THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Introduction to heat transfer

This paper presents a monolithic mechanically-bistable mechanism that does not rely on residual stress for its bistability. The typical implementation of this mechanism is two curved centrally-clamped parallel beams, hereafter referred to as "double curved beams". Modal analysis and finite element analysis (FEA) simulation of the curved beam are used to predict, explain, and design its bistable behavior. Microscale double curved beams are fabricated by deep-reactive ion etching (DRIE) and their test results agree well with the analytic predictions. Approaches to tailor the bistable behavior of the curved beams are also presented.

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A curved-beam bistable mechanism

The monitoring of acceleration is essential for a variety of applications ranging from inertial navigation to consumer electronics. Typical accelerometer operation involves the sensitive displacement measurement of a flexibly mounted test mass, which can be realized using capacitive, piezo-electric, tunnel-current or optical methods. Although optical detection provides superior displacement resolution, resilience to electromagnetic interference and long-range readout, current optical accelerometers either do not allow for chip-scale integration or utilize relatively bulky test mass sensors of low bandwidth. Here, we demonstrate an optomechanical accelerometer that makes use of ultrasensitive displacement readout using a photonic-crystal nanocavity monolithically integrated with a nanotethered test mass of high mechanical Q-factor This device achieves an acceleration resolution of 10 µg Hz^(−1/2) with submilliwatt optical power, bandwidth greater than 20 kHz and a dynamic range of greater than 40 dB. Moreover, the nanogram test masses used here allow for strong optomechanical backaction, setting the stage for a new class of motional sensors.

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A high-resolution microchip optomechanical accelerometer

Introduction to Surface Chemistry and Catalysis

We have successfully demonstrated a series of results that push the limits of optical sensing, acceleration sensing and lithography. Previously, we built some of the most sensitive displacement sensors with displacement sensitivities as low as 12 fm / Hz at 1 kHz. Using reference detection circuitry in conjunction with correlated double sampling methods, we lowered the 1/f noise floor to 10 mHz, hence improving the detection limit at low frequencies (10 mHz) by 77 dB to 50 fm / Hz . We converted these highly sensitive displacement sensors to highly sensitive acceleration sensors through a direct mass integration processes. Our accelerometers have resonant frequencies as low as 36 Hz and thermal noise floors as low as 8 nG / Hz (where 1 G = 9.8 m/s2). We have pushed the limits of shaker table experiments to independently verify acceleration measurements as low as 10 μ G / Hz . Direct measurements with our integrated sub-wavelength optical nano-grating accelerometers have shown device sensitivities of 590 V/G and noise floors corresponding to 17 nG / Hz (at 1 Hz).

In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor

We present a high coupling coefficient, k eff 2 , micromechanical resonator based on the propagation of SH0 Lamb waves in thin, suspended plates of single crystal X-cut lithium niobate (LiNbO 3 ). The thin plates are fabricated using ion implantation of He to create a damaged layer of LiNbO 3 below the wafer surface. This damaged layer is selectively wet etched in a hydrofluoric (HF) acid based chemistry to form thin, suspended plates of LiNbO 3 without the wafer bonding, layer fracturing and chemical mechanical polishing in previously reported LiNbO 3 microfabrication approaches. The highest coupling coefficient is found for resonators with acoustic propagation rotated 170° from the y -axis, where a fundamental mode SH0 Lamb wave resonator with a plate width of 20 μm and a corresponding resonant frequency of 101 MHz achieves a k eff 2 of 12.4%, a quality factor of 1300 and a resonator figure of merit ( M ) of 185. The k eff 2 and M are among the highest reported for micromechanical resonators.

A high electromechanical coupling coefficient SH0 Lamb wave lithium niobate micromechanical resonator and a method for fabrication

Bistable behavior is desirable for a variety of applications because power is applied only during switching, and the mechanism state remains the same regardless of any power interruptions. The low variability in the stable positions also makes accurate open-loop control of many systems possible, and the precise switching characteristics make them valuable in sensing arrays. In this paper, fully-compliant bistable micromechanisms were modeled using finite elements. This model was then coupled with an optimization program, allowing extensive exploration of the design space. Three designs within this space were generated by minimizing the layout size of the devices subject to force constraints. These designs were subsequently manufactured and tested to verify bistability, with each mechanism snapping as expected between the two stable positions. The design space was then further explored to determine the behavior of the device as the maximum force output increased. This study revealed that the minimum layout size increases with the maximum force output.

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Design optimization of a fully-compliant bistable micro-mechanism

This paper describes the development of aluminum nitride (AlN) resonant accelerometers that can be integrated directly over foundry CMOS circuitry. Acceleration is measured by a change in resonant frequency of AlN double-ended tuning-fork (DETF) resonators. The DETF resonators and an attached proof mass are composed of a 1-mum-thick piezoelectric AlN layer. Utilizing piezoelectric coupling for the resonator drive and sense, DETFs at 890 kHz have been realized with quality factors (Q) of 5090 and a maximum power handling of 1 muW. The linear drive of the piezoelectric coupling reduces upconversion of 1/f amplifier noise into 1/f 3 phase noise close to the oscillator carrier. This results in lower oscillator phase noise, -96 dBc/Hz at 100-Hz offset from the carrier, and improved sensor resolution when the DETF resonators are oscillated by the readout electronics. Attached to a 110-ng proof mass, the accelerometer microsystem has a measured sensitivity of 3.4 Hz/G and a resolution of 0.9 mG/radicHz from 10 to 200 Hz, where the accelerometer bandwidth is limited by the measurement setup. Theoretical calculations predict an upper limit on the accelerometer bandwidth of 1.4 kHz.

Michael S. Baker

Papers

In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor

A high electromechanical coupling coefficient SH0 Lamb wave lithium niobate micromechanical resonator and a method for fabrication

Design optimization of a fully-compliant bistable micro-mechanism

Post-CMOS-Compatible Aluminum Nitride Resonant MEMS Accelerometers

Post-CMOS Compatible Aluminum Nitride Resonant MEMS Accelerometers.