The invention also concerns a system for controlling the interelectrode distance of micromechanical components.

In many types of micromechanical components and sensors implemented by silicon techniques, a vital part is formed by an electrode structure comprising two, typically planar electrodes whose interelectrode distance is arranged variable by means of an electrostatic force. Generally, the interelectrode distance has been varied by controlling the AC or DC voltage applied over the electrodes. Herein, the control range of inter- electrode distance is limited by the so-called pull-in voltage Upi. When the control voltage exceeds this value, the electrodes will hit each other under the electrostatic force pulling them together.

In the art are known methods based on driving the interelectrode distance of a moving- electrode capacitor by means of controlling the DC charge imposed over the electrodes.

Although this technique is capable of reducing the risk of electrode pull-in, a practicable construction thereof requires a galvanic contact to the electrodes.

It is an object of the present invention to overcome the disadvantages of the above- described techniques and to provide an entirely novel method for electrical control of interelectrode distance in micromechanically fabricated electrode structures.

The goal of the invention is achieved by virtue of controlling the interelectrode distance by virtue of controlling the level of AC current passed through the electrodes.

More specifically, the method according to the invention is characterized by what is stated in the characterizing part of claim 1.

Furthermore, the system according to the invention is characterized by what is stated in the characterizing part of claim 8.

The invention offers significant benefits.

In addition to offering an efficient method of controlling the interelectrode distance without a risk of electrode pull-in, the novel control technique can be implemented in a capacitive or inductive manner without a galvanic contact. Particularly in silicon micro- mechanical constructions, this control technique can provide significant benefits, since the fabrication of any galvanic control signal contacts to electrodes tends to complicate a micromechanical construction beyond the limits of acceptable production cost efficiency.

Advantageous applications of the invention can be found in new silicon micromechanical voltage transfer standards and Fabry-Perot interferometers in which the control span of the interelectrode distance can be increased up to three-fold as compared to the conventional voltage control technique.

Moreover, embodiments of the invention equipped with tuned circuits according to the invention can offer a significantly boost toward a high efficiency of control.

In the following, the invention will be examined in greater detail with the help of exem- plifying embodiments illustrated in the appended drawings, in which Figure 1 shows the block diagram of an AC current control circuit configuration according to the invention; Figure 2 shows a plot of the capacitor voltage-charge characteristic as measured in the circuit configuration of Fig. 1; Figure 3 shows a circuit configuration particularly suited for use in the method according to the invention;

Figure 4 shows a plot of interelectrode forces as a function of capacitor plate deviation; Figure 5 shows a plot of interelectrode forces in a frequency-control-based embodiment according to the invention; Figure 6 shows the block diagram of a control system according to the invention; and Figure 7 shows a plot of interelectrode distance as a function of control voltage for constant-frequency operation of a tuning circuit according to the invention.

In short, the invention relates to a method for controlling the interelectrode distance in a moving-electrode capacitor. The invention may also be applied to micromechanical alternating-current transfer standards suited for use in miniature and cost-efficient con- structions of precision electronics.

In an ideal moving-plate capacitor (MPC) having planar electrodes, the capacitance is C=a/(d-x),(d-x), where x is deviation of the moving electrode (ME) from its static position under electrostatic forces and (d-x) is the interelectrode distance. The displacement of the moving electrode ME is determined by the equation of a forced harmonic oscillator: <BR> <BR> <BR> <BR> d²x dx<BR> m + # + kx = Fel (1)<BR> dt² dt<BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> written using the symbols according to the standard convention of physics. If a sinusoidal current i = iosinwt is passed via a capacitor, the charge of the capacitor is <BR> <BR> <BR> <BR> q = (lo/0) (1-cosat) + qo, where qo is the capacitor charge at instant t = 0. The<BR> <BR> <BR> <BR> <BR> <BR> electrostatic force between the planar electrodes is Fel = q2/(2&4). Then, the exact steady-state solution of Eq. (1) is x=- lfl+A (2w) cos2cot+B (2w) sin2cot], (2) where <BR> <BR> <BR> where<BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> B-1(#) = Qm(1-#²)² / # + Qm-1 # # Qm#³ ,and

Herein, an assumption has been made that whereby the average electrostatic energy stored in the capacitor is minimized so that the DC voltage component over the capacitor is zero. Herein, the terms containing A and <BR> <BR> <BR> <BR> B (co) can be neglected provided that the frequency co of the alternating control current is substantially high in regard to the mechanical resonant frequency coo of the capacitor, in <BR> <BR> <BR> <BR> other words meaning that 8 » l, a condition called later in the text as a high operating frequency assumption.

Then, the pseudostatic value of the electrostatic force is 7=/(2),(2a) and the interelectrode distance is x = q²#/ (2#Ak). (2b) While Fel is not related to the interelectrode distance in a current-controlled capacitor, <BR> <BR> <BR> <BR> the value of Fel in a voltage-controlled capacitor increases drastically as the inter- electrode distance closes to zero thus causing the pull-in effect of the opposed electrodes.

The amplitude of the AC voltage over the capacitor is <BR> 8<BR> where C0 = #A/d and upi² = kd²/C0. From Eq. (3) can be seen that the amplitude Ma ;<BR> 27

has a maximum value 3<BR> when q# = qmax # 3C0µpi . This characteristic amplitude value Mmax can be used as a reference voltage, because a change in the value <BR> <BR> <BR> <BR> of io does not have a first-degree effect on the value of ûmax. If the amplitude inaccuracy of the current causing the voltage is Aio, the relative inaccuracy of the voltage at its <BR> <BR> <BR> <BR> maximum value is A,,, 3/1, 2. To verify these relationships, also the effect of stray capacitance and spectral purity of current source waveform have been investigated by the inventors using numerical simulations.

In preliminary tests, measurements were performed using an AC current control system illustrated in Fig. 1, wherein the planar capacitor 1 was fabricated using surface micro- mechanical techniques. The tested capacitive sensor comprises a moving electrode 7 and a stationary electrode 8. An operational amplifier 2 was used as a voltage-to-current converter. The AC current to the capacitor 1 was supplied by a signal generator 3, whose output voltage was converted by a current-to-voltage converter 2 into an AC current control signal. In the actual circuit configuration, the AC current control of the sensor 1 was implemented by placing the sensor 1 on the feedback path of the current- to-voltage converter 2. The exemplifying component values in the circuit configuration of Fig. 1 were: Rf = 22 Mohm, Ri = 10 kohm, Ro = 100 ohm and Ci = 100 nF. The current passing through the capacitor 1 was estimated as l0 = Vi,/R, and the voltage over the capacitor 1 as (VOU'-Vjn). The measurements were performed by measuring the values of Vjn and VOUt when Vjn was increased slowly.

In curve 5 of Fig. 2 is shown a plot of the voltage measured over the capacitor 1 of the circuit shown in Fig. 1 as a function of q, Furthermore, in curve 6 of Fig. 2 is shown with a dashed line the voltage theoretically computed from Eq. 3. Curve 5 representing the measured voltage exhibits a sudden dip at 130pC (rms), caused by the tendency of the planar capacitor electrodes 7 and 8 to pull in until they hit the spacers made in the interelectrode space. This pull-in effect is a result of the sensor stray capacitance and the nonzero condition of DC voltage over the capacitor. In order to cope with these anomalies resulting from the nonideal behaviour of the capacitor, the

horizontal and vertical axes of the theoretically computed curve are scaled with correction factors having values of 0.95 and 0.80, respectively.

In a static situation, the force imposed by the DC charge on the moving electrode ME is <BR> <BR> <BR> <BR> Fe, _ sAu z l (d-x) 2 = q2 12s4, whereby it can be computed from the equation of an equilibrium situation <BR> <BR> <BR> <BR> 2k<BR> u² = dx (1-x/d)². (4) C0 that the DC voltage u over the capacitor attains a maximum value u = upi when x = d/3.

On the same principle, it is also possible to realize DC and AC voltage transfer standards based on the shift of the mechanical resonant frequency of micromechanical oscillators having a high Q value.

In the present application, the term AC current is used when reference is made generally to a cyclic alternating-current waveform having a frequency typically selected to be substantially higher than the effective mechanical resonant frequency of the capacitive electrode structure. Herein, the term effective resonant frequency is preferredly used inasmuch the inherent mechanical resonant frequency of the electrode construction can be varied by means of, e. g., a DC control voltage applied between the electrodes. <BR> <BR> <BR> <BR> <BR> <BR> <BR> <P>In a plurality of applications, it is advantageous to make the values of Fe, and qdv = itV/computed from Eq. (2a) dependent on the interelectrode distance in a manner that aids the stabilization of the desired interelectrode distance. This goal can be attained by means of a resonant-tuned AC current control circuit.

Referring to Fig. 3, the circuit shown therein may be tuned to the resonant frequency of the control system, whereby the interelectrode distance can be controlled using minimal control energy. As shown in the diagram, an inductor 11 and a capacitor 12 are connect- ed in series and tuned to resonance by a suitably selected inductance value of the inductor 11. In the diagram, the circuit element 10 represents the series resistance of the inductor 11, while the circuit element 13 represents the stray capacitance of the capacitor 12.

If the Q value of the resonant circuit is made high, very low values of the AC control voltage Vi,, are sufficient to create an electrostatic force which is dependent on the alternating control current passed via the electrodes. This is because a tuned circuit has an inherent property contributing to easier control of the interelectrode distance, namely, the electrostatic force acting between the electrodes is highest when the interelectrode distance and, hence, the capacitance determined by said distance is modulated so that the effective resonant frequency of the structure is equal to the frequency of the applied alternating control current. Resultingly, the interelectrode distance can be altered by controlling the frequency of the control current.

Assuming the high operating frequency condition, the effective value of the control voltage applied over the electrodes is where Ct = C + Cstray. Then, the electrostatic force between the electrodes is <BR> <BR> <BR> Fel 4V² inRMS C² 1<BR> = x<BR> <BR> kd 27u² piC²o #²R²C²t + (#²LCt-1)², whereby the electrical resonant frequency is where At resonance, the quality factor is where Referring to Fig. 4, therein are plotted the forces acting on the electrode of a moving electrode capacitor in a pseudostatic situation. The curves are computed using the parameter values Cs, ray = 0 and Qo = 40. Using conventional circuit analysis techniques, it can be seen that when co/wo = 0.65 (V,"RMs = 0. 04upl), the solutions plotted in the diagram are stable for x = xB, while the intersection point x = xA represents an unstable <BR> <BR> <BR> solution. When col =1.2 (V", RMS = upr) there is only one pseudostatic solution that is stable. Herefrom, it is easy to see that the electrical resonant frequency of a current drive circuit for a moving-plate capacitor operating in a stable working point must be lower than the actual drive frequency.

On the basis of the above treatise, it is obvious that when 6)/ > 1, a desired inter- electrode distance x in the range 0 < x < can can set set controlling controlling voltage voltage Vi,.

Besides in the ideal case when Cstray = 0, this is also true for cases where Cstray is not very large in respect to Co.

In addition to the control of electrode movement, the interelectrode distance control based on operation essentially close to the resonant frequency of tuned drive circuit may also advantageously be used for clamping electrode movement in a force-balanced configuration. Thus, it is possible to compensate for the force imposed by a pressure differential, for instance, over an electrode acting as the sensor diaphragm.

If the interelectrode distance control is implemented using a resonant circuit tuned to a frequency higher than the mechanical resonant frequency of the electrode system, a situation is created in which the change of the interelectrode distance is an almost linear function of the control voltage over a large control range. Herein, the electrical resonant frequency of the current drive circuit of the moving-electrode must again be set lower than the actual drive frequency in order to obtain a stable working point. <BR> <BR> <BR> <BR> <BR> <BR> <P>When the circuit shown in Fig. 3 is operated in resonance, the force Fl is multiplied by a factor Q2. By virtue of this phenomenon, large electrostatic forces can be generated using minimal drive voltages.

In Fig. 5 is shown a configuration suitable for using a constant-amplitude drive voltage, whose frequency is controlled so that the circuit operation is all the time confined to within the limits of the resonant frequency curve of the resonant circuit of Fig. 3, whereby a small control voltage can be used to achieve the maximal value of electrostatic force between electrodes 7 and 8 of the force transducer 1.

Referring to Fig. 6, therein is illustrated the basic concept of the invention for configuring a system in which the signal of an alternating current source 15 is converted in a converter 16 such that the interelectrode force, which under the control of a conventional voltage control system behaves as a force inversely proportional to the

square of the distance between the electrodes thus readily causing a pull-in effect on the electrodes of a sensor 1, is converted in said converter into an alternating control current which is not dependent on the interelectrode distance and thus is not subject to the pull- in effect between the electrodes. Alternatively, the converter 16 can be replaced by a tuned resonant circuit shown in Fig. 3 or even using a more complicated tunable circuit, whereby a conventional voltage control signal Vin can be converted into an alternating current capable of inducing a deflection force that inherently diminishes with a small interelectrode distances, thus stabilizing the control of the interelectrode distance. This arrangement offers a substantially linear control of interelectrode distance as a function of the control voltage Vin. A third alternative is that the converter 16 includes a tuned resonant circuit and a frequency-control unit, whereby the interelectrode distance in the sensor 1 is set such that makes the respective electrical resonant frequency of the circuit to be slightly below the actual control frequency. Then, the interelectrode distance can be controlled by altering the control frequency.

In Fig. 7 is shown the deflection x of the planar electrode as a function of the control voltage Vi;"R,,s. The plotted curve is obtained when the control voltage is applied over the resonant circuit with the following parameter values:/o = 1. 5,values:/o = 1. 5, and Cro = 0. The linearity of the control function x over the deflection range 0.15<x<1 is +1. 1 %.