Piezoelectric Biochemical Sensors

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1 1 Piezoelectric Biochemical Sensors Outline Piezoelectricity Mechanical Resonance Bulk Acoustic Wave (BAW) devices Quartz Crystal Microbalance (QCM) Surface Acoustic Wave (SAW) devices Love Acoustic Wave (LAW) devices Plate Acoustic Wave (PAW) devices

2 2 Piezoresonators as Biochemical Sensors How does it work a resonator? A change in mass or elastic properties of a resonator modifies the resonant freuency Ideal transducers for affinity interactions which do not necessarily involve redox reactions or variations in the charge state of the system. - Immunoreceptors (antigen/antibody) -Some transmembrane proteins (Acetylcholine, Lectins, ) -DNA How does mass loading affect the resonant freuency? Different types of resonant sensing devices

3 3 Piezoelectricity at a glance Greek ancient: Greek term piezin means to press 188 : The Curie brothers found that Rochelle salt crystals produce electricity when pressure is applied in certain crystallographic directions (piezoelectric effect) : Lippman predicted that an applied electric potential would produce a mechanical deformation (reverse piezoelectric effect) : Lord Rayleigh published On waves propagating along the plane of an elastic solid 1917 : Langevin uartz crystals used as transducers / receivers of ultrasound in water (SONAR) 1919 : First demonstrations of loud speakers, microphones 1921: Cady : uartz resonator for stabilizing electronic oscillations Increase of the resonant freuency by drawing pencil marks on the electrodes, and decrease of the freuency by rubbing electrode material off with an eraser 1946 : Cady: Piezoelectricity Electric polarization produced by mechanical strain in crystals belonging to certain classes, the polarization being proportional to the strain and changing sign with it 1959 : Sauerbrey the freuency shift of a uartz crystal resonator is directly proportional to the added mass : White, Voltmer Direct piezoelectric coupling to surface acoustic waves Today: Piezoelectric devices in watches, TVs, radios, radar, communication satellites, mobile phones, car sensors, biosensors!!

4 4 The Piezoelectric effect. Review of concepts Deformation of a material is forced by applying a stress, Displacement, u, is used as a deformation measurement T = F A ( force) ( area) Stress induces a corresponding strain, S, which is the rate of change of the displacement. Elastic/inelastic used to defined materials which recovers/or not the original shape and size upon removal of the stress Strain and stress can also be defined as: dilatational/compressional mode : deformation increases along an axis in the direction of the applied stress applied stress deformation direction shear mode : deformation occurs in a plane with its normal parallel to the applied force. applied stress deformation directions

5 5 The Piezoelectric effect. Review of concepts Resonance : With stress applied to an elastic isotropic material, individual atoms are moved from their resting position, increasing the potential energy (E P ) of the system. - The structure and bonding of the material influence the displacement and the force reuired for that deformation. Removing the stress accelerates the atoms back to their original position, where the velocity (kinetic energy, E K ) is maximum. Then the material overshoots, E K is reconverted to E P, and the material is deformed in the opposite direction. ideal resonator: u displacement u sin( ωt) Viscosity, resistance to deformation of the material. The system energy is converted to heat and the motion is damped. u = u max sin( ωt) u = u exp( t / τ ) max τ η (viscosity) displacement time damped resonator

6 6 Piezoelectricity How does a mechanical deformation produce an electric potential? uartz crystal Si O compression in one direction increases the polarization (or charge separation) between the electronegative O and the electropositive Si atoms. charge separation selecting the direction of applied stress with respect to the crystallographic axes of a uartz crystal, a difference in surface potential across the material can be induced. compressional stress when a positive potential is applied to the surface, Si atoms are forced away, producing a mechanical deformation (reverse piezoelectric effect)

7 7 Quartz Crystal Structure X plate crystals: large voltage generated when compressed and decrease in freuency with T increases Y plate crystals: large voltage generated by shear stress and increase in freuency with T increases X cuts exhibits an extensional vibration mode with AC voltage AT cuts (35 degrees off the Y axis) vibrates in the thickness shear mode

8 8 Piezoelectricity Only specific materials, belonging to certain crystal classes, show the piezoelectric effect - uartz, cadmium sulphide, lithium niobate, lithium tantalate, zinc oxide, lead zirconium titanate (PZT), III-nitrides group (GaN, AlGaN) Constitutive euations : T D T = cs e E = es + ε E applied stress electric displacement (polarization) S induced strain E electric field c stiffness coefficient matrix e piezoelectric constant matrix ε permittivity (dielectric constant) matrix

9 9 Mechanical resonance How does a mechanical resonance result in acoustic waves [periodic particle displacement: u =u sin(ωt) ]? voltage pulse δv x= displacement displacement t < t = distance distance δv causes an initial displacement, u, in the direction of E. Then, the system relax to the initial position as a damped resonator. Time-varying mechanical displacement. In addition, due to the piezoelectricity of the material, a charge separation is forced, and therefore a time-varying electric field in phase with the mechanical displacement. Resonance is obtained if this induced electric field is reapplied to the device in phase with the displacement displacement voltage pulses polarization time

10 1 Mechanical resonance The resonance condition generation of an acoustic pulse by applying an electric potential pulse via electrodes. the generated wave will propagate until it reaches a boundary and is reflected. The reflected wave will generate an electric potential in the electrode. the new electric signal regenerated an acoustic wave. - outgoing and returning waves are not in phase destructive interference wave cancellation - outgoing and returning waves are in phase constructive interference standing wave wavelength (λ) in a certain relationship to the physical size of the medium no net gain or loss in energy through the process of generation, propagation, and regeneration. Due to the damped wave motion (frictional losses, ), an extra electric energy has to be supplied to each regenerated wave. Z PE measures signal attenuation θ arg( Z ) = PE delay between applied field and induced displacement V =A x V i

11 11 Mechanical resonance The resonance condition V =A x V i feedback fraction β = Z Z PE PE + R V A = β V for continuous oscillation V f = V i βa = 1 βa βa <1 >1 amplitude decay continuous amplitude increase loop gain condition In addition, and because Z PE is arg A = 2n complex, V f and V i must be in phase ( β ) π loop phase condition Changes in the environment of the piezoelectric device perturbing i) acoustic wavelength or velocity change in resonance freuency ii) energy stored or lost change the gain reuired to maintain constant amplitude

12 12 Piezoelectric resonator euivalent circuit C C m L m R m C static capacitance of uartz Energy stored through electric polarization can be modeled by a capacitance (C m ), which is related to the material elasticity and any coupling of the surface to an elastic medium. resonant system The inductance (L m ) models the inertia arising from material mass and viscosity, and it depends on the mass loading and any coupling of the surface motion to a viscous medium. The frictional losses are represented by the resistance R m, related to the amount of material in motion. R m increases whenever acoustic energy is coupled to the surroundings. Z = R + ( X X ) m L C X ω L = ωl = m L 1 m C m X C 1 = ωc m resonance freuency

13 13 Bulk Acoustic Wave (BAW) sensors The first piezoresonator employed as a chemical sensor was a AT-uartz resonator Two metal electrodes deposited on a thin slice of uartz cut with a specific orientation relative to the crystallographic axes (AT-cut) Displacement in a thickness-shear mode, in which the entire material is subject to particle displacement Quartz Crystal Microbalance (QCM) resonant condition: thickness eual to an odd number of a half wavelength d λ 2d = n λ =, n = 1,3, n ν b shear wave velocity (~ 32m/s for uartz) f ν = b = λ ν b n 2d [For a typical thickness d =.2 mm typical resonant freuency ~ 9MHz ]

14 14 Mass sensitivity of QCM Sauerbrey (1959) - For small mass changes, the added mass can be treated as an additional mass of uartz with its corresponding added thickness d The change in thickness, d, causes a change in the oscillation freuency, f. An increase in thickness and mass produces a decrease in freuency. f ν b = 2d d d f f = d d M = ρ Ad For uartz, ρ = 2.64 g / cm ν b = 3,33cm / f =1MHz, A = 1cm 2 f M = 23 Hz/µg s 3 f = 2 f 2 1 ρ ν b M A f f M = M f f f M 2 = ρ Aν ν b = 2d b f

15 15 Liuid operation Initially it was believed that QCM could not be operated in liuid due to excessive wave damping by acoustic coupling into the liuid. However, stable resonance can be obtained if only one face of the QCM resonator is in contact with the liuid. Due to the strong adhesive forces between the liuid phase and the surface there is a strong coupling of the wave motion from the surface into the liuid Due to the moderate cohesive forces in the liuid (much smaller than in a solid), the motion damping is very accentuated. The decay rate of the liuid compressional waves, and the amount of energy coupled to the liuid depends on the liuid viscosity. The lost of acoustic energy results in a change in freuency and/or attenuation.

16 16 Liuid operation freuency shift f = f 3 2 l, refers to liuid ηl ρl πρ µ ηl viscosity µ elasticity ν b = µ ρ important: films of biological origin (nucleic acids, proteins) can have viscoelastic properties such that large f can be observed, even under circumstances where only minimal mass change is expected real-time studies of protein-protein, protein-small molecule, and protein-nucleic acid interactions.

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