
the point of observation at timet [219]. For the waves to be in phase and add constructively thenφ = 2mπ , where m is an integer. The intensity of scattered waves is the square of the total amplitude, which is given by the summation of the amplitudes of the electromagnetic fields from all points in space (by the principle of superposition). When the phase of scat- tered waves at a point is exactly out of phase (φ = π), then complete cancellation occurs (destructive interference).
4.1.2
The Diffraction Grating Equation
Diffraction effects are easily observed by examining the transmission of light through multiple slits. By considering the interference of light propagating from each slit using ray optics the diffraction grating equation may be derived. An equivalent situation is to consider the interference of light reflected from a periodic array of reflectors, such as depicted in Figure 4.1. The diffraction grating equation describes the angle of an intensity maximum of the light diffracted from the scattering aperture (or surface), related to the order of the interference
4.1 Principles of Diffraction Analysis 96 pattern, the regular spacing of the contributing sources in the array and the wavelength of light used.
Figure 4.1: Rays scattered parallel with respect to each other are of the same diffraction order of wavelength path difference.
Parallel coherent light rays (for example, from a laser), are incident at an angle θi on the
plane of adjacent lines of a diffraction grating which are separated by a distance d. Rays that scatter in a parallel direction belong to the same diffraction order (see Figure 4.1). The parallel scattered rays are aligned at an angleθm to the normal of the plane. At the point
of observation any difference in the optical path length travelled between interfering rays, is a consequence of their diffraction being from different lines.
Figure 4.2: There is an optical path length difference introduced between incident and diffracted beams.
The optical path length difference on incidence (∆i) between two light rays incident on
adjacent lines separated by a distance d is ∆i = dsinθi (see Figure 4.2). The difference in
To form an intensity maximum all the rays of the same order (i.e. rays that have scattered parallel to each other) must interfere constructively. Hence the total path difference ∆ =mλ, wheremis an integer, so that all the waves are in phase and their path difference is a whole number of wavelengths.
The total optical path length difference (∆) between incident and scattered rays necessary for constructive interference is ∆ = ∆m−∆i =mλ :
d(sinθm−sinθi) =mλ (4.1)
This is called the diffraction grating equation [220]. The diffraction grating equation specifies the angular location of the principal maximum of the mth diffraction order [221]. The equation relates the angle θm of diffraction order m to the grating period d, for a given
wavelengthλ of light incident upon the grating at an angle of θi [222]. Under the condition
of an infinite array of diffracting slits, or scattering points, then the superposition of light rays will cancel everywhere except where the path difference is exactly mλ. This leads to a diffraction pattern of sharply defined points; intensity maxima. When there is a finite number of scattering points in the array there will not be exact cancellation at all points in between maxima, and the points will be ‘blurred’ or broadened. In this case, the grating equation specifies the location of the centres of the intensity maxima relative to one another.
A pattern that has small features in real space, of the same order of magnitude as the wavelength of light, will produce a diffraction pattern that is broad in reciprocal space compared to features which are several orders of magnitude larger than the wavelength, which will produce narrow features in a diffraction pattern. The greater the number of scattering points involved in generating the diffraction pattern, the narrower the angular width of the intensity maxima will be in reciprocal space.