82 Sen.wrs und Achrarors A, 37-38 (1993) 82-85

High accuracy pressure measurement with a silicon resonant sensor

John Greenwood and Troy Wray Druck Lusted, Ar Tree Lane, Groby, Las LE6 OFH (UK)

Abstract

The sources of error when measurmg pressure urlth a slhcon resonant sensor are described m the context of a new preclnon barometer

The sensor

The sensing element, which has been described before [ 1, 21 1s fabncated from silicon wafers by arusotroplc etching using the boron etch stop The resonator chip 1s bonded to a substrate chip by a layer of screen printed glass, the two chips are pressed together and heated to reflow the glass A glass tube IS bonded to the exhaust hole m the substrate and the cavity contalmng the resonator IS evacuated The resonator IS electrostatically excited via electrodes on the substrate

After fabncatlon the sensing element 1s mounted on a earner together wth a temperature sensing &ode It 1s now gven an mitral test with an open loop frequency scan using a frequency response analyser The reso- nance IS found and then scanned with sufficient resolu- tlon to measure the gam and the Q factor, the latter bemg typically greater than 40 000 The gap between the resonator and the drive electrodes has to be small enough not to reqmre an excessive amplifier gain, which 1s approxnnately proportional to the 4th power of the gap On the other hand d the gap 1s too small the

transfer characterlstlc becomes less smooth and the residual errors Increase and the sensltlvlty of the fre- quency to bias voltage also increases

Next the sensing element on Its earner IS mounted on a PCB urlth the drive electronics It 1s enclosed by a pressure block and IS then ready for cahbratlon The structure IS shown dlagrammatlcally m cross section m Fig 1

Calihra~on of the sensor

Cahbratlon IS done automatically with a ng which mcorporates a traceable pressure cahbrator Each sen- sor IS calibrated over the whole of the pressure and temperature range Readings are taken at 25 mbar steps from 10 to 1300mbar and at temperature Intervals of 10 “C from -20 to 70 “C In both cases d few readmgs are taken on the way down to check for hysteresis Normally this calibration IS repeated after a burn-m period of two weeks to check dnft Figure 2 shows the uncorrected curve of frequency against pressure

DIAPHRAGM WIRE BOND

PRESSURE BLOCK

PUMP OUT STE

ADHESIVE

TEMPERATURE SENSOR

Fig 1 Dlagrammatlc cross sectIon of the complete sensor

0924-4247/93/$6 00 @ 1993 - Elsevler Sequoia All nghts reserved

83

36500

0 200 400 BOO

Rg 2 Resonant frequency YS apphed pressure

Resonant and analogue sensors are used m dflerent ways Analogue sensors are usually linear and are typl- tally tnmmed by addmg adJustable components

In contrast resonant sensors are inherently non-hnear and would be difficult to trun as this would reqmre modlfymg the shape of the resonator which 1s rather maccesslble Instead the frequency IS measured and the corrected output 1s obtamed by calculation We are using a two-dunenslonal polynonnal m frequency and temperature represented by diode voltage

1=4

Pressure = i= 3 KJ(f-fo)‘(~d - Vo)’ r=O

J=o

where f = frequency, f0 = nommal frequency, V, = diode voltage, V, = nominal diode voltage

T~s equation has a set of coefficients which 1s dtier- ent for every sensor The results from the cahbratlon are processed and the set of coefficients are calculated by making a least-squares fit of the equation to the data

The calibration data will not be perfectly represented by the algonthm and the devlatlon 1s the curve fit error The fit can be improved by mcreasmg the number of coefficients but at the expense of mcreasmg the compu- tatlon The choice of the algonthm 1s thus a compro- nuse between accuracy and computation speed Figure 3 1s a plot of these residual errors

Temperature effects are of the order of 30 to 50 ppm “C-’ which would not be resolved m Rg 2 Figure 4 shows residual error after the pressure has been fitted but not temperature

Perform-

We see a small amount of hysteresis which 1s very vanable from device to device It can Just be seen in Fig 4 In general the pressure hysteresis IS usually less than 10 ppm but the temperature hysteresis can be up to 100 ppm At present the target spec&atlon for this device 1s a total error of 0 13 mbar and 0 26 mbar after 12 months Results so far Indicate that this can be improved upon

The total error 1s the sum of curve fit, noise, hys- teresis and dnft errors Possible sources of error are l strams transmitted from the package l strams set up by curmg of the mounting adhesive l contammation on the outside of the sensing element l contammants inside the sensmg element l plastic effects m the element matenals, Sl and glass l changes m the electromc arcmt

It has been suggested that there are long term changes m boron-doped structures We see httle evidence for ths but there are high temperature treatments after an- lsotroplc etchmg which may anneal out this hypothetical excessive strain

We thmk that the most potent source of error IS strams from mounting Thus there 1s a marked nnprovement with burn-m Grosscontammatlononthedlaphragmdoes have some effect on the resonator charactenstics but the present devices have only been operated m relatively clean air We do not expect there to be any gas density effects

Application

The first apphcatlon of ths device has been m our own instruments of which one 1s a preclslon barometer The

84

0 100

Residual

0 060 Error (mbar)

0 060

-0 060

-0100 , Apphed pressure (mbara)

I

FCS

12

1

08

06

04

02

0

-0 2

-0 4

-0 6

0 000 200 000 400 000 600 000 600 000 1000 000 1200000 1400 000

3 Residual error -25 to 75 “C

Error

0 200 400 600 600 1000 1200 1400

TemDerature - -20 - 5 - 20 - 40 -70 1

Fig 4 Residual error Hrlthout temperature compensation

present device has exposed electrical connections so that conclusions it 1s smtable for the environment mslde such instruments but would not tolerate condensmg water A modified We have described the calibration and compensation version of this sensor with these connections isolated of a resonant s&on absolute pressure sensor over the from the pressure medmm 1s m an advanced state of range lo- 1300 mbar wth a resolution of 10 ppm and a development total error of less than 100 ppm Each sensor IS calibrated

a5

over the whole pressure and temperature range and a polynomial IS fitted to the data Each sensor has a unique set of coefficients and m use the pressure reading IS calculated from the sensor frequency using this poly- nomlal Fourteen years after it was first proposed [ 31 this

References

1 The ongmal development of this sensor was carned out at STL (now BNR Europe), Harlow, UK

2 J C Greenwood and D W Satchel], A mmiature s&on resonant pressure sensor, IEE Proc , 135 (5) (1988) 369-372

sensor IS finding application m precision barometry 3 J C Greenwood, Br Parent No 1588669 (1978)