The Z match technique

Miller and Bolef (1968) treated the quartz oscillator and coating system as a single-dimensional, coherent acoustic resonator. Lu and Lewis (1972) developed the simplified Z match equation on that basis. Simultaneous advances in electronics, particularly the microprocessor, made it possible to solve the Z match equation in real time. Most coating process control units sold today use this sophisticated equation, which takes into account the acoustic properties of the quartz oscillator/coating system  

Uq = shear module, quartz Uf = shear module, film 

This led to basic understanding of the conversion of frequency shift into thickness which enabled correct results in a practical lime frame for process control. To achieve this high degree of accuracy, the user must only enter an additional material parameter Z, for the coating material. The validity of the equation was confirmed for many materials and it applies to frequency shifts up to AF 0.4 Fq Note that equation 6.2 was only valid up to AF 0.02 Fq. And equation 6.3 only up to AF 0.05 Fq. 

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One must be aware of the limits of this technique. Since the assessment of Z depends on frequency shifts of two modes, any minimal shift leads to errors due to substantial mechanical or thermal stresses. It is not necessary to mention that under such circumstances the Z match technique, too, leads to similar errors. Nevertheless, the automatic Z value determination of the Z match technique is somewhat more reliable regarding occurrence of errors because the amplitude distribution of the (102) mode is asymmetric over the active crystal surface and that of the (100) mode is symmetric. 

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