CN103697876B - Based on the static driven formula bulk acoustic wave solid fluctuation microthrust test of silicon surface manufacturing process - Google Patents
Based on the static driven formula bulk acoustic wave solid fluctuation microthrust test of silicon surface manufacturing process Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
- G01C19/56—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces
- G01C19/567—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces using the phase shift of a vibration node or antinode
- G01C19/5677—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces using the phase shift of a vibration node or antinode of essentially two-dimensional vibrators, e.g. ring-shaped vibrators
- G01C19/5684—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces using the phase shift of a vibration node or antinode of essentially two-dimensional vibrators, e.g. ring-shaped vibrators the devices involving a micromechanical structure
Abstract
The present invention provides a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process, comprise: a rectangular parallelepiped matrix, a square harmonic oscillator with four beams, four driving electrodes and four detecting electrodes, wherein: four drive the distribution configuration along matrix internal surface sidewall corresponding to both sides, four angles, square harmonic oscillator top respectively of electrodes and four detecting electrodes, by arranging that it is applied generating positive and negative voltage by metal wire on the beam connecting square harmonic oscillator, thus coordinate and drive electrode and detecting electrode to realize static driven and detection. The present invention utilizes the special vibration mode of square harmonic oscillator to carry out work, and its driven-mode and sensed-mode match each other. The present invention adopts MEMS technology to make, and structure is simple, volume is little and the surface manufacturing process of silicon compatible and is convenient to encapsulation.
Description
Technical field
The present invention relates to the solid fluctuation mode vectors correlation gyro of a kind of field of micro electromechanical technology, specifically, it relates to a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process.
Background technology
Gyrostat be a kind of can the inertia device of sensitive carrier angle or circular frequency, have extremely important effect in fields such as gesture stability and navigation location. Along with the development of science and techniques of defence and aviation, space industry, inertial navigation system also develops to low cost, small volume, high precision, multiaxis detection, high reliability, the direction that can adapt to various severe environment for the requirement of gyrostat. Gyroscope based on MEMS technology adopts the processing of micro-nano batch fabrication techniques, its cost, size, power consumption are all very low, and environmental compatibility, working life, reliability, integrated level have great raising compared with conventional art, thus MEMS microthrust test has become an important directions of the extensive investigation and application exploitation of MEMS technology in the last few years.
Solid ripple is a kind of mechanical wave in solid, the deformation that in solid, certain a bit or partly causes by the disturbance of power or other reasons, such as volume deformation or shear deformation, propagates into other parts of solid with the form fluctuated. In wave propagation process, the particle in solid, except having small vibration on the position original at it, does not produce permanent displacement. Because solid is flexible, elastic force has the deformation that disturbance is caused to return to the ability of undeformed state, so forming fluctuation. Elasticity is the major cause that can form fluctuation in solid.
At present, most of MEMS solid fluctuation micromechanical gyro and silicon process technology are not compatible, even if having employed the technique of silicon processing, majority adopts 3-D Bulk micro machining, and manufacturing process is complicated, causes cost higher, is not suitable for producing in enormous quantities.
Summary of the invention
For defect of the prior art, it is an object of the invention to provide a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process, this gyroscope structure is simple, volume is little, shock resistance, there is high q-factor and be convenient to encapsulation.
For realizing above object, the present invention provides a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process, comprising:
A rectangular parallelepiped matrix;
A square harmonic oscillator with four beams;
The driving electrode of four configurations that distribute along rectangular parallelepiped matrix internal surface sidewall corresponding to side, four angles, square harmonic oscillator top;
The detecting electrode of four configurations that distribute along rectangular parallelepiped matrix internal surface sidewall corresponding to side, four angles, square harmonic oscillator top;
Wherein, drive electrode, detecting electrode and the equal noncontact of square harmonic oscillator, and the locus of the locus of four driving electrodes and four detecting electrodes is orthogonal.
Preferably, described microthrust test comprises connection metal pin further and drives the metal wire of electrode, detecting electrode, and the electrical signal introducing of outside is driven electrode or the electrical signal by the generation of detecting electrode 4 place to be derived by metal wire by metal wire by described metal pins.
Preferably, described square harmonic oscillator is provided with conductive layer, and this conductive layer is the silicon single crystal of ion doping, has electric action; Depositing layer of metal on this conductive layer, this layer of metal and metal pins, metal wire are that the same layer metal by deposition on rectangular parallelepiped matrix is formed after mask, etching.
Preferably, described square harmonic oscillator, in four sidewalls, namely different with end face and bottom surface plane orthogonal medullary ray is applied fixing by four beams.
Preferably, described square harmonic oscillator material is silicon single crystal, it may also be useful to capacitive sensing effect carries out driving and detecting.
Preferably, four described driving electrode materialss are the silicon single crystal of doping, along the interior side-wall surface distribution in 2*2 array parallel to each other of rectangular parallelepiped matrix, for encouraging square harmonic oscillator to produce the driven-mode vibration shape.
Preferably, four described detecting electrode materials are the silicon single crystal of doping, along the interior side-wall surface distribution in 2*2 array parallel to each other of rectangular parallelepiped matrix, and drive electrodes spatially orthogonal with four, for detecting on square harmonic oscillator that the circular frequency being perpendicular to rectangular parallelepiped matrix bottom surface plane and z-axis direction causes and detecting electrode the capacitance variations due to the generation of capacitive sensing effect.
Preferably, when two relative driving electrodes in four described driving electrodes are applied in voltage of alternating current, the vibration of square harmonic oscillator at driven-mode is produced by capacitive sensing effect; When there is input angular velocity, the vibration shape of square harmonic oscillator changes to sensed-mode, and the sensitive electrical signal utilizing detecting electrode place capacitive sensing effect to produce carries out signal detection; Above-mentioned driven-mode and sensed-mode match each other.
The present invention utilizes the special mode of square harmonic oscillator as with reference to vibration, angle, four, square harmonic oscillator top vibrates along four edge directions under this mode. To driving, electrode applies sinusoidal voltage by four driving electrodes one, produce the vibration of square harmonic oscillator at driven-mode by capacitive sensing effect. When there being the turning rate input being perpendicular to bottom square harmonic oscillator, under the effect of Coriolis power, the resonance manner of square harmonic oscillator can change from driven-mode to sensed-mode, and sensed-mode is directly proportional along the square resonance amplitude of four edge directions to the size of input angular velocity. By the change of the inductance capacitance between four detecting electrodes detecting on square harmonic oscillator and matrix internal surface sidewall, so that it may detection is perpendicular to the size of square harmonic oscillator bottom surface plane angle speed.
Compared with prior art, the present invention has following useful effect:
1, silicon surface manufacturing process is adopted, compatible with existing silicon process technology, and, relative to the gyro that body processing technology makes, technique is simple, and cost is lower;
2, ion doping can be carried out once, be formed and drive electrode and detecting electrode;
3, can deposit once, etch metal and form wire and pin, and pin is symmetrical, the edge that neatly is distributed in rectangular parallelepiped base, is convenient to encapsulation;
4, utilizing square resonator moving as driving and sensed-mode along fixed beam direction, resonator stiffness relatively greatly, has good shock resistance;
5, driven-mode that the vibration shape is completely the same and sensed-mode is adopted so that temperature variation is the same for driven-mode with the impact of sensed-mode, because this reducing temperature sensitivity.
Accompanying drawing explanation
By reading with reference to the detailed description that non-limiting example is done by the following drawings, the other features, objects and advantages of the present invention will become more obvious:
Fig. 1 is the present embodiment perspective view;
Fig. 2 be the present embodiment on rectangular parallelepiped matrix in order to form the conductive layer of harmonic oscillator, to drive the area schematic of electrode and detecting electrode;
Fig. 3 is that the present embodiment deposits the structural representation after layer of metal layer also etches on rectangular parallelepiped matrix;
Fig. 4 is the present embodiment three-dimensional arrangement sectional view;
Fig. 5 is that the present embodiment obtains the driven-mode vibration shape emulation schematic diagram of square harmonic oscillator by the method for finite element analysis;
Fig. 6 is the rough schematic view of the driven-mode vibration shape of Fig. 5;
Fig. 7 is the three-dimensional vibration shape schematic diagram that the vibration shape of the square harmonic oscillator of the present embodiment is changed to sensed-mode by driven-mode;
Fig. 8 is that the present embodiment obtains the sensed-mode vibration shape emulation schematic diagram of square harmonic oscillator by the method for finite element analysis;
Fig. 9 is the rough schematic view of the sensed-mode vibration shape of Fig. 8;
The voltage's distribiuting ANSYS that Figure 10 is the present embodiment driven-mode emulates schematic diagram;
The voltage's distribiuting ANSYS that Figure 11 is the present embodiment sensed-mode emulates schematic diagram;
In figure: 1 is rectangular parallelepiped matrix, 2 is square harmonic oscillator, and 3 for driving electrode, and 4 is detecting electrode, and 5 is metal pins, and 6 is metal wire, and 7 is conductive layer, and 8 is silicon single crystal, and 9 is the silicon single crystal after doping, and 10 is the metal level of deposition-etch on doped monocrystalline silicon.
Embodiment
Below in conjunction with specific embodiment, the present invention is described in detail. The technician contributing to this area is understood the present invention by following examples further, but does not limit the present invention in any form. It should be appreciated that to those skilled in the art, without departing from the inventive concept of the premise, it is also possible to make some distortion and improvement. These all belong to protection scope of the present invention.
As shown in Figure 1, the present embodiment provides a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process, comprising:
A rectangular parallelepiped matrix 1;
A square harmonic oscillator 2 with four beams;
The driving electrode 3 of four configurations that distribute along rectangular parallelepiped matrix 1 internal surface sidewall corresponding to the side, four angles, top of square harmonic oscillator 2;
The detecting electrode 4 of four configurations that distribute along rectangular parallelepiped matrix 1 internal surface sidewall corresponding to the side, four angles, top of square harmonic oscillator 2;
It is distributed in the metal pins 5 of rectangular parallelepiped matrix 1 top surface edge;
Connection metal pin 5 and the metal wire 6 driving electrode 3, detecting electrode 4;
The conductive layer 7 of square harmonic oscillator 2;
Wherein: drive electrode 3 and the noncontact of square harmonic oscillator 2, detecting electrode 4 and the noncontact of square harmonic oscillator 2, and the locus of the locus of four driving electrodes 3 and four detecting electrodes 4 is orthogonal.
In the present embodiment, the electrical signal of outside can be introduced the silicon single crystal after driving electrode 3(ion doping by metal wire 6 by described metal pins 5, there is electric action) or by the silicon single crystal after detecting electrode 4(ion doping, there is electric action) place produce electrical signal derived by metal wire 6, can, so that packaging process and the microelectronics IC packaging process of the present invention are compatible, be convenient to utilize prior art to encapsulate by arranging metal pins 5.
In the present embodiment, described conductive layer 7 is the silicon single crystal of ion doping, has electric action. Depositing layer of metal on it, this layer of metal and metal pins 5, metal wire 6 are that the same layer metal by deposition on rectangular parallelepiped matrix 1 is formed after mask, etching.
Varied clearance motivating force refers to that static driven power is at the force component being perpendicular to the generation of electrode plane direction. If it is standard that order is perpendicular to electrode plane direction, then electrode plane is directly proportional to the voltage squared being applied in two electrode plane at the reactive force that this side up, such that it is able to utilize this effect to be driven by vibrating mass.
Tested mechanical quantity, the effect being converted to electric capacitance change such as displacement, pressure etc. is called capacitive sensing effect. Its most frequently used form is made up of two parallel poles, be the electrical condenser of medium taking air between pole. If ignoring fringing effect, the electric capacity of plate condenser is �� A/ ��, and in formula, �� is the specific inductivity of contrasted between solid dielectric, and A is the useful area that two electrodes cover mutually, and �� is the distance between two electrodes. In ��, A, �� tri-parameters, the change of any one all will cause electric capacitance change, and can be used for measuring. Therefore capacity type probe can be divided into pole apart from change type, area change type, media variations type three class. Pole generally is used for measuring small line shift or the pole that causes due to power, pressure, vibration etc. apart from change (see capacitive pressure sensor) apart from change type. Area change type is generally used for the line shift of measured angular displacement or bigger. Media variations type is usually used in the mensuration of the temperature of level gauging and various medium, density, humidity. What the present embodiment adopted is exactly the capacitive sensing of pole apart from change type.
In the present embodiment, square harmonic oscillator 2, in four sidewalls, on the vertical center line of namely different with end face and bottom surface plane, applies fixing by four beams (as, in Fig. 1, driven the silicon single crystal crossbeam between electrode 3 or detecting electrode 4).
In the present embodiment, the material of square harmonic oscillator 2 is silicon single crystal.
In the present embodiment, four drive the material of electrode 3 to be doped monocrystalline silicon, along the interior side-wall surface distribution in 2*2 array parallel to each other of rectangular parallelepiped matrix 1, for adopting capacitive sensing effect to encourage square harmonic oscillator 2 to produce the driven-mode vibration shape.
In the present embodiment, the material of four detecting electrodes 4 is doped monocrystalline silicon, along the interior side-wall surface distribution in 2*2 array parallel to each other of rectangular parallelepiped matrix 1, and each detecting electrode 4 is positioned at each side driving electrode 3, four detecting electrodes 3 and four driving electrodes 4 are spatially orthogonal, for adopting capacitive sensing effect detection to be perpendicular to the size of square harmonic oscillator 2 bottom surface plane (z-axis) direction angle speed.
As shown in Figure 2, wherein 3 for driving electrode part, by silicon single crystal formed after boron ion or phosphonium ion adulterate certain thickness can conductive region, it is possible to by metal wire 6(as shown in fig. 1) by metal pins 5(as shown in fig. 1) external electric signal at place introduces; 4 is detecting electrode part, by silicon single crystal formed after boron ion or phosphonium ion adulterate certain thickness can conductive region, it is possible to by metal wire 6(as shown in fig. 1) electrical signal that this electrode produces is exported to metal pins 5(as shown in fig. 1) place. 7 is the conductive layer of square harmonic oscillator, by silicon single crystal formed after boron ion or phosphonium ion adulterate certain thickness can conductive region, layer of metal 10(finally can be deposited as shown in Figure 4) above it, by this harmonic oscillator being applied the voltage of a change, it just can be made to produce vibration two under driving the motivating force between electrode, when there being external angular velocity to input, so that it may to produce the change of corresponding electrical signal between two pairs of detecting electrodes.
Fig. 3 is that the present embodiment deposits the structural representation after layer of metal layer also etches on rectangular parallelepiped matrix; The conductive layer etc. of driving electrode in Fig. 2, detecting electrode, square harmonic oscillator is that can be formed after boron ion or phosphonium ion adulterate by silicon single crystal in corresponding position certain thickness can conductive region, in order to realize introducing or the derivation of electrical signal, it is necessary to deposit layer of metal in these positions and be connected to corresponding metal pins 5 place by metal wire 6. The present invention can be deposited by disposable metal layer, etch. Namely the upper surface of shown rectangular parallelepiped matrix 1 deposits layer of metal layer 10(as shown in Figure 4 in figure 3), and 3,4,5,6,7 positions are etched into the shape of needs in the drawings.
Fig. 4 is the present embodiment three-dimensional arrangement sectional view; Wherein, 8 is silicon single crystal, rectangular parallelepiped matrix 1 one-piece construction in the present invention is silicon single crystal, when can be formed after boron ion or phosphonium ion adulterate in a certain position certain thickness can conductive region, namely become the silicon single crystal 9 after ion doping, it is used as to drive the conductive layer etc. of electrode, detecting electrode, square harmonic oscillator; 10 is the metal level deposited on doped monocrystalline silicon and the metal level being used as metal wire 6 and metal pins 5. By at the upper surface metal refining of rectangular parallelepiped matrix 1 and etch formation.
The method by finite element analysis that is illustrated in figure 5 obtains the driven-mode vibration shape analogous diagram of square harmonic oscillator 2; It is illustrated in figure 6 the rough schematic view of the driven-mode vibration shape of Fig. 5, by driving in electrode 3 at four, off-diagonal any two relative driving electrodes 3 apply identical sine voltage signal, making to drive and produce driven-mode vibration by electrostatic force between electrode 3 and square harmonic oscillator 2, now four drift angles of square harmonic oscillator 2 vibrate on four edge directions.
When there being the z-axis direction turning rate input being perpendicular to square harmonic oscillator 2 bottom surface plane, gyro vibration direction on by power as shown in Figure 7. Under the effect of Coriolis power, square harmonic oscillator 2 is vibrated by the driven-mode vibration shape to the change of the sensed-mode vibration shape, and amplitude and the input angular velocity of vibration are directly proportional.
The method by finite element analysis that is illustrated in figure 8 obtains the sensed-mode vibration shape analogous diagram of square harmonic oscillator 2; It is illustrated in figure 7 the rough schematic view of Fig. 8 sensed-mode vibration shape. When there being the z-axis direction turning rate input being perpendicular to square harmonic oscillator 2 bottom surface plane, square harmonic oscillator 2 produces the vibration of the sensed-mode vibration shape, by measuring the capacitive sensing effect capacitance variations that four detecting electrodes 4 produce, the size of the direction angle speed being perpendicular to square harmonic oscillator 2 bottom surface (z-axis) can be detected.
Driven-mode and the sensed-mode of square harmonic oscillator 2 as shown in Figure 5 and Figure 8 match each other, and its implication is: driven-mode is similar with the vibration shape of sensed-mode, the angle that only difference is certain mutually; Not vibrating mode containing other in the middle of driven-mode and sensed-mode, frequency splitting is little. When the top surface space symmetr of the square harmonic oscillator 2 in the present embodiment, form mode vectors correlation; When the top surface spatial dissymmetry of the square harmonic oscillator 2 in the present embodiment, mode vectors correlation cannot be formed.
It is the voltage's distribiuting ANSYS emulation schematic diagram of the present embodiment driven-mode as shown in Figure 10; It is the voltage's distribiuting ANSYS emulation schematic diagram of the present embodiment sensed-mode as shown in figure 11; Figure 10,11 describes under driven-mode and sensed-mode, the charge distribution situation that prop drawing shape harmonic oscillator produces due to piezoelectric effect.
A kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process described in the present embodiment, it may also be useful to single crystal silicon substrate, adopts silicon surface manufacturing process, forms monocrystalline silicon conductive layer by ion doping, drives electrode and detecting electrode; Then, deposit thereon, etch layer of metal, form the metal wire of metal pins and connection metal pin and electrode; Finally, for the square harmonic oscillator peripheral circuit of welding and carry out final encapsulation and obtain GYROCHIP finished product.
Above specific embodiments of the invention are described. It is understood that the present invention is not limited to above-mentioned particular implementation, those skilled in the art can make various distortion or amendment within the scope of the claims, and this does not affect the flesh and blood of the present invention.
Claims (8)
1. the static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process, it is characterised in that, comprising:
A rectangular parallelepiped matrix;
A square harmonic oscillator with four beams;
The driving electrode of four configurations that distribute along rectangular parallelepiped matrix internal surface sidewall corresponding to side, four angles, square harmonic oscillator top;
The detecting electrode of four configurations that distribute along rectangular parallelepiped matrix internal surface sidewall corresponding to side, four angles, square harmonic oscillator top;
Wherein, drive electrode and the equal noncontact of square harmonic oscillator, detecting electrode and the equal noncontact of square harmonic oscillator, and the locus of the locus of four driving electrodes and four detecting electrodes is orthogonal;
Described microthrust test utilizes the driven-mode of square harmonic oscillator and the mode vectors correlation of sensed-mode as with reference to vibration, angle, four, square harmonic oscillator top vibrates along four edge directions under this mode; By driving in electrode at four, off-diagonal any two relative driving electrodes apply sinusoidal voltage, produce the vibration of square harmonic oscillator at driven-mode by capacitive sensing effect; When there being the turning rate input being perpendicular to bottom square harmonic oscillator, under the effect of Coriolis power, the resonance manner of square harmonic oscillator can change from driven-mode to sensed-mode, and sensed-mode is directly proportional along the square resonance amplitude of four edge directions to the size of input angular velocity; By the change of the inductance capacitance between four detecting electrodes detecting on square harmonic oscillator and rectangular base internal surface sidewall, so that it may detection is perpendicular to the size of square harmonic oscillator bottom surface plane angle speed.
2. a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process according to claim 1, it is characterized in that, described microthrust test comprises connection metal pin further and drives the metal wire of electrode, detecting electrode, and the electrical signal introducing of outside is driven electrode or the electrical signal by the generation of detecting electrode 4 place to be derived by metal wire by metal wire by described metal pins.
3. a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process according to claim 2, it is characterised in that, described square harmonic oscillator is provided with conductive layer, and this conductive layer is the silicon single crystal of ion doping, has electric action; Depositing layer of metal on this conductive layer, this layer of metal and metal pins, metal wire are that the same layer metal by deposition on rectangular parallelepiped matrix is formed after mask, etching.
4. a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process according to the arbitrary item of claim 1-3, it is characterized in that, described square harmonic oscillator, in four sidewalls, namely different with end face and bottom surface plane orthogonal medullary ray is applied fixing by four beams.
5. a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process according to claim 4, it is characterised in that, described square harmonic oscillator material is silicon single crystal, it may also be useful to capacitive sensing effect carries out driving and detecting.
6. a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process according to the arbitrary item of claim 1-3, it is characterized in that, four described driving electrode materialss are the silicon single crystal of doping, along the interior side-wall surface distribution in 2*2 array parallel to each other of rectangular parallelepiped matrix, for encouraging square harmonic oscillator to produce the driven-mode vibration shape.
7. a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process according to the arbitrary item of claim 1-3, it is characterized in that, four described detecting electrode materials are the silicon single crystal of doping, along the interior side-wall surface distribution in 2*2 array parallel to each other of rectangular parallelepiped matrix, and drive electrodes spatially orthogonal with four, for detecting on square harmonic oscillator that the circular frequency being perpendicular to rectangular parallelepiped matrix bottom surface plane and z-axis direction causes and detecting electrode the capacitance variations due to the generation of capacitive sensing effect.
8. a kind of static driven formula bulk acoustic wave solid fluctuation microthrust test based on silicon surface manufacturing process according to the arbitrary item of claim 1-3, it is characterized in that, when two relative driving electrodes in four described driving electrodes are applied in voltage of alternating current, produce the vibration of square harmonic oscillator at driven-mode by capacitive sensing effect; When there is input angular velocity, the vibration shape of square harmonic oscillator changes to sensed-mode, and the sensitive electrical signal utilizing detecting electrode place capacitive sensing effect to produce carries out signal detection; Above-mentioned driven-mode and sensed-mode match each other.
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| EP2078925A2 (en) * | 2008-01-08 | 2009-07-15 | Northrop Grumman Guidance and Electronics Company, Inc. | Capacitive bulk acoustic wave disk gyroscopes with self-calibration |
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