Fundamentals of Vacuum Technology (1248463), страница 55
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The new system is insensitive to mode hopping and theresultant inaccuracy. It is fast and precise. The crystal frequency isdetermined 10 times a second with an accuracy to less than 0.0005 Hz.The ability of the system to initially identify and then measure a certainmode opens up new opportunities thanks to the advantages of theadditional information content of these modes. This new, "intelligent"measuring device makes use of the phase/frequency properties of thequartz crystal to determine the resonance frequency. It works by applying asynthesized sinus wave of a certain frequency to the crystal and measuringthe phase difference between the applied signal voltage and the currentflowing through the crystal.
In the case of series resonance, this differenceis exactly zero degrees; then the crystal behaves like an ohmic resistance.By disconnecting the applied voltage and the current that returns from thecrystal, one can determine with a phase comparator whether the appliedfrequency is higher or lower than the crystal resonance point.The crystal impedance is capacitive at frequencies below the fundamentalwave and inductive at frequencies above the resonance. This information isuseful if the resonance frequency of a crystal is unknown.
A brief frequencysweep is carried out until the phase comparator changes over and thusmarks the resonance. For AT quartzes we know that the lowest usablefrequency is the fundamental wave. The anharmonics are slightly abovethat. This information is not only important for the beginning, but also in therare case that the instrument loses ÒtrackÓ of the fundamental wave. Oncethe frequency spectrum of the crystal is determined, the instrument musttrack the shift in resonance frequency, constantly carry out frequencymeasurements and then convert them into thickness.Use of the ÒintelligentÓ measuring system has a number of obviousFig. 6.7Oscillations of a thickly coated crystal128HomeThin film controllers/control unitsadvantages over the earlier generation of active oscillators, primarilyinsensitivity to mode hopping as well as speed and accuracy ofmeasurement.
This technique also enables the introduction of sophisticatedproperties which were not even conceivable with an active oscillator setup.The same device that permits the new technology to identify thefundamental wave with one sweep can also be used to identify otheroscillation modes, such as the anharmonics or quasi-harmonics. The unitnot only has a device for constantly tracking the fundamental wave, but canalso be employed to jump back and forth between two or more modes.
Thisquery of different modes can take place for two modes with 10 Hz on thesame crystal.of the anharmonic in relation to the fundamental oscillation.If one side of the quartz is coated with material, the spectrum of theresonances is shifted to lower frequencies. It has been observed that thethree above mentioned modes have a somewhat differing mass sensitivityand thus experience somewhat different frequency shifts. This difference isutilized to determine the Z value of the material.
By using the equations forthe individual modes and observing the frequencies for the (100) and the(102) mode, one can calculate the ratio of the two elastic constants C60 andC55. These two elastic constants are based on the shear motion. The keyelement in WajidÕs theory is the following equation:(C55 / C66 )coated1≈(C55 / C66 )uncoated (1 + M ⋅ Z )6.8Auto Z match techniqueThe only catch in the use of equation 6.4 is that the acoustic impedancemust be known.
There are a number of cases where a compromise has tobe made with accuracy due to incomplete or restricted knowledge of thematerial constants of the coating material:1) The Z values of the solid material often deviate from those of a coating.Thin coatings are very sensitive to process parameters, especially in asputter environment. As a result, the existing values for solid materialare not adequate.withM ... area mass/density ratio (ratio of coating mass to quartz mass per areaunit)Z ... Z valueIt is a fortunate coincidence that the product M ¹ Z also appears in the LuLewis equation (equation 6.4).
It can be used to assess the effective Zvalue from the following equations: F Ftg M ⋅ Z ⋅ π ⋅ c + Z ⋅ tg π ⋅ c = 0Fq Fq 2) For many exotic substances, including alloys, the Z value is not knownand not easy to determine.3) It is repeatedly necessary to carry out a precise coating thicknessmeasurement for multiple coating with the same crystal sensor. Thisapplies in particular to optical multiple and semi-conductor coatings witha high temperature coefficient TC. However, the effective Z value of themixture of multiple coatings is unknown.In such a case, therefore, the only effective method is to assume a Z valueof 1, i.e. to ignore reality with respect to wave propagation in multisubstance systems.
This incorrect assumption causes errors in theprediction of thickness and rate. The magnitude of the error depends on thecoating thickness and the amount of deviation from the actual Z value.In 1989 A. Wajid invented the mode-lock oscillator. He presumed that aconnection existed between the fundamental wave and one of theanharmonics, similar to that ascertained by Benes between thefundamental oscillation and the third quasi-harmonic oscillation. Thefrequencies of the fundamental and the anharmonic oscillations are verysimilar and they solve the problem of the capacity of long cables.
He foundthe necessary considerations for establishing this connection in works byWilson (1954) as well as Tiersten and Smythe (1979).The contour of the crystal, i.e. the spherical shape of one side, has theeffect of separating the individual modes further from each other andpreventing energy transfer from one mode to another.
The usual method ofidentification is to designate the fundamental oscillation as (100), the lowestanharmonic frequency as (102) and the next higher anharmonic as (120).These three indices of the mode nomenclature are based on the number ofphase reversals in the wave motion along the three crystal axes. The abovementioned works by Wilson, Tiersten and Smythe examine the properties ofthe modes by studying the influence of the radius of the cut on the position(6.5)orZ=−tg M ⋅ Z ⋅ π ⋅tg π ⋅(6.6)Fc Fq Fc Fq Here Fq and Fc are the frequencies of the non-coated or coated quartz inthe (100) mode of the fundamental wave.
Because of the ambiguity of themathematical functions used, the Z value calculated in this way is notalways a positively defined variable. This has no consequences of anysignificance because M is determined in another way by assessing Z andmeasuring the frequency shift. Therefore, the thickness and rate of thecoating are calculated one after the other from the known M.One must be aware of the limits of this technique. Since the assessment ofZ depends on frequency shifts of two modes, any minimal shift leads toerrors due to substantial mechanical or thermal stresses.
It is not necessaryto mention that under such circumstances the Z match technique, too,leads to similar errors. Nevertheless, the automatic Z value determination ofthe Z match technique is somewhat more reliable regarding occurrence oferrors because the amplitude distribution of the (102) mode is asymmetricover the active crystal surface and that of the (100) mode is symmetric.According to our experience, coating-related stresses have the mostunfavorable effect on the crystal. This effect is particularly pronounced inthe presence of gas, e.g.
in sputter processes or reactive vacuum coatingor sputter processes. If the Z value for solid material is known, it is better touse it than to carry out automatic determination of the Òauto Z ratioÓ. Incases of parallel coating and coating sequences, however, automatic Zdetermination is significantly better.129HomeThin film controllers/control units6.9Coating thickness regulationThe last point to be treated here is the theory of the closed loop for coatingthickness measuring units to effect coating growth at a controlled (constant)growth rate.
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