Our requirements required many special considerations due to the thinness of the material, the aspect ratios and dimensions we were looking for, and the fragility of our membrane devices. The piezoresistive response of the device in liquid was demonstrated through the use of the pulsating fluid machine.
Overview: Mechanical Sensors for Biology
Force spectroscopy is not limited to research into interaction forces, but has also been applied to the study of conformational changes, for example of the enzyme lysozyme8 and of the unfolding of the protein titin.9 Force spectroscopy has also been used to study DNA hybridization processes. 10. Clearly, force spectroscopy has proven to be an extremely fruitful approach for studying biomolecular interactions.
Motion Transduction via Piezoresistive Sensing
In both cases, the signal arises from a change in the dynamic, fluid-coupled response function of the device as a direct consequence of the binding of the analytes under study. Biosensing with NEMS is based on effecting a change in the dynamic properties of the device when a target analyte is captured.
BioNEMS Detection Based on a Change in Device Damping
The binding of an analyte will lead to a change in the effective spring constant of the cantilever if its immobilization forms a structural bridge between the movement element and another body. The immobilization of a target analyte causes increased attenuation, which can be detected by the resulting change in the response function of the device.
Coupled, Multiple-Cantilever Devices
In this modality, the biomolecular coupling induces additional motional correlations between two cantilevers—correlations that exceed the "parasitic" one. Both of these concepts can be translated into realistic two-cantilever biosensor protocols in several ways.
Practical Considerations
Specificity and the Stochastic Nature of Single-Analyte Binding Events
Throughout this thesis x will be referred to the displacement of the cantilever point. The effective mass of the device including liquid charge is discussed in section 2.2.3, as well as the effective damping coefficient, γeff.
BioNEMS Displacement Response Function
In this approximation, the fluidic forces at each frequency and on each section of the cantilever are proportional to the displacement at that point. This is analogous to the response function of a resonant device in vacuum, except that in the latter case the effective mass and damping are frequency independent.).
Cantilever 2
- Calculation of the Spring Constant and comparison with simulations
- Calculation of the Cantilever’s Effective Mass in Vacuum
- Piezoresistivity: an Overview
- Maximal Transducer Current Bias
In deriving the spring constant we have shown that the tension at position y along the length of the cantilever is given by. Knowing these parameters, we now estimate the coupled force sensitivity of the prototype system.
Frequency [MHz]
Low Frequency Transducer Noise
Based on numerical calculations of the depletion length, the number of carriers in the doped region is estimated to be 1.2x104 for cantilever 3.†. At the heart of the device is the piezoresistive console shown in the lower part of Fig. Soitec is one of the leading suppliers of silicon on insulator [SOI] thin film (<340 nm) conductors.
Once bonded, the combined thickness of the oxide layer from each of the two wafers forms the buried oxide. Nevertheless, the residual damage from the hydrogen ions is expected to be much less than that for the thermal oxidation process.1 The disadvantage of the wafer bonding process is that the bonded wafers generally suffer.
Complete Fabrication Procedure for Early Foundry Runs (PHSMEMS, SA)
For the original prototypes fabricated in-house, liftoff techniques were used to form the electrode patterns. The passivation was patterned photolithographically and etched via wet etching in buffered oxide etchant (BOE). Then, 30 nm of chromium was deposited over the passivation, patterned via photolithography and defined by wet etching.
The backside was then cleaned and the backside oxide patterned (by masking and dry etching). A DRY was performed up to the buried oxide, which was then removed with a wet etch.
Improved Fabrication Procedure for Foundry Runs (Tronics, SA)
Timing requires strict control as overetching/undercutting leads to distortion of the shape of the trenches which are exaggerated during DRIE. Since the processing adjustments, the standard deviation of resistance for devices of the same dimensions is ~9%. To achieve the latter, the tungsten layer is shaped to protrude beneath the gold at the tip of the electrodes (see Fig. 3.1.E).
Timing requires strict control as excessive etching/undercutting leads to trench shape deformation that is exaggerated during DRIE. In the absence of the tungsten interface, there would be a high risk of mechanical fractures in the gold coating in the interface.
Nanofabrication Processes Performed at Caltech
A mask thickness of 350 nm is used for a silicon thickness of 110 nm and a mask of 30 nm for a silicon thickness of 30 nm. The PMMA mask will not withstand ECR etching, so µRIE is used instead. Carbon tetrafluoride is used for µRIE etching at a flow rate of 18 sccm and a pressure of 100 mTorr.
This PMMA mask is etched in an oxygen plasma with a flow rate of 10 sccm and a pressure of 90 mTorr. The fragility of these devices raises concerns about the applicability of these devices as they are intended for use in liquids.
Fabrication of the Microfluidics
Piezoresistors are designed to have a thin layer of heavily doped silicon on top of the nominally intrinsic silicon.
Summary of the Calculation of the Doping Profile in Doped Silicon with Two Different Doping Levels
Summary of Conclusions
An expression relating the expected resistance change for a given displacement of the cantilever tip was calculated in the previous section. The piezoresistive response of the device is characterized using an AFM to displace the cantilever tip by a known amount. A positive tip displacement corresponds to a downward movement of the cantilever tip from the neutral position.
This custom preamplifier was used for many of the silicon piezoresistive devices and is featured below. A direct estimate of the effective number of carriers involved in conduction, based on the device geometry and depletion length calculations of section 3.3, provides an estimate for the effective number of carriers in the 6x106 legs.
Measurement of Noise Floor in Fluid
The current path runs along the two outer silicon "legs"; a central Au-coated silicon “line” running longitudinally along the center of the device enables biosensor applications.3 (b) Voltage noise spectral density obtained at room temperature with a bias of 0.3 V, measured at the output terminals of the device. Prior to the nanofabrication steps, the oxide layer is removed from the back side of the trenches by buffer oxide etching. The effect of a gold electrode patterned along the center of the device was included in these simulations.
To evaluate the temperature-dependent force sensitivity of the device, evaluation of the actual device temperature is required, which can be affected by pre-current induced heating. The temperature dependence of the mechanical properties of the device is determined by the phonon temperature (Tph).
Experimental Configuration for Temperature Control
The average speed of sound for silicon is given by s 3 2 3 3. at 73K) where is the sum of the propagation modes and the average is the direction of propagation.12 Here is the effective mean free path of the phonon. Based on previous studies of low-temperature thermal transport in nanometer-scale beams with a geometry similar to the piezoresistive arm used here,13 we assume a limited scattering value at the boundary ~ 1.12 A. Here, A is the cross-sectional area of the beam.14 Using these formulas, we conclude that the average temperature in the steady-state leg region (at current deviation) for all data below 40 K.
Above 40K, the Debye formula ceases to be valid for determining thermal conductivity - however, for the full range of biases used in this work, we have verified that bias heating is negligible in this regime. A silicon diode thermometer is mounted on the opposite side of the copper block at a comparable distance from the heating resistor as the micropower device.
Experimental Validation of Heating Model
The diode thermometer and heating element were controlled using a Lakeshore 340 temperature controller. relatively large) values of the bias power, as shown in the table. In both cases, the agreement between the local temperature increase measured from resonant frequency shifts and that estimated from the above calculations is within 7% for temperatures up to 15K and all applied bias powers (up to 47 µW). To is the initial temperature (before heating), ∆Tmeas is the temperature rise as determined by the resonant frequency shift (Fig.
2 (a)), and ∆Tkalk is the temperature rise estimated from the thermal conductivity calculations discussed in the text.
Experimental Results: Temperature Dependence of the Quality Factor, Gauge Factor and Thermomechanical Noise
Here T =RT ( /Q Ko) is the group system responsivity, the product of the converter and mechanical responsivities at resonance, SVJ =4k T RB h d is the (Johnson) voltage noise of the converters, and Th is the effective temperature of the holes. The heat capacities of the hole gas and resonator phonons are Ch and Cph, respectively. The temperature profile of the phonons is determined by Eq. 4) where the heat transferred is Q now.
The temperature dependence of the optimal force sensitivity obtained by this procedure is shown in Fig. At low bias power, the responsiveness of the transducer decreases, leading to an increase in the effective power noise (referenced to the input).
A Comparison of Thermal Conduction Pathways
For ambient temperatures below 1K, thermal conduction is dominated by hole diffusion at low bias powers (<10pW). A crossover to phonon-mediated thermal conduction occurs at a bias power of ~10pW (at this crossover the phonon and hole temperatures are ~1.7K and ~3.5K, respectively). For higher ambient temperatures, such as the 4K ambient shown in (b), the higher ambient temperature places the device above the transition from hole diffusion thermal transport to phonon mediated thermal transport, even for arbitrarily low bias power.
Phonon-assisted heat transport To=0.1K Phonon-assisted heat transport Na=1K Heat transport via hole diffusion Na=0.1K Heat transport via hole diffusion Na=1K. 0 shows the thermal conductivity via the two paths at the optimum bias power over a temperature range of 0.1K to 10K.
Thermal Conduction via Hole Diffusion under Experimental Conditions
The presence of such a voltage will lead to sinusoidal heating in the conductive layer of the device. This heating and the resulting thermal expansion of the conductive (surface layer) of the device leads to a surface tension in the device (Fig. For small power levels, the temperature of the device is in turn linearly proportional to the power which depends on the square of the applied voltage.
To order δRd, the measured signal is the voltage across the device, v (= VA-VB in Fig. a) Heating the conductive region of the device leads to a surface voltage. V V the dominant component of the signal is out of phase while the background is completely in phase.
Magnetic Actuation
- Estimation of Coil – Magnetic Cantilever Tip Force
- First Estimate of Coil-Cantilever Magnetic Force
- Estimation of Magnetic Force, Taking into Account the Tip Geometry
- Experimental Results for Magnetic Drive in Vacuum and Ensuing Force Estimation
- Magnetic Driven Response in Air
- Piezoelectric Driven Response in Vacuum
- Piezoelectric driven Response In Air
- Cantilevers with Silicon Piezoresistive Elements
Next, we need to determine the magnetic moment of the material at the tip of the cantilever. The surface at the top of the core has been ignored (this is ~3 cm from the region of interest compared to the tip which is ~50µm; its effect is therefore negligible). The parameters listed on the chart above are used to calculate the filing from the magnetic tip.
In this section, we discuss the results for one of the larger cantilevers shown in Fig. The discrepancy is attributed to the assumption in the calculation that the magnetic core in the middle of the coil is saturated.
