Determination of doping and temperature-dependent elastic constants of degenerately doped silicon from MEMS resonators

Jaakkola, Antti; Prunnila, Mika; Pensala, Tuomas; Dekker, J.; Pekko, Panu

doi:10.1109/tuffc.2014.3007

Cited by 54 publications

(34 citation statements)

References 12 publications

(30 reference statements)

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“…This results in an additional electronic contribution to the elasticity that should be observable as a carrier concentration dependence in the Young's elastic modulus. [19] Semiconductors with different dopant concentrations have been observed to have different Young's modului [20], in rough agreement with Keyes' theory. However, direct measurements of the carrier concentration dependent Young's modulus have not been made.…”

Section: Introductionsupporting

confidence: 65%

Near-Surface Electronic Contribution to Semiconductor Elasticity

et al. 2017

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The influence of the carrier concentration on the elasticity is measured for a microscale silicon resonator. UV radiation is used to generate a surface charge that gates the underlying carrier concentration, as indicated by the device resistance. Correlated with the carrier concentration change is a drop in the resonant frequency that persists for 60 hours following exposure. Model calculations show that the change in resonant frequency is due to the modification of the elastic modulus in the near-surface region. This effect becomes increasingly important as device dimensions are reduced to the nanometer scale, and contributes an important source of instability for micro and nano scale electro mechanical devices operating in radiation environments.

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Section: Introductionsupporting

confidence: 65%

Near-Surface Electronic Contribution to Semiconductor Elasticity

et al. 2017

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“…It has been demonstrated that the TCF of the [100]-oriented silicon resonators is nonlinear, and there is a turnover temperature point [24,25] at which the TCF is equal to zero. The turnover point can be tuned by the doping level [26]. The oven-controlled N ++ [100] length-extensional mode silicon resonator has been previously reported by the authors [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Oven-Controlled MEMS Oscillator with Integrated Micro-Evaporation Trimming

Pei

Sun

Yang

et al. 2020

Sensors

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This study reports an oven-controlled microelectromechanical systems oscillator with integrated micro-evaporation trimming that achieves frequency stability over the industrial temperature range and permanent frequency trimming after vacuum packaging. The length-extensional-mode resonator is micro-oven controlled and doped degenerately with phosphorous to achieve a frequency instability of ±2.6 parts per million (ppm) in a temperature range of −40 to 85 °C. The micro-evaporators are bonded to the resonator, integrated face-to-face, and encapsulated in vacuum. During trimming, the micro-evaporators are heated electrically, and the aluminum layers on their surfaces are evaporated and deposited on the surface of the resonator that trims the resonant frequency of the resonator permanently. The impact of the frequency trimming on the temperature stability is very small. The temperature drift increases from ±2.6 ppm within the industrial temperature range before trimming to ±3.3 ppm after a permanent trimming of −426 ppm based on the local evaporation of Al. The trimming rate can be controlled by electric power. A resonator is coarse-trimmed by approximately −807 ppm with an evaporation power of 960 mW for 0.5 h, and fine-trimmed by approximately −815 ppm with an evaporation power of 456 mW for 1 h. Though the Q-factor decreases after trimming, a Q-factor of 304,240 is achieved after the trimming of −1442 ppm.

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“…Thirdly, the technique doping a dopant into silicon has been employed in many areas, e.g, in polycrystalline Si thin films phononic crystal nanopatterning for thermoelectric applications 27 or temperature-induced frequency stability of silicon-based MEMS resonators. 23,24,28 Obviously, the pattern of air hole in PnC-based MEMS resonators can reduce thermal conductance. 29 However, this doping mechanism can be employed for any type of silicon-based MEMS resonators to obtain a turnover point 23 which avoids to drift the operating frequency of the resonators.…”

Section: Introductionmentioning

confidence: 99%

A phononic crystal strip based on silicon for support tether applications in silicon-based MEMS resonators and effects of temperature and dopant on its band gap characteristics

Bao

2016

AIP Advances

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Phononic crystals (PnCs) and n-type doped silicon technique have been widely employed in silicon-based MEMS resonators to obtain high quality factor (Q) as well as temperature-induced frequency stability. For the PnCs, their band gaps play an important role in the acoustic wave propagation. Also, the temperature and dopant doped into silicon can cause the change in its material properties such as elastic constants, Young’s modulus. Therefore, in order to design the simultaneous high Q and frequency stability silicon-based MEMS resonators by two these techniques, a careful design should study effects of temperature and dopant on the band gap characteristics to examine the acoustic wave propagation in the PnC. Based on these, this paper presents (1) a proposed silicon-based PnC strip structure for support tether applications in low frequency silicon-based MEMS resonators, (2) influences of temperature and dopant on band gap characteristics of the PnC strips. The simulation results show that the largest band gap can achieve up to 33.56 at 57.59 MHz and increase 1280.13 % (also increase 131.89 % for ratio of the widest gaps) compared with the counterpart without hole. The band gap properties of the PnC strips is insignificantly effected by temperature and electron doping concentration. Also, the quality factor of two designed length extensional mode MEMS resonators with proposed PnC strip based support tethers is up to 1084.59% and 43846.36% over the same resonators with PnC strip without hole and circled corners, respectively. This theoretical study uses the finite element analysis in COMSOL Multiphysics and MATLAB softwares as simulation tools. This findings provides a background in combination of PnC and dopant techniques for high performance silicon-based MEMS resonators as well as PnC-based MEMS devices.

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Determination of doping and temperature-dependent elastic constants of degenerately doped silicon from MEMS resonators

Cited by 54 publications

References 12 publications

Near-Surface Electronic Contribution to Semiconductor Elasticity

Near-Surface Electronic Contribution to Semiconductor Elasticity

Oven-Controlled MEMS Oscillator with Integrated Micro-Evaporation Trimming

A phononic crystal strip based on silicon for support tether applications in silicon-based MEMS resonators and effects of temperature and dopant on its band gap characteristics

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