Page 245 - An Introduction to Microelectromechanical Systems Engineering

224 Packaging and Reliability Considerations for MEMS

Calibration and Compensation

The performance characteristics of precision sensors, especially pressure, flow,
acceleration, and yaw-rate sensors, often must be calibrated in order to meet the
required specifications. Errors frequently arise due to small deviations in the manu-
facturing process. For example, the sensitivity of a pressure sensor varies with the
square of the membrane thickness. A typical error of ±0.25 µmona10-µm thick
membrane produces a ±5% error in sensitivity that must be often trimmed to less
than ±1%. Additionally, any temperature dependence of the output signal must be
compensated.
One compensation and calibration scheme utilizes a network of laser-trimmed
resistors with near-zero TCR to offset errors in the sensor [5]. The approach
employs all-passive components and is an attractive low-cost solution. The resistors
can be either thin film (<1 µm thick) or thick film (~ 25 µm thick) [6] and are
trimmed by laser ablation. Thin-film resistors, frequently used in analog integrated
circuits such as precision operational amplifiers, are sputtered or evaporated directly
on the silicon die and are usually made of nickel-chromium or tantalum-nitride.
These materials have a sheet resistance of about 100 to 200Ω per square, and a very
low TCR of ±0.005% per degree Celsius. Nickel-chromium can corrode if not passi-
vated with quartz or silicon monoxide (SiO), but tantalum nitride self passivates by
baking in air for a few minutes. Thick-film resistors, by contrast, are typically fired
on thick ceramic substrates and consist of chains of metal-oxide particles embedded
in a glass matrix. Ruthenium dioxide (RuO ) and bismuth ruthenate (BiRu O ) are
2 2 7
examples of active metal oxides. Blending the metal oxides with the glass in different
proportions produces sheet resistances with a range of values from 10 to 10 Ω per
6
square. Their TCR is typically in the range of ±0.01% per degree Celsius. Trimming
using a neodymium-doped yttrium-aluminum-garnet (Nd:YAG) laser at a wave-
length of 1.06 µm produces precise geometrical cuts in the thin- or thick-film resis-
tor, hence adjusting its resistance value. The laser is part of a closed-loop system that
continuously monitors the value of the resistance and compares it to a desired target
value.
Laser ablation is also useful to calibrate critical mechanical dimensions by direct
removal of material. For instance, a laser selectively ablates minute amounts of sili-
con to calibrate the two resonant modes of the Daimler Benz tuning fork yaw-rate
sensor (see Chapter 4). Laser ablation can also be a useful process to precisely cali-
brate the flow of a liquid through a micromachined channel. For some drug delivery
applications, such as insulin injection, the flow must be calibrated to within ±0.5%.
Given the inverse cubic dependence of flow resistance on channel depth, this trans-
lates to an etch depth precision of better than ±0.17%, equivalent to 166 nm in a
100-µm deep channel. This is impossible to achieve using most, if not all, silicon-
etching methods. A laser ablation step can control the size of a critical orifice under
closed-loop measurement of the flow to yield the required precision.
As the integration of circuits and sensors becomes more prevalent, the trend has
been to perform, when possible, calibration and compensation electronically. Many
modern commercial sensors, including pressure, flow, acceleration, and yaw-rate
sensors, now incorporate application-specific integrated circuits (ASICs) to calibrate
the sensor’s output and compensate for any errors. Correction coefficients are stored
in on-chip permanent memory such as EEPROM.