DE19737880C1 - Complex elasticity or shear modulus evaluation method for thin polymer layers - Google Patents

Abstract

The elasticity or shear modulus of a thin layer is evaluated by attaching a number of identical electromechanical resonators to the thin layer, caused to oscillate at the characteristic frequency, with measurement of the effective acoustic impedance of the thin layer via at least 2 resonance frequencies. The effective acoustic impedance of a double layer provided by the measured layer and a layer with a known acoustic impedance is used with the previous measurement for providing the characteristic acoustic impedance of the measured layer, used for calculating the elasticity and shear modulus.

Description

The invention relates to a method and a device for determining the complex Elasticity or shear modulus of a thin layer using oscillators. With the procedure and the associated device, these material parameters can be determined without the Thickness of the thin layer is known. The invention is particularly useful for determining the complex shear module of thin polymer layers can be used, but not in their applicability limited to this application. In particular, the method is also for such materials can be used where the loss share (imaginary part) of the complex elastic or Shear module assumes comparable values compared to the real part.

In the description and the claims, the effective acoustic impedance Z _{eff of} a thin layer is to be understood as a quantity calculated according to equation 1 given below.

Accordingly, the characteristic acoustic impedance Z _{char of} a thin layer should be understood to mean a quantity calculated according to equation 2 given below. A layer is understood to be firmly adhering to an object, which can also be a layer, if the layer does not slide on the object.

A method for micro-weighing thin rigid layers has long been known, in which a Quartz crystal is the frequency-determining component of an oscillator circuit and the mass of one applied to the quartz crystal from the change in the natural frequency of the Quartz crystal is determined during the coating. This procedure is only for thin rigid layers designed, otherwise material properties of the thin layer influence the measurement result.

It is known that this disadvantageous influence of the material properties for the micro-weighing the determination of physical parameters of substances can be used. It is based on the The fact that the acoustic wave propagation in a medium in addition to geometric sizes how the layer thickness also depends on material parameters. The theoretical description the acoustic wave propagation in a multilayer arrangement with a piezoelectric Layer and one or more non-piezoelectric layers is e.g. B. by Martin (J. Appl. Phys. 75 (1993) 1319-1329). Both the  Derive the preconditions for micro-weighing as well as the influence of material parameters thinner Calculate layers on the electrical signal of a piezoelectric transducer.

US 4,312,228 describes a method and a device for detection with acoustic Surface waves are presented, with the physical parameters of substances such as fluids and Polymers, or their change, e.g. B. by temperature change, solvent release or absorption, or derived quantities, such as glass transition, crystallization or crosslinking, are determined can be. The method is based on the fact that the physical parameters of a substance, which is in contact with a surface acoustic wave element, the propagation conditions of the surface acoustic wave changes what changes in amplitude or phase shift the acoustic wave that is generated and detected by the surface wave element becomes. The ambiguity of the method is disadvantageous, since a large number of different ones physical parameters lead to similar changes in the surface acoustic wave can. In the case of determining the shear modulus of a thin layer, all must therefore other parameters are known and kept constant.

In SU 1078315 A, the elastic modulus of individual layers in a multi-layer arrangement by exciting a torsional oscillation and gradually removing the examined layers determined when measuring the natural frequency. With this method, mass and Dimension of the sample to be determined before each measurement. It is comparatively thick Layers.

A special form of use of the dependence of the propagation conditions acoustic Waves of physical parameters of substances is the determination of the viscosity of Liquid samples or derived quantities, such as the concentration of a component in one Liquid mixture (e.g. US 4,741,200, DE 29 08 469 A1)

US 4,741,200 describes a method and a device for determining the viscosity of Liquids with piezoelectric shear transducers are proposed. Because of the extreme shallow depth of penetration of a shear wave into a liquid, the thin, The liquid layer adjacent to the shear oscillator has been examined, which means that it is also acoustic effective thickness of the foreign layer is defined. The characteristic properties of the Scherschwingers depend on the density and viscosity of the adjacent liquid. The The method remains limited to determining the viscosity of liquids. This basic disadvantage also has the device according to DE 44 24 422, which for Determining the concentration of a mixture of at least two liquids is used, though  with this device the reproducibility of the measurements is significantly increased. The The device consists of a measuring quartz which can be wetted and sealed by the liquid mixture Thick shear vibrations is excited and its resonance frequency changes depending on the Concentration changes, and a reference quartz, which is in a reference liquid. The device uses the property of the mechanical thickness shear resonator, its Resonance frequency depending on the density and viscosity of the adjacent Change fluid.

In addition to US 4,312,228, e.g. B. in the publications by Martin (Martin SJ et al., 1991 Ultrasonics Symp. Proc., New York: IEEE, pp. 393-398) and Lucklum (Lucklum, R, et al., J. Phys. D: Appl Phys. 30 (1997) 346-356) showed that the material parameters of solid thin layers can also be determined with the aid of thickness shear transducers. In contrast to liquids, solid substances can have complex elasticity and shear modules, which can be split into a storage part (real part) and a loss part (imaginary part). Furthermore, the acoustically effective thickness of the thin solid layer is generally not determined by the depth of penetration of the acoustic shear wave, but by the geometric thickness of the thin layer. The swing properties of the thickness shear transducer are thus determined by the material properties and the thickness of the thin layer. If the thickness is generally insufficiently known, the method becomes ambiguous. The influence of these quantities of a single thin layer is generally summarized in the so-called effective acoustic impedance or surface impedance Z _{eff of} the thin layer according to equation 1:

ρ _s is the density of the thin layer, G _S = G ' _S + jG'' _S is the complex shear module of the thin layer with the storage module G _S ' and the loss module G _S "and d _S its thickness, ω is the angular frequency of the Dickenscherschwingers.

Z _char is the characteristic impedance of a substance and is defined by Equation 2:

Because of the transcendent nature of Z _eff , the complex shear module cannot be isolated. Therefore, the complex shear modulus must be determined by adapting theoretically calculated values for Z _eff to the experimental data. This calculation is complex and gives z. T. considerable deviations from reference values. These disadvantages affect the applicability of the method.

The statements made above using the example of a shear wave are also up Longitudinal waves in thin layers and thus on the determination of the complex Modulus of elasticity transferable.

The invention is therefore based on the object of a method and an apparatus for Determination of the real part and the imaginary part of the complex elastic or shear modulus to create thin layers by which these material parameters with sufficient accuracy determined without determining the thickness of the thin layer and without parameter adjustments can be.

This object is achieved by the features of claim 1 and claim 7 solved.

Characterized in that in the method according to the invention from the resonance frequencies of the oscillators, which occur in the electromechanical resonators vibrating with different phase positions, both the effective acoustic impedance of the thin layer Z _eff1 and the effective acoustic impedance of a double layer Z _eff12 , consisting of the thin one Layer and a second layer with known effective acoustic impedance Z _eff2 , a determination equation can be established for the characteristic acoustic impedance Z _{char of} the thin layer, which is independent of the thickness of the thin layer (Equation 3):

In equation 3 mean:
f1.1 resonance frequency of the oscillator 1 for the resonator coated with a thin layer,
f2.1 resonance frequency of the oscillator 2 for the resonator coated with a thin layer,
f1.12 resonance frequency of the oscillator 1 for the resonator coated with a double layer,
f2,12 resonance frequency of the oscillator 2 for the resonator coated with a double layer.

At the same time, the transcendent equation for the effective acoustic impedance (Equation 1) to derive the complex shear modulus. From the The method according to the invention thus has three advantages:

• 1. The need to know the thickness of the thin layer or the ambiguity of the by Lucklum (Lucklum, R, et al., J. Phys. D: Appl. Phys. 30 (1997) 346-356) The process with unknown thickness of the thin layer is eliminated, the complex one The shear modulus of the thin layer can be clearly determined from the characteristic impedance of the determine thin layer according to a generally known relationship (equation 2).
• 2. The equations for the real and imaginary part of the complex elastic modulus are algebraic functions, so there is no need for the described adjustment theoretically calculated values on measured values.
• 3. To determine the modulus of elasticity or shear of the thin layer, only the frequencies f _1.1 and f _{2.1 of} the electrical oscillators, which set the resonators coated with the thin layer in vibration, and the measurement of the frequencies are necessary f _1.12 and f _2.12 , which set the resonators coated with the double layer in vibration. The otherwise necessary, complex measurement of the electrical impedance of the electromechanical resonator is eliminated.

As electromechanical resonators, thickness shear vibrations are preferred excited piezoelectric quartz disks are used, which is the frequency determining element of the Quartz oscillators are and guarantee sufficient frequency stability. The frequency measurement can e.g. B. by simply counting those executed in a defined time interval Vibrations and digital processing take place.

In this case, the real and imaginary part of the complex shear modulus of the thin layer.

The frequencies f _1.1 , f _2.1 , f _1.12 , f _2.12 are determined either in succession or advantageously simultaneously, in that at least two resonators are coated identically only with the thin layer and are thus excited to oscillate by oscillators that these oscillate at a sufficiently different phase position, and at least two further resonators, which were coated identically to the first two with the thin layer and additionally with a second layer with known effective acoustic impedance, and likewise excited by oscillators to oscillate in a sufficiently different phase position will. The structure can be optimally realized with a 4-element array on a substrate. The resonant frequencies of the oscillators can be used to calculate the effective acoustic impedance from generally known equations of four-pole theory and suitable models (here: a piezoelectric element), from which, as described above, the complex shear parameters can be derived. The quartz parameters and the phase position at which the oscillators oscillate must be known.

The invention, including its mode of operation, is described below using an exemplary embodiment be explained in more detail that the determination of the complex shear modulus of a thin Polymer layer concerns.

As mechanical resonators, four oscillated at about 5 MHz in natural resonance Quartz crystals of approx. 2.5 cm in diameter are used. The thin approx. 1 µm thick polymer layer was applied identically to the resonators by using a spin coating a solution of the polymer in a suitable solvent and subsequently the Solvent was evaporated. In accordance with the method according to the invention the thickness of the polymer layer thus obtained was not measured.

According to the invention, a 6 nm thick layer of gold was then applied to two quartz crystals to form the double layer on the surface of the polymer layer. The effective acoustic impedance Z _{eff2 of} this second layer was calculated from material data and the thickness of the gold layer.

The crystals prepared in this way were then integrated into two identical oscillators, which worked at 0 ° or -40 ° phase rotation of the crystals, in a measuring cell with a controllable atmosphere, each heated to the measuring temperature, which in the described case was between -50 and 150 ° C lay, and the four resonance frequencies f _1.1 , f _2.1 , f _1.12 , f _{2.12 of} the oscillators measured. From the measured frequencies, the effective acoustic impedances Z _eff1 and Z _{eff12 were} calculated, and with the known effective acoustic impedance Z _{eff2 of} the layer of gold, the characteristic acoustic impedance Z _{char of} the thin polymer layer could be calculated using equation 3 without the thickness thereof was known.

Finally, the shear parameters sought could be separated from them according to the storage share and Loss share, can be determined.

Claims (8)

1. A method for determining the complex elastic or shear modulus of a thin layer, in which the thin layer is firmly adhered to one or more electromechanical resonators so that the layer is identical in terms of properties in the case of several electromechanical resonators, the resonators using electrical oscillators are continuously excited in their natural frequency by the following steps:

• 1. Determination of the effective acoustic impedance of the thin layer Z _eff1 from at least two resonance frequencies of oscillators which oscillate at sufficiently different, known phase positions, the frequency-determining element of which is a resonator coated with the thin layer,
• 2. Determination of the effective acoustic impedance of a double layer Z _eff12 , the double layer consisting of said thin layer and a second layer with sufficiently well known effective acoustic impedance Z _eff2 , which adheres firmly to the free surface of said thin layer at least during the measurement period is applied, from at least two resonance frequencies of oscillators oscillating at sufficiently different phase positions, the frequency-determining element of which is a resonator coated with the double layer,
• 3. The characteristic acoustic impedance Z _{char of} the thin layer mentioned is subsequently calculated from these values, from which the real part and / or the imaginary part of the complex elasticity or shear module of the thin layer is calculated by means of a known physical relationship.

2. The method according to claim 1, characterized in that for the simultaneous measurement of Frequency values of several oscillators are used, the frequency-determining element are electromechanical resonators, of which at least two are only with the thin Layer and at least two are coated with said double layer.   3. The method according to claim 2, characterized in that the frequency values f _1.1 and f _2.1 are measured by two oscillators, the frequency-determining element are each electromechanical resonators, which are coated only with the thin layer, and the frequency values f _{1 , 12} and f _2.12 are measured by two oscillators, the frequency-determining element of which are respectively electromechanical resonators which are coated with the double layer. 4. The method according to any one of the preceding claims, characterized in that the electromechanical resonators are operated in the same vibration mode and the Resonance frequencies are similar. 5. The method according to any one of the preceding claims, characterized in that the second layer of a thin rigid material or a liquid layer with a sufficient minimum thickness and the materials of the thin layer and the second Layer are not soluble in each other. 6. The method according to any one of the preceding claims, characterized in that the electromechanical resonators, preferably Dickenscherschwinger, z. B. piezoelectric Quartz disks with a resonance frequency between 500 kHz and 50 MHz. 7. The device for performing the method according to claim 1, characterized by a Arrangement for measuring the resonance frequencies of electromechanical resonators, those of electrical oscillators vibrating at sufficiently different phase positions are continuously excited in their associated natural frequency, the electromechanical resonators the frequency-determining element of the oscillator circuits are and are provided with the thin layer or the double layer. 8. The device according to claim 7, characterized in that the electromechanical Dickenscherschwinger resonators in a 4-element array, e.g. B. on one piezoelectric quartz substrate, with a resonance frequency between 500 kHz and 50 MHz, are.