A novel technique is used to distinguish the charging of the surface from that of the bulk of the dielectrics of different types of RF MEMS capacitive switches under different electric fields and humidity levels. In general, bulk charging dominates in dry air, while surface charging increases linearly with increasing humidity. Under comparable electric fields and humidity levels, switches made of silicon dioxide are less susceptible to surface charging than switches made of silicon nitride. These quantitative results not only underscore the importance of packaging the switches in a dry ambient atmosphere, but also validate the novel technique for evaluating the effectiveness of dielectric preparation and packaging.
This paper presents a study of the variation of the piezoresistive coefficients over several devices on the same die, the same wafer, and finally at different doping levels. The sensor test vehicles are fully documented, and a thorough error analysis on the method of applying a known uniaxial state of stress is presented. The results show that individual stress sensor calibration is required if the uncertainty in the absolute values of the measured stresses need to be less than 15%. If the uncertainty only needs to be less than 50% then one device per wafer can be calibrated, or an equation relating the unstressed resistance values to the piezoresistive coefficients can be used.
Piezoresistive Coefficient Variation StudvAlthough the study of the piezoresistive effect in silicon has been investigated for some time now, the variation of the piezoresistive coefficients associated with piezoresistive-based integrated circuit stress sensors has not yet been addressed with any great certainty in the literature. The motivation for a thorough understanding of these coefficients and their variation with doping density, dopant type, temperature, and other physical parameters, is driven by the present need to individually calibrate the sensors to obtain accurate stress measurements [51[61[71[81[91. Present stress sensing chips designed to measure the distribution of a single stress component over a die can contain over twenty resistors [lo], each of which needs calibration to assure accuracy of subsequent stress measurements. This number of resistors can further increase if it is desired to measure biaxial or triaxial stress states at each point of interest. This places an excessive burden on the calibration process if enough stress sensing chips are to be obtained to be able to qualify a process sequence or packaging technology.In order to determine the number of calibrations required for a specific error tolerance, an analysis of the piezoresistive coefficient variation over many devices is required. If it is found that the coefficients vary only a small percentage over an entire wafer, then one calibration step could suffice for that entire wafer. If the coefficients vary only slightly from wafer to wafer then possibly one device per lot could suffice for the calibration needs. Understanding these variations of the coefficients is essential to determining the calibration requirements of a specific application.The following sections of this paper address the observed variations of the calibrated piezoresistive coefficients versus doping density as well as quantifying the experimental error associated with the four-point bend (4PB) stress fixture used in the calibration experiments.
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