DESIGN OF A PROXIMITY SENSOR USING INDUCTORS,
COMPATIBLE WITH INTEGRATED CIRCUIT FABRICATION
by
Vikas Inderpal Gupta, B.E.
Thesis
Presented to the Faculty of the Graduate School
of The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science in Engineering
The University of Texas at Austin
August 1995
Abstract
SUPERVISOR: Dean P. Neikirk
This work consists of designing an eddy-current proximity sensor, using a planar inductor as it's transducer. The sensor is capable of measuring distances between a metal target and it's transducer. Single coil designs for the transducer are studied. Methods to calculate the self inductance and resistance of these coils and the mutual inductance between the coils and the target are discussed. The effect of scaling these coils down to microelectronic dimensions is studied.
Two coil transformer designs are studied as an alternative to the single coil designs. The scaling of single coil designs causes the resistance of these coils to increase affecting their performance. This can be circumvented by using a two coil design.
Various fabrication issues which arise due to the specific application of the eddy-current proximity sensor are also studied.
Copyright by Vikas Inderpal Gupta 1995
Acknowledgments v
Abstract vi
Table of Contents vii
List of Figures x
1.1.0 Proximity Sensors 1
1.1.1 Mechanical Proximity Sensors 2
1.1.2 Laser Interferometry 2
1.1.3 Ultrasonic Proximity Sensors 4
1.1.4 Capacitive Proximity Sensors 4
1.1.5 Magnetic Proximity Sensors 5
1.1.6 Eddy-current Proximity Sensors 5
1.2.0 Motivation 7
1.3.0 Summary of Chapters 10
References 12
Chapter 2 : Single Coil Design 13
2.1.0 Resistance Calculation 13
2.2.0 Coil Inductance Calculation 14
2.3.0 Calculation of Mutual Inductance between Plate and Coil 19
2.4.0 Measurements 23
2.4.1 Image theory revisited 33
2.4.2 Conclusions from Measurements 37
2.5.0 The Discontinuity 38
2.6.0 Effect of change in Dielectric between the Coil and the Metal Plate 42
2.7.0 Effect of change in resistance of Metal Plate 44
2.8.0 The Scaling Issue 47
2.8.1 Scaling number of segments (n) 48
2.8.2 Scaling of distance between segments (d) 49
2.8.3 Scaling of width of segment (w) 51
2.8.4 Total Coil Scale 53
2.9.0 Circuits 56
2.9.1 A self excited oscillator test instrument 56
2.9.2 An AC Bridge 57
2.10.0 Summary 58
References 59
Chapter 3 : Two Coil Design 61
3.1.0 Measurements 61
3.2.0 PSpice® Model 69
3.2.1 Calculation of Rplate 71
3.2.2 PSpice® Simulation 73
3.2.3 Effect of variations in Rprimary (Rsecondary) 74
3.2.4 Effect of variations in Lplate and Rplate 77
3.2.5 Simulation results 81
3.3.0 Circuit 85
3.4.0 Potential Applications 87
3.4.1 An Electromagnetic Accelerometer 87
3.4.2 An Electromagnetic Bearing Wear Sensor 87
3.5.0 Summary 88
References 90
Chapter 4 : Fabrication Issues 91
4.1.0 The Membrane 93
4.2.0 The Overhang Problem 93
4.3.0 Photoresist Profiles 95
4.4.0 Exposure 100
4.5.0 Patterning along the side walls 102
4.6.0 Summary 104
References 105
5.1.0 Summary 106
5.2.0 Work to be done 107
Bibliography 109
Vita 113
List of Figures
Fig. (1-1): A schematic diagram of a laser interferometer. 3
Fig. (1-2): Pattern of magnetic field in eddy-current and magnetic sensors 7
Fig. (1-3): Cross-section of a Journal Bearing. 8
Fig. (1-4): The Slider Bearing approximation. 9
Fig. (2-1): Explanation of Greenhouse's model. 16
Fig. (2-2): Calculation of the mutual inductance between two segments of different lengths. 19
Fig. (2-3): A conductor over a ground plane is replaced by the conductor and it's image. M is the mutual inductance between the conductor and the ground plane, which equal to the mutual inductance between the conductor and it's image. 20
Fig. (2-4): Model for Rosa's calculation of GMD between two segments of different cross section. 21
Fig. (2-5): Single coil mask designs. 24
Fig. (2-6): Compensating short to eliminate the effect due to the contact pads. 25
Fig. (2-7): Inductance and resistance graphs for the spiral coil. 27
Fig. (2-8): Inductance and resistance graphs for the zigzag coil. 28
Fig. (2-9): Inductance and resistance graphs for the parallel coil. 29
Fig. (2-10): Single coil transformer to represent the coil and plate system. R1 and L1 represent the coil, R2 and L2 represent the plate and Zdiscontinuity represents the discontinuity in the current flow in the plate. 31
Fig. (2-11): Circuit model for image theory. 34
Fig. (2-12): Connection schemes for the transformer model. 35
Fig. (2-13): Experimental data vs. calculation results for inductance vs. gap 38
Fig. (2-14): Coil with it's image and the discontinuity. 39
Fig. (2-15): Reduced coil showing position of slits in the metal plate with respect to the coil 40
Fig. (2-16): Inductance and resistance graphs for discontinuity. 41
Fig. (2-17): Inductance and resistance graph for different dielectrics. 43
Fig. (2-18): Inductance and resistance graphs for metal plates of different resistances. 45
Fig. (2-19): Scaling the number of segments (n) of the coil. 48
Fig. (2-20): Effect of scaling the distance between segments on inductance of the coil (unoptimized and optimized). 49
Fig. (2-21): Effect of scaling of distance between segments on the resistance of the coil (unoptimized and optimized). 50
Fig. (2-22): Effect of scaling the width of the segment on the inductance of the coil (unoptimized and optimized) 51
Fig. (2-23): Scaling of the width of the segment (resistance) 52
Fig. (2-24): Effect of a total coil scale on the inductance and resistance of the coil. 54
Fig. (2-25): Graph of the frequency at which the Q-factor equals 1 (or vL = R) versus the scaling of the length of the segment. 55
Fig. (2-26): A self-excited oscillator instrument. 56
Fig. (2-27): The AC Bridge circuit. 57
Fig. (3-1): Two-coil mask designs. 62
Fig. (3-2): Test set-up for measuring gain and phase of the voltage across the primary coil versus the output voltage across the secondary coil for different gaps between the coils and the plate. 63
Fig. (3-3): Gain and phase measurements for the zigzag coil. 65
Fig. (3-4): Gain and phase measurement for the finger coil (1). 66
Fig. (3-5): Gain and phase measurement for finger coil (2). 67
Fig. (3-6): Gain and phase measurement for spiral coil. 68
Fig. (3-7): PSpice® model for a two-coil planar transformer with the metal plate. 70
Fig. (3-8): The "w+6h" model developed by Tuncer and Neikirk, used to calculate Rplate. 72
Fig. (3-9): PSpice® Simulation Program 73
Fig. (3-10): Phase and gain plots for variation in Rprimary (and Rsecondary). 76
Fig. (3-11): Phase and gain plots (using PSpice®) for a variation in Lplate. 78
Fig. (3-12): Phase and gain plots (using PSpice®) for a variation in Rplate 80
Fig. (3-13): Inductance and resistance graphs for the primary coil with the secondary coil open. 82
Fig. (3-14): PSpice® values to match the experimental graphs 83
Fig. (3-15): PSpice® vs. calculated values for Lplate and Rplate 84
Fig. (3-16): Block diagram for phase detection circuit 86
Fig. (3-17): An accelerometer 87
Fig. (3-18): Bearing wear sensor 88
Fig. (4-1): Schematic diagram of the proximity sensor. 92
Fig. (4-2): Schematic of the two-coil transformer. 92
Fig. (4-3): Overhang produced due to the circular mask hole used to etch the masking dielectric on the back of the wafer. 94
Fig. (4-4): Top view of the photoresist spun on a sample with two holes. 96
Fig. (4-5): Top view of the photoresist spun on a sample with four holes. 97
Fig. (4-6): Photoresist profiles inside the etched hole of a four hole sample. 99
Fig. (4-7): Photoresist patterning on back-side of membrane. 100
Fig. (4-8): The conventional exposure system. 101
Fig. (4-9): Exposure through the membrane. 102
Fig. (4-10): Using the "autofocus" function of the RDI Pattern Generator to expose patterns along the side walls of the etched hole. 103