WO2004072664A1 - Method and apparatus for measuring characteristics of materials with improved accuracy - Google Patents

Abstract

The invention relates to an apparatus and method for measuring thickness and deviations from the thickness of very thin conductive/non-conductive coatings on various non-conductive substrates. The apparatus (120) consists of an inductive coil (134) having specific parameters and miniature dimensions, an external AC generator (128), and a measuring instrument (130) for measuring output of the sensor (122). The invention is based on the principle that inductive coil of the sensor, active resistance (136) of the coil winding, inherent capacitance of the inductive coil, and the AC generator form a parallel oscillating circuit. The apparatus operates on very hit resonance frequencies, preferably within the range of 100 to 200 MHz, at which a capacitive coupling is established between the coil of the oscillating circuit and the thin films being measured. By measuring the parameters of the resonance oscillating circuit, it becomes possible to measure film thickness below 500 Angstroms.

Description

Patent Application of

Boris Kesil, Leonid Velikov, and Yuri Vorobyev for

METHOD AND APPARATUS FOR MEASURING CHARACTERISTICS OF

MATERIALS WITH IMPROVED ACCURACY

FIELD OF THE INVENTION

The present invention relates to the field of measurement of film thickness, more specifically, to measuring thickness of conductive films on various conductive substrates or of non-conductive films on various conductive substrates. In particular, the invention may find use in measuring thickness of coating films on semiconductor wafers, hard drive disks, or the like.

BACKGROUND OF THE INVENTION

There exists a great variety of methods and apparatuses used in the industry for measuring thickness of coating films and layers applied or laid onto substrates. These methods and apparatuses can be classified in accordance with different criteria. Classification of one type divides these methods into direct and indirect. An example of the direct method is measurement of a thickness in thin metal coating films by means of so-called X-ray reflectivity. One of these methods is based on a principle that X-rays and gamma rays are absorbed by matter. When a beam of rays passes through a material, the amount of the beam absorbed depends on what elements the material consists of, and how much of the material the beam has to pass through. This phenomenon is used to measure the thickness or density of a material. The advantage of measuring in this way is that the gauge does not have to touch the material it is measuring. In other words, in thickness measurement, the surface of a web or strip product will not be scratched. The instrument for this method is e.g., RMS1000 Radiometric System produced by Staplethome Ltd (UK). The instrument uses a suitable radiation source and one or more radiation detectors installed in a mechanical housing which also provides high quality radiological shielding. The source may be an X-ray tube or a radioactive source. The instrument also uses a set of beam-defining collimators and one or more radiation detectors. The detectors measure the radiation absorbed within the object or flow being measured and output of the signal data to a computer. For thickness gauging, the collimators usually define a single, narrow beam. This gives optimum spatial resolution.

A disadvantage of radiation methods is the use of X-ray or gamma radiation that requires special safety measures for protection of the users against the radiation. The instruments of this type are the most expensive as compared to metrological equipment of other systems.

Another example of direct measurement is a method of optical interferometry, described e.g., by I. Herman in Optical Diagnostics for Thin Film Processing", Academic Press, 1996, Chapter 9. Although the optical interferometry method produces the most accurate results in measuring the thickness of a coating film, it has a limitation. More specifically, for conductive films, to which the present invention pertains, this method is limited to measurement of extremely thin coating films which are thin to the extent that a nontransparent material, such as metal, functions as transparent. In other words, this method is unsuitable or is difficult to use for measuring conductive films thicker than 200 A to 500 A.

Another example of direct measurement methods is measuring thickness of a film in situ in the course of its formation, e.g., in sputtering, magnetron target sputtering, CVD, PVD, etc. These methods, which are also described in the aforementioned book of I. Herman, may involve the use of the aforementioned optical interferometry or ellipsometry. However, in this case measurement is carried out with reference to both the surface of the substrate and the surface of the growing layer. Therefore, this method is inapplicable to measuring-thickness of the film that has been already deposited.

In view of the problems associated with direct methods, indirect non-destructive methods are more popular for measuring thickness of ready-made films. An example of a well-known non-destructive indirect method used for measuring thickness of a film is the so-called "four-point probe method". This method is based on the use of four contacts, which are brought into physical contact with the surface of the film being measured. As a rule, all four contacts are equally spaced and arranged in line, although this is not a compulsory requirement. Detailed description of the four-point probe method can be found in "Semiconductor Material and Device Characterization" John Wiley & Sons, Inc., N.Y., 1990, pp. 2-40, by D. Schroder. The same book describes how to interpret the results of measurements. This method is classified as indirect because the results of measurement are indirectly related to the thickness of the film. It is understood that each measurement of electric characteristics has to correlated with the actual thickness of the film in each particular measurement, e.g., by cutting a sample from the object and measuring the thickness of the film in a cross-section of the sample, e.g., with the use of an optical or electron microscope. Nevertheless, in view of its simplicity, low cost, and convenience of handling, the four-point probe method is the most popular in the semiconductor industry.

However, the four-point method has some disadvantages. The main problem associated with the aforementioned four-point probe method is that in each measurement it is required to ensure reliable contact in each measurement point. This is difficult to achieve since conditions of contact vary from sample to sample as well as between the four pointed contact elements of the probe itself in repeated measurement with the same probe. Such non-uniformity affects the results of measurements and makes it impøssibleto perform precision calibration.

Known in the art are also methods for measuring film thickness with the use of inductive sensors. For example, US Patent 6,072,313 issued in 2000 to L. Li et al. describes in-situ monitoring and control of conductive films by detecting changes in induced eddy currents. More specifically, the change in thickness of a film on an underlying body such as a semiconductor substrate is monitored in situ by inducing a current in the film, and as the thickness of the film changes (either increase or decrease), the changes in the current are detected. With a conductive film, eddy currents are induced in the film by generating an alternating electromagnetic field with a sensor, which includes a capacitor and an inductor. The main idea of the apparatus of US Patent 6,072,313 consists in using a resistor and a capacitor in a parallel resonance circuit. The resonance is caused by means of an oscillator. The inductive coupling between the oscillation circuit and the Eddy current inducted in the coating is used for improving a signal/noise ratio and can be used for improving quality of measurements. In fact, this is a method well known in the radioelectronics for measuring under conditions of the electrical resonance. The above patent describes the aforementioned inductive method for measuring thickness of a film in chemical mechanical polishing (CMP).

A similar inductive method, which was used for measuring thickness of a slag, is disclosed in US Patent 5,781 ,008 issued in 1998 to J. Muller et al. The invention relates to an apparatus for measuring the thickness of a slag layer on a metal melt in a metallurgical vessel. The apparatus comprises a first inductive eddy current sensor which indicates the distance of the apparatus from the metal melt as it is moved toward the melt. A second sensor detects when the apparatus reaches a predetermined distance relative to or contacts the slag layer and triggers the inductive eddy-current sensor when sueh distance is attained. The sensors are arranged in a predetermined spatial relation, and the thickness of the slag layer is determined by an evaluation device, which analyzes the received signals. The apparatus permits measurement of the thickness of the slag layer without the need of additional equipment (e.g. mechanical lance movement or distance measurement).

The method and apparatus of US Patent 5,781 ,008 relate to macro- measurements of thick layers, and the sensors used in the apparatus of this invention are inapplicable for measuring thickness of thin-film coatings on such objects as semiconductor wafers and hard-drive disks. Furthermore, once the second sensor has detected that the apparatus reached a predetermined distance relative to or contacts the slag layer, this distance remains unchanged during the measurement procedure. This condition is unacceptable for measuring thickness of a thin film with microscopic thickness, which moves relative to the sensor, e.g., for mapping, i.e., for determining deviations of the thickness over the substrate. In order to understand why the use of known eddy-current sensor systems utilizing a measurement eddy-current sensor and a proximity sensor cannot be easily and directly applicable to measurement of microscopically-thin film coatings on conductive or non-conductive substrates, let us consider constructions and operations of the aforementioned known systems in more detail.

Generally speaking, an inductive sensor is based on the principle that in its simplest form an inductive sensor comprises a conductive coil, which is located in close proximity to a conductive film to be measured and in which an electric current is induced. The conductive film can be considered as a short-circuited virtual coil turn with a predetermined electrical resistance. Since a mutual inductance exists between the aforementioned conductive coil and the virtual coil turn, an electric current is generated in the virtual coil turn. This current is known as eddy current or Foucault current. Resistance of the virtual coil turn, which depends on the material of the conductive film and, naturally, on its thickness, influences the amplitude of the alternating current induced in the virtual turn. It is understood that the amplitude of the aforementioned current will depend also on the thickness of the conductive film.

However, realization of a method and apparatus based on the above principle in application to thin films is not obvious. This is because such realization would involve a number of important variable parameters which depend on a specific mode of realization and which are interrelated so that their relationships not always can be realized in a practical device.

In order to substantiate the above statement, let us consider the construction of an inductive sensor of the aforementioned type in more detail. Fig. 1 is a schematic view of a known inductive sensor used, e.g., for positioning an inductive sensor 22 relative to the surface S of an object 24. Let us assume that the surface S of the object 24 is conductive. The inductive sensor comprises an electromagnetic coil 26 connected to an electronic unit 28, which, in turn, is connected to a signal-processing unit 30. The latter can be connected, e.g., to a computer (not shown). The electronic unit 28 may contain a signal oscillator (not shown), which induces in the electromagnetic coil 26 an alternating current with a frequency within the range from several kHz to several hundred KHz. In Fig. 1 , symbol D designates the distance between the electromagnetic coil 26 and the surface S.

In a simplified form, the sensor of Fig. 1 can be represented by a model shown in Fig. 2. In this model, L1 designates inductance of the electromagnetic coil 26; R1 designates resistance of the coil 26; L2 designates inductance of the aforementioned virtual coil turn 27 (Fig. 1 ); and R2 is electrical resistance of the aforementioned virtual coil turn 27. M designates mutual induction between L1 and L2.

It can be seen from the model of Fig. 2 that the amplitude of current I generated in coil 26 will depend on R1, L1, L2, R2 and M. It is also understood that in this influence M is the most important parameter since it directly depends on the distance D (Fig. 1 ) from the inductive sensor 22 to the surface S.

Fig. 3 is further simplification of the model of Fig. 2. Parameters L and R are functions that can be expressed in terms of L1 , L2, M, R1 , and R2. Therefore, as shown in Fig. 3, these parameters can be considered as functions L(D) and R(D), where D is the aforementioned distance (Fig. 1). The model of Fig. 3 can also be characterized by a quality factor Q, which is directly proportional to the frequency of the current in the sensor coil 26, to inductance of the sensor of Fig. 3, and is inversely proportional to a distance D (Fig. 1) from the sensor coil 26 to the surface S. The higher is the value of Q, the higher is stability of the measurement system and the higher is the measuring accuracy. Thus it is clear that in order to achieve a higher value of Q, it is necessary to operate on higher frequencies of the alternating currents in the inductance coil 26. Analysis of relationships between Q, L, and R for a fixed distance D was made by S. Roach in article "Designing and Building an Eddy Current Position Sensor" at http://www.sensormag.com/articies/0998/ edd0998/main.shtml. S. Roach introduces an important parameter, i.e., a ratio of D to the diameter of the sensor eøii-26,^nd shows that R does not practically depend on the above ratio, while the increase of this parameter leads to the growth in L and Q. When distance D becomes equal approximately to the diameter of the coil 26, all three parameters, i.e., L, Q, and R are stabilized, i.e., further increase in the distance practically does not change these parameters. In his important work, S. Roach generalized the relationships between the aforementioned parameters and showed that, irrespective of actual dimensions of the sensor, "the rapid loss of sensitivity with distance strictly limits the range of eddy current sensor to about the coil diameter and constitutes the most important limitation of this type of sensing".

The impedance of the coil also depends on such factors as film thickness, flatness of the film, transverse dimensions, temperature of the film and coil, coil geometry and DC resistance, operating frequency, magnetic and electric properties of the film, etc.

As far as the operating frequency of the inductive coil is concerned, the sensor possesses a self-resonance frequency, which is generated by an oscillating circuit formed by the power-supply cable and the capacitor. As has been shown by S. Roach, in order to improve sensitivity, it is recommended to increase the quality factor Q and hence the frequency. However, the sensor must operate on frequencies at least a factor of three below the self-resonant frequency. Thus, practical frequency values for air core coils typically lie between 10 kHz and 10 MHz.

The depth of penetration of the electromagnetic field, into the conductive film is also important for understanding the principle of operation of an inductive sensor. It is known that when an alternating electromagnetic field propagates from non- conductive medium into a conductive medium, it is dampened according to an exponential law. For the case of propagation through the flat interface, electric and magnetic components of the alternating electromagnetic field can be expressed by the following formulae:

E = Eo exp (-αx)

H = Ho exp (-αx),

where α = (πfμσ)^1/2, f is oscillation frequency of the electromagnetic field, σ is conductivity of the medium, and μ = μo = 1.26 x 10^"6 H/m (for non-magnetic materials).

Distance x from the interface, which is equal to

x =_δ = 1/_α = 1/(_πf_μσ)^1/2 (1)

and at which the amplitude of the electromagnetic wave decreases by e times, is called the depth of penetration or a skin layer thickness. Based on formula (1 ), for copper on frequency of 10 kHz the skin depth δ is equal approximately to 650 μm, on frequency of 100 kHz to 200 μm, on frequency of 1 MHz to 65μm, on frequency of 10 MHz to 20 μm, on frequency 100 MHz to 6.5 μm, and on frequency 10 GHz to 0.65 μm.

The above values show that for the films used in the semiconductor industry, which are typically with the thickness on the order of 1 μm or thinner, the electromagnetic field can be considered practically as uniform. This is because on any frequency in the range from 10 KHz to 10 MHz the electromagnetic waves begin to dampen on much greater depth than the thickness of the aforementioned films. It is only on frequencies substantially greater than 100 MHz (e.g., 10 GHz), the depth of penetration of the electromagnetic fields becomes comparable with the thickness of the film.

Similar trend is observed in the films made from other metals, where the skin layer is even thicker because of lower conductivity. At the same time, deviations from uniformity in the thickness of the conductive coating films used in the semiconductor industry, e.g., copper or aluminum layers on the surface of silicon substrates, should not exceed 5%, and in some cases 2% of the average thickness of the layer. In other words, the deviations should be measured in hundreds of Angstroms. It is understood that conventional inductive sensors of the types described above and used in a conventional manner are inapplicable for the solution of the above problem. Furthermore, in order to match conditions of semiconductor production, such sensors must have miniature constructions in order to be installed in close proximity to the measurement site. The distance between the measurement element of the inductive sensor and the surface of the film being measured also becomes a critical issue. Due to high sensitivity, the sensor becomes very sensitive to the influence of the environment, especially, mechanical vibrations, variations in temperature, etc.

In their previous U.S. Patent No. 6,593,738 issued on July 15, 2003, the applicants made an attempt to solve the above problems by developing a method and apparatus for measuring thickness and deviations from the thickness of thin conductive coatings on various substrates, e.g., metal coating films on semiconductor wafers or hard drive disks. The thickness of the films may be as small as fractions of microns. The apparatus consists of an inductive sensor and a proximity sensor, which are rigidly interconnected though a piezo-actuator used for displacements of the inductive sensor with respect to the surface of the object being measured. Based on the results of the operation of the proximity sensor, the inductive sensor is maintained at a constant distance from the controlled surface. Variations in the thickness of the coating film and in the distance between the inductive sensor and the coating film change the current in the inductive coil of the sensor. The inductive sensor is calibrated so that, for a predetermined-objeGt-with a predetermined meta eoating and thickness of the coating, variations in the amplitude of the inductive sensor current reflect fluctuations in the thickness of the coating. The distinguishing feature of the invention resides in the actuating mechanism of microdisplacements and in the measurement and control units that realize interconnection between the proximity sensor and the inductive sensor via the actuating mechanism. The actuating mechanism is a piezo actuator. Measurement of the film thickness in the submicron range becomes possible due to highly accurate dynamic stabilization of the aforementioned distance between the inductive sensor and the object. According to one embodiment, the distance is controlled optically with the use of a miniature interferometer, which is rigidly connected to the inductive sensor. According to another embodiment, the distance is controlled with the use of a capacitance sensor, which is also rigidly connected to the inductive sensor.

However, the sensor disclosed in the aforementioned patent could not completely solve the problems associated with accurate measurement of super- thin films, e.g., of those thinner than 500 Angstroms. This is because the construction of the aforementioned sensor is limited with regard to the range of operation frequencies, i.e., the sensor cannot be use in frequencies exceeding 30 MHz. Furthermore, the aforementioned sensor requires the use of a complicated distance-stabilization system. The above problems restrict practical application of the method and apparatus of U.S. Patent No. 6,593,738 for measuring thickness of very thin films and deviations from the thickness in the aforementioned films. Furthermore, it is obvious that the aforementioned method and apparatus do not allow thickness measurement of non-conductive films. The sensor has relatively large overall dimensions and comprises a stationary measurement instrument.

Another disadvantage of the sensor of the aforementioned application is that it is very sensitive to the distance between the sensor and the film. This requirement dictates the use of expensive and complicated distance-measurement means such as microinterferometers or microscopes.

Furthermore, it is understood that for measuring a 1000 Angstroms-thick film, even with 5% accuracy, the sensor should depict thickness deviations at least within 50 Angstroms. It is also understood that improvement in the accuracy of measurement of super-thin films with specific electromagnetic sensors can be achieved by increasing the frequency of electromagnetic radiation (up to microwave frequency) utilized by such sensors for testing. An example of such a sensor is the one disclosed in U.S. Patent No. 5,334,941 issued in 1994 to R. King. Although the aforementioned sensor is described in application for measuring complex impedance characteristics of the surface, one can assume that such a resonance sensor can be used also for measuring thickness of thin films. The sensor system consists of a microwave source with a frequency that can be swept within a limited range, a radio-reflectometer bridge, a microwaveguide line that connects the reflectometer bridge with the resonance sensor, and a ratio meter or scalar network analyzer connected to the microwave source and the radio-reflectometer bridge for visual presentation and data monitoring of the test operation. The sensor has a special slit-like structure, which comprises a metal microstrip dipole resonator etched on the surface of a dielectric substrate, which is bonded to a copper ground. This dipole resonator is electromagnetically driven by mutual inductive coupling to a short nonresonant feed slot formed in the ground plane. The slot is driven by a coaxial feed line or a microstrip feed line extending from a swept microwave frequency source, which excites the incident wave. Measurement of the resonant frequency and input coupling factor determines small changes in real and imaginary parts of the dielectric constant or in conductivity for highly conductive materials, such as metals.

In spite-of the fact that the microwave reflection resonator sensor described in U.S. Patent No. 5,334,941 is a device which after a special calibration procedure may appear to be highly efficient and accurate for measuring sufficiently thin films (down to 1000 Angstroms), this sensor may operate only in physical contact with the test object, which is not always permitted in the semiconductor industry where the use of contactless test sensors is preferable.

Thus, an inexpensive, simple, high-accurate and efficient contactless microwave resonance sensor system suitable for measuring film thicknesses below 500 Angstroms is unknown.

SUMMARY OF THE INVENTION

It is an object of the invention to provide an apparatus and method for measuring thickness and thickness fluctuation in coating films, in particular in very thin films, e.g., below 500 Angstroms. It is another object to provide the method and apparatus for measuring thickness of very thin conductive films on a non- conductive substrate, or of non-conductive films in conductive substrates. Still anther object is to provide a sensor of the aforementioned type, which is simple in construction and can be produced in the form of a portable miniature device which can be mounted on platforms of optical measurement instruments such as interferometers, spectrophotometers, ellipsometers, or the like. Still another object is to provide an apparatus of the aforementioned type, which is less sensitive to a distance between the sensor and the surface of the film being measured. It is another object to provide a method and apparatus for contactless measurement of film thicknesses below 500 Angstroms by means of a microwave resonance sensor.

According to one embodiment, the invention provides an apparatus for measuring thickness and deviations from the thickness of very thin conductive coatings on various non-conductive substrates, or of very thin non-conductive coatings on conductive substrates. The apparatus consists of an inductive coil having specific parameters, an external AC generator operating on frequencies, e.g., from 50 MHz to 2.5 GHz, preferably from 100 MHz to 200 MHz, and a' measuring instrument, such as an oscilloscope, voltmeter, etc. for measuring output of the sensor. The coil has miniature dimensions. The invention is based on the principle that inductive coil of the sensor, active resistance of the coil winding, capacitance of the inductive coil (or a separate capacitor built into the sensor's circuit), and the aforementioned AC generator form an oscillating circuit. The main distinction of the sensor of the invention from all conventional devices of this type is that it operates on very high resonance frequencies or on frequencies close to very high resonance, preferably within the range of 100 to 200 MHz. In order to maintain the aforementioned high frequency range, the oscillating circuit should have specific values of inductance L (several nano- Henries) and capacitance C (several pico-Farades), and in order to provide accurate measurements, the Q-factor on the above frequencies should exceed 10. It has also been found that on such frequencies the inductive-type coupling that exists in conventional Eddy-current sensors for measuring film thickness acquires a secondary meaning, and that the primary role is transferred mainly to a capacitive coupling between the coil of the oscillating circuit and the thin films being measured. This capacitive coupling determines new relationship between the parameters of the film, mainly the film thickness, and parameters of the resonance oscillating circuit. By measuring the parameters of the resonance oscillating circuit, it becomes possible to measure film thickness below 500 Angstroms.

In accordance with another embodiment, the invention provides an apparatus that comprises a special resonator unit in the form of an open-bottom cylinder, which is connected to a microwave swept frequency microwave source via decoupler and a matching unit installed in a waveguide that connects the resonator unit with the microwave source. The microwave generator is fed from a power supply unit through a frequency modulator that may sweep the frequency of microwaves generated by the microwave generator. All the controls can be observed with the use of a display, such as, e.g., a monitor of a personal computer, which may be connected to the microwaveguide line, e.g., via a directed branched waveguide line for directing waves reflected from the resonator, via a reflected wave detector, an amplifier, a synchronous detector, an A/D converter, and a digital voltmeter. A feedback line is going from a direct wave detector, which is installed in a line branched from the microwaveguide between the decoupler and the matching unit, to the power supply unit. The operation resonance frequency of the resonator sensor unit should be somewhere within the range of swept frequencies of the microwave generator.

During operation of the apparatus, the thin metal film F, which is to be measured, does not contact the end face of the open bottom of the cylindrical resonator sensor unit and functions as a bottom of the cylindrical body. In designing the cylindrical resonator, it is necessary to choose inner diameter d and the inner length a of the cylindrical body in such a ratio that excludes generation, near the resonance frequency, of modes other than the basic operation mode. Another design requirement of the resonator dimensions is to provide the highest possible Q-factor.

In operation, the microwave generator generates electromagnetic waves in a certain sweeping range that induces in the resonator sensor unit oscillations on the resonance frequency with a Q-factor on the order of 10⁴ or higher. A distinguishing feature of the resonator of the invention is that the design parameters of the resonator unit allow to achieve the aforementioned high Q- factor without physical contact of the sensor unit with the film to be tested. As the surface of the film to be measured constitutes the inner surface of the resonator unit, even a slightest deviation in conductivity will exert a significant influence on the Q-factor. The Q-factor, in turn, defines the height of the resonance peak. As the conductivity directly related to the film thickness, it is understood that measurement of the film thickness is reduced to measurement of the resonance peak amplitudes. This means that superhigh accuracy inherent in measurement of the resonance peaks is directly applicable to the measurement of the film thickness or film thickness deviations.

A common feature of the apparatus and methods of the present is that they are based on so-called Resonance Sensor Technology (hereinafter referred to as RST) developed by the applicants. The RST is characterized by the following features: 1 ) the measurement system of an RST sensor, the objects being tested form an indispensable part of the resonance oscillation measurement circuit; 2) in contrast to the majority of known inductive sensors, the RST sensors operate on resonance conditions; 3) there exist several resonance conditions, and the RST sensors operate mainly under conditions of complete resonance; 4) under conditions of complete resonance, the Q-factor of the system "sensor-object" may be significantly higher than the Q-factor of a single inductive sensor.

Incorporation of the aforementioned four features into the structure of the measurement system results in significant improvement of sensitivity and repeatability of measurements and makes it possible to measure characteristics of the film in a wide ranges of thicknesses from hundreds Angstroms to several tens of microns.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a schematic view of a known inductive sensor.

Fig. 2 is an equivalent electric circuit of the sensor of Fig. 1.

Fig. 3 is a simplified equivalent electrical circuit of the sensor of Figs. 1 and 2.

Fig. 4 is a schematic diagram of the apparatus of the invention for measuring thickness of a thin film.

Fig. 5 is a side view of the apparatus of the invention illustrating arrangement of a sensor with respect to the object being measured.

Fig. 6 is an equivalent electric circuit of the apparatus of the invention.

Fig. 7 is a block diagram of the apparatus of the invention with measurement and control units. Fig. 8 is one embodiment of an electronic circuit of the apparatus of the invention.

Fig. 9 is another embodiment of an electronic circuit of the apparatus of the invention.

Fig. 10 is a top view that illustrates the sensor of the apparatus of the invention in the form of a flat spiral pattern on the end face of the probe.

Fig. 11 is a side view that illustrates the sensor of the apparatus of the invention in the form of a helical body on the end of the probe.

Fig. 12 is a general block-diagram view of the apparatus according to the second embodiment based on the use of a cylindrical microwave resonator.

Fig. 13A is a schematic vertical sectional view of the cylindrical resonator unit of Fig. 12.

Fig. 13B is sectional view of the resonator unit along lines XIIIB-XIIIB of Fig. 13A.

Fig. 14A is a vertical sectional view of a modified resonator unit of the invention.

Fig. 14B is a sectional view of the modified resonator unit along the line XIVB- XIVB of Fig. 14 A.

Fig. 15A is a graph that shows dependence of the output power of the klystron from the voltage applied to the klystron reflector in the apparatus of the invention. Fig. 15B is a graph that illustrates dependence of frequency deviation from a certain generation frequency that corresponds to a constant voltage on the klystron reflector.

Fig. 15C shows an image that corresponds to the signal from the directed diode in the apparatus of the invention.

Fig. 16 illustrates a system for stabilization of the gap between the lower end face of the resonator unit and the film to be measured in the apparatus of the invention, where the resonator unit and the film form plates of a capacitor.

DETAILED DESCRIPTION OF THE INVENTION

Figs. 4-11. Embodiment of the Device with Resonance Sensor for Operation on Frequencies up to Few GHz

A schematic diagram of an apparatus of the invention for measuring thickness of a thin film is shown in Fig. 4. The apparatus, which in general is designated by reference numeral 120, consists of a sensor 122 connected in parallel with an amplifier 124 connected to a power source 126, a high-frequency AC generator 128 with an amplitude modulator M, and a measurement unit 130. The sensor 122 comprises a resonance oscillating circuit formed by a capacitor 132, an inductance 134, and a resistor 136 connected in series. The inductance comprises the winding of the inductive coil. Although the capacitor 132 and resistor 136 are shown as separate physical element, they may comprise the inherent capacitance and resistance of the inductive coil 136. The aforementioned oscillating circuit may also be characterized by a specific inherent resonance frequency. The circuit that contains the amplifier consists of the amplifier 124 and the power supply 126 and is connected in parallel across the ground G and the sensor 122. The circuit that consists of the high-frequency AC generator 128 with the amplitude modulator M is connected in parallel between the ground G and the sensor 122.

The measurement unit 130 may consist of a voltmeter 140 included into the circuit of the apparatus as shown in Fig. 4.

In an actual construction of the apparatus of the invention, which is shown in Fig. 5, the inductive coil 136, the capacitor 132, and the resistor 136, which may be represented by the capacitance and the resistance of the coil, respectively, may be built into a thin rod that projects outer the sensor's body 142. Reference numeral 144 designates a mounting frame that supports the sensor's body 142. Position of the sensor body 142 relative to the mounting frame can be adjusted by means of a micro-adjustment mechanism, e.g., a screw 146. Accuracy of micro-adjustment (about 5 microns or less) for positioning the tip of the rod 122 with respect to the surface of the film F with the use of the screw 146 is sufficient for accurate measurements. This is because the distance D between the tip of the rod 122 and the surface of the film is about 100 to 300 microns and because, as has been mentioned above, the capacitance between tip of the probe 122 and the surface of the film F is inversely proportional to the distance between the both. Respectively, the electrical resistance for alternating current through the gap D between the tip of the probe 122 and the surface of the film F will drop proportionally to a decrease in the distance D.

It is understood that the schematic presentation shown in Fig. 5 is given only as an example and that in view of miniature dimensions of the sensor 122 it can be held by any appropriate holder that can be stationary and rigidly fixed in place. For better understanding the principle of the present invention, it would be advantageous to consider some theoretical issues incorporated into the apparatus of the invention.

In the range of frequencies in which the apparatus of the invention operates (hundreds of MHz), a system "sensor/film" can be represented by an equivalent electric circuit 147, which is shown in Fig. 6 and which is essentially different from the electrical equivalent circuit of a conventional Eddy-current sensor shown in Fig. 3. The resonance oscillating circuit 147 of Fig. 6 comprises a typical parallel resonance oscillating circuit with losses. The resonance circuit 147 of Fig. 6 consists of an inductance in the form of a coil 148, an active resistance 150 of the coil 148, a capacitor 152, which may comprise capacitance of the coil 148 and of the aforementioned gap between the tip of the probe 122 and the surface of the film F, a high-frequency AC generator, and the active resistance R2 on the portion of the film F which is included into the resonance oscillating circuit shown in Fig. 6. The inherent capacitance of the coil 148 may have a value from fractions of a picoFarade to several pico-Farades. With the distance D on the order of hundreds of microns, the capacitance between the sensor and the film may be on the same order as, or even higher than, the inherent capacitance of the inductive coil 148. Therefore, the resonance of the oscillating circuit 147 of Fig. 6 will to a large extent be determined by the capacitance in the "sensor/film" system, as well as by the resistance of the resistor R₂, i.e., by the electrical resistance of the film F.

It is also appreciated that the resistance R₂ of the part of film F which passes the current depends on the thickness of the film F. Therefore the thickness of the film can be expressed in terms of the resonance frequency and the Q-factor of the resonance oscillating circuit of Fig. 6. Let us consider how the frequency characteristics of the aforementioned oscillating circuit 147 depend on the loss of energy in the active elements of the circuit 147. The resonance frequency of the resonance oscillating circuit shown in Fig. 6 is determined with the use of the complex conductivity equation:

Y = YRL + YRC = 1/( ι + jωL ) + 1/(R₂ + j/ωC ).

This equation can be converted into the following form:

Y= (Ri - jωL)/[R²ι + (ωL)²] + ωC(R₂ωC + 1 )/[( R₂ωC)² + 1] = α - jβ

The imaginary part of the obtained expression determines reactive conductivity β = ωL/[ R²ι + (ωL)²] - ωC/[( RzωC)² + 1].

As is known, the resonance frequency may exist under condition β = 0, or ωL/[ R²ι + (ωL)²] - ωC/[( R₂ωC)² + 1] = 0.

Based on simple calculations, one can obtained the resonance frequency as follows:

ω₀ = 1/(LC)^1/2 x [(I - R²iC)/(l - R² ₂C)]^1/2 (1 a)

Analysis of equation (1a) allows us to make an important conclusion, i.e., at relatively high values of Ri or R₂, or of both, non-resonance condition may occur. However, the value of R-i may be reduced by selecting a material and thickness of the probe wire that determine inductance L. Within the range of operating parameters of the resonance circuits (L, C, ω), the values R₂ that could provide resonance-free conditions were not experimentally obtained. It is understood that R₂ can be easily derived from equation (1 ) as follows: R² ₂ = L/C + (R²ι/LC - 1 /C²)/ ω₀ ² (2).

All values located in the right side of equation (2) can be measured. However, measurement of induced capacitance C may present a problem. Therefore, in order to simplify determination of R₂, it would be advantageous to precalibrate the circuit, the more so, it is not exactly known how R₂ is related to the actual thickness of the film being measured. The calibration process may be carried out by measuring R₂ in films of different thickness but of the same material, e.g., by means of the aforementioned X-ray analysis.

A block diagram of the apparatus of the invention for measuring the thickness of a thin film, e.g., thinner than 500 Angstroms by the method of the invention is shown in Fig. 7. The system consists of the following main units: the probe 122 (the inherent capacitance and active resistance of the coil itself are not shown) with the coil 148, which is connected with an amplifier 154, which, in turn, is connected to a demodulator 156. The demodulator 156 is coupled to an audiofrequency amplifier 58, and the latter is connected to the measurement unit 130. One of the main parts of the system of Fig. 7 is a carrier-frequency generator 160 (e.g., from 100 to 300 MHz). This can be a variable-frequency or a constant- frequency generator for generating frequency that corresponds to the resonance frequency of the oscillating circuit of Fig. 6. Reference numeral 162 designates an audio-frequency generator for a variable frequency, e.g., of 400 Hz to 25 KHz. The output signals of both generators 160 and 162 are mixed in a signal modulator 164, which excites an AC current in the coil 148 of the sensor via appropriate electric circuits (not shown).

Examples of principle electronic circuits of the apparatus of the invention are shown in Fig. 8 and Fig. 9. The circuit of Fig. 8 is based on measuring direct current obtained by rectifying harmonic or non-harmonic audio signals in the aforementioned range of 400 Hz to 25 KHz and by amplifying the obtained DC signal with the use of an amplifier 165 (OP-77). This signal is then measured by means of an analog or digital voltmeter 167 with subsequent processing on a computer (not shown). In the generator 162, the sinusoidal signals of the frequency to be measured are generated by unit 168 (ICL8038). In the circuit of Fig. 8, the main units of the block diagram of Fig. 7 are shown by broken-line blocks and are designated by the same reference numerals. The unit formed by the generator of the carrier frequency and the modulator (160, 164), and the demodulator 156 are built on the same transistors 170a and 170b (2N2222A). The RF amplifier 154 utilizes the transistor 172 (2SC1923). The audio-frequency amplifier 158 & builtαn the use of ajohip 174j(L 3fifi).

The circuit of Fig. 9 in general is similar to the circuit of Fig. 8 but is based on measuring harmonic or non-harmonic audio signals in the aforementioned range of 400 Hz to 25 KHz with the use of an oscilloscope or oscilloscope-computer 166 with digital data processing of the signals. Those units and elements of circuits of Figs. 8 and 9, which are identical, are designated by the same reference numerals with an addition of symbol "a" for elements of Fig. 9. In addition to unit 168 (ICL8038) of the circuit of Fig. 8, the circuit of Fig. 9 may use a pulse generator 176 (SA555P). Furthermore, the unit formed by the generator of the carrier frequency and the modulator (160a, 164a) is based on the use of two transistors.

Fig. 10 illustrates an example of the sensor 122. The coil 148 of the sensor is formed by the methods of submicron lithography in the form of a flat spiral pattern on the end face of the probe of the sensor 122. The gaps between the turns and the thickness of the turns in the spiral pattern may vary from 0.1 micrometer to several micrometers. Resistance Ri (Fig. 6) of the sensor is determined by the number of turns and may be on the order of several Ohms. The number of turns may vary, e.g., from 1 to 50. Inductance L (Fig. 6) of the sensor may vary, e.g., from 1 nano-Henry to 200 nano-Henries. A preferable material for the coil 148 is gold.

Fig. 11 shows another embodiment of the sensor 122. The coil 148a of this sensor has a cylindrical helical shape. The diameter of the coil may be, e.g., with the range of 0. 3 to 3 mm, and the height of the coil may vary, e.g., from 0.5 to 3 mm. The coil can be made from a copper wire having a diameter not exceeding 10 micrometers.

The apparatus of.lne embodiment shown in Fig, 4-11 operates as follows. First the sensor 122 (Fig. 5) is calibrated by fixing it with respect to the reference film F_R SO that a gap D within the range of 10 to 100 micrometers is established between the coil 148 (148a) (Figs. 10 and 11 ) and the surface of the film F_R. The parameters of the reference film F_R (thickness, material, etc.) are known. The probe 122 is moved with the use of the micro-adjustment mechanism 146 until an appropriate direct current signal is obtained on the output of the analog or digital voltmeter 167 (Fig. 8) or until the characteristic oscillogram will be obtained on the oscilloscope 168a (Fig. 9). The calibration curve plotted for amplitude versus the film thickness (or another characteristic parameter such as a dielectric constant) is obtained for films of different thickness. The resonance oscillagram of the same type is then established for the film F to be measured, and the thickness of the film is determined by measuring, e.g., the amplitude of the signals on the oscillogram. Then the results of measurements are compared with the oscillogram obtained on the reference film. For measuring deviations from the film thickness uniformity, the aforementioned procedure is repeated in different measurement points. The case described above related to measurement of thickness in a conductive thin film on a nonconductive substrate. However, the apparatus and method of the invention of this embodiment are equally applicable to measurement of thickness in a nonconductive film on a conductive substrate. In this case, calibration is carried out on a number of identical conductive substrates of the same thickness which are coated with dielectric films having different thickness. The thickness of the thin dielectric films on the conductive substrate is determined, e.g., in terms of C-V characteristics, or with the use of an ellipsometer, spectrophotometer, or the like. The same specimens are used for measuring resonance frequency and Q-factor by the apparatus of this embodiment under the following conditions: the distance D between the sensor winding 148 and t e surface of the conductive substrate with and without the dielectric coating film. These measurements are carried out on the same conductive substrates and dielectric films as in the aforementioned measurements performed by the apparatuses and methods other than in the present embodiment (ellipsometeric, spectrophotometric measurements, etc.). Relationships are then established between the values of the resonance frequency and Q-factor and corresponding thicknesses of the dielectric films. The thickness of a dielectric coating on a conductive substrate of a product, which has to be tested, is then determined by measuring at least the resonance frequency of the target object. As can be seen from formula (1a) given above, the resonance frequency depends on the capacitance C in the gap between the inductance of the sensor winding 148 and the surface of the conductive body, i.e., the conductive substrate or film. In other words, by measuring the aforementioned capacitance C, one can measure the thickness of a dielectric coating on a conductive film by using the calibration procedure described above.

Furthermore, the apparatus of the invention is suitable for measuring characteristics of materials of object and films other than thickness. For example the principle of the invention is applicable for measuring characteristics of a material such characteristics as a surface electrical resistance, a dielectric constant, ,and a coefficient of magnetic permeability of the films and bulk materials.

Figs. 12-16. Embodiment of the Device with Resonance Sensor for Operation on Freguencies from Few GHz to 120 GHz

Fig. 12 is a general block-diagram view of the apparatus according to the second embodiment based on the use of a cylindrical microwave resonator. The apparatus, which as a whole is designated by reference numeral 200, will be described in general in order to show main components and their interconnections, and then the main units will be described separately in more detail. It should be understood that the specific components and their arrangement shown in Fig. 12 represent only one possible example of the apparatus, which can be embodied in a variety of other acceptable modifications.

The main unit or heart of the apparatus is a cylindrical microwave resonator unit 222, which functions as a film-thickness sensor unit for measuring the thickness of a thin film F₂ placed on a non-conductive substrate SB. The resonator unit 222 comprises a cylindrical body with one end 224 (which faces the film F₂) open and another end covered by a membrane 226 with an opening 228 for connection of one end of a microwaveguide line 230. The opposite end of the microwaveguide line 230 is connected to a microwave generator 232, e.g., a Klystron-type microwave generator or a Gunn-type microwave diode, via a matching unit 234 and an isolator or decoupling unit 236. The function of the microwave generator is to generate microwave power on a sweeping microwave frequency for transmission through a microwaveguide line 230 to the cylindrical microwave resonator unit 222, while the decoupling unit 236 prevents penetration of the waves reflected from the cylindrical microwave resonator unit 222 to the microwave generator 232.

A wavelength measuring device 238 may be branched by means of a branched waveguide 240 from the microwaveguide line 230 on a section thereof between the decoupling unit2 36 and the matching unit 234.

The microwave generator 232 is fed from a power supply unit 242 through a frequency modulator 244 that may sweep the frequency of microwaves generated by the microwave generator 232.

All the controls can be observed with the use of a dispjay, such as, e.g., a monitor 246 of a personal computer which is connected to microwaveguide line 230 via a directed branched waveguide line 248 for directing waves reflected from the resonator unit 222, via a reflected wave detector 251, an amplifier 250, a synchronous detector 252, an A/D converter 254, and a digital voltmeter 256 to the monitor 246.

The apparatus is also provided with an oscilloscope 258. The modulator 244 is connected to the synchronous detector 252 through a phase-shifting decoupling unit 262. A microwaveguide line 264 with a detector 266 is branched from the waveguide line 230 on a portion thereof between the matching unit 234 and the decoupling unit 236 in order to supply the detected signal of the microwave generator 232 to an oscilloscope 258 for signal control and through a feedback line 237 to the power supply unit 242 for stabilization of frequency, if necessary. The line 230 contains a microwave-length detector 260, which is connected to a wavelength measuring device 238 for measuring the wavelength of the microwaves generated by the generator 232 and to the oscilloscope for control and observation. The oscilloscope 258 is also used for observing and controlling resonance signals reflected from the resonance sensor unit 222. For this purpose, a line 257 is provided between the oscilloscope 258 and the reflected wave detector 251.

As has been mentioned above, one of the main units of the apparatus 200 of the invention is a cylindrical resonator unit 222 with an open bottom. During operation of the apparatus, the function of the bottom that closes the cylindrical resonator unit 222 is fulfilled by the thin metal film F₂, the thickness of which is to be measured. In designing the cylindrical resonator unit 222, it is necessary to choose inner diameter d and the inner length a of the cylindrical body 268 in such a ratio that excludes generation of other modes near the inherent resonance frequency. Dimensions d and a are shown in Fig. 13A, which is a schematic vertical sectional view of the cylindrical resonator unit 222. Fig. 13B is sectional view of the resonator unit 22 in lines XIIIB-XIIB of Fig. 13A. As will be shown later, measurement accuracy of the method of this embodiment depends, among other factors, on the so-called load-free Q-factor Q_u. Among a variety of various definitions of the Q-factor, the one most convenient for use in conjunction with a microwave cylindrical resonator unit is based on a general energy relation that links the Q-factor with a reactive energy accumulated in the system (resonator), when the latter works in the mode of steady-state oscillations with the energy that dissipates though the system during one oscillation period T. This condition can be written as follows:

W_accum accum where W_aCcum de) Q₀ = 2π 3 accumula= ω₀ norgy, Wdiss (0 b) iates the dissipated energy, ^_di_ss de (Wdiss) T power ^diss, ated in the resonator unit 222, and ω₀ is an inherent resonance frequency equal to 2π/T. Let us use equation (1) for a general case of a hollow resonator unit. The energy accumulated in the resonator unit is constant and is equal to the sum of energies of electrical and magnetic fields. Let us chose the moment when the magnetic field passes through the maximum and, hence, when the electric field in the resonator is equal to zero. In this case, the accumulated energy is expressed through the amplitude of the magnetic field intensity H as follows:

W_accum = j_v0.5 x μ μ₀ |H|² dV (2b)

where V is the volume of the resonator unit, and μ is the relative permeability of the dielectric that fills the resonator unit In a majority of practical cases for nonmagnetic materials, it can be assumed that μ = 1.

If the resonator unit is filled with a dielectric substance without losses, then dissipation of energy is associated only with the Joulean losses in the resonator walls (see Landau-Lifshitz, Vol. 8, paragraphs 59 and 87). As follows from equation (2b), with reference to the surface effect, resistance on the unit surface of the resonator's wall R_SUr_f is equal to 1/σ_DCδ, where σ_DC is a specific conductivity of the material of the resonator walls measured on direct current, δ is the depth of penetration of the field to the wall.

The magnitude of thermal losses of power averaged for one period can be determined by integrating over the entire inner surface S of the resonator walls:

Pd,ss = Is 0.5 x |J|² x Rsurf dS (3b), where |J| is a modulus of the surface current density amplitude in the resonator wall. In equation (3b), |J| can be replaced by the modulus of the tangential component of high-frequency magnetic field |H_t| near the resonator walls.

The value of H_t is determined from wave equations assuming that the resonator walls have ideal conductivity.

The entire energy dissipated in the resonator unit during a single period is equal to:

(W_diss)_τ = P_di_ss x T = ( T/ 2σ_DC δ) x Is |H_t|² dS (4b),

The aforementioned equation can be simplified by expressing active conductivity of the resonator walls σ_DC in terms of the surface layer thickness δ

σ_Dc = 2/(δ² ω μ_Dc μo) (5b),

where μ_DC is a relative magnetic permeability of the material of the resonator wall. In the case of non-magnetic films, μ_DC is always equal to 1.

Thus, according to equation (1b) with reference to equations (2b) and (3b), inherent Q-factor of the resonator can be expressed as follows:

Q = (2/δ) X (μ/μ_DC) x (J_v |H|² dV)/( J, |H_t|² dS) (6b). Based on the assumption that neither the resonator walls nor the dielectric substance that fills the resonator possesses magnetic properties, i.e., that μ_DC=l, the following can be written:

Q = (2/δ) x (Jv |H|² dV)/( |H_t|² dS) (7b).

If equations of the field generated in a hollow resonator unit have been determined, equation (7b) can be used for calculating parameters of an evacuated or gas-filled hollow resonator unit.

In order to evaluate the quality of the obtained equations, let us assume that the field generated in the resonator unit is free of variations, i.e., that |H| = |H_t| = Const. Then the following- expression (8b) can be derived from equation (7b):

Q = (2/δ) x (V/S) (8b).

Thus, in a first approximation the inherent Q-factor of the hollow resonator unit is proportional to a ratio of the resonator volume to the resonator surface. As a rule, linear dimensions of the resonator are proportional to the working wavelength λ. Thus, it can be concluded that V » λ³ and S« λ². With the accuracy up to a- small constant multiplier, equation (8b) can be simplified into equation (9b) given below:

Q * λ/δ (9b).

Knowing the wavelength λ and assuming that the walls of the resonator are made from a metal of high electrical conductivity, one can easily find that in the centimeter range of the wavelength the value of δ will be on the order of several microns or fractions of micron. This means that Q₀ may be equal to about 10⁵. In the embodiment of Figs. 11-16, the apparatus 220 of the invention utilizes the cylindrical resonator unit 222 with modes TE₀n, since it has sufficiently high Q- factor Q_u and since no electric currents flow between the resonator walls and the resonator end face. As is known, each mode is characterized by a specific pattern of the electric and magnetic fields. Mode TEon is shown in Figs. 2A and 2B. More specifically, the spatial distribution of electrical and magnetic fields is shown in Figs. 13A and 13B in cross-sections of the resonator unit 222, where lines of electrical fields are shown in Fig. 13A by plus signs and small circles and where lines of the magnetic field H are shown in Fig. 13B by arrows directed radially inwardly. It can be seen that electric current flows neither in longitudinal direction of the resonator nor in the radial direction, but only in the azimuthal direction φ. Distribution of electric current density (J_φ) in the resonator unit wall is shown by the distribution curves on the right side of resonator unit image in Fig. 13A and under the resonator unit image in Fig. 13B. Such directions of the electrical and magnetic fields make it possible to use the test film F₃ on the substrate SB as an end-face plate of the resonator unit 222 (Figs. 4 and 5A).

Fig. 14A is a vertical sectional view of a modified resonator unit 222a of the invention. Fig. 14B is a sectional view of the modified resonator unit along the line XIV-XIV of Fig. 14A. As shown in Fig. 14A, the resonance frequency ω₀ of the resonator unit 222a can be adjusted within some range if the resonator unit 222a is provided with a plunger 270 that forms the upper end face of the resonator body 268a. In such a construction, the resonance frequency ω₀ will depend on the vertical position of the plunger 270 in the resonator. The plunger 270 can be moved vertically by screwing or unscrewing via threaded interconnection between the plunger and the cylindrical part of the resonator body 268a. In this case, the resonator unit 222a is excited through a slit 272 in the sidewall of the resonator. Reference numeral 273 designates a lock nut for locking the plunger 270 in the adjusted position.

The arrangement of electrical and magnetic fields shown in Figs. 14A and 14B makes good electrical contact, between the test film F₃ (Fig. 13A) on the substrate SB and the end face of the cylindrical body 268, unnecessary.

If a gap 274 (Fig. 13A) is left between the lower end face of the cylindrical part 168 of the resonator and the film F₃, then other modes will also be suppressed, as the aforementioned gap will not allow the passage of surface currents. What is important is that the mode TMm, which has the current flow through the resonator walls, which may coexist with the aforementioned mode TEQH, will also be suppressed because the flow of current through the gap 274 is impossible.

Formula (5b) allows to make an important conclusion that for providing the resonator with the maximal Q-factor, the length a of the cylindrical resonator 222 (Fig. 13A) should be approximately equal to its diameter d.

As has been mentioned above, the test film F₃ functions as the lower end face of the microwave resonator unit 222. It is known that the depth δ of penetration of an electromagnetic field into metal can be represented by the following expression (10b) (see formula (5b)):

δ = [2/(ω μ_Dc μo σ_DC)]^1/2 (10b).

With reference to the depth of penetration of the electromagnetic field into the material of the resonator walls, unit surface resistance R_surf on the inner surface of the microwave resonator can be expressed as follows: Rsur_f = 1/σ_DC δ (11 b) ,

where, as defined above, σ_DC is a specific conductivity of the material of the resonator walls measured on direct current. Base on this expression, resistance of the metal layer having thickness δ and the unit length and unit width, i.e., the specific surface resistance or the actual part of the surface impedance (see Landau-Lifshitz, paragraphs 59, 87), can be expressed by the following formula:

Rsurf = (ω μ_DC μ₀/2σ_DC)^1/2 (12b).

For the microwave resonator unit with the geometry of the maximal Q-faetor, the surface resistance on side walls is represented by the following equation:

Rc_yl = πd² (ω μ_DC μ₀ /2σ_DC )]^1/2 (13b),

while surface resistance on the end faces will be expressed as follows:

R_t = πd²/2 (ω μ_DC μ₀/2σ_DC)]^1/2 (14b).

Taking into account the equations (1b), (3b), (13b) and (14b), it can be concluded that even a slightest variation in R_t may cause significant variations in Qu. This means that for Q_u within the range of 10⁴ to 10⁵, variation in R_t by several percents or a fraction of one percent may exert a significant influence on the Q- factor and can be measured by the above-described method of the invention with sufficiently high accuracy. Depth of penetration of electromagnetic fields operating on various frequencies into copper and aluminum films calculated by formula (10b) is shown in Table 1 (data for copper included into Table 1 has been given above).

Table 1

Skin depth δ in microns for various metals and frequencies

It can be assumed from Table 1 that for metal films of the type used at the present time in semiconductor chips and having-a-thiekness of- less than 0.5 μm, accurate measurements require frequencies that exceed 20 GHz. The method and apparatus of the invention are applicable for films even thinner than 0.1 μm. In fact, if the film thickness Δ is less than the depth of the skin layer δ, then in formula (11) δ should be replaced by Δ, and the specific surface resistance will be represented by the following equation:

Rsurf - 1 (σ_Dc ^• Δ) (15b).

Formulae (6b) and (7b) can also be converted by the above replacement, while formulae (8b) and (9b) remain unchanged. In this case, all previous conclusions remain true.

During operation of the apparatus 220 (Fig. 12) , the microwave generator 232 is activated by means of the power supply unit 242 with the modulator 244. The sweeping frequency range of the microwaves generated by generator 232 is selected so as to overlap the resonance frequency ω₀ of the resonator unit 222, which is excited from the generator 232 via the microwave guide 230. Figs. 15A, 15B, and 15C illustrate operation of the generator 232 in form of a klystron, although microwave generator of any other suitable type can be used. More specifically, Fig. 15A shows dependence of output power P_k of the klystron from the voltage applied to the klystron reflector (not shown). It can be seen that if a sinusoidal voltage is applied to the klystron with the amplitude of voltage variable from U_rι to U_r2 for an average (constant) value of 200 V, the output power P_k will vary periodically in accordance with the pattern shown Fig. 15A with the sweeping period.

Fig. 15B illustrates dependence of frequency deviation Δf from a certain generation frequency that corresponds to a constant voltage U^on the klystron reflector. Let us assume that the resonance frequency of the resonator unit 222 corresponds to Δf = 0. Then the signal from the directed diode 251 (Fig. 12) will correspond to the image shown in Fig. 15C. Signals shown in Figs. 15A and 15C can be observed on the oscilloscope 258, provided that the sweep of the signal on the oscillographscope 258 is carried out under control of the modulator unit 244.

During measurement, the amplitude of modulation or sweeping, i.e., the sweeping amplitude on the klystron reflector (not shown), is reduced to the level that corresponds to resonance or half-resonance on the resonator unit (see broken lines in Fig. 15C).

The procedure of measuring the thickness of film F₃ is, in fact, measurement of the. amplitude of the signal (e.g., current signal on diode 251 ) under resonance conditions. The procedure of synchronous detection makes it possible to further improve the accuracy of measurements since measurements are carried out on the sweeping frequency. In the method and apparatus of the invention, the magnitude of the gap 274 (Fig. 13A) between the film F₃ and the end face of the resonator unit 222 that faces the film F₃ is an important parameter. This is because variations in the gap 274 leads to variations in the volume of the resonator unit and hence in the intrinsic resonance frequency ω₀. However, variations in Q-factor associated with variations in ω₀, are insignificant as compared to changes caused by losses under the effect of variations in the resonance frequency. Therefore, the microwave generator 232 should be of the type that allows adjustment of frequency in a certain small range.

On. the other hand, significant improvement in the accuracy of measurement may be achieved by stabilizing the gap 274. Mechanisms suitable for stabilization of the gap 274 are described in the aforementioned U. S. Patent 6,593,738. For example, as shown in Fig. 16, which illustrates a system for stabilization of the gap 274 in the apparatus 220 of the invention, the resonator unit 322 and the film F1 to be measured may form plates of a capacitor 323 which is included into an oscillation circuit 319 that contains an inductance coil 325, an AC generator 327, and a measurement instrument, e.g., an ampermeter 329, is connected to an actuating mechanism 331 via a controller 333 installed in a feedback circuit 335. The actuating mechanism 331 may comprise a piezoactuator 331 for controlling relative positions between the resonator unit 322 and the film F1. It is important that the operation frequency of the oscillating circuit 319 be noticeably distinctive from the resonance frequency ω₀ of the generator 232, e.g., lower than ω₀, but significantly greater than the sweeping frequency of the generator 232 (Fig. 12). This is needed for exclusion of interferences between the respective frequencies.

Another item important for the method and apparatus of the invention is the magnitude of the film area tested in one measurement. As can be seen from aforementioned formulae (8b) and (9b), the value of the Q-factor decreases with an increase in the working frequency of the resonator unit 222. However, evaluation shows that the method and apparatus of the embodiment shown in Figs. 12-16 are practically applicable to frequencies up to 120 GHz. At higher frequencies the method and apparatus encounter a problem associated with manufacturing accuracy of the resonator system, especially with regard to the membrane 226 with an opening 228 (Fig. 12) in the upper part of the resonator unit 22. For resonator units 222 working at frequencies exceeding 120 GHz the size of the test area diameter on the film F will become close to 1 mm. On lower frequencies, e.g., at 10 GHz, the test area may have a diameter equal to about 1 cm or more.

Although the invention has been shown and described with reference to specific embodiments, it is understood that these embodiments should not be construed as limiting the areas of application of the invention and that any changes and modifications are possible, provided these changes and modifications do not depart from the scope of the attached patent claims. For example, the circuits of Figs. 8 and 9 may be assembled from elements different from those shown in the drawings. For improving accuracy of measurements, these circuits may incorporate quartz resonators, which will stabilize the carrier frequency. The apparatus and method of the invention is also applicable to measuring the thickness and non-uniformity of a thin conductive film on a thick conductive substrate of uniform properties. Although the description and examples related to very thin films with the thickness below 500 Angstroms, it is understood that the apparatus and method of the invention are equally applied to thicker films, e.g., up to 2 μm. The apparatus system shown in Fig. 12 is given in a simplified form sufficient for understanding the principle of the invention, and it is understood that all the components of this system as well as their arrangement may be modified and changed, provided that the main component of the system, i.e., the open-end cylindrical resonator unit 222 may fulfill its functions under control of the aforementioned components. For example, the generator 232 may be of an avalanche transit-time diode. A commercial scalar network analyzer can be used for data analysis instead of the synchronous detector 252, A/D converter 254, etc. The measurement components and components of the waveguides, such as the wavelength detector 266, decouplers 236, 240, 248, etc. may be either excluded or replaced by members combined into an integrated microstrip. The entire system of Fig. 12 may be produced as a compact integral module with the resonator unit and the macrowave generator. Externally such a unit may have only a remote control and connectors to the power supply. The resonator unit 222 may have a toroidal shape and may work on a mode different from TEon,-e.g,, on the E0₄₂ mode. The method and apparatus of the invention may control thickness in non-conductive films, provided that they are supported on conductive substrates. Although the second embodiment described above was considered in implementation to films with non-magnetic properties, the principle of the invention may be applicable to measuring the contents of magnetic components, provided that the thickness of the test film is known. The apparatus of the invention may be realized in the form of a portable instrument or a stationary machine with a sample table having appropriate adjustments. If the thickness of the film is known, the apparatus and method of the invention can be used for precision measurement of any properties associated with conductivity.

Claims

CLAIMS:

1. An apparatus for measuring characteristics of a material of an object comprising: sensor means comprising a resonance oscillating circuit characterized by inherent inductance, inherent capacitance, and an inherent resonance frequency; a high-frequency AC generator with a signal modulator connected to said sensor means; and an amplifier connected to said sensor means; a-measurement unit.connected to said sensor; and a resonance control means; said resonance oscillating circuit having such a relationship between said inherent inductance and inherent capacitance that provides an inductive and capacitive couplings between said sensor and said material of said object.

2. The apparatus of Claim 1 , wherein said object comprises a substrate with at least one coating film, wherein said materials of said substrate and of said coating films are selected from the group of materials comprising a metal, a dielectric, and a semiconductor.

3. The apparatus of Claim 2, wherein said inherent resonance frequency is within the range of 50 MHz to 2.5 GHz.

4. The apparatus of Claim 2, wherein said inherent resonance frequency is within the range of 100 MHz to 200 MHz.

5. The apparatus of Claim 2, wherein said inherent inductance is within the range from 0.1 to 200 nano-Henries and inherent capacitance is within the range of 0.1 to 100 pico-Farades.

6. The apparatus of Claim 4, wherein said inherent inductance is within the range from 0.1 to 200 nano-Henries and inherent capacitance is within the range of 0.1 to 100 pico-Farades.

7. The apparatus of Claim 5, wherein said inherent inductance is within the range from 0.1 to 200 nano-Henries and inherent capacitance is within the range of 0.1 to 100 pico-Farades.

8. The apparatus of Claim 2, wherein said sensor has a sensor winding which is characterized by said inherent inductance, said inherent resistance, and said inherent resonance, said sensor winding being made in the form selected from the group consisting of a flat spiral winding with at least one spiral turn and a helical winding formed by at least two cylindrical helical turns.

9. The apparatus of Claim 8, wherein said at least one spiral turn has a diameter not exceeding 0.5 mm, an wherein said at least two cylindrical helical turns have a diameter within the range from 0.3 mm to 3 mm.

10. The apparatus of Claim 5, wherein said sensor has a sensor winding which is characterized by said inherent inductance, said inherent resistance, and said inherent resonance, said sensor winding being made in the form selected from the group consisting of a flat spiral winding with at least one spiral turn and a helical winding formed by at least two cylindrical helical turns.

11. The apparatus of Claim 10, wherein said at least one spiral turn has a diameter not exceeding 0.5 mm, an wherein said at least two cylindrical helical turns have a diameter within the range from 0.3 mm to 3 mm.

12. The apparatus of Claim 2, wherein said characteristics of a material are selected from the group consisting of a thickness of said coating film, a surface electrical resistance of said material of said object, a surface electrical resistance of said material of said coating film, a dielectric constant of said material of said object, a dielectric constant of said coating film, a coefficieint of magnetic permeability of said material of said object, and a magnetic permeability of said coating. film.

13. A method for measuring characteristics of the material of an object, said method comprising the steps of: providing an apparatus comprising a sensor with a resonance oscillating circuit which has a sensor body characterized by inherent inductance, inherent capacitance, and an inherent resonance frequency; a high-frequency an AC generator with an amplitude modulator connected to said sensor means; an amplifier connected to said sensor means; and a measurement unit connected to said sensor; providing said sensor body with calibration data obtained by a plurality of measurement procedures, each consisting of fixing said sensor body with a calibration gap relative to a reference conductive body with calibration parameters known for different values of said characteristics; energizing said resonance oscillating circuit to generate resonance conditions in said sensor body and approaching said sensor body towards said reference conductive body until an inductive and capacitive relationships are established between said sensor winding and said measurement surface of said reference conductive body; fixing said sensor body relative to said measurement surface at a distance equal to said calibration gap; measuring characteristics of said material of said object with the use of said measurement unit for obtaining characteristic measurement data; and determining the characteristics of said material of said object by comparing said characteristic measurement data with said calibration data.

14. The method of Claim 13, wherein said sensor body comprises a sensor winding, said object comprises a substrate with at least one coating film, wherein said materials of .said substrate and of said coating films are selected from the group of materials comprising a metal, a dielectric, and a semiconductor.

15. The method of Claim 14, wherein said calibration parameters are selected from the group consisting of a thickness of said coating film, a surface electrical resistance of said material of said object, a surface electrical resistance of said material of said coating film, a dielectric constant of said material of said object, a dielectric constant of said coating film, a coefficient of magnetic permeability of said material of said object, and a magnetic permeability of said coating film.

16. The method of Claim 13, wherein said conductive body is a conductive coating film on a dielectric substrate.

17. The method of Claim 15, wherein said conductive body is a conductive coating film on a dielectric substrate.

18. The method of Claim 13, wherein said film is said nonconductive body and said substrate is a conductive body.

19. The method of Claim 15, wherein said conductive body is a conductive coating film on a dielectric substrate.

20. The method of Claim 13, wherein said inherent resonance frequency is within the range of 50 MHz to 2.5 GHz.

21. The method of Claim 13, wherein said inherent resonance frequency is within the range of 100 MHz to 200 MHz.

22. The method of Claim 13, wherein said inherent inductance is within the range from 0.1 to 200 nano-Henries and inherent capacitance is within the range of 0.1 to 100 pico-Farades.

23. The method of Claim 20, wherein said inherent inductance is within the range from 0.1 to 200 nano-Henries and inherent capacitance is within the range of 0.1 to 100 pico-Farades.

24. The method of Claim 21 , wherein said inherent inductance is within the range from 0.1 to 200 nano-Henries and inherent capacitance is within the range of 0.1 to 100 pico-Farades.

25. The apparatus of Claim 1 , wherein said high-frequency AC generator comprises a source of microwave energy; said sensor means comprises a microwave resonator unit and is made as a hollow cylindrical body with an open end on the side facing said object during measurement and a close end on the side opposite to said open end, so that, when said open end approaches said object during measurement and forms a gap with said object, said gap and said object function as a resonator wall that in combination with said hollow cylindrical body forms a closed microwave resonance circuit; said apparatus further comprising linking means for linking said microwave resonator unit with said source of microwave energy and with said resonance control means; said object comprising a material selected from the group consisting of a bulk material and a coating film on a substrate, wherein said bulk material is a conductive material, and when one of said film and said substrate is a conductive material, the other one of said film and said substrate is a dielectric material.

26. The apparatus of Claim 25, wherein said closed end is a membrane and said linking means comprises an opening formed in said membrane.

2.7, The apparatus rf Claim 25, wherein said hollow-cylindrical body has a side wall and said linking means comprises a slit formed in said side wall.

28. The apparatus of Claim 27, wherein said closed end comprises a plunger adjustable in said hollow cylindrical body.

29. The apparatus of Claim 25, wherein said hollow cylindrical body has an inner diameter and an inner height equal to a distance from said open end to said closed end inside said hollow cylindrical body, said inner diameter being substantially equal to said inner height.

30. The apparatus of Claim 25, wherein said source of microwave energy generates microwaves with a frequency within the range from 2.5 GHz to 120 GHz.

31. The apparatus of Claim 25, wherein said source of microwave energy generates microwaves with a frequency within the range from 60 GHz to 90 GHz.

32. The apparatus of Claim 25, wherein said microwave resonator unit has an operation resonance mode TEon.

33. The apparatus of Claim 29, wherein said microwave resonator unit has an operation resonance mode TEon.

34. The apparatus of Claim 30, wherein said microwave resonator unit has an operation resonance mode TEon.

35. The apparatus of Claim 31 , wherein said microwave resonator unit has an operation resonance mode TE₀n.

36. The apparatus of Claim 25, further comprising gap adjustment means for maintaining said gap at a constant value for stabilization of said resonance frequency.

37. The apparatus of Claim 29, further comprising gap adjustment means for maintaining said gap at a constant value for stabilization of said resonance frequency.

38. The apparatus of Claim 30, further comprising gap adjustment means for maintaining said gap at a constant value for stabilization of said resonance frequency.

39. The apparatus of Claim 31^', further comprising gap adjustment means for maintaining said gap at a constant value for stabilization of said resonance frequency.

40. The apparatus of Claim 25, wherein said microwave resonator unit has a Q- factor within the range of 10³ to 10⁵.

41. The apparatus of Claim 32, wherein said microwave resonator unit has a Q- factor within the range of 10³ to 10⁵.

42. The apparatus of Claim 33, wherein said microwave resonator unit has a Q- factor within the range of 10³ to 10⁵.

43. The apparatus of Claim 34, wherein said microwave resonator unit has a Q- factor within the range of 10³ to 10⁵.

44. The apparatus of Claim 43, wherein said microwave resonator unit has a Q- factor within the range of 10³ to 10⁵.

45. The method of Claim 13, wherein said high-frequency AC generator comprises a source of microwave energy, said sensor body comprises a microwave resonator unit and is made as a hollow cylindrical body with an open end on the side facing said object during measurement and a close end on the side opposite to said open end; said apparatus further comprising linking means for linking said microwave resonator unit with said source of microwave energy and with said resonance control means; said object comprising a material selected from the group consisting of a bulk material and a coating film on a substrate, wherein said bulk material is a conductive material, and when one of said film and said substrate is a conductive material, the other one of said film and said substrate is a dielectric material; said method further comprising the steps of: energizing said microwave resonance unit by supplying thereto a microwave energy from said microwave energy source; positioning said open end of said hollow cylindrical body close to said thin film with a gap at which said thin film functions as a resonator wall that closes the microwave resonance circuit with a current flowing through said resonator wall of said microwave resonator unit; exciting in said microwave resonance unit a resonance mode; measuring resonance characteristics of said microwave resonance circuit; and determining said characteristics of said object by comparing the resonance characteristics of said microwave resonance circuit with said calibration data.

46. The method of Claim 45, further comprising the step of preventing penetration of modes other than said resonance mode into said microwave resonance unit

47. The method of Claim 46, providing means for moving said closed end of said hollow cylindrical body by making it in the form of a plunger adjustable in said hollow cylindrical body.

48. The method of Claim 45, wherein source of microwave energy generates microwaves with a frequency within the range from 2.5 GHz to 120 GHz.

49. The method of Claim 48, wherein said microwave resonator unit has an operation resonance mode TEon.

50. The method of Claim 49, providing means for moving said closed end of said hollow cylindrical body by making it in the form of a plunger adjustable in said hollow cylindrical body.

51. The method of Claim 45, further comprising the step of maintaining said gap at a constant value for stabilization of said resonance frequency.

52. The method of Claim 48, further comprising the step of maintaining said gap at a constant value for stabilization of said resonance frequency.

53. The method of Claim 49, further comprising the step of maintaining said gap at a constant value for stabilization of said resonance frequency.

54. The method of Claim 45, said microwave resonator unit operates with a Q- factor within the range of 10³ to 10⁵.

55. The method of Claim 48, said microwave resonator unit operates with a Q- factor within the range of 10³ to 10⁵.

56. The method of Claim 49, said microwave resonator unit operates with a Q- factor within the range of 10³ to 10⁵.