Microwave Ondestructive Testing of Thin Multilayers Conductive StructuresValeri V. Gavriline, Dr. Eng., CashCodeCorresponding Author Contact: Email: valeri@cashcode.com |
Among the non-destructive methods for the control of layers parameters in various electronic products to measure the parameters in structures based on semiconductor layers and metallic films, the microwave and electromagnetic methods of investigation open up certain possibilities.
Thin Multi Layers Conductive Structures are characterized by a number of parameters: thickness, specific conductivity of each separate layer or film, diffusion depth, impurity density, structure of the film (island - type, mesh, porous ), etc. Consequently, the practice of measurement calls forth the necessity of having a preliminary option of a microwave and electromagnetic method and instrument for the control of each given type of structure in the optimum frequency band.
The solution of this task appears possible when a more general single characteristic is chosen, which would be valid for all structures employed and would determine their properties in electromagnetic fields of a certain frequency, by the magnitude of which the distribution of the complex structures employed is to be effected. In the present report, the possibility will be discussed of solving such a task of a more general nature on the basis of impedance relationships analysis including impedance surfaces technique analysis for a Multi Layers Structures with thin conducting discontinuous films.
The development and application of nondestructive techniques for electromagnetic testing of Thin Conductive Multi Layers Structures involves the problem of field calculations, which is a difficult one because of the ambiguous nature of field propagation in thin films having a complex discrete composition (island-type, mesh, porous, etc.) and the impossibility of setting up the actual boundary conditions for the surfaces of films forming the thin-film structure (because of the indeterminacy of the surfaces proper in discontinuous thin films).
Even such a simple notion as "thickness" appears to be indeterminate in the case of a thin films and depends on the method of definition, since discrete films thicknesses determined in terms of weight, geometrical, optical, or electrical parameters may substantially vary among themselves.
Provided, however, that the effective conventional thickness of the film (de) is far less than the effective depth of electromagnetic field penetration into the film (e) and the effective electromagnetic wave length (e),
(1) |
such thin film, when interacting with an electromagnetic wave, may be regarded as an impedance surface with a square impedance of Zs, the latter depending, in the general case, on the field frequency. The value of Zs of the film essentially determines the nature of its interaction with the field.
In case of simple homogeneous conducting layers with a geometrical thickness (d) and electrical conductivity (), surface square impedance (Zs) of the film in the an electromagnetic field with frequency () may be written in a simple way as follows:
(2) |
But for the discrete films with complex discrete composition, as was mentioned above, it is difficult to determine the real parameters of thin films such as thickness and conductivity. And the only parameter essentially determines the nature of film interaction with the electromagnetic field is the value of Zs - surface complex square impedance.
The boundary conditions for the tangential components of electromagnetic field penetrating through the film with a surface impedance Zs , provided the conditions (1) obeyed, can be expressed as :
E1tg = E2tg ; H1tg - H2tg = E1tg / Zs | (3) |
Using these boundary conditions theoretical relationships were obtained for microwave nondestructive testing by solving electrodynamics equations when calculating the interactions of the field of microwave transducers with thin-film structure comprising discrete films with undetermined interfaces.
In the case of Thin Multi Layers Conductive Structure interaction with a plane electromagnetic wave, which is more easily realized in the microwave and infra-red bands, the value of the input impedance Zin on the boundary (i) fully determines the electrophysical properties of the structure under control on the boundary (i).
For non-uniform fields (eddy-current and specific waveguide transducers), such approach must be given a more precise definition. But in some well-conducting structures, provided the approximate LEONTOVICH's boundary conditions are obeyed, the wave within the structure may be considered to be plane , and the nature of the interaction will be also determined by the value of the input impedance for the plane wave Zin .
In the case of thin conducting films, the thickness of which is considerably less than the penetration depth and wavelength in the material of the film (1), the films in the Multi Layers Structure may be looked upon as impedance surfaces with the surface impedances Zsi which unambiguously determine their properties upon interaction with electromagnetic fields of any configuration over a wide range of frequencies.
Thus, for a number of structures, the diversity of their properties in electromagnetic fields is likely to come to a change in the parameter of the input impedance, the value of which, at the given frequency, unambiguously determines these properties.
In the case of thin plane conducting film Zsi placed on the boundary (i) of the structure with input impedance Zin(i-1) total input impedance of such a structure, using boundary conditions (3) may be written as follows:
1/Zin i = 1/Zin(i-1) + 1/Zsi | (4) |
If there are sandwich type (n) thin films (Zsi) structure, conditions (1) may be rewritten as:
(5) |
and we obtain for total input impedance on the boundary with n - thin films on it :
(6) |
were: Zin i - input impedance on the boundary (i) of the same structure without thin films.
The surface impedance Zsi values could be established for each film type at a given electromagnetic field frequency. The techniques suggested considerably simplify the estimation of the structure and the electromagnetic wave interaction.
Let us now consider impedance relationships for a several Multi Layers Structures containing thin conducting films in interaction with an electromagnetic field of the waveguide and an open resonator-type microwave transducers.
The "Impedance Surface Techniques" was used in design new methods for remote inspection of parameters for Large-area Conducting Planar Structures upon transmitted microwave signal by means of a real horn-type radiator and receiver.
Partial elimination of the effect of sample side travel in the working gap is shown to be possible in the case of partial misalignment in the horn-type waveguide transducer's system (the reflection coefficients of the horns are taken as non-zero).
The horn-type waveguide transducer's system shown in Fig.1 is used to measure properties (transmission coefficient (t) , and (or) surface impedance Zs ) of thin plane conductive structure (3) located on the distance (l) from radiator (1) in the working gap (L) (distance between the radiator (1) and receiver (3) horns with reflection coefficients 1 and 2 accordingly).
Fig 1: Example of the horn-type waveguide system. |
The relations between the power transmition T = [ E_{3} / E_{0}] ^{2} coefficient and the position (l) of the sample (t, Rs) in the working gap (0, L) of the system (were simplified taken as reflection coefficients 1=1, 2=2 < 0.5; t =t ) are shown in Fig.2 (L= n /2 ) and Fig.3 (L= (2n+1) /4 ) for 3 samples: (1) - t = 0.7; (2) - t = 0.5; (3) - t = 0.3.
Fig 2: Theoretical diagram for T(l) , when L=n/2. |
Fig 3: Theoretical diagram for T(l), when L=(2n+1)/4. |
You can see that if the working gap in the horn-type waveguide transducer system determined as L=(2n+1) /4 (Fig.3) we have a maximal effect of elimination of sample side travel (change of ( l ) ) in the process of measurement. The experimental results of an investigation for the real conducting structures with Rs from 50 to 1500 Ohm / (conducting paper) in the frequency bands (=8mm, 3cm.) are shown on Fig. 4,5 correspond to a theoretical conclusions and open possibilities of design a new microwave methods for measuring surface impedance of thin conducting films during the process of manufacture.
Fig 4: Experimental relations between Power Transmission Coefficient T and an active Surface Impedance Rs if L=(2n+1) /4. | Fig 5: Experimental relations between Power Transmission Coefficient T and an active Surface Impedance Rs if L = n/2 |
"Surface Impedance Technique" was used to calculate the interaction of a plane electromagnetic wave in the open resonator with ultra thin conducting , semiconducting films and dielectric layers. If the resonator's mirrors have the Power Transmission Coefficient (tm <<1) and Zo is the impedance of working gap (0, L) between the mirrors were conducting film (Rs) is located, the Open Resonator Transmission Coefficient can be written as follows:
(7) |
were:
Rs - active surface impedance of thin conducting films (2), located on the distance (l) in the working gap (L) between the mirrors (1,3) (as shown on Fig.1)
The theoretical diagrams for T(Rs) are shown on Fig.6 for 6 types of mirrors: (1) - tm = 0.3 ; (2) - tm = 0.2 ; (3) - tm = 0.1 ; (4) - tm = 0.05 ; (5) - tm = 0.03 ; (6) - tm = 0.01.
The experimental diagram for resistor ultra thin coating on dielectric film is shown on Fig.7.
Fig 6: Theoretical diagram for Power Transmission Coefficient of Open Resonator (T) with thin conducting film (Rs). | Fig 7: Experimental relations between the Power Transmission Coefficient of Open Resonator (T) and the surface resistance of thin conducting film (Rs). |
Choosing the different mirrors with the different coefficients (tm) the optimum control of real thin conducting films (optimum range of Rs (Ohm/()), semiconducting and dielectric layers can be developed by the way of measuring the open resonator transmission coefficient in microwave band.
Microwave techniques utilizing open resonator-type transducers were developed for measuring Ultra-Thin Films Surface Square Impedance within the range of 10^{3} - 10^{12} Ohm as well as parameters of semiconducting and dielectric layers of small losses.
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