Design and optimization of a novel tri-axial miniature ear-plug piezoresistive accelerometer with nanoscale piezoresistors

Contents

Abstract

Acknowledgement

List of Figures

List of Tables

Chapter
1 INTRODUCTION
1.1 Introduction
1.2 Motivation
1.3 Thesis Aim and Objectives
1.4 Conclusion
1.5 Thesis structure

Chapter
2 LITERATURE REVIEW
2.1 Introduction
2.2 Overview of earplug accelerometer
2.3 Instrumented helmets
2.4 Earpiece accelerometer
2.5 Acceleration Sensor
2.5.1 Piezoresistive Accelerometers
2.6 Piezoresistance
2.6.1 Piezoresistance of p-type and n-type single crystal silicon
2.6.2 Giant Piezoresistance in Silicon Nanowires
2.6.3 Fabrication processes of silicon nanowires
2.7 Gap in Knowledge
2.8 Conclusion

Chapter
3 DESIGN, MODELLING AND OPTIMIZATION OF A BIO-MECHANIC PIEZORESISTIVE ACCELEROMETER WITH SILICON NANOWIRES
3.1 Introduction
3.2 Accelerometer design concept and considerations
3.3 Accelerometer model
3.3.1 Mathematical model
3.3.2 Finite element modelling
3.4 Accelerometer Geometry Optimization
3.4.1 Accelerometer shape optimization
3.4.2 Size optimization of the candidate shapes
3.4.3 Overload End Stops Design
3.5 Results and discussion
3.5.1 Shape optimization
3.5.2 Size optimization
3.6 Conclusion

Chapter
4 ELECTRICAL PERFORMACE OF NANOSCALE PIEZORESISTORS COMPARED TO CONVENTIONAL MICROSCALE PIEZORESISTORS
4.1 Introduction
4.2 Methodology
4.2.1 FEM model
4.2.2 Measurement circuit
4.2.3 Electrical Sensitivity and cross-axis sensitivity
4.2.4 Nonlinearity
4.2.5 Damping
4.2.6 Bandwidth
4.2.7 Noise and resolution
4.3 Results and discussion
4.3.1 Structural analysis
4.3.2 Electrical sensitivity and cross-sensitivity
4.3.3 Nonlinearity, damping and bandwidth
4.3.4 Noise and resolution
4.3.5 Discussion
4.4 Conclusion

Chapter
5 INFLUENCE OF VARIATIONS IN THE MASS MOMENT OF INERTIA INTO THE PERFORMANCE OF A TRI-AXIAL PIEZORESISTIVE ACCELEROMETER
5.1 Introduction
5.2 FE Modelling and input validation
5.3 Design optimization approach
5.4 Results
5.4.1 Design Concept Type A: Curved beams
5.4.2 Design Concept Type B: Straight beams
5.4.3 Effect on performance of beam geometry
5.5 Optimum design selection
5.6 Conclusion

Chapter
6 PROPOSED OPTIMAL ACCELEROMETER DESIGN
6.1 Introduction
6.2 Optimization strategy
6.3 FE Modelling
6.4 Results and discussion
6.4.1 FEA results - nanowires as piezoresistors
6.4.2 FEA results - conventional microscale piezoresistors
6.5 Conclusion

Chapter
7 A FEASIBILITY STUDY ON THE FABRICATION OF SILICON NANOWIRES FOR NANOSCALE PIEZORESISTORS
7.1 Introduction
7.2 Design of samples
7.3 Experiments
7.3.1 Materials
7.3.2 Fabrication
7.4 Results and discussion
7.4.1 Focus Ion beams experiment results
7.4.2 Nanowire growth experiment results
7.5 Conclusion

Chapter
8 CONCLUSION AND FUTURE WORK

REFERENCES

APPENDIX A. TECHNICAL SPECIFICATIONS OF THE ACCELERATION SENSOR

APPENDIX B. ACCELEROMETER MECHANICAL STRUCTURE - SHAPES STUDY RESULTS

APPENDIX C. SIZE OPTIMIZATION RESULTS OF ACCELEROMETER MECHANICAL STRUCTURES

APPENDIX D. PROBE STRESS ANALYSIS RESULTS UNDER 250g ACCELERATION

APPENDIX E. PACKAGING, 8 LEAD 2X2 DFN-EP

APPENDIX F. ACCELEROMETER FABRICATION

APPENDIX G. PIEZORESISTIVE ACCELROMETER MEASUREMENT CIRCUITS

APPENDIX H. DOPING CONCENTRATION AND ORIENTATION OF PIEZORESISTORS

APPENDIX I. TABLES CHAPTER 5 AND

APPENDIX J. SINGLE CRYSTAL SILICON MATERIAL PROPERTIES

APPENDIX K. CHARACTERIZATION AND TESTING OF SAMPLES

ACHIEVEMENTS

Abstract

This work aims at the advancement of state-of-art accelerometer design and optimization methodology by developing an ear-plug accelerometer for race car drivers based on a novel mechanical principle. The accelerometer is used for the measurements of head acceleration when an injurious event occurs. Main requirements for such sensor are miniaturization (2×2 mm), because the device must be placed into the driver earpiece, and its measurement accuracy (i.e. high sensitivity, low crosstalk and low nonlinearity) since the device is used for safety monitoring purpose.

A micro-electro-mechanical system (MEMS)-based (bulk micromachined) piezoresistive accelerometer was selected as enabling technology for the development of the sensor. The primary accelerometer elements that can be manipulated during the design stage are: the sensing element (piezoresistors), the micromechanical structure and the measurements circuit. Each of these elements has been specifically designed in order to maximize the sensor performance and to achieve the miniaturization required for the studied application.

To achieve accelerometer high sensitivity and miniaturization silicon nanowires (SiNWs) as nanometer scale piezoresistors are adopted as sensing elements. Currently this technology is at an infancy stage, but very promising through the exploitation of the “Giant piezoresistance effect” of SiNWs. This work then measures the potential of the SiNWs as nanoscale piezoresistors by calculating the major performance indexes, both electrical and mechanical, of the novel accelerometer. The results clearly demonstrate that the use of nanoscale piezoresistors boosts the sensitivity by 30 times in comparison to conventional microscale piezoresistors. A feasibility study on nanowires fabrication by both top-down and bottom-up approaches is also carried out.

The micromechanical structure used for the design of the accelerometer is an optimized highly symmetric geometry chosen for its self-cancelling property. This work, for the first time, presents an optimization process of the accelerometer micromechanical structure based on a novel mechanical principle, which simultaneously increases the sensitivity and reduces the cross-sensitivity progressively. In the open literature among highly symmetric geometries no other study has to date reported enhancement of the electrical sensitivity and reduction of the cross-talk at the same time. Moreover the novel mechanical principle represents advancement in the accelerometer design and optimization methodology by studying the influence of a uniform mass moment of inertia of the accelerometer proof mass on the sensor performance. Finally, an optimal accelerometer design is proposed and an optimized measurement circuit is also specifically designed to maximize the performance of the accelerometer.

The new proposed accelerometer design is capable of increasing the sensor sensitivity of all axes, in particular the Z-axis increases of almost 5 times in respect to the current state-of-art-technology in piezoresistive accelerometer. This occurs thanks to the particular newly developed approach of combination of beams, proof mass geometry and measurement circuit design, together with the use of silicon nanowires as nanoscale piezoresistors. Furthermore the cross-sensitivity is simultaneously minimized for a maximal performance. The sum of the cross-sensitivity of all axes is equal to 0.4%, well below the more than 5% of the state-of-art technology counterpart reported in the literature. Future work is finally outlined and includes the electro-mechanical characterization of the silicon nanowires and the fabrication of the proposed accelerometer prototype that embeds bottom up SiNWs as nanoscale piezoresistors .

Acknowledgement

First of all, I would like to thank my supervisor, Dr. James Njuguna, for his valuable academic guidance throughout all three years of work at the Cranfield University. Secondly, I want to thank all people that helped me technically for the success of my work, such as Vaifro Dariol of EM Motorsport Ltd. for the technical advices during hand calculations, Andrew Dyer for the FIB processing; Dr. Christopher Shaw facility manager of Microsystems and Nanotechnology Centre for the processing in the cleanroom; Dr. Alois Lugstein and Stefan Wagesreither of the Institute for solid state electronics of Vienna University of Technology for the nanowires grow; Dr. Robert Wright, Dr. Paul Kirby of Microsystems and Nanotechnology Centre and Prof. Robert Dorey professor of Nanomaterials for the fruitful assistance and useful conversation. Furthermore I would like to thank all my academic panel members, such as, Dr. Ahmed Al-Ashaab and Dr. Jeffry Alcock for their superb work during my reviews.

Finally I would like to thank the support of my wife, Rini, and my two amazing daughters, Alisha and Aurora, during difficult times occurred in these three years of work far from them.

List of Figures

Figure 1-1. Relationship between relative sensitivity and typical

Figure 1-2. Schematic of the methodology adopted to address the thesis aim. As it can be seen the FEM of highly symmetric mechanical structures are first optimized by obtaining a possible candidate then a further optimization is attempted by a new optimization approach based on the influence of the mass moment of inertia. Finally the device with maximum performance is obtained as output.

Figure 2-1. (a) Photo of outer ear that shows the length of different ear parts [133]; (b) Image of outer and inner ear [155].

Figure 2-2. Ear shapes [133]

Figure 2-3. Moulded earpiece [156]

Figure 2-4. DESS and the smaller Endevco earplug [31]

Figure 2-5. (a) Close-up of the 7273GT die mounted on a flex [118]. (b) Complete in-ear triaxial shock measurement system (Endevco) [118].

Figure 2-6. Z-axis Piezoresistive Accelerometer [32]

Figure 2-7. Typical frequency response of accelerometer [33]

Figure 2-8. Convective Heat Transfer Accelerometer (MX2125) [128]

Figure 2-9. Silicon Micromachined MOEMS device [129]

Figure 2-10. Piezoresistive Factor comparison at room temperature [53]

Figure 3-1. (a) Mass-spring-damper system; (b) Graphical representation of the electromechanical physical model involved in the sensing (K, K1, K2 are the constants)

Figure 3-2. Simple 1-DOF accelerometer with a beam and suspended proof mass.

Figure 3-3. Five shapes selected as possible candidates for further optimization. The beams are deformed under Z-axis acceleration.

Figure 3-4. (a) Graph that shows the results of the DOE optimization process under Z-axis acceleration. All points above 5 KHz are feasible design points. Notice the Pareto frontier in the graph that is the boundary of the feasible points region. (b) Graph that shows the results of the optimization process under X-axis acceleration. Similar results are obtained for Y-axis acceleration

Figure 3-5. (a) Geometry Dimensions Shape no. 2. (b) Geometry Dimensions Shape no. 4

Figure 4-1. (a) Current state-of-art accelerometer mechanical structure [6, 93]; (b) Typical accelerometer under stress due to external forces (Z-axis acceleration and blue frame fixed). The red colour corresponds to the maximum displacement of the proof mass. In blue is the surrounding frame which is undeformed.

Figure 4-2. (a) Piezoresistors location.16 nanoscale piezoresistors, in orange, are placed in strategic locations where the maximum stress is present in order to maximize the sensitivity and minimize the cross-sensitivity (top view). (b) Nanoscale Piezoresistor model. In blue is the nanowire and in green are the contacts

Figure 4-3. Measurement circuit design type A. (a) Ax-, Ay-bridge and (b) Az- Wheatstone Bridge measurement circuit

Figure 4-4. Typical cantilever noise spectrum showing Johnson and 1/f noise [53].

Figure 4-5. Noise spectral density of piezoresistive accelerometer [60]

Figure 4-6. Optimized mechanical structure geometry

Figure 4-7. (a) Overload End Stop (Top view). The colour defines the total deformation of the structure under Z-axis acceleration. In red the maximum deformation and in blue the undeformed section. (b) Overload End Stop (Detail). The gap of 5 microns for in-plane acceleration allows a movement of the proof mass under a maximum of 500g of acceleration.

Figure 4-8. Validation of the model sensitivity by comparing to the demonstrator performance of Dao et al. [19].

Figure 4-9. Temperature drift – Output Voltage vs. X- or Y-axis and Z-axis Acceleration. It was observed that the sensitivity is progressively reduced due to temperature increase.

Figure 5-1. (a) Evolutionary design approach of mechanical structures type A (curved beams). Design A1: square, Design A2: octagon, Design A3: circle. (b) Evolutionary design approach of mechanical structures type B (straight beams). Design B1: square, Design B2: octagon, Design B3: circle.

Figure 5-2. Evolutionary design approach. The MMI under biaxial acceleration at each step of optimization become more and more similar to the MMI under uniaxial acceleration. Therefore the sensitivity, since it is proportional to the MMI, in the last step of optimization is the same for uniaxial and biaxial acceleration improving the measurement accuracy.

Figure 5-3. Sensitivity comparison of three designs using silicon nanowires as nanoscale piezoresistors. Due to geometry effect the octagon design (A2) presents higher sensitivity under Z-axis acceleration. The circle design (A3) due to curved beams presents higher transversal stress than the octagon geometry A2; therefore the sensitivity under Z-axis acceleration is reduced.

Figure 5-4. Cross-axis sensitivity of three designs using silicon nanowires as nanoscale piezoresistors. Beam geometry determines the superior performance of the octagon geometry (A2) with the lower cross-talk. The circle design (A3) due to curved beams (higher transversal stress) presents higher cross-talk than the octagon geometry (A2).

Figure 5-5. (a) Octagonal geometry sensor (top view). (b) Octagonal geometry sensor (isometric view with mesh).

Figure 5-6. (a) Piezoresistors locations on the top surface of the chip (Design B1). (b) Measurement circuit type B. -(a) X, Y-axis Wheatstone bridge; (b) Z-axis Wheatstone bridge.

Figure 5-7. Cross-axis sensitivity of three designs type B with nanowires. As it can be seen optimization process not improves the performance from geometry B1 to geometry B2 but improves in B3 due to circular proof mass and straight beams.

Figure 5-8. Circle design with straight beams (Top view)

Figure 5-9. Sensitivity comparison among the various geometries analysed in the study. As can be seen square mass with straight beams gives similar sensitivity performance except under Z-axis acceleration due to the different measurement circuit used. The octagonal proof mass geometry with octagonal beams compared to straight beams is superior under all different acceleration directions, again the high improvement under Z-axis acceleration is related to the measurement circuit used and also the bend angle. Finally, the geometry with circular proof mass and circular beams shows slightly higher sensitivity levels than the geometry with circular proof mass and straight beams.

Figure 6-1. Flow chart of the design optimization approach. As it can be seen the geometry optimization starts with a square proof mass (Design A1/B1) and then it becomes octagonal (Design A2 and B2) and finally a circle (Design A3 and B3). Two types of beams are used straight and curved. The final design is obtained after a performance analysis that indicates the superior geometries (Design A2 and B3).

Figure 6-2. (a) Optimal design (top view). The design is obtained from the combination of the octagon geometry type A and circle geometry type B and utilizing the measurement circuit of type A. (b) Meshed optimal design (isometric view). As it can be seen the beams have a much more dense mesh for accuracy enhancement.

Figure 6-3. (a) Curved+circle geometry. The beams have a concave geometry. (b) Curved+circle2 geometry. The beams have convex geometry. (c) Doughnut geometry. The proof mass is empty in the middle.

Figure 6-4. Sensitivity comparison of different design. The proposed optimal design due to combination of parameters, such as octagonal beams, circular proof mass, measurement circuit type A and the use of nanowires determines the maximum performance.

Figure 6-5. Cross-sensitivity comparison. The proposed optimal design presents lower cross-sensitivity.

Figure 6-6. Sensitivity comparison with conventional microscale piezoresistors. The final optimal design and the new beam geometries (curved+circle and curve+circle2) present higher sensitivity. The doughnut geometry presents the lower sensitivity compared to the other geoemtries.

Figure 6-7. Cross-sensitivity comparison with conventional microscale piezoresistors. The new geometries (curved+circle,curved+circle2 and doughnut) present higher cross-talk. The final design results superior to all geometries studied.

Figure 7-1. Sample and nanowires design. The samples are specifically designed to fit in the characterization station (see Appendix K). The nanowires grown to be 3 microns with contacts of 100 square microns. As it can be seen a set of three pairs of nanowires are placed into the middle of the sample microstructure in order to have with 20 N a maximum of 100MPa of stress.

Figure 7-2. Masks design sketch. As it can be seen from the image three flats are designed for the mask layout in order to be possibly able to make nanowires on different direction just rotating the wafer relatively to the mask.

Figure 7-3. (a) Front mask design. In the inset on the left it can be seen the middle of the sample layout where the contacts are designed. On the inset on the right the mask aligner mark is shown. (b) Back mask design. The inset on the right shows the mask aligner mark.

Figure 7-4. (a) FIB processing (top view). The thickness of the structure is around 1 micron. (b) FIB processing (side view). The sidewall of the structure is here visible with a thickness of around 2 microns. (c) FIB processing (isometric view). The isometric view is showing the entire stracture.

Figure 7-5. (a) Pair of contacts. The contacts shown in the picture are not completely separated. (b) Zoom on the gap between contacts not completely separated.

Figure 7-6. (a) Gap between contacts. As it can be seen from the image the gap is completely separated. (b) Two pairs of contacts perfectly separated.

Figure 7-7. Back side ready for DRIE. Three samples are designed in a single wafer in order to efficiently exploit the available space of 3 inches.

Figure 7-8. (a) Complete DRIE etching of a hole. The white color in the hole shows that the etching has reached the BOX. (b) The dark colour is the photoresist that remained after the DRIE etching.

Figure 7-9. (a) Final released sample structure. (b) Misalignment of the central region with the contacts.

Figure 7-10. Growth of 1D structures by VLS mechanism [154]. (a) Metal catalyst thin-film deposition of Au catalyst by sputtering, (b) liquid alloy droplets formed by the metal catalyst by absorbing vapour components, (c-d) the alloy is supersaturated and precipitates at the liquid-solid interface growing the 1D structure.

Figure 7-11. (a) Pairs of contacts with nanowires grown between them, see contacts in the middle. As it can be seen five different positions are chosen in contact gap to grow the nanowires. The sample broke during handling. (b) Five windows were opened in the contact gap and the nanowires grown in between.

Figure 7-12. (a) Ion beam milling with higher current. (b) Ion beam milling with lower current. As it can be seen the trench edges were more sharp using lower beam current.

Figure 7-13. Best milling achieved. The maximum width achievable with the FIB is of around 100 manometers.

Figure 7-14. (a) Nanowires grown on both sides of the gap due to the short gap width that do not allow deposition of the gold on one side only. Therefore the nanowires grown from both sidewalls of the gap width interfering with each other during growth. (b) Due to the nanowires growth from both sidewalls only few nanowires are able to form a bridge structure.

Figure 7-15. The nanowire grows and sticks on the opposite sidewall and finally forming a solid bridge structure that withstands high strain.

Figure 7-16. (a) Nanowires bridge structures between contacts gap. (b) The length of the two nanowires is of 2.10 µm which is smaller than the designed gap (3 µm).

Figure 7-17. Two nanowires bridge structures. The nanowire width reduces during grow due to the change in size of the gold droplet.

Figure 7-18. Nanowire bridge structure starting 112.3 nm wide and ending 73.8 nm wide in a direction different from <111>.

Figure 8-1. Diagram of the methodology adopted to address the first research aim. Notice that this work addresses only the first step of the research methodology that is the design and fabrication of test-chips in order to study the feasibility of sensor fabrication.

Figure B-1. Cross-beam Single-mass Accelerometer

Figure B-2. Deformed structure Z-axis Acceleration

Figure B-3. Deformed structure X-axis Acceleration

Figure B-4. Picture-frame Accelerometer

Figure B-5. Deformed structure Z-axis Acceleration

Figure B-6. Deformed structure X-axis Acceleration

Figure B-7. Picture-frame Accelerometer type 2

Figure B-8. Deformed structure Z-axis Acceleration

Figure B-9. Deformed structure X-axis Acceleration

Figure B-10. Picture-frame Accelerometer type 3

Figure B-11. Deformed structure Z-axis Acceleration

Figure B-12. Deformed structure X-axis Acceleration

Figure B-13. Cross-inset beams Accelerometer

Figure B-14. Deformed structure Z-axis Acceleration

Figure B-15. Deformed structure X-axis Acceleration

Figure B-16. Surrounded-cross inset beams Accelerometer

Figure B-17. Deformed structure Z-axis Acceleration

Figure B-18. Deformed structure X-axis Acceleration

Figure B-19. Surrounded-cross inset beams Accelerometer type 2

Figure B-20. Deformed structure Z-axis Acceleration

Figure B-21. Deformed structure X-axis Acceleration

Figure B-22. Surrounded-cross inset beams Picture-frame Accelerometer type 3

Figure B-23. Deformed structure Z-axis Acceleration

Figure B-24. Deformed structure X-axis Acceleration

Figure B-25. Surrounded beams Picture-frame Accelerometer type 4

Figure B-26. Deformed structure Z-axis Acceleration

Figure B-27. Deformed structure X-axis Acceleration

Figure C-1. Optimization Shape n. 2, Z-axis acceleration

Figure C-2. Optimization Shape n. 2, X-axis acceleration

Figure C-3. Optimization Shape n. 3, Z-axis acceleration

Figure C-4. Optimization Shape n. 3, X-axis acceleration

Figure C-5. Optimization Shape n. 4, Z-axis acceleration

Figure C-6. Optimization Shape n. 4, X-axis acceleration

Figure C-7. Optimization Shape n. 5, Z-axis acceleration

Figure C-8. Optimization Shape n. 5, X-axis acceleration

Figure C-9. Optimization Shape n. 9, Z-axis acceleration

Figure C-10. Optimization Shape n. 9, X-axis acceleration

Figure F-1. .GDS file of the octagonal geometry sensor.

Figure F-2. Metallization layers. (a) Layer 1, (b) Layer 2.

Figure F-3. .GDS file of the circular geometry sensor with nanowires

Figure F-4. .GDS file of circular geometry sensor with conventional piezoresistors

Figure F-5. Conventional piezoresistor design (Fraunhofer IZM)

Figure F-6. Conventional piezoresistor process flow (Fraunhofer IZM)

Figure F-7. Conventional piezoresistor process flow part 2 (Fraunhofer IZM)

Figure F-8. Sensor before and after packaging (Fraunhofer IZM)

Figure G-1. Wheatstone bridge and equations [32]

Figure G-2. Output voltage and linearity error for constant voltage drive bridge configuration [32]

Figure H-1. Room temperature piezoresistive coefficients in the (100) plane of p-type silicon. This graphic

Figure H-2. n-type (100) oriented wafer showing the primary and secondary flats [73]

Figure H-3. Illustration identifying various planes in a wafer of {100} orientation (the wafer thickness is exaggerated) [73]

Figure H-4. Notation for Smith’s test configurations [48]

Figure H-5. Dependence of π44 on the doping level at room temperature

Figure H-6. Temperature coefficient of π44 for a p-Si material.

Figure H-7. Piezoresistive Factor vs. p-Si concentration at different temperatures

Figure H-8. Piezoresistive Factor comparison at room temperature [53]

Figure H-9. Fitting Function at room temperature [53]

Figure J-1. Silicon crystal structure: Different crystal orientations are indicated with Miller indexes with [100] coinciding with x-axis. Also shown is (100)-plane (that is plane orthogonal to [100] direction) and crystal unit cell (red box) [52].

Figure K-1. Nanowire 2-points contacts [3]

Figure K-2. (a) Prototype tensile kit, equipped with horizontal gripping jaws for conventional tensile testing [78]. (b) Prototype tensile stage kit, equipped with vertical gripping jaws and point tip for bending experiment. In the inset the pushing tip is shown in contact with a metal sample [78].

List of Tables

Table 2-1. Earhole dimension, age group and percentile (mm) [132]

Table 2-2. Earhole dimension, age group and percentile (mm) [133]

Table 2-3. Arithmetic mean of the anthropometric data

Table 2-4. DESS Specification

Table 2-5. Piezoresistivity components for single-crystal silicon under certain doping values.

Table 2-6. Formula for transverse and longitudinal piezoresistive coefficient for various commonly encountered resistor configurations.

Table 2-7. p-type silicon nanowires experiments

Table 3-1. Target sensor technical specifications

Table 3-2. FEM analysis set up

Table 3-3. Highly symmetric shapes selected for the analysis

Table 3-4. Performance comparison of shapes selected

Table 3-5. Best geometry design candidates

Table 4-1. Inputs material parameters used in the developed FEM

Table 4-2. Input geometry parameters used in the developed FEM for sensitivity validation.

Table 4-3. Resistance change due to unbalanced bridge

Table 4-4. Final geometry size and performance

Table 4-5. Temperature drift - sensitivity

Table 4-6. Voltage Noise – Sensitivity – Resolution

Table 4-7. Sensor comparison

Table 5-1. Sensitivity and cross-sensitivity of three designs type B with conventional piezoresistors

Table 5-2. Measurement circuit performance comparison between Square geometry type A1 and Square geometry type B1

Table 5-3. Sensor performance comparison of Octagon geometry type A2 and Circle geometry type B3

Table 6-1. Model material and geometrical properties

Table B-1. FEA results shape 1 under Z-axis acceleration

Table B-2. FEA results shape 1 under X- or Y-axis acceleraiotn

Table B-3. Mode of operation shape 1

Table B-4. FEA results shape 2 under Z-axis acceleration

Table B-5. FEA results shape 2 under X- or Y-axis acceleration

Table B-6. Mode of operation shape 2

Table B-7. FEA results shape 3 under Z-axis acceleration

Table B-8. FEA results shape 3 under X- or Y-axis acceleration

Table B-9. Mode of operation shape 3

Table B-10. FEA results shape 4 under Z-axis acceleration

Table B-11. FEA results shape 4 under X- or Y-axis acceleration

Table B-12. Mode of operation shape 4

Table B-13. FEA results shape 5 under Z-axis acceleration

Table B-14. FEA results shape 5 under X- ot Y-axis acceleraiotn

Table B-15. Mode of operation shape 5

Table B-16. FEA results shape 6 under Z-axis acceleration

Table B-17. FEA results shape 6 under X- or Y-axis acceleration

Table B-18. Mode of operation shape 6

Table B-19. FEA results shape 7 under Z-axis acceleration

Table B-20. FEA results shape 7 under X- or Y-axis acceleration

Table B-21. Mode of operation shape 7

Table B-22. FEA results shape 8 under Z-axis acceleration

Table B-23. FEA results shape 8 under X- or Y-axis acceleration

Table B-24. Mode of operation shape 8

Table B-25. FEA results shape 9 under Z-axis acceelration

Table B-26. FEA results shape 9 under X- or Y-axis acceleration

Table B-27. Mode of operation shape 9

Table C-1. Optimized design points candidate shape 2

Table C-2. Optimized design points candidate shape 3

Table C-3. Optimized design points candidate shape 4

Table C-4. Optimized design points candidate shape 5

Table C-5. Optimized design points candidate shape 9

Table I-1. Sensitivity and cross-sensitivity of three designs type A with nanowires

Table I-2. Sensitivity and cross-sensitivity of three designs type B with nanowires

Table I-3. Sensitivity and cross-sensitivity of three designs type A and final design with nanowires

Table I-4. Sensitivity and cross-sensitivity of three designs type A, final design and two new geometries with conventional microscale piezoresistors

Table J-1. Young's modulus in [100], [110] and [111] direction [54]

Chapter 1

1 INTRODUCTION

1.1 Introduction

Since silicon devices have dominated IC chips for many decades, to date silicon is the most significant semiconductor currently available. Silicon nanowires devices can transport electrons and holes with enhanced opto-electro-mechanical properties, as known today due to the quantum confinement effect. Due to their enhanced features they could function as building blocks for nanoelectronics and advanced devices [1]. Furthermore, they present a very large piezoresistance effect [2-7], which is suitable for enhancing the mechanical sensors performance. Currently, other areas of study of this device are to improve silicon transistors [8, 9]. Silicon nanowires are also attractive for applications in the field-emission devices, photonics, chemical sensors and spintronics [10].

The piezoresistive effect is a simple way used for converting, for example, acceleration in an electrical output. After an inertial force is applied to the sensor the strain on the piezoresistive material (silicon) changes its electrical resistance proportionally, the correspondent voltage change is a measure of the acceleration by less than a constant of proportionality.

Currently, in the design and development of an accelerometer the main effort is to set the right trade-off between size and sensitivity that may satisfy the requirements of the device application. Conventional technology is limiting the fabrication of accelerometer below 1 square millimetre due to the drastic loss in sensitivity [11, 12]. Basically when the miniaturization is the main concern of the application, sensitivity is the main issue to address, since the smaller is the device the lower will be its sensitivity. Obviously reduced sensitivity will drastically affect the accuracy of the device since a low signal to noise ratio is obtained. Much of MEMS technology currently face this issue by simply introducing an amplifier at the output level, sometimes monolithically as in capacitive pick-off (the way the acceleration is converted to an electrical signal) or in a complete different device as in piezoresistive pick-off (hybrid system partitioning). Introducing an amplifier results into a relative signal noise that inevitably worsens the accuracy of the measurement.

This research intends to address this issue in a different way by avoiding the use of an amplifier. In particular, the study exploits a phenomenon observed when the dimension of a piezoresistor shrinks down to the nanoscale, called in the literature “Giant Piezoresistance” [3]. By implementing the accelerometer with nanoscale piezoresistors (i.e. nanowires or quantum wires) the traditional design trade-off explained earlier using conventional microscale piezoresistors is overcame, due to the high sensitivity and the minuscule size achievable (see Figure 1-1). This is demonstrated in this work by designing a novel tri-axial miniature accelerometer based on nanoscale piezoresistors for applications in head injury detection of race car drivers.

illustration not visible in this excerpt

Figure 1 - 1 . Relationship between relative sensitivity and typical dimension of a piezoresistive accelerometer [12]

1.2 Motivation

Traumatic brain injuries (TBI) due to impacts are common in helmeted sports, such as hockey, football and motorsport. Therefore, significant research effort has been made in the past decade in order to monitor and prevent head injuries in these sports, especially in motorsport where the high speeds and forces mean that crashes are inevitable. In the past there have been many deaths and injuries to race drivers, one of the most famous was Ayrton Senna on May 1, 1994 at the San Marino GP in Imola when he died for a fatal massive brain injury due to a high speed impact with the wall. The drivers were not monitored, therefore links between accelerations of specific body parts and injury could not be rigorously made.

The first solutions introduced in the late 90s were instrumented helmets, mounting sensors capable to measure the amplitude of a crash through accelerometers. These instrumented helmets may not accurately measure the actual acceleration experienced by the head due to mainly helmet-to-head fit and helmet liner properties. In the latter case, the shell of the helmet distributes the impact force over a large surface area, and the helmet liner absorbs the acceleration forces, thereby reducing the acceleration of the head to non-concussive levels. [15, 16, 17, 18, 19, 20, 21]

Therefore, if the helmet shell or liner is instrumented, it is very difficult to estimate the amount of acceleration passed to the head. Helmets are designed to reduce the amount of acceleration experienced by the head; therefore, instrumented helmets may not reflect acceleration of the head [22, 23, 24], they overestimate the actual acceleration forces experienced by the head [22].

As accurate measuring of head accelerations is an important aspect in predicting head injury, it is important that the measuring sensor be well-coupled to the head. Therefore the instrumented helmet solution has been soon replaced in the new century, by a mouthpiece accelerometer in the football [25] and by attaching the accelerometer to an earpiece and not to the helmet in the motorsport [26, 27] . With these novel solutions the effects of the shell and liner properties are eliminated, allowing for the direct assessment of acceleration experienced by the head.

A version of these types of earpieces, the Delphi Earpiece Sensor System [28], was adopted by the Indy Racing League and Championship Auto Race Teams (CART) in 2003. In 2006, Begeman, Melvin, Troxel (Wayne State University) and Mellor (FIA Institute) [29] reported that signals from these earplugs mounted in post mortem human specimens (PMHS) showed a progressive phase lag from 50 to 100 Hz vibration when compared to skull measurement (rigidly mounted head accelerometers). These tests indicate less than perfect skull coupling for the earplugs mounted in the outer ear canal for high rate excitations. A step further has been made towards the improvement of the design of the ear-plug in order to obtain much more accurate measurement at high rate and magnitude exposure by stiffening the coupling between the ear and the head.

One explored solution has been to developing a miniaturized tri-axial accelerometer that is small enough to be placed in the ear canal portion of the earpieces [30]. The sensor measurement was well correlated to the reference sensor and therefore, demonstrated improved coupling to the head over the Delphi version that were perceived too bulky [31]. Moreover other advices for improving the accuracy of the measurements is by improving the positioning technique and mounting material, a stiff material is recommended [30].

Currently there is still a need for research in this area of study in order to develop a more precise and reliable earplug accelerometer mainly used for biomechanics measurements, e.g. in helmeted sports. At the time of writing, no device on the market is available that is able to measure medium-g impact values with the size of few millimetres, because of the technical issues mentioned earlier. The only available micro-accelerometer on the market of the size of 2×2mm, e.g. from Bosch or ST, are low-g devices that incorporate an amplifier within it. Furthermore, the only attempt made so far in fabricating miniature prototypes with nanowires has been made for measuring low-g impacts with the sensitivity being of the same order of magnitude of the state-of-art sensors counterparts [6, 13, 14].

Other major applications of such novel sensors based on enhanced nanoscale piezoresistors are in the biomedical arena, such as implantable devices for motion/vibration sensing. Examples are in hearing aid systems (implantable sound sensor for cochlear implants [122]), heart wall motion measurement for cardiac artificial pacemakers (an adaptive control system that detects the human body activity level in order to adjust accordingly the pacemaker rate response [102]) and head injury monitoring of military soldiers in case of blast (the sensor is placed inside the helmet).

This study attempts a further improvement in the earplug sensor design by investigating possible ways of enhancing sensor performances and miniaturization, with the objective of achieving a more accurate response in case of medium-g impact crashes not achievable in state-of-art sensors. The data gathered from this new sensor would benefit all the stakeholders involved in the motorsports community.

First of all the race drivers that would wear the sensor would benefit from a more accurate safety system. When an injurious event occurs a better and fast diagnosis of the traumatic brain injury (TBI) would be possible to the medical personnel.

Medical, automotive researchers as well as engineers may use the data collected to evaluate how safety improvements like shoulder harnesses, helmets, seat belts and head and neck restraints commonly used in all forms of racing are helping prevent head injuries and eventually design better driver restraint systems and safety devices.

1.3 Thesis Aim and Objectives

The aim of this thesis is to advance current state-of-art knowledge of accelerometer design and optimization by developing a novel enhanced miniature accelerometer of 2 × 2 mm2 characterized by improved sensitivity and cross-sensitivity.

The thesis objectives are:

- To conduct literature survey to establish current state-of-art earplug accelerometer and nanoscale piezoresistors technology.
- To design, model and optimize the novel accelerometer.
- To develop ear-plug accelerometer’s circuits to enhance the performance of the devices.
- To evaluate the silicon nanowires as accelerometer sensing elements

1.4 Conclusion

The thesis aim is addressed by designing and modelling a novel accelerometer that embeds silicon nanowires as nanometer scale piezoresistors and by also designing a tailored measurement circuit that maximizes sensor performance. Accelerometer design has been addressed based on the flow chart presented in Figure 1-2. To start with, the accelerometer design is modelled based on highly symmetric geometries with four surrounding beams. These types of geometries have been chosen for their low cross-sensitivity due to their self-cancelled feature. Many geometries have been developed and analysed by finite element analysis technique, then the data have been collected and the design performances calculated (e.g., sensitivity, cross-sensitivity analysis, natural frequency). The design was set such that if the accelerometer performance is above or equal to the predefined technical specification for the device, the particular design is selected as a possible candidate, if not the design process is iterated. Furthermore, the possible candidate design is further modified based on an optimization method, where the mass moment of inertia of the proof mass becomes progressively uniform. The hypothesis demonstrated in this study is that with a uniform or even mass moment of inertia the performance of the accelerometer design is enhanced. Finally when the maximum performance is achieved a final new proposed design for the accelerometer is obtained otherwise the design is rejected, as illustrated in the schematic diagram on Figure 1-2.

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Figure 1-2. Schematic of the methodology adopted to address the thesis aim. As it can be seen the FEM of highly symmetric mechanical structures are first optimized by obtaining a possible candidate (Chapter 3 and 4) then a further optimization is attempted by a new optimization approach based on the influence of the mass moment of inertia (Chapter 5). Finally the device with maximum performance is obtained as output (Chapter 6).

1.5 Thesis structure

The thesis is structured in literature review in Chapter 2, where state-of-art earplug accelerometer, piezoresistive accelerometers, piezoresistance and giant piezoresistance are addressed, with identified gap in knowledge and conclusion. The design, modelling and optimization of the accelerometer is presented in chapter 3, where also the potential of silicon nanowires as nanoscale piezoresistors is evaluated based on previous experimental work on silicon nanowires. In Chapter 4, all major electrical and mechanical performance indexes of the device are calculated and a comparison between conventional microscale piezoresistors and novel nanoscale piezoresistors is presented. Then in Chapter 5, a further design step is undertaken in order to enhance the performance of the device. This optimization process is based on the mechanical principle that even mass moment of inertia determines even electrical sensitivity and therefore improves measurement accuracy. The Chapter 6 presents the final geometry version of the device which represents the optimal solution output of the optimization process adopted. Chapter 7 deals with the experiments undertaken to verify the fabrication feasibility of silicon nanowires used in the simulation studies conducted in the thesis. Firstly, the nanowires processing made by focus ion bean direct milling is presented and then followed by self-assembled fabrication process. Finally the present work is completed by Chapter 8 on conclusion and future work.

Chapter 2

2 LITERATURE REVIEW

2.1 Introduction

This chapter addresses the latest scientific developments related to ear-plug accelerometer and then presents the different types of acceleration sensor currently available. The chapter then focuses on the piezoresistive accelerometer technology for the ear accelerometer design. Finally, piezoresistance developments followed by the recent giant piezoresistance discovery and fabrication processes of silicon nanowires are addressed, before completing the chapter with the identified gap in knowledge and conclusion of the literature review.

2.2 Overview of earplug accelerometer

The earplug accelerometer is a miniature sensor specifically designed to be inserted inside the ear by an earpiece. An ear plug accelerometer must be small enough to fit in the earpiece.

According to Sanders and McCormick (1993) [130], ergonomic product design refers to “designing for human beings.” Accordingly, designing ergonomically ear-related products requires data on the dimensions and shapes of human ears. The anthropometric dimensions of outer ears, specifically the earhole length, the ear connection length, and the length of the pinna and the ear canal (see Figure 2-1 (a)), play a key development role in the design of our earpiece. However, human physical dimensions vary considerably with age, gender, race group, occupation, weight, height and so on [131] and the target users of our earpiece are different in gender, age, ethnicity, weight and height, therefore trying to accommodate all users is virtually impossible and costs increase proportionally with any effort to do so [132]. Therefore for cost effectiveness one needs to identify a typical target user at onset of the earplug accelerometer design.

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Figure 2 - 1 . (a) Photo of outer ear that shows the length of different ear parts [133]; (b) Image of outer and inner ear [155].

Not many studies have been done to examine the correlation among the anthropometric dimension of the ear, the human physical dimension and age. Hwa S. Jung and Hyung-Shik Jung (2003) [133] selected six hundred male and female Korean subjects aged 17–89 for their study, four different points of the outer ear (the lengths of the pinna, the ear connection point, the earhole and the lobule thickness) were measured and analyzed along with demographic data, including age, stature and weight. When they examine the correlation among each variable they found that age, regardless of gender difference, had a greater effect on the dimensions of ears than weight and height. As for the age group where the increase rate is highest, results show that the dimensions of ears increase in all age groups except the dimension of the earhole which decreases from the age of forty to fifty. Bor-Shong Liu (2008) [132] in his research of two hundred subjects aged 20–59 found that the coefficient of correlations between the three different dimensions of the outer ear (the earhole length, the ear connection length, the length of the pinna) and stature were very low (0.27, 0.27, and 0.29 respectively). In addition, the results showed that all ear dimensions had significant gender effects. From these studies seems that stature and weight play a minor role in the determination of the ear dimension. Age and sex are the most relevant variables that effect the growing of the ear. Concerning different ethnicity, Hwa S. Jung and Hyung-Shik Jung [133] in 2003, point out the shape and dimension dissimilarity of the ears between Koreans and Caucasians. Most of the Korean men have bigger ears with the shape of Disposition Nature, instead the ears of most Westerners had the shape of Bone Nature with few having Nutrition Nature or Disposition Nature (Figure 2-2).

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Figure 2 - 2 . Ear shapes [133]

Based on the studies of the dimension and shape of the ears, we can apply the findings to the manufacturing of our ear plug accelerometer to ensure it fits properly. It is recommended that the length of the earhole be applied for designing our earpiece since it will resemble a earphone (see Figure 2-3). The main problem of many earphone users is that the earphone slips off, this was found especially to people in their 20s using a current model [133]. From this finding we concluded that in order to fit both big and small earholes, the earpiece should be made oblong and elongated inside the ear canal where the accelerometer would be placed (Figure 2-3).

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Figure 2 - 3 . Moulded earpiece [156]

We assume the race driver to be an adult male of an age from 20 to 50 years old. From this assumption we can identify the mean dimension of the earhole, considering that the human ear canal extends from the pinna to the eardrum and is about 26 mm in length and 7 mm in diameter in adults and it is slightly S-shaped (see Figure 2-1(b)). Below are listed the main results related to the earhole of the two studies examined above (Table 2-2 and Table 2-3) and the arithmetic mean obtained by merging the data from these studies (Table 2-4).

Table 2-1. Earhole dimension, age group and percentile (mm) [132]

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Table 2-2. Earhole dimension, age group and percentile (mm) [133]

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Table 2-3. Arithmetic mean of the anthropometric data

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From the data above we obtain the arithmetic mean of the earhole dimensions of around 16.2 mm. This dimension is close to the 75th percentile for all males based on anthropometric data of the research of Liu and 50th percentile for people in their 20s, 25th percentile for people in their 30s, 10th for people in their 40s and 5th percentile for people in their 50s in the research of Jung and Jung. In engineering design, percentiles are the most used anthropometric data. A percentile value for an anthropometric dimension represents the percentage of a population with a body dimension of a certain size or smaller [131]. From the percentiles obtained by Jung and Jung seems that an earpiece should be slightly bigger in order to cover a wider population. We can therefore recommend a 2-mm increment in earpiece diameter, with the length of the earhole applied to 50th percentile data of all males. However, earphones are made slightly bigger than the earholes to ensure a perfect fit. From this finding we can conclude that in order to fit both big and small earholes, the earpiece should be measuring around 18.2 mm×16.2 mm, based on the fact that an oval shape felt better, fitted more comfortably and without slip off.

2.3 Instrumented helmets

In the late 1990s for the first time in helmeted sports were introduced instrumented helmets mounting accelerometers to measure the severity of a head injury. The actual acceleration experienced by the head may not accurately be measured by these instrumented helmets due to mainly helmet-to-head fit and helmet liner properties. In the latter case, the impact force is distributed over a large surface area by the shell of the helmet, and the helmet liner absorbs the acceleration forces, thereby reducing the acceleration of the head to non-concussive levels [15, 16, 17, 18, 19, 20, 21]. Therefore, if the helmet shell or liner is instrumented, the measured acceleration would not be the actual acceleration passed to the head [22, 23, 24], basically they overestimate the actual acceleration forces experienced by the head [22].

It is important that the measuring sensor be well-coupled to the head as in predicting head injury accurate measuring of head accelerations represents a key aspect. Therefore in the new century the instrumented helmet solution has been soon replaced, by a mouthpiece accelerometer in the football [25] and by attaching the accelerometer to an earpiece and not to the helmet in the motorsport [26, 27] . With these novel solutions the effects of the shell and liner properties are eliminated, allowing for the direct assessment of acceleration experienced by the head.

2.4 Earpiece accelerometer

In 2000, as the importance of the measurement accuracy was crucial the instrumented helmeted solution has been replaced by introducing the accelerometer in the ear together with an earpiece [26, 27]. Instrumented earplugs were first introduced in 2000 by the Air Force Research Lab (AFRL) as a means of measuring head accelerations in race car drivers after it was shown that instrumented helmets slipped on the head during impact events. The helmet moves relative to the head and it did not produce an accurate reading of head forces. A version of these earplugs, the Delphi Earpiece Sensor System (DESS), was adopted by the Indy Racing League and Championship Auto Race Teams (CART) in 2003 (Figure 2-4). For the first time researchers were able to collect data on the dynamic forces impacting a race car driver’s head during an accident.

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Figure 2 - 4 . DESS and the smaller Endevco earplug [31]

The sensing system was consisting of 3 accelerometers (Analog Devices ADXL193), one for each axis and two circuit boards. The system had to fit inside the earpiece alongside the transducer for the radio receiver. The DESS is a variable-capacitance MEMS-based accelerometer. When the proof mass moves, with control provided by the springs, interleaving capacitive-sensing fingers detect minuscule changes in capacitance, which then get converted electronically to an acceleration reading. The following table summarizes the DESS specifications.

Table 2-4. DESS Specification

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In 2006, Begeman et al. [29] reported that signals from DESS earplugs mounted in cadavers showed a phase shift at 50 and 100 Hz vibration, indicating less than perfect coupling with the head. This led to the development of a new miniature tri-axial accelerometer that is small enough to be placed in the ear canal portion of communication earplugs (earpieces), thereby improving the coupling and thus the reliability of the recordings from drivers undergoing multi-axial crash events.

Jesse Bonfeld in 2009 proposed to develop this mini-triaxis device. The AFRL/RHPA (Biomechanics Branch) team collaborated with Bonfeld to build the new sensors and provide the validation testing and comparison with the current operational sensors [31]. The new 7273GT sensors were mounted in molded earplugs and subjected to impacts as high as 300g with very short durations in multiple axes. They were also subjected to vibrations up to 100 Hz. The earplugs were mounted in artificial ears which were mounted on rigid blocks and on manikin heads. The sensors showed good correlation with reference sensors and demonstrated improved coupling to the head over the current generation of earplug accelerometers [31, 118] (Figure 2-5(a) and (b)).

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Figure 2 - 5 . (a) Close-up of the 7273GT die mounted on a flex [118]. (b) Complete in-ear triaxial shock measurement system (Endevco) [118].

After the findings of Begeman (2006) [29] other studies have been undertaken in order to investigate the mechanical coupling between human head acceleration and a small tri-axial accelerometer package inserted into the ear bony canal. In 2009 Panzer at al. [107] used post mortem human specimens (PMHS) to carry out impact tests over a broad range of frequency inputs using moderate rate drop tests and high rate shock tube tests. The measurements profile used were historically been used to quantify head injury risk. The result was a good agreement between sensors measurements due to an improvement of sensor positioning within the bony canal. Another work during the same period suggests to enhancing the measurement accuracy of the earplug by improving the position techniques and by using a stiff material for the mounting plug [30].

Recently, in 2012, a 3-axis acceleration switch of 3×3-mm specifically designed for traumatic brain injury was developed as an early warning capable to power up only when an injurious event occurs [108]. A novel three-axial biomechanic piezoresistive accelerometer enhanced by silicon nanowires as nanoscale piezoresistor as an implanted device for head injury g-loads detection for racecar drivers was also proposed in 2012 [134].

2.5 Acceleration Sensor

A sensor is a device that converts a physical phenomenon input into an electrical signal output. Acceleration sensors are sensing devices that provide an output proportional to acceleration, vibration, shock and seismic waves as input, measured in g-force. These sensors have found a wide variety of applications in both research and development arenas along with everyday use. In addition to the very technical test and measurement applications, such as modal analysis (the study of the dynamic properties of structures under vibrational excitation), NVH (noise, vibration and harshness - the study and modification of the noise and vibration characteristics of vehicles), and package testing, accelerometers are also used in everyday devices. They are widely used in automotive and space (airbag sensors and automotive security alarms, crash detection, stability control and navigation [88]), biomedical (activity monitoring [90, 91, 92], surgical instrument tracking [87]), consumer electronics (portable computing, cameras lens stabilization, cellular phones), robotics (control and stability [89]), structural health monitoring, and military and sports applications (i.e. football, boxing, hockey and racing) for real-time health monitoring of traumatic brain injuries (TBI) due to impacts or blasts [32].

Currently there are three main different technologies of accelerometers and each has unique characteristics, advantages and disadvantages. These accelerometers are different regarding the output (integrated electronic piezoelectric - IEPE output, charge output, voltage output, 4-20mA output, velocity output), the design (shear type, flexural type, single ended compression type) and the technology (piezo-electric, capacitive, convection heat transfer, optical, piezo-resistive and servo). Many manufacturers use their own trade name to referring to sensor with built-in electronics, such as ICP® (PCB Piezotronics), Deltatron (Bruel & Kjaer), Piezotron (Kistler Instruments), Isotron [37], and LIVM (Low Impedance Voltage Mode), to name a few. IEPE sensors incorporate monolithically built signal conditioning electronics that convert the high-impedance signal output generated by the piezoelectric sensing element into a usable low-impedence voltage signal that can be easily transmitted, over ordinary cable, to any voltage readout or recording device. The charge output has also a high-impedance output because the electrical signal is generated directly by the piezoelectric sensing element. Therefore a signal conditioning is required in order to condition the signal to a low-impedance voltage [33]. Tribo-electric noise in the cable is a drawback determined by the high-impedance signal, therefore special treated cable should be used [32]. In industrial process control the analog 4-20 mA output is commonly used. The key advantage of this type of accelerometer output is that the signal accuracy is not affected by voltage drop in the line, and the loop can supply continuously operating power to the device [81]. Velocity output is commonly used to evaluate the health of a machine and the accelerometers with this type of output are typically used in condition monitoring applications. Velocity is also used in very low frequency applications where the vibration amplitude is too small to measure and the velocity vibration is of higher and more meaningful value. Velocity output accelerometers are mainly effective if the vibration frequency is higher than 2 Hz and ideally 5Hz [34].

To perform the transduction principles of a piezoelectric accelerometer different mechanical configurations are currently available [33]. These configurations are different in the way the piezoelectric material is excited by the inertial forces of an accelerated mass. In the shear mode of operation under acceleration the mass applies a shear stress to the sensing crystals. Shear accelerometers excel in rejecting thermal transient and base strain sensitivity [33]. Furthermore, the shear geometry favours itself to a small size, which promotes high frequency response while minimizing mass loading effects on test structure [32]. Flexural mode designs utilize crystals shaped as beams that are supported to create strain on them when accelerated. This type of design is characterized by insensitivity to transverse motion, therefore they are well suited for low gravitational acceleration and low frequency applications such as structural testing [32]. The compression mode accelerometers represent the historical accelerometer design; they provide high rigidity combined to a simple structure. There are mainly three types of compression designs: upright, inverted and isolated.

2.5.1 Piezoresistive Accelerometers

In the piezoresistive accelerometers the piezoresistive effect describes the change of a material’s electrical resistance caused by an applied mechanical stress proportional to the applied inertial forces. The piezoresistive effect determines a change in resistance of piezoresistors (gauges) connected electrically in a Wheatstone bridge circuit [85] (e.g., Z-axis piezoresistive accelerometer with four gages in a full-bridge configuration, see Figure 2-8) by the inertial force exerted by the seismic (or proof) mass (2 gages in tension, 2 gages in compression in the Figure 2-8) due to acceleration (see Appendix G). The unbalanced Wheatstone bridge network detects the fractional resistance change producing a proportional output voltage; this is true in a full Wheatstone bridge because other types of bridge introduce nonlinearities (see Appendix G for details). This type of technology, differently from the piezoelectric one, allows for a response down to DC (i.e., they respond to steady-state accelerations).

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Figure 2 - 6 . Z-axis Piezoresistive Accelerometer [32]

At frequencies close to 0 Hz, piezoelectric accelerometers cannot, when high accuracy is required, measure the acceleration an object is subject to. A static force results in a fixed amount of charges on the piezoelectric material and working with conventional electronics, not perfect insulating materials, and reduction in internal sensor resistance results in a constant loss of electrons, yielding an inaccurate signal [160]. When this slight inaccuracy is integrated in order to determine velocity, displacement and tilt, it becomes quite large. As a result, the velocity and displacement data are then inaccurate. For a static or quasi-static acceleration signal measurement, it is preferable to use either a piezoresistive or variable-capacitance accelerometer [37].

Many and diverse technologies are utilized in the piezoresistive accelerometer fabrication. Generally, in the bulk micromachining fabrication process the sequence of steps are: to grow the single crystal silicon; the ingot is trimmed, sliced, polished, and cleaned to obtain wafer; a mask layout on the wafer is patterned by a photoresist deposited film for diffusion or ion implantation of a dopant into a defined surface region; places defined by the mask are etched, followed by removal of the photoresist; and isotropic and/or anisotropic wet or plasma chemicals are used for releasing the structure by etching. The piezoresistive coefficients of the silicon are determined by the resultant stress distribution in the piezoresistors, the doping concentration and finally the orientation of the silicon wafer. The advantages of an accelerometer built in this way are: a high stiffness, resulting in a high resonant frequency (ω) which means a large usable frequency response. Other desirable features of such device fabrication are miniaturization, relatively large sensitivity (semiconductor strain gages have a gage factor 25 to 50 times that of metal), good linearity. Temperature compensation allows such devices to operate over a temperature range of -65 to +250ºF [32].

Roylance and Angell introduced the first fully integrated piezoresistive micromachined accelerometers in 1978 for biomedical applications [38, 39]. A comprehensive review on micromachined piezoresistive accelerometers was provided by Yazdi et al. [119]. Monolithic integration of piezoresistive accelerometers with CMOS circuitry that improves the output and compensates also temperature drift were developed in early 1990s [120, 121]. More recently a novel wafer-level package technique has been developed by encapsulating the die with a thick polysilicon epitaxial cup that protects the piezoresistors from dicing and plasma processing. Some devices that implement such novel encapsulation technique are the ones of Kwon and Park [123] which fabricated a three-axes piezoresistive accelerometer by using bulk micromachining and silicon direct bonding technology with a polysilicon layer. Also Partridge et al. [124] and Park et al. [125] for the piezoresistors used oblique ion-implantation and deep reactive ion etching (DRIE) to fabricate devices designed for lateral acceleration sensing; moreover they adopted encapsulation technique in their devices. Park et al. developed a sub-mm single axis piezoresistive accelerometer as a sound sensor for a cochlear implant. This technology is a possible alternative for implantable hearing aids [122]. For wireless structural monitoring Lynch et al. [126] combined a planar piezoresistive accelerometer with wireless sensing unit.

Many different 3-DOF (degree of freedom) piezoresistive accelerometer designs with highly symmetric geometry have been developed in the past. Currently they can be divided in accelerometers with cross beams, cross-inset beams or surrounding beams designs.

Most of the structures with highly symmetric geometry present a cross [94, 96, 97, 98, 100, 101, 103] or a cross-inset beams [95, 99, 102, 105] due to the higher stress obtained during deformation. Even though surrounding beams design [2, 93, 104] presents a lower stress profile compared to the cross-inset beams counterpart, the surrounding beams design presents the advantage of reducing the beams deformation. Reduced deformation determines a lower nonlinearity and cross-sensitivity effect; therefore a higher accuracy of the measurement is expected at the expense of mechanical structure sensitivity. Another option for further sensitivity increasing of the mechanical structure is to combine the cross-inset beams design to the surrounding beams design as in the work of Amarasinghe et al. [106].

Regarding different types of pick-off in the piezoelectric accelerometers the piezoelectric effect of quartz or ceramic crystals triggers an electrical output when subject to compression, flexion or shear forces. A force applied to a quartz crystal lattice structure modifies alignment of positive and negative ions, determining an accumulation of these charged ions on an electrode. In an accelerometer, the stress on the crystals occurs by the seismic mass applying a force upon the crystal. On the usable frequency range, this structure obeys Newton's second law of motion. Therefore, the total amount of charge accumulated is proportional to the applied force to the seismic mass, and the applied force is proportional to acceleration, therefore ultimately the voltage output is a measure of the applied acceleration [33].

The frequency response of the sensor is determined by the resonant frequency of the sensor, which occurs when the sensor is excited at his natural frequency (Figure 2-7). The resonant frequency (ωo) of the sensor can be calculated by:

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Figure 2 - 7 . Typical frequency response of accelerometer [33]

The usable frequency response as depicted in the Figure 2-7 is the flat area of the frequency response curve and extends to approximately ⅓ to ½ of the natural frequency [34].

The natural frequency of an accelerometer is the frequency at its highest peak (Figure 2-7). From a frequency of around ⅓ to ½ of the natural frequency the ratio of output to input or transfer function becomes non-linear and therefore the measurement is difficult to be interpreted. A higher natural frequency of an accelerometer frequency response is preferable since it is wider the band of frequencies that can be measured. It can be seen from the formula of the resonant frequency that as the mass decreases the natural frequency increases which is good for the measurement, but a small mass typically determine a lower sensitivity and this is true for most high frequency accelerometers [34].

In capacitive accelerometers the acceleration is a measure of an unbalanced bridge, measuring a change in capacitance. The pick-off element is formed by two parallel capacitors that work in a differential mode. These capacitors operate in a bridge configuration and are dependent on a carrier demodulator circuit to produce an electrical output proportional to acceleration. These types of accelerometer are built in a surface micromachining process [36] and typically a monolithically built electronic circuit is required for proper operation of a capacitive accelerometer. One of the major advantages of capacitive accelerometers is to measure low level (less than 2g), low frequency (down to DC) acceleration with high shock survivability, typically 5,000g or greater, and high accuracy [32].

In convectional heat transfer accelerometers a single heating element is centred in a substrate and suspended across a cavity with temperature sensors positioned in all four sides of the suspended heating element (Figure 2-8). Under zero acceleration the heat gradient will be symmetrical, which means that all the temperature sensors measure the same temperature. Due to convection heat transfer the acceleration in any direction causes the heat gradient to become asymmetrical and the unbalanced temperature sensors would represent a measure of the acceleration [35]. Simple electronics is typically used to converts the temperature measurements into signals.

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Figure 2 - 8 . Convective Heat Transfer Accelerometer (MX2125) [128]

In the optical pick-off type of accelerometers the acceleration is converted in an electrical signal based on an optical intensity modulation techniques. There are two main categories of these devices. The first consist of two fibres attached to a substrate with supporting bars, one completely attached and the other one is a cantilever-like fibre beam. The other category is based on movable shutter fabricated by micromachined processes (MOEMS) [41]. An example is illustrated in the Figure 2-9.

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Figure 2 - 9 . Silicon Micromachined MOEMS device [129]

The servo or force-rebalance type of accelerometer, which integrate a control system with feedback, is the most sensitive (capable of sensing distant earthquakes in micro-g's) and most precise (used in navigation of spacecraft) accelerometer. All type of open-loop sensors described so far may have a certain actuation system that works as force-rebalance. Typically the accelerometer that implements such system is the variable-capacitance accelerometer since the actuation is straightforward.

2.6 Piezoresistance

The piezoresistance effect can be described in a matrix form where each of the six fractional resistivity changes relates to each of the six stress components [40] (see Appendix H). Kanda [72] generalized the fractional resistivity change by [40]:

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where ω is a fixed voltage and current orientation and λ the stress orientation.

Mathematically this yields a matrix of 36 coefficients. By definition, the elements of this matrix are called piezoresistance coefficients, πωλ, (ω, λ =1 to 6), expressed in Pa-1.

Generally, two piezoresistors’ contacts are formed by masked-ion implantation method, and lie on very thin surface layer, the beam [32]. Therefore, only two piezoresistance coefficients, i.e. π’11 and π’12 are relevant for calculation. π'11 corresponding to the case the stress parallel with the direction of electric field and current density, thus it is called the longitudinal piezoresistance coefficient, denoted by π l. Similarly, π’12 relating to the case the applied stress perpendicular to the electrical field and current density, hence it is called transverse piezoresistance coefficient, π t. The shearing stress is neglected since it is much smaller than the others. These two coefficients are expressed through three fundamental piezoresistance coefficients π11, π12, π44, and directional cosines (l, m, n) for arbitrary crystal orientation by the general formulation for longitudinal (πl = π’11) and transversal (πt = π’12) piezoresistive coefficient by Mason and Thurston [70]:

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Based on the theory and equation above, the resistance change can be calculated as a function of the beam stress. In the accelerometer the piezoresistors are located on the surface of a thin beam, therefore the material is stressed mainly in two dimensions at the surface plane. The mechanical stresses are considered constant over the piezoresistors; the fractional resistance change is simply given by:

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where σl and σt are longitudinal and transversal stress, the shearing stress is neglected since very low respect to the others. It is noted that the above equation is only valid for uniform stress fields or if the piezoresistor dimensions are small compared to the beam size [71 , 40].

The first materials widely used as piezoresistors were single crystal germanium and silicon because with diamond lattice crystal structure. In 1954 in these semiconductor crystals Smith [48] reported the first measurements of large piezoresistive coefficients noting that this phenomenon could be explained by the work of Bardeen and Shockley [157], and later Herring [110, 111]. Smith measured the piezoresistive coefficients for (100) samples along the <100> and <110> crystal directions. Longitudinal and transverse coefficients for the fundamental crystal axes were determined directly. Shear piezoresistive coefficients were inferred. By these measurements and considering the crystal symmetry, Smith fully characterized the piezoresistive tensor of 7.8 Ω-cm at low p-Si concentration. At light concentrations (1.7×1015 cm-3), Smith [48] found the p-type longitudinal piezoresistive coefficient in the [110] direction for bulk silicon to be relatively constant at 72×10-11 Pa-1 [(π11+π12+π44)/2]. His results have been showed graphically by Kanda [72] (see Appendix H). In other words, p -type piezoresistors must be oriented along the <110> directions to measure stress and thus should be either aligned or perpendicular to the wafer primary flat [73]. The piezoresistance coefficient magnitude decreases significantly with the doping concentration and the temperature. The first systematic experimental study on piezoresistance over a broad temperature range (-90°C to 100°C) and doping concentration levels was carried out by Tufte and Stelzer [69] in the early 1960s. Subsequent studies by many investigators have generally confirmed the trend of their results. Kanda [72] has theoretically discussed the dependence of the piezoresistive coefficient on the impurity concentration and temperature. He concluded that the piezoresistive coefficient with a doping concentration of N at a temperature T, Π (N, T), can be generally expressed as:

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where Π (300K) is the piezoresistive coefficient at room temperature (300 K or 25°C) for low doped material of the same conductive type and P(N,T) is a factor indicating the dependence of the piezoresistive coefficient on the doping level and temperature. Based on the multi-valley theory of semiconductor energy bands, the factor P(N,T) has been calculated. The calculated values of the P(N,T), agree well with the experimental values obtained by Mason [70] for doping concentrations less than 1×1017 cm-3, over the temperature range of 50°C to 150°C, but differ by 21% at a concentration of 3×1019 cm-3 at room temperature. The error was attributed to dopant ions scattering for high dopant concentrations, whereas the calculation only considered lattice scattering. Harley and Kenny [53] later evaluated data from several researchers (see Figure 2-10) and provided an empirical fit of piezoresistance vs. concentration that better estimates the sensitivity for higher concentration devices.

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Figure 2 - 10 . Piezoresistive Factor comparison at room temperature [53]

The theory underlying the physics of the piezoresistive effect of semiconductors are grounded in one-dimensional descriptions of electron and hole transport in crystalline structures under strain. During that period the existing theories were based on bandgap energies shifts, and the change in mobility with the lattice strain was explained as band warping or bending and the non-uniform density of states [109 – 112]. The many-valley model of Herring [110, 111] is the main model used for explaining the physics underlying the piezoresistive effect of n-type silicon. In 1988, Lin [113] explained the large mobility degradation at higher transverse electric field by the scattering mechanisms of quantized subbands at (100) silicon planes. The physics of p-type silicon piezoresistance has been almost unknown for decades due to the inherent complexity of valence band structure [114], most of the research and commercial piezoresistive devices had therefore been mainly based on experimental studies. However, only recently computational advances allowed improving the understanding of the p-type silicon piezoresistance effect [115 – 117].

2.6.1 Piezoresistance of p-type and n-type single crystal silicon

The doping concentration [69, 161], type of dopant [69, 161], and temperature of the substrate [69, 72] influence the piezoresistive coefficients of single-crystal silicon that are not constants. Different elements of the π matrix (π11, π12 and π44) are affected differently by temperature and doping concentrations. With increasing temperature and doping concentrations the value of the piezoresistive coefficient decreases for both p- and n-type silicon. The values of π11, π12 and π44 for single-crystalline silicon under certain doping concentration and dopant types have been experimentally characterized. Several typical values for selected doping concentrations are listed in Table 2-5.

Table 2-5. Piezoresistivity components for single-crystal silicon under certain doping values.

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However, all 36 of the coefficients in the coefficient matrix [π] may be nonzero when referring to a Cartesian system of arbitrary orientation relative to the crystallographic axes [162]. In the case of silicon, the components of the matrix change if the x-, y-, and z-axes are not aligned to <100> directions.

In the most commonly occurring cases, when the piezoresistor points in <100>, <110> or <111> directions [72, 163] the effective longitudinal and transverse piezoresistive coefficients are summarizes in Table 2-6.

Table 2-6. Formula for transverse and longitudinal piezoresistive coefficient for various commonly encountered resistor configurations.

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Combining the results in Table 2-5 and the formula of the piezoresistive coefficients in Table 2-6 it is possible to estimate the fractional resistance change (Eq. 2.5) for n-type and p-type piezoresistors in the <100> and <110> direction. N-type piezoresistors in the <100> direction with a resistivity of 11.7 Ω cm have a fractional resistance change equal to:

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Equation 2.7 shows the fractional resistance change as function of only the longitudinal piezoresistive coefficient and that the fractional resistance change is zero for a transversal stress twice the longitudinal stress. Therefore n-type piezoresistors in the <100> direction are suitable for measuring acceleration when the longitudinal stress is the main stress component as in uniaxial stress application. Clearly the p-type piezoresitors in this direction with a resistivity of 7.8 Ωcm are not suitable for measurements due to the very low piezoresistive coefficients.

In the <110> direction the n-type piezoresistors have a longitudinal coefficient of -31.2×10-11 Pa-1 and a transversal coefficient of -17.6×10-11 Pa-1. This configuration is in general not prefered for measurements due to the low piezoresistive coefficents compared to the <100> direction. P-type pezoresistors in the <110> direction with a resistivity of 7.8 Ωcm show a fractional resistance change given by:

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where π11 and π12 are considered zero due to their very low value compared to the π44. This configuration is suitable for measurements and used in this study. P-type piezoresistors in the <110> direction are preferred in this work compared to the n-type in the <100> direction because is a convenient crystallographic orientation from a fabrication standpoint [53], moreover boron is the most common used dopant. In a (100)-oriented wafer the p-type piezoresistors in the <110> direction are orthogonal to each other, therefore fabricating the piezoresistors in the X and Y-axis pointing to the <110> direction it is possible to measure the in-plane acceleration by simple Wheatstone bridges circuits (see Appendix G and H for details).

2.6.2 Giant Piezoresistance in Silicon Nanowires

In the last decade experimental studies on piezoresistance effect of silicon nanowires agreed that SiNWs under uniaxial stress offers an enhanced piezoresistance effect respect to the bulk counterparts [2-7].

The origin and behaviour of this phenomenon called in the literature “Giant Piezoresistance” is currently not clearly understood. The origin of the giant piezoresistance effect was examined in numerous works [12, 45-47, 140-149]. Alongside with the quantum confinement [45, 137-139] the nature of the giant piezoresistance [3, 140] was explained by the following reasons: strong strain-dependence of effective masses of holes [46], strain modulation of the surface potential [47, 149], interface trapping of charged carriers [140] and stress concentration regions [150]. Existence of the giant piezoresistance in nanowires [3] was contested in work [79]. To date, relatively few reports on the development of silicon nanowire-based sensors are available [42]. However, p-type single crystalline SiNWs have been studied for sensor applications [2, 13, 14, 43, 44, 134, 136].

Toriyama et al. studied silicon nanowire piezoresistors have been fabricated by separation by implanted oxygen (SIMOX), thermal diffusion, electron beam (EB) direct writing, and reactive ion etching (RIE) [43]. Longitudinal and transverse piezoresistive coefficients, πl <110> and πt <110> , are both dependant on the cross sectional area of the nanowires. The πl <110> of the nanowire piezoresistors increased (up to 60%) with a decrease in the cross sectional area, while πt <110> decreased with an increase in the aspect ratio of the cross sectional area. The enhancement behaviour of the πl <110> was explained qualitatively using 1-D hole transfer and hole conduction mass shift mechanisms. The decrease in the πt <110> with increase in the aspect ratio of the cross sectional area is explained due to decrease in the stress transmission from substrate to the nanowire. The maximum value, πl <110> of 48 x 10-11 Pa-1 at a surface concentration of 5 x 1019 cm-3, suggests enough sensitivity for sensing applications (see Table II, [43]). Dao et al. incorporated these p-type silicon nanowires as piezoresistive elements in a miniaturized 3-degrees-of-freedom (3-DOF) accelerometer [2, 6]. Initial experimental studies undertaken by He and Yang [3] reported a very high piezoresistive effect (increased up to 3,776%) of self-assembled single crystal silicon nanowires in the <111> crystallographic orientation. Reck et al. later on used a lift-off and an electron beam lithography (EBL) technique to fabricate silicon test chips and study the piezoresistive properties of crystalline and polycrystalline nanowires as a function of stress and temperature [4]. They found that the piezoresistive effect in the <110> direction greatly increases as the silicon nanowire diameter decreases (up to 633%), consistent with the results from He and Yang [3]. Finally, Passi et al. [7] recently obtained an increase of piezoresistance of up to 2,140% respect to the bulk-Si in the same crystallographic direction, the <110>.

Some hypotheses have been speculated on the origin of such phenomenon, initially it was explained based on transconductance data as being due to enhanced strain modulation of carrier mobility in the p-type <111> and <110> SiNWs [3]. However, first-principle calculations later on point out surface states being the main culprit in p-type <111> silicon nanowires [46, 47]. But in 2009 first-principles results on piezoresistive effect in silicon nanowires in the <111>, <110> and <100> directions carried out by Nakamura et al. [12, 45, 137-139] were in contrast to the calculation by Cao et al. [46] that the hole transport occurs on the wire wall in p-type <111> SiNWs with dangling bond. Nakamura et al. [12, 45, 137-139] in their simulation model find out that the hole transport occurs stably in the interior of p-type <111> SiNWs without dangling bond. They conclude that the <100> direction is the most suitable one for integrating p-type SiNW without dangling bond as nanoscale piezoresistors and allege the origin of such Giant Piezoresistance in this direction (πl<100>= 588 × 10-11 Pa-1) can be explained in terms of orbital interactions theory [6, 12]. Finally in this study they obtained that the p-type <111> SiNWs without dangling bonds (H-terminated wire wall) have small piezoresistive coefficients, which is contradictory to the experimental results obtained by He and Yang [3] and in contrast to those in the case of p-type bare-walled <111> SiNW with dangling bonds, reported by Cao et al. [46]. Therefore Nakamura et al. [12, 45, 137-139] predict that <111>-oriented SiNWs will not be suitable candidate for nanoscale piezoresistors. In conclusion it may be asserted that conductivity of p-type <111> SiNW differs greatly between wire walls with or without dangling bonds and then it is natural for SiNW with a giant piezoresistance coefficient to be under an irregular wall-termination condition [45]. Finally, recently experimental findings adduced the giant effect of being a surface induces effect with {110} surfaces inducing much larger piezoresistance than {100} surfaces [5], showing a clear aspect ratio dependence of piezoresistance coefficient. This work supports the computational work of Cao et al. [46] and Rowe [47] pointing towards surface states being the source of giant piezoresistance. In particular Rowe identifies the origin of this phenomenon in the partial depletion of the conduction channel.

Recently research by Milne et al. [79] claimed that this phenomenon may not exist after all The France-Switzerland research team claimed that the observations of giant piezoresistance were probably artefacts and caused by surface trapping of charges (also known as dielectric relaxation) that takes place in the Si/SiO2 interface and induced by the voltage applied to measure the resistance. The charge trapping results in partial depletion of the nanowires determining the giant effect. The team by applying a heterodyne detection (an oscillating stress to its samples) were able to separate any non-stress-related drift in the resistance value from that caused by the applied stress. In this way the stress repeatedly increases and then decreases as function of time. According to Rowe [158], heterodyne techniques were never applied before to piezoresistance measurement before, so previous measurements revealed large (but not stress-related) resistance change in the silicon nanowires. Yang replied [158] to the results of Rowe [47, 79] by saying that they reported piezoresistance measurements on top-down micro and nanowires while in their measurements they used bottom-up grown nanowires. Since bottom-up synthetic bridging nanowires have quite different strain levels, surface states and dopant profiles from those of top-down fabricated ones the results obtained are of different nature. Moreover, the team of research guided by Yang [86] recently demonstrated the first resonator piezoresistively transduced with very high frequency (100 MHz) using silicon nanowire with on-chip electronic actuation at room temperature. Yang claimed that their resonator would not be possible without enhanced piezoresistance effect [86].

Another study undertaken by Koumela et al. [80] showed that top-down nanowires appear in general to have a gauge factors close to bulk, except for low doped suspended nanowires with a gauge factor twice as high as the bulk. Top-down nanowires [5, 79] have shown much lower piezoresistive coefficients than the ones observed for bottom-up devices [3]. The results of this study support the work of Milne [79] and Barwicz [5] where no giant effect was observed. Table 2-7 summarizes the major experiments undertaken on p-type silicon nanowires under stress/strain.

The modelling of the silicon nanowires based on first principle simulation have revealed a piezoresistance effect higher than in the bulk counterparts in the <100> direction and similar to the bulk counterparts in the <111> [10, 12, 45, 46, 137-139]. These results are in contrast to the experimental work carried out so far. Therefore, future modelling and experimental work need to be conducted in conjunction in order to clarify the origin and to better describe the phenomenon under study.

Table 2-7. p-type silicon nanowires experiments

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*SiNW embedded in an accelerometer

2.6.3 Fabrication processes of silicon nanowires

Currently there are two main technologies for the fabrication/growth of nanowires: self-assembly and top-down approach. The self-assembly technology is a growth mechanism. The more common growth mechanisms are vapour-liquid-solid (VLS) and oxide-assisted growth (OAG) mechanisms [10]. In the VLS model, the nanowire grows from a metal-catalyst droplet during silicon vapour deposition. The metal particles are present at the tips of the Si NWs. This mechanism is used by He and Yang [3] for growing their nanowires in the <111> and <110> direction using Pt as catalyst and SiCl4 as precursor at 900°C. The oxide-assisted growth process produces metal-free SiNWs. The mechanism does not require metal catalyst and the oxide is continuously needed throughout the entire nucleation and growth process [10]. Main problem of the use of this technology is the integration of the silicon nanowires growth into the MEMS fabrications steps.

The top-down approach of fabrication of nanowires comprises mainly two different technologies: electron beam lithography (EBL) and nanoimprint lithography (NIL). These are currently part of standard industrial micro/nano fabrication. Both technologies have sub-10 nm resolution, a limit of 3-5nm resolution is achievable with both technologies [50, 51]. EBL consists of a focused electron beam with nanometre spot size that is scanned across the surface to be patterned. EBL is a maskless lithography, where the electron beam directly creates the fine patterns with random shapes in positive and negative electron beam sensitive resists [51]. Because of serial pattern generation EBL suffers from serious throughput limitations. It is typically ideal for research and development and small volume production. The EBL is followed by RIE etching or lift-off as pattern transfer. For industrial scale nanowire fabrication, NIL is a more suitable technology. Ultraviolet nanoimprint is a mechanical molding technique. A template made from quartz or a flexible elastomer with a 3D relief is brought into intimate contact with a UV-curable resist spin-coated on top of a substrate. Applying low imprint pressure at room temperature, features are filled within seconds due to the low viscosity of the imprint resist. Alignment of template and wafer is carried out with high precision and the resist is hardened via UV-light through the backside of the template. Finally substrate and template are separated. The replicated resist relief can further be transferred into the substrate via RIE-process or used as functional element [50]. These two technologies can be combined, in particular the EBL is used to fabricate efficient moulds for nanoimprinting structures with high density moulds [50, 51].

2.7 Gap in Knowledge

All of the studies reported in this study agreed that low doping and surface-to-volume ratio represent the main parameters that boost the piezoresistance effect of SiNWs. Some hypotheses have been speculated on the origin of such phenomenon [42]. Recently the major culprit has been indicated to be surface-state induced effect for nanowires smaller than 70 nm width, and enhanced strain modulation of carrier mobility for larger nanowires [43].

In this work the author intends to investigate experimentally the suitability of p-type SiNW in the <111> direction as nanoscale piezoresistors for mechanical sensors, by fabricating nanotechnology samples.

From the literature review outlined in the Table 2-5, the following summarized considerations have been made:

a. No experimental data are available for SiNWs with feature around 5 nm in any of the <111>, <110> and <100> directions.

Mainly because of technology difficulties in the downscale of SiNWs.

b. No experimental data are available for p-type SiNW in the <100> direction under only uniaxial stress

Because of the very low piezoresistive effect of the bulk piezoresistor counterparts in the <100> crystallographic direction

c. No experiment has been undertaken on bottom-up silicon nanowires applying an oscillating stress.

The surface charge trapping of SiNW was unknown before the study of Milne at al. [79]

d. Not clear explanation has been given on the giant effect origin (surface induced or carrier mobility modulation or orbital interaction) and two studies [79, 80] did not observe this phenomenon at all.

There are controversial results and explanations of previous theoretical and experimental studies.

The p-type <100>, <111> SiNW showed Giant effect in first-principles calculations [10, 12, 45, 46, 49],

BUT:

1 The p-type <100>, <111> SiNW are suitable as piezoresistor?

2 The bottom-up silicon nanowires under oscillating stress do they show an enhanced piezoresistance effect?

The experimental work undertaken in this study aims to answers part of the first question demonstrating the feasibility of fabricating silicon nanowires as nanoscale piezoresistors in the <111> direction.

2.8 Conclusion

The investigation carried out on silicon nanowires will ultimately allow the development of inertial sensors (e.g. accelerometer) with a very tiny footprint being characterized by high sensitivity not achievable before. Traditionally a trade-off between miniaturization and sensor sensitivity has limited the miniaturization and together the accuracy achievable. To date no tri-axis accelerometer are commercially available with a size below 2×2 mm capable to measure impacts events of >250g; besides, none of them can avoid amplification of the output signal, mainly because the relative high thermo-mechanical noise due to small proof mass size. The sensitivity achievable by the incorporation of quantum wires that benefits giant effect within the sensor (two orders of magnitude larger than that of bulk silicon, [6]) will permit to obtain an electrical sensitivity (static response) such that the device will not require any kind of amplification (high accuracy of measurements) and will allow to achieve a miniaturization level not permitted before. Obviously, sensors that avoid amplifier enjoy a much higher sensing accuracy. This study will predict the advent of a new class of electro-mechanical-system devices in the nanoscale dimension (NEMS) with a footprint less than 1 square millimetre with high sensitivity and accuracy.

Major applications of such novel sensor based on enhanced nanoscale piezoresistors are in the biomedical arena, such as implantable devices for motion/vibration sensing. Examples are in hearing aid systems (implantable sound sensor for cochlear implants [112]), heart wall motion measurement for cardiac artificial pacemakers (an adaptive control system that detects the human body activity level in order to adjust accordingly the pacemaker rate response [102]) and head injury monitoring of military soldiers and race car drivers in case of blast and crash respectively (an earplug sensor placed in the inner ear canal). It is presumed that such devices, with these amazing technical characteristics driven by nanotechnology, will spread also in the area of consumer products as can be observed already with conventional accelerometers.

Moreover, shrinking the miniaturization size in the sub-millimetre will pull the fabrication cost down due to the higher number of devices fabricated per silicon wafer (batch fabrication) and at the same time will increase the systems integration in a single chip allowing the development of increasingly intelligent sensors. Currently the most time and cost effective nanofabrication process of nanowires that seems more suitable for high volume manufacturing processes in the area of top-down fabrication technology is the nanoimprint lithography (NIL). The electron beam lithography (EBL) in comparison is much more time-consuming process and with higher cost obtaining similar or less resolution than NIL. Other option is to grow the nanowires as self-assemble devices, which is the technique used in this work. Currently most of the work on silicon nanowires as nanoscale piezoresistors has been carried out on top-down fabricated sensors, therefore the few study on bottom-up silicon nanowires are not exhaustive, and this work intends to progress the knowledge on this type of sensors.

All the historical findings since the experimental work of Smith [48], graphically described by Kanda [72] first and then improved by a fitting function of Harley and Kenny [53] that perfectly describes the work of Mason et al. [70], Tufte et al. [69] and Kerr et al.[75] have been presented. The effort to explain the physics behind the piezoresistive phenomenon by Herring [110, 111] with his many-valley model and by Lin [113] with his scattering mechanism of subbands theory has been highlighted. The most recent advancement on the piezoresistive effect in the nanoscale dimension outlining all major experiments on p-type silicon nanowires and first-principle calculation by simulation models proposed by Nakamura et al. [12, 45, 137-139] have been addressed. The latest developments of Milne [79] and Koumela [80] on possible explanations of the giant effect as apparent phenomenon due to dielectric relaxation are also considered. The work done so far on the giant piezoresistance effect is:

a. Limited to nanowires size above 5 nm in the <110> and <111> directions,
b. No experiments are currently available on bottom-up silicon nanowires applying oscillating stress.
c. The work carried out on explaining this phenomenon, if really exists, by first-principal simulations contradicts the results of various experimental studies.

The next chapter deals with the design and simulation of a novel accelerometer that embeds silicon nanowires as nanoscale piezoresistors. Moreover in order to highlight the potential of the nanowires, a comparison to conventional microscale piezoresistors is proposed.

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