The Silicon Oscillating Accelerometer:
`A High-Performance MEMS Accelerometer for Precision
`Navigation and Strategic Guidance Applications
`
`
`by
`R. Hopkins, J. Miola, R. Setterlund, B. Dow, W. Sawyer
`Draper Laboratory
`
`
`
`
`ABSTRACT
`
`(ICBM) and
`intercontinental ballistic missile
`The
`submarine-launched strategic missiles developed over the
`past 50 years have employed successive generations of
`increasingly accurate inertial guidance systems. The
`comparatively short time of guided flight and high
`acceleration levels characteristic of the ballistic missile
`application place
`a premium on
`accelerometer
`performance to achieve desired weapon system accuracy.
`Currently, the U.S. strategic missile arsenal relies on
`variants of the pendulous integrating gyro accelerometer
`(PIGA) to meet the high-performance, radiation-hard
`requirements of the weapon system.
`
`Likewise, precision navigation systems, such as the
`currently deployed SSBN Ship Inertial Navigation
`Systems (SINS), employ highly specialized and complex
`electromechanical instruments that, like the PIGA, present
`a system life-cycle cost and maintenance challenge.
`
`The PIGA and the Electromagnetic Accelerometer (EMA)
`demonstrate unsurpassed performance, however, their
`life-cycle cost has motivated a search for a high-
`performance, solid-state, strategic accelerometer.
`
`The Draper Laboratory is currently in the process of
`developing the Silicon Oscillating Accelerometer (SOA),
`a MEMS-based sensor
`that has demonstrated
`in
`laboratory testing the part-per-million (ppm)/(cid:541)g scale-
`factor and bias performance stability required of precision
`guidance navigation applications.
`
`The ICBM and SSBN applications have significantly
`different environmental, acceleration dynamic range, and
`resolution requirements
`that are best satisfied by
`optimizing the SOA geometry for each application. The
`design flexibility and wafer-scale fabrication methods of
`the silicon MEMS process enable manufacturing both
`
`
`instrument designs with essentially zero incremental cost
`associated with the additional instrument assembly line.
`That is, the SOAs developed for the ICBM guidance and
`SSBN navigation applications share a common sensor
`package, electronics architecture, main housing and
`instrument assembly process. This paper will give an
`overview of the Draper SOA and compare and contrast
`performance data taken to date on both versions of the
`SOA.
`
`INTRODUCTION
`SOA Applications and Performance Goals
`
`the most
`ICBM/SLBM strategic missile has
`The
`demanding
`requirements of any
`inertial guidance
`application. The high degree of accuracy required of the
`weapon system, combined with the high acceleration
`levels and large velocity at reentry body deployment place
`an especially stringent performance requirement on the
`guidance system accelerometers. The SSBN SINS system
`requires similarly precise inertial performance from the
`navigation system accelerometers, although compared
`with the missile application, the SINS accelerometers
`enjoy a more benign operational environment and a
`smaller dynamic range requirement (Ref. [5]).
`
`Although there are many system-derived performance
`parameters specified for inertial grade accelerometers (see
`Table 1), in broad terms, accelerometer performance can
`be characterized with two parameters: bias and scale-
`factor (SF) stability. Accelerometer bias is the DC offset
`indicated from the instrument output under zero applied
`acceleration. Scale factor is the instrument gain or
`sensitivity that relates the applied acceleration to the
`instrument output signal (e.g., V/g, Hz/g, etc.).
`
`guidance
`missile
`high-performance
`Typically,
`applications require accelerometer bias stability on the
`order of 1 (cid:541)g, and SF stability on the order of 1 ppm. The
`
`
`
`
`ION 61st Annual Meeting
`The MITRE Corporation & Draper Laboratory,
`27-29 June 2005, Cambridge, MA
`
`1043
`Page 1 of 10
`
`HAPTIC EX2018
`
`

`

`SINS accelerometer requirements are similar to the
`ICBM/SLBM guidance requirements (see Table 1),
`however, the missile and SINS applications differ in two
`important aspects: 1) the reduced operational dynamic
`range of the SINS systems (maximum acceleration of 2
`g), and 2) the very low readout noise specified for the
`SINS navigator processing.
`
`Table 1. Typical SOA Performance Goals.
`
`Parameter
`
`Units
`
`Missile
`Guidance
`
`High-
`Performance
`Navigation
`
`1
`
`0.5
`
`10
`
`5
`TBD
`1
`
`TBD
`
`0.0014
`1
`
`TBD
`
`0.4
`TBD
`TBD
`2
`TBD
`
`Consequently, the missile guidance community is seeking
`a low-cost alternative to the PIGA for next-generation
`high-performance missile systems, and a similarly
`simplified, low-maintenance accelerometer design for the
`next generation of SINS navigator systems. Both
`applications
`hold
`the
`important
`provision
`that
`performance remain uncompromised in candidate design
`alternatives.
`
`in process of
`is currently
`The Draper Laboratory
`developing the SOA a Microelectromechanical Systems
`(MEMS)-based sensor that has demonstrated the ppm/µg
`performance stability required of the SINS navigator and
`missile applications. The MEMS technology is low cost
`and offers a rapidly expanding commercial business base
`to leverage and sustain accelerometer production and
`deployment in next-generation guidance systems.
`
`the generic category of
`to
`The SOA belongs
`accelerometers known as Vibrating Beam Accelerometers
`(VBA), which sense acceleration by measuring the
`change in the resonant frequency of beam oscillators
`under the inertial loading of a proof mass. The SOA
`differs from conventional VBAs in one important respect;
`namely, the SOA is a silicon MEMS based device, as
`opposed to VBAs, which typically are bulk-fabricated
`quartz devices.
`
`The silicon MEMS process offers several advantages over
`quartz that enable superior accelerometer design features:
`1) semiconductor-grade, single-crystal silicon
`is a
`perfectly elastic structural material that can be produced
`with extremely low levels of impurities; 2) the MEMS
`process enables fabrication of very small (millimeter scale
`in the case of the SOA) resonator elements that are well
`isolated from
`the
`influence of parasitic
`instrument
`package stresses, and 3) capacitively based, electrostatic
`resonator actuation and sensing, which offers greater
`design flexibility than the piezoelectric quartz technology.
`
`The SSBN navigation and missile guidance applications
`have significantly different environmental, acceleration
`dynamic range, and resolution requirements that are best
`satisfied by optimizing the SOA geometry for each
`application. The design flexibility and wafer-scale
`fabrication methods of the silicon MEMS process enable
`manufacturing both instrument designs with essentially
`zero incremental cost associated with the additional
`instrument assembly line. That is, both versions of the
`SOA share a common sensor package, electronics
`architecture, main housing and instrument assembly
`process.
`
`The next sections describe the operational principles of
`the SOA, the MEMS fabrication process, and present a
`summary of performance data taken to date on both the
`
`
`1 - 100
`
`1 - 5
`
`1 - 100
`
`1 - 5
`TBD
`0.1 - 0.2
`
`
`µg
`
`µg
`
`ppm
`
`ppm
`ppm
`µg/g2
`
`µg/g3
`
`ft/s/√h
`µg/√Hz
`
`arcsec
`
`TBD
`0.014 -
`0.030
`10 - 22
`
`0.1 - 5
`
`• Bias
`-- Long-Term
`Stability*
`-- Short-Term
`Stability**
`• Scale Factor
`-- Long-Term
`Stability*
`-- Short-Term
`Stability**
`-- Asymmetry
`-- g2
`(Compensated)
`-- g3
`(Compensated)
`• VRW
`• White Noise
`• Misalignment
`-- Long-Term
`Stability*
`-- Short-Term
`0.1 - 2
`arcsec
`Stability**
`µg/(grms)2
`• Vibration Rect.
`<1
`• Bandwidth
`Hz
`100
`• Max DC
`15 - 120
`g
`Acceleration
`• Peak Shock
`g
`70 - 170
` *Long-term stability = 1σ over 90 days
`**Short-term stability = 1σ over 10 h
`
`To date, strategic-grade performance has been achieved
`over the ICBM/SLBM mission times and hostile flight
`environments only
`in
`the PIGA, a highly refined
`instrument that has been employed successfully in every
`U.S. strategic missile deployed since the inception of
`ICBM weapon systems. The complexity of PIGA
`accelerometers and their specialized technologies, such as
`gas bearing wheels, ultrastable ball bearings, precision
`electromagnetic components, and “designer chemical”
`flotation fluids require a costly support infrastructure for
`production and system life-cycle maintenance. Likewise,
`the EMA deployed in the SSBM fleet SINS systems
`satisfies
`the accelerometer navigation performance
`parameters specified in Table 1, but like the PIGA the
`EMA is also a highly specialized design that requires a
`costly life-cycle maintenance infrastructure.
`
`
`ION 61st Annual Meeting
`The MITRE Corporation & Draper Laboratory,
`27-29 June 2005, Cambridge, MA
`
`1044
`
`Page 2 of 10
`
`

`

`Figure 2. SOA Oscillator Detail.
`
`
`
`stability is required of a 100-Hz/g SF unit to resolve 1-µg.
`A 10-Hz/g unit has a 10 times more restrictive frequency
`stability requirement (10 µHz) to resolve the same 1 µg
`input.
`
`It can be shown (Ref. [3]) that the lateral stiffness of an
`axially loaded beam with fixed ends is:
`
`IE
`12
`12
`π2
`3
`L
`
`[1]
`
`
`
`LP
`
`
`
`K
`
`=
`
`+
`
`K = stiffness
`E = Young’s modulus
`I = moment of inertia
`L = beam length
`P = axial load
`
`where
`
`
`
`
`
`
`If a lumped mass is supported between two beams, the
`natural frequency of the mass-beam system as a function
`of axial load is given by:
`
`
`
`
`[2]
`
`[3]
`
`LP
`
`IE
`12
`12
`3 +
`L
`π2
`
`2
`m
`
`f
`
`=
`
`
`
`f = resonant frequency
`m = mass of lumped oscillator
`
`
`
`where
`
`
`
`Rearranging [2] gives:
`
`
`f
`
`=
`
`f
`
`o
`
`2
`L
`1
`+
`IE
`2
`π
`
`P
`
`f = resonant frequency
`fo = nominal unloaded (bias) resonant frequency
`
`IE
`24
`Lm
`3
`
`
`
` =
`
`
`
`where
`
`
`
`missile guidance and SSBN navigation versions of the
`SOA.
`
`SOA Functional Description
`
`The SOA developed by Draper Laboratory is a miniature
`silicon VBA
`fabricated
`using
`silicon MEMS
`micromachining technology. Figure 1 is a schematic
`representation of the SOA sensor, showing a pair of
`double-ended tuning-fork oscillators connected to a
`common proof mass. These elements form a monolithic
`silicon structure that is supported above, and anodically
`bonded to a glass substrate as shown.
`
`
`
`AnchoredAnchored
`
`ComponentComponent
`
`
`SuspendedSuspended
`
`ComponentComponent
`
`
`ElectrostaticElectrostatic
`
`ComponentComponent
`
`
`
`Figure 1. SOA Schematic.
`
`The SOA input axis lies in plane as indicated in Figure 1;
`under acceleration, the proof mass axially loads the two
`resonator pairs. The vibration frequency of each resonator
`changes under the applied load. This frequency change is
`measured and serves and the indicated acceleration output
`of the SOA. Note that the resonators are arranged so they
`are loaded differentially by the proof mass. That is, one
`resonator is placed in tension, the other in compression.
`This differential design doubles the sensitivity or scale
`factor of the accelerometer and furnishes a cancellation of
`error sources common to both resonators.
`
`The resonators are excited by an electrostatic comb drive
`(Refs. [1], [2]), similar
`to
`that used
`in Draper’s
`micromechanical tuning-fork gyro (TFG). The comb
`drive has both inner and outer motor stator combs that are
`fixed to the glass substrate. The outer motor combs apply
`the drive force; the inner motor combs sense the drive
`amplitude and frequency. A detail of the comb geometry
`is shown in Figure 2.
`
`The goal of the SOA design is to achieve a high scale
`factor, high Q resonator to achieve high-performance.
`Large scale factor is desirable because it decreases the
`degree of frequency stability required to resolve a given
`acceleration level. For example, 0.1-mHz frequency
`
`ION 61st Annual Meeting
`The MITRE Corporation & Draper Laboratory,
`27-29 June 2005, Cambridge, MA
`
`1045
`
`Page 3 of 10
`
`

`

`= -50 ppm/°C), as it is an order of magnitude larger than
`silicon’s thermal coefficient of expansion (TCE) (2.5
`ppm/°C), the parameter that would control the resonator
`dimensional stability. Given the square root relationship,
`the linear SF temperature coefficient is approximately 25
`ppm/°C, indicating that 0.01°C temperature control will
`maintain better than 1-ppm SF performance.
`
`From [4] and [5], the values of the g2 and g3 coefficients
`(K2, K3) can be expressed by the linear SF (K1) and bias
`frequency (fo):
`
`
`m = resonator mass
`L = beam length
`E = Young’s modulus
`I = beam inertia
`P = applied axial load
`
`
`
`
`
`
`
`Note that the frequency versus applied acceleration load
`relationship in the SOA is nonlinear as indicated by [3]
`and shown in Figure 3.
`
`
`
`
`Frequency (Hz)Frequency (Hz)
`
`
`
`Linear SF (Hz/g)Linear SF (Hz/g)
`
`
`
`ff
`
`
`
`==
`
`
`
`ff
`
`
`
`0 1+0 1+
`
`
`22
`
`LL
`
`IEIE
`
`π2π2
`
`
`
` gM gM
`
`
`
`Bias Frequency f0Bias Frequency f0
`
`
`
`Buckling LoadBuckling Load
`
`
`
`Input Acceleration (g)Input Acceleration (g)
`
`
`
`Figure 3. SOA Frequency vs. Acceleration Curve.
`
` A
`
` series expansion of [3] can be used to determine the
`linearized SOA scale factor (the slope about zero
`acceleration in Figure 3) and higher order g-coefficients:
`
`
`
`
`f
`
`=
`
`f
`
`o
`
`PSPS
`2
`−
`
`2
`
`+
`
`[4]
`
`[7]
`
`[8]
`
`
`021
`fK
`
`21
`
`K
`
`2
`
`−=
`
`
`
`2031
`fK
`
`21
`
`K
`
`3
`
`=
`
`
`
`
`
`
`
`
`For a 100-Hz/g (per side) SF, 20-kHz nominal bias
`frequency unit, [7] and [8] project g2 and g3 coefficients
`
`of 0.25 Hz/g2 and 0.0125 Hz/g3. Normalizing these
`coefficients by dividing by the linear SF gives 2500 µg/g2
`and 12.5 µg/g3, respectively.
`
`Compensating these coefficients to the sub-µg level is
`feasible because their stability will be of the order of the
`linear SF and bias. Differentiation of [7] and [8] gives:
`
`
`K
`Δ
`K
`
`2
`
`2
`
`=
`
`2
`
`SF
`Δ
`SF
`
`−
`
`Δ
`f
`
`f
`
`0
`
`0
`
`K
`Δ
`K
`
`2
`
`2
`
`=
`
`3
`
`SF
`Δ
`SF
`
`−
`
`2
`
`Δ
`f
`
`f
`
`0
`
`[9]
`
`[10]
`
`0
`
`
`
`
`
`
`
`
`1
`16
`
`⎤
`3
`3
`−
`LPS
`⎥⎦
`
`
`
`21
`
`⎡
`1
`+
`⎢⎣
`
`where S = L2/π2EI.
`
`Equation [4] can be rewritten as:
`
`
`81
`
`
`
`f
`
`2
`gKgKgKf
`+=
`+
`+
`1
`2
`3
`o
`
`3
`L−
`
`[5]
`
`
`
`Kn = K1bn(K1/fo)n-1 (Hz/gn)
`bn = bn-1 (3-2n)/n
`K1 = S/2
`b1 = 1
`g = acceleration
`
`
`
`where
`
`
`
`
`
`
`Note that the values of the g2 and g3 coefficients (K2, K3)
`are controlled by the linear SF (K1) and bias frequency
`linearized SF
`is dependent on resonator
`(fo). The
`dimensions, Young’s modulus and the mass of the
`resonator (m) and proof mass (M):
`
`
`
`
`K
`
`1 =
`
`M
`π8
`
`L
`mIE
`
`[6]
`
`
`The SF stability of the SOA will be largely controlled by
`the Young’s modulus sensitivity to temperature (ΔE/E/ΔT
`
`
`
`Note that 1-µg performance implies a resonator frequency
`stability (Δf/f) on the order of 5 ppb (given a 100-Hz/g
`
`per side SF and 20-kHz nominal frequency unit).
`Combined with 1-ppm SF stability, this implies that the
`above SF nonlinearity coefficients should be stable to
`approximately 2 to 3 ppm. This high degree of stability
`should
`enable
`compensating
`the
`raw nonlinear
`coefficients to sub-µg levels (although calibrating the
`higher-order g-coefficients will
`require precision
`the net SOA g2
`centrifuge
`testing). Additionally,
`coefficient and other even order terms will be reduced as
`the g2 contribution from each resonator will be common
`mode differenced in the net SOA output.
`
`SOA Electronics
`
`Figure 4 shows the SOA electronics block diagram. As
`mentioned above, the SOA employs an electrostatic comb
`
`ION 61st Annual Meeting
`The MITRE Corporation & Draper Laboratory,
`27-29 June 2005, Cambridge, MA
`
`1046
`
`Page 4 of 10
`
`

`

`
`
`Δ
`f
`
`f
`
`=
`
`o
`
`[13]
`
`2
`
`x
`
`x
`Δ
`x
`
`KK
`43
`
`3
`
`
`From [12] and [13] it can be seen that a small drive
`amplitude will minimize the resonator frequency variance
`
`from drive amplitude instability and noise. An alternate
`means of maximizing frequency stability is to minimize
`the amount of nonlinear stiffening, i.e., design a resonator
`with a low K3 coefficient.
`
`The resolution or noise floor of the SOA can be estimated
`by calculating the amplitude and phase noise associated
`with the sense comb frequency readout. From Ref. [1],
`the capacitance across a set of engaged comb drive
`fingers is given by:
`
`
`
`
`C
`
`L
`
`[14]
`
`
`
`GAINGAIN
`
`
`
`X1X1
`
`
`
`-X1-X1
`
`
`PROOFPROOF
`
`MASSMASS
`
`
`
`GAINGAIN
`
`
`
`X1X1
`
`
`
`-X1-X1
`
`
`9090
`
`degdeg
`
`
`DRIVEDRIVE
`
`GENGEN
`
`
`9090
`
`degdeg
`
`
`DRIVEDRIVE
`
`GENGEN
`
`
`
`--
`
`
`
`--
`
`
`FREQFREQ
`
`DETDET
`
`
`AMPLAMPL
`
`DETDET
`
`
`
`C(s)C(s)
`
`
`FREQFREQ
`
`DETDET
`
`
`AMPLAMPL
`
`DETDET
`
`
`
`C(s)C(s)
`
`
`
`FaFa
`
`
`
`++
`
`
`
`FbFb
`
`
`
`++
`
`
`
`REFREF
`
`
`
`REFREF
`
`
`
`gt
`
`=
`
` N
`
`2
`εα
`
`o
`
`Figure 4. SOA Electronics Block Diagram.
`
`drive to excite the resonators and to pick off the resonator
`displacement. The electrostatic drive force is given by:
`
`
`
`
`F
`
`=
`
`2
`
`[11]
`
`dC
`dxV
`
`12
`
`F = drive force
`dC/dx = comb position sensitivity
`V = applied voltage
`
`
`where
`
`
`
`
`The drive amplitude stability furnished by the electronics
`is critical to maintaining nominal resonator frequency
`stability. The resonator beams stiffen with
`lateral
`deflection, causing a dependence of
`the
`resonant
`frequency with drive amplitude. This nonlinear stiffening
`effect introduces a bias uncertainty from the resonator
`drive amplitude instability.
`
`It can be shown (Ref. [4]) that if the resonator is modeled
`as a linear plus cubic stiffness element, the resonator
`frequency dependence on amplitude is given by:
`
`
`
`
`
`where
`
`
`
`
`
`
`
`
`The capacitance sensitivity to position (i.e. engaged
`length) is given by:
`
`
`C = capacitance
`εo = permittivity of air
`N = Number of teeth per side
`α = fringing factor
`t = comb finger thickness
`g = air gap between fingers
`L = engaged length of fingers
`
`gt
`
` N
`
`= 2
`oεα
`
`
`
`
`
`[15]
`
`
`
`dC
`dx
`
`
`where: dC/dx = sensitivity to position
`
`Equation [12] gives the relationship between resonator
`amplitude and frequency, which gives the resonator
`frequency power spectral density (PSD) as:
`
`
`[16]
`
`φ
`
`A
`
`⎟⎠⎞
`
`X
`
`KK
`43
`⎜⎝⎛
`
`3
`
`φ
`
`f
`
`=
`
`f
`
`o
`
`
`
`φf = frequency PSD in Hz/√Hz
`x = nominal drive amplitude
`φA = amplitude noise PSD
`fo = nominal resonant frequency
`K3/K = stiffness coefficient ratio
`
`
`
`where
`
`
`
`
`
`
`The contribution of phase noise in the drive frequency
`electronics can also be estimated. The PSD of the
`
`2
`
`3
`
`K
`xK
`
`⎤
`⎥⎦
`
`[12]
`
`
`
`83
`
`
`
`f
`
`=
`
`f o
`
`⎡ +
`1
`⎢⎣
`
`f = frequency at amplitude x
`fo = nominal resonant frequency
`K = linear stiffness of resonator
`K3 = cubic stiffness coefficient
`x = drive amplitude
`
`
`
`
`where
`
`
`
`
`
`
`The stability requirement on the drive amplitude can be
`determined by differentiating [12] to get:
`
`
`ION 61st Annual Meeting
`The MITRE Corporation & Draper Laboratory,
`27-29 June 2005, Cambridge, MA
`
`1047
`
`Page 5 of 10
`
`

`

`The geometries of the two different SOAs are optimized
`for each application by adjusting oscillator and proof
`mass geometry. The advantages of the silicon MEMS
`design approach is apparent as two different applications
`can be serviced with only the incremental expense of the
`MEMS photo-maskset needed to fabricate the application-
`specific SOA sensor element. The design flexibility and
`wafer-scale fabrication methods of the silicon MEMS
`process enable manufacturing both instrument designs
`with essentially zero incremental cost associated with the
`additional sensor design. That is, both versions of the
`SOA share a common sensor package, electronics
`architecture, main housing, and instrument assembly
`process. The only difference between the two instrument
`assembly processes is the use of a different MEMS photo-
`maskset in the fabrication of the SOA sensor element.
`
`Draper uses the silicon-on-glass dissolved-wafer process
`to fabricate the SOA (Refs. [6]), a mature MEMS
`fabrication process that Draper employs elsewhere in
`MEMS-based inertial technology (Ref. [2]).
`
`The main process steps of the dissolved wafer process are
`illustrated in Figure 6. The starting wafers used in
`processing are a boron-doped epitaxial silicon layer
`grown on an undoped silicon handle layer. The thickness
`of the epitaxial layer determines the final thickness of the
`silicon device layer. The first process step is to etch mesas
`in the epitaxial silicon layer; this step defines the eventual
`operating air gap between the suspended silicon sensor
`element structures and the glass substrate.
`
`
`
`
`
`
`SiliconSiliconSilicon
`
`
`
`p++ Epitaxial Growthp++ Epitaxial Growth
`
`
`
`Glass WaferGlass Wafer
`
`
`
`Form MesasForm Mesas
`
`
`
`MetalizationMetalization
`
`
`
`Deep Trench EtchDeep Trench Etch
`
`
`
`EDP EtchEDP Etch
`
`
`
`Anodic BondAnodic Bond
`
`
`
` Figure 6. SOA Fabrication Process.
`
`The device structural layer is then photolithographically
`patterned on the silicon and the wafers are etched using
`high-aspect-ratio micromachining in a Reactive ion Etch
`(RIE) machine. This step forms the 2-D geometry of the
`
`oscillator phase noise is approximately equal to the PSD
`of the amplitude noise divided by the peak amplitude.
`
`At resonance, the phase noise is related to frequency noise
`by:
`
`
`φ φ φωω
`n
`Q
`2
`
`
`
`[17]
`
`p
`
`=
`
`dd
`
`φ
`
`=
`
`f
`
`p
`
`
`
`φf = frequency noise PSD
`φp = phase noise PSD
`ωn = nominal resonant frequency
`Q = Q of resonator
`
`
`where
`
`
`
`
`
`The high Q’s achieved in the SOA oscillators (~100,000)
`significantly reduce the frequency noise in the output
`from phase jitter. The net frequency noise in the SOA
`readout is dominated by oscillator amplitude noise.
`Consequently, frequency readout resolution is improved
`with
`increasing bias voltage and decreasing drive
`amplitude.
`
`SOA MEMS Sensor Design, Fabrication,
`and Screening
`
`The ICBM application and the SSBN SINS system have
`significantly
`different
`environmental,
`acceleration
`dynamic range, and resolution requirements as mentioned
`above (Table 1). The SOA instrument can be easily
`adapted to either application by adjusting the SOA
`MEMS sensor element geometry for
`the specific
`operating acceleration range required. Figure 5 is similar
`to Figure 3 and shows the load vs. acceleration curve for
`two different SOA designs: a higher g-capable design
`suitable for ICBM/submarine-launched ballistic missile
`(SLBM) environments and a lower g design tailored for
`the more benign SINS environment. Note that the higher
`sensitivity (higher SF) SINS design has a correspondingly
`lower buckling load. This is a consequence of beam
`mechanics and is a fundamental design trade-off in
`selecting SOA acceleration sensitivity.
`
`
`
`
`ff
`
`
`
`==
`
`
`
`ff
`
`
`
`0 1+0 1+
`
`
`22
`
`LL
`
`IEIE
`
`π2π2
`
`
`
` gM gM
`
`
`
`Frequency (Hz)Frequency (Hz)
`
`
`
`Low-gLow-g
`
`
`
`High-gHigh-g
`
`
`
`Linear SF (Hz/g)Linear SF (Hz/g)
`
`
`
`Bias Frequency f0Bias Frequency f0
`
`
`Buckling LoadBuckling Load
` Figure 5. SOA Dynamic Range.
`
`
`
`Input Acceleration (g)Input Acceleration (g)
`
`
`
`ION 61st Annual Meeting
`The MITRE Corporation & Draper Laboratory,
`27-29 June 2005, Cambridge, MA
`
`1048
`
`Page 6 of 10
`
`

`

`
`
` Figure 8. SOA Instrument.
`
`to exploit the reduced dynamic range environment of the
`SSBN application. The SINS SOA sensor design also
`incorporates design features to maximize longer time
`scale drift stability.
`
`The contrast in the performance of both versions of the
`SOA is best captured by the acceleration resolution
`capability demonstrated via the noise PSD plots shown in
`Figure 9. Note that both units have a white noise floor on
`the order of 10-11 g2/Hz, however, the SINS design
`maintains the resolution capability over longer time scales
`(i.e., lower frequency bands). The missile guidance SOA
`shows a noise PSD that starts to break upward with a 1/f
`signature in the 10-1 Hz to 10-2 Hz decade. The SINS SOA
`shows the white noise floor extending another decade or
`two before exhibiting a 1/f signature.
`
`
`Figure 9. SOA Acceleration Noise PSD.
`
`
`
`
`SOA silicon sensor element. Recent advances in RIE
`etching technology have enabled a very high degree of
`feature size control (e.g., beam width uniformity, side
`wall perpendicularity, etc.) in MEMS processing, a
`critical factor affecting as-built SOA sensor performance.
`
`The patterned wafers are then anodically bonded to glass
`substrates that have been metallized with the SOA
`electrode pattern. Finally, the silicon wafer is dissolved
`in an anisotropic wet etchant such as Ethylenediamine
`Pyrocatechol (EDP), which removes the silicon handle
`layer. The boron doping in the epitaxial layer stops the
`chemical etching action of the EDP, leaving the finished
`device layer array on the glass wafer substrate. Individual
`SOA sensors are then diced and screened prior to
`packaging.
`
`The first screening step performed on the SOA MEMS
`sensor die is a particle and defect inspection, followed by
`electrical probing for proper resistance and continuity.
`Units passing this step are “wiggle tested” by energizing
`the oscillator elements to verify oscillator freedom at the
`expected drive frequency.
`
`After probe testing, SOAs with satisfactory performance
`are packaged and vacuum sealed in an aluminum oxide
`leadless ceramic chip carrier (LCCC). The residual
`pressure achieved in the LCCC after vacuum seal is less
`than one mTorr, which ensures high oscillator Q factors.
`A plot of Q vs. pressure for a typical SOA is shown in
`Figure 7, indicating that oscillator drive Q’s on the order
`of 100,000 are achieved with this process. The packaged
`SOA is mated to a front-end preamplifier electronics
`module and subsequently mounted in an instrument main
`housing assembly. The final SOA instrument assembly is
`shown in Figure 8.
`
`
`Q vs. Pressure
`
`0.1
`
`10
`1
`Log Pressure (mTorr)
`
`100
`
`1000
`
`
`
`1000000
`
`100000
`
`10000
`
`Log Q
`
`1000
`0.01
`
`Figure 7. Q vs. Pressure Relationship.
`
`Missile Guidance and SINS SOA Performance
`Test Data
`
`Both versions of the SOA demonstrate the performance
`required for their respective applications. As mentioned
`above, the SINS SOA is tailored with a higher sensitivity
`
`ION 61st Annual Meeting
`The MITRE Corporation & Draper Laboratory,
`27-29 June 2005, Cambridge, MA
`
`1049
`
`Page 7 of 10
`
`

`

`
`White Noise (-1/2 slope)White Noise (-1/2 slope)
`
`φ = 4.5 μg/√Hzφ = 4.5 μg/√Hz
`
`VRW = 0.006 ft/s/√hVRW = 0.006 ft/s/√h
`
`
`
`10-510-5
`
`
`
`10-610-6
`
`
`Missile Guidance SOAMissile Guidance SOA
`
`sn 036 IA vertical drift 1/24/03 Green Chartsn 036 IA vertical drift 1/24/03 Green Chart
`
`
`
`at 84.4 minutes unc = 0.45 ug at 84.4 minutes unc = 0.45 ug
`
`
`
`1 μg1 μg
`
`
`
`0.5 μg0.5 μg
`
`
`
`10-410-4
`
`
`
`10-510-5
`
`
`
`10-610-6
`
`
`
`gg
`
`
`
`10-710-7
`
`
`SOA-SINSSOA-SINS
`
`SN 063 IA Vertical drift 9/13/04 SN 063 IA Vertical drift 9/13/04
`
`
`
`1 μg1 μg
`
`
`
`0.08 μg0.08 μg
`
`AccelerationUncertainty (g)
`AccelerationUncertainty (g)
`
`
`
`gg
`
`
`10-710-7
`
`100100
`
`
`
`101101
`
`
`
`102102
`103103
`
`time (seconds)time (seconds)
`
`
`
`104104
`
`
`10-810-8
`
`
`105105
`100100
`
`
`
`101101
`
`
`
`102102
`103103
`
`time (seconds)time (seconds)
`
`
`
`104104
`
`
`
`105105
`
`
`
`Figure 10. SOA Allan Variance.
`
`indicative of an
`is
`This 1/f (or “flicker”) noise
`acceleration drift instability that limits the net resolution
`capability of the accelerometer. This is also characterized
`by the Allan variance charts calculated from the PSD
`measurements shown in Figure 10. The missile guidance
`SOA resolution is limited to 0.5 µg, which is achieved
`over 100-s averaging times. Longer averaging times do
`not further improve resolution in the missile guidance
`SOA because of the 1/f drift instability, but the low-
`frequency extension of white noise floor of the SINS
`SOA enables 80 nano-g resolution, which is achieved
`after 1000 s of averaging.
`
`The Allan variance plots the standard deviation of
`indicated acceleration against data averaging time. The
`white noise floor of the corresponding PSD can be
`determined from the portion of the Allan variance having
`a minus one half slope on the log scale. The equivalent
`white noise PSD can be calculated from a point on the
`minus one half slope line from:
`
`
`noise PSD of 4.5 µg/√Hz, which is equivalent to a
`velocity random walk coefficient of 0.006 ft/s/√h.
`
`Figure 11 shows SOA bias and SF uncertainty measured
`on a missile guidance SOA in a 2-position test, and Figure
`12 shows SF and bias uncertainty measured on an SOA-
`SINS unit in a 4-position test. The SF and bias data shown
`in these figures is uncompensated SOA output and are the
`average values over a 30-min dwell as determined from 1-
`s averaged data. The data shown extend over a roughly 3-
`day period and show 1σ standard deviations in SF and
`bias of 0.56 ppm and 0.92 µg, respectively, for the missile
`guidance SOA. The quieter SOA-SINS unit demonstrates
`1σ uncertainty in SF and bias of 0.14 ppm and 0.19 µg,
`respectively.
`
`
`
`SF (ppm)SF (ppm)
`
`Bias (µg)Bias (µg)
`
`
`
`
`SF (1σ) = 0.56 ppmSF (1σ) = 0.56 ppm
`
`Bias (1σ) = 0.92 micro-gBias (1σ) = 0.92 micro-g
`
`
`
`2.02.0
`
`
`
`1.51.5
`
`
`
`1.01.0
`
`
`
`0.50.5
`
`
`
`0.00.0
`
`
`
`-0.5-0.5
`
`
`
`-1.0-1.0
`
`
`
`-1.5-1.5
`
`SF (ppm) & Bias (µg)
`SF (ppm) & Bias (µg)
`
`
`-2.0-2.0
`
`0.000.00
`
`
`
`20.0020.00
`
`
`40.0040.00
`
`Time (h)Time (h)
`
`
`
`60.0060.00
`
`
`
`80.0080.00
`
`Figure 11. Missile Guidance SOA SF and Bias Stability.
`
`
`2 φ
`σ =
`T2
`
`
`
`
`
`[18]
`
`σ = acceleration standard deviation
`φ = white noise PSD
`T = averaging time
`
`
`where
`
`
`
`
`The data from both versions of the SOA (Figure 10) in the
`minus-one-half slope region indicates (from [18]) a white
`
`ION 61st Annual Meeting
`The MITRE Corporation & Draper Laboratory,
`27-29 June 2005, Cambridge, MA
`
`1050
`
`Page 8 of 10
`
`

`

`Table 2. Multiposition Tumble Results.
`
`
`
`Tumble about OA
`Nominal
`Std.
`Value
`Dev.
`(1σ)
`0.354
`µg
`0.989
`ppm
`0.652
`µg/g2
`1.324
`µg/g3
`0.629
`µg/g2
`0.295
`µrad
`
`797.965
`Hz
`126.697
`Hz/g
`121.33
`µg/g2
`6.167
`µg/g3
`-7.293
`µg/g2
`2.34 mrad
`
`Tumble about MA
`Nominal
`Std.
`Value
`Dev.
`(1σ)
`0.295
`µg
`0.822
`ppm
`0.542
`µg/g2
`1.10
`µg/g3
`0.523
`µg/g2
`0.245
`µrad
`
`797.724
`Hz
`126.722
`Hz/g
`117.49
`µg/g2
`0.24 µg/g3
`
`-6.65
`µg/g2
`28.3 mrad
`
`
`
`
`
`0.50.50.5
`
`
`
`
`
`0.40.40.4
`
`
`
`
`
`0.30.30.3
`
`
`
`
`
`0.20.20.2
`
`
`
`
`
`0.10.10.1
`
`
`4 Position Calibration4 Position Calibration
`
`SF (1σ) = 0.14 PPMSF (1σ) = 0.14 PPM
`
`Bias (1σ) = 0.19 µgBias (1σ) = 0.19 µg
`
`
`
`
`
`000
`
`SF (ppm) & Bias (µg)
`SF (ppm) & Bias (µg)
`SF (ppm) & Bias (µg)
`
`
`
`
`
`-0.1-0.1-0.1
`
`
`
`
`
`-0.2-0.2-0.2
`
`
`
`
`
`-0.3-0.3-0.3
`
`
`
`
`
`-0.4-0.4-0.4
`
`
`
`
`
`-0.5-0.5-0.5
`
`
`
`
`
`000
`
`
`
`
`
`101010
`
`
`
`
`
`202020
`
`
`
`
`
`404040
`
`
`
`303030
`
`
`Time (h)Time (h)Time (h)
`
`
`
`
`
`505050
`
`
`
`
`
`606060
`
`
`
`
`
`707070
`
`
`
`Figure 12. SOA-SINS SF and Bias Stability.
`
`The SOA also demonstrates sub-ppm and sub-µg
`performance across multiposition
`tumble
`tests. The
`following error model was used to fit the tumble data:
`
`
`=
`
`=
`
`+
`
`+
`
`Parameter
`
`
`
`SF (ppm)SF (ppm)SF (ppm)
`
`
`Bias (µg)Bias (µg)Bias (µg)
`
`Bias
`
`Scale Factor
`
`K2
`
`K3
`
`Kim/Kio
`
`Misalignment
`
`
`
`
`
`2.02.0
`
`
`
`1.51.5
`
`
`
`1.01.0
`
`
`
`0.50.5
`
`
`
`
`
`
`OA TumbleOA Tumble
`
`MA TumbleMA Tumble
`
`
`
`00
`
`
`
`100100
`
`
`
`200200
`
`
`
`300300
`
`
`
`400400
`
`
`
`Table Angle (deg)Table Angle (deg)
`
`
`OA Residual (1σ) = 0.95 μgOA Residual (1σ) = 0.95 μg
`
`MA Residual (1σ) = 0.79 μgMA Residual (1σ) = 0.79 μg
`
`
`
`0.00.0
`
`
`
`-0.5-0.5
`
`
`
`-1.0-1.0
`
`
`
`-1.5-1.5
`
`
`
`-2.0-2.0
`
`Residual (µg)
`Residual (µg)
`
`Figure 13. Multiposition Tumble Residuals.
`
`Finally, Figures 14 and 15 show long-term (30-day) SF
`and bias stability measured on two SOA-SINS units (S/Ns
`028 and 063). The better of the two units demonstrates a
`1σ SF stability of 0.73 ppm and a 1σ bias stability of
`approximately 2 µg over 30 days.
`
`
`
`S/N 028 Avg. SF = 247.4 Hz/gS/N 028 Avg. SF = 247.4 Hz/g
`
`S/N 063 Avg. SF = 258.8 Hz/gS/N 063 Avg. SF = 258.8 Hz/g
`
`2.02.0
`
`
`
`SOA- SINS Long Term SF StabilitySOA- SINS Long Term SF Stability
`
`
`S/N 028 SF (1σ) = 0.73 ppmS/N 028 SF (1σ) = 0.73 ppm
`
`S/N 063 SF (1σ) = 1.22 ppmS/N 063 SF (1σ) = 1.22 ppm
`
`
`SF 063SF 063
`
`SF 028SF 028
`
`Linear (SF 028)Linear (SF 028)
`
`Linear (SF 063)Linear (SF 063)
`
`
`
`dSF/SF = -0.102 ppm/daydSF/SF = -0.102 ppm/day
`
`
`
`dSF/SF = 0.011 ppm/daydSF/SF = 0.011 ppm/day
`
`
`
`1.51.5
`
`
`
`1.01.0
`
`
`
`0.50.5
`
`
`
`0.00.0
`
`ppm
`ppm
`
`
`
`-0.5-0.5
`
`
`
`-1.0-1.0
`
`
`
`-1.5-1.5
`
`
`
`-2.0-2.0
`
`
`
`00
`
`
`
`55
`
`
`
`1010
`
`
`
`1515
`
`
`2020
`
`daysdays
`
`
`
`2525
`
`
`
`3030
`
`
`
`3535
`
`
`
`4040
`
`Figure 14. Long-Term SOA-SINS SF Stability.
`
`2
` Bias
`aKa
`+
`+
`i
`i
`2
`
`3
`aK
`i
`3
`
`aaK
`mi
`im
`
`
`
`+
`
`aaK
`oi
`io
`
`+
`
`2
`aK
`o
`oo
`
`[19]
`
`aind = indicated acceleration output
`f = net (differenced) SOA frequency output
`SF = SOA scale factor (Hz/g)
`Bias = SOA bias frequency
`ai = input axis applied acceleration
`am, ao = cross axis applied accelerations
`K2, K3 = second and third order SF nonlinearity
`Kim , Kio = cross-axis coupling coefficients
`Kmm , Koo = cross-axis nonlinearity coefficients
`
`a
`ind
`
`
`
`f
`SF
`2
`aK
`+
`
`m
`mm
`
`
`
`
`where
`
`
`
`
`
`
`
`
`
`
`the above
`the nominal values of
`Table 2 shows
`parameters for the SOA as determined in