Modeling of Electromagnetic Behavior of Composite Thin Layers using Genetic Algorithm

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The 5th International Conference on Electrical Engineering – Boumerdes (ICEE-B) October 29-31, 2017, Boumerdes, Algeria.

Modeling of Electromagnetic Behavior of Composite Thin Layers using Genetic Algorithm

Abdelmalek Reddaf^1,2, Karim Ferroudji¹, Mounir Boudjerda¹,Khaled Hamdi Chérif¹, Isslam Bouchachi¹

1Research Center in Industrial Technologies CRTI. P.O.

Box 64, Cheraga 16014 Algiers, Algeria

Fatima Djerfaf²

2Semiconductors and functional materials, Laboratory, University Amar Telidji Laghouat Algeria

Abstract— In this paper, we present a new model using the high frequency electromagnetic simulator for several binary mixtures where the load is in the lossless thin film form with a permittivity of (έ = 100, 200, 300, and 400) and for various thickness values in a range of 10 µm to 250 µm with respect to the host matrix. The model operates in a variety of frequencies from 8.2 GHz to 12.4 GHz. The effective permittivity of composites is evaluated using Nicholson Ross Weir (NRW) algorithm in a rectangular waveguide. The implementation of NRW algorithm is conducted on various samples simulated by HFSS, in order to estimate the dielectric composite behavior. Furthermore, we employ a genetic algorithm methodology (GA) for the filling factor optimization of the proposed model by Mosallaei. The obtained results show a good agreement with the theoretical models, which ensure the validity of our proposed model for characterizing the electromagnetic behaviour of dielectric thin films.

Keywords— Thin films, electromagnetic behaviour, dielectric mixtures ,Genetic optimization ,mico wave.

I. INTRODUCTION

MIM (Metal Insulating Metal) capacitors are commonly used for dielectric characterization of thin films [1]. However, at high frequencies or in the case of high permittivity, propagation phenomena appear and reduce the apparent permittivity. YILDIZ et al. [2] use the Conformal mapping method to calculate the effective permittivity of a composite in two phases, including a thin layer. This method suffers from a major drawback in the calculation of the permittivity which is not precise when the thickness of the thin layer is less than 10 μm.

The measurement technique in rectangular waveguide [3]

has the advantage of being broadband, particularly in the X-and [8.2 - 12.4] GHz. On the other hand, the sample material to be characterized is placed in the interior of the structure of propagation (refer to Fig. 1).

We used HFSS software in the electromagnetic study of waveguide and broadband technique characterization of materials. This software is based on solving Maxwell's equations, using the finite element method FEM, in the frequency domain. The simulator calculates the S parameters which are used to define the effective permittivity of samples using Nicholson Ross Weir (NRW) algorithm [4].

Mosallaei, H et al. [5] have proposed a mathematical model refer to (9) to calculate the effective permittivity of a binary composite in which the binary composite is repetitive in the periodic or random structure. In theory, Wiener mixing law refer to (8) reflects this kind of multilayer structures in series or in parallel

Wiener law is a generalized law of the model proposed by Mosallaei. Our model uses genetic algorithm to define the filling factors of model and compare them with the factors of Mosallaei model.

Figure. 1. The rectangular waveguide with the sample to be characterized

(MUT).

Figure. 2. Sample load with a thin layer (thin film).

II. METHOD A. The method of NRW

The electrical properties are obtained from S parameters.

We describe the theoretical aspects of NRW method to obtain the effective permittivity for both the substrate and the thin layers (using different types of materials). The effective dielectric constant can be obtained from [3]:

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

 



 Γ

−

= 1² Γ ₂ ²₂

11 1

) 1 (

T R T

S (1)



 



 Γ

−

= 2² Γ ₂ ²₂

22 1

) 1 (

T R T

S ₍₂₎



 



 Γ

− Γ

= −

= 12 2 1 ₂ ²₂

21 1

) 1 (

T R T

R S

S ⁽³⁾

With :

R

₁

= e

⁻^γ⁰^d¹^, 2 ⁰ ²

e

d

R =

⁻^γ ^and

T = e

⁻^γ^d

d1 is the distance between the material and port 1, d2 is the distance between the material and port 2, and d is the thickness of the sample. The present work concerns the non-magnetic materials (µr =1) as well as d is known (d = 10 mm). Also, for isotropic materials S12 = S21. We can solve the equations in various combinations eg if the position of the reference planes is not precisely known, then d1 and d2 can be eliminated from the equations invariant reference planes. Here Ross Nicholson and Weiner combined equations S11 and S12 after they arrived at the formula that determines the permittivity of materials as follows:

For the reflection coefficient (Г):

2

− 1

±

=

Γ A A

⁽⁴⁾

Where:

11 221 211

2

1 S

S

A= S − + ⁽⁵⁾

For the transmission coefficient (T):

Γ +

−

Γ

−

=1 (+₁₁ ₁₂)

12 11

S S

S

T S ₍₆₎

We will achieve the following formula:











  −



 



=  ₂

2 2

0

) 1 ln(1 2

1

c

r λ πd T λ

ε ⁽⁷⁾

B. Wiener’s model

Wiener [6] proposed a descriptive model of the effective permittivity of a composite for n components given by:

= (8)

ɛi is the relative permittivity of each layer;

ɛeff isthe equivalent permittivity of the multilayer;

C. Mosallaei’s model

The permittivity of the multi-layer substrate is given by H.

Mosallaei [4], for a two layers we obtain:

= + (9)

= ℎ

ℎ + ℎ (10)

= ℎ

ℎ + ℎ (11)

ɛ1 and ɛ2 are the relative permittivities of each layer;

h1, h2 are he thicknesses of each layer;

ɛeff is the equivalent permittivity of the multilayer;

III. GENETIC OPTIMIZATION (GA)

GA algorithm is a population-based stochastic search method, it belongs to the family of evolutionary algorithms [8- 9]. The simulated model with different thickness of the thin layer and the relative permittivity of the material is used to create a database. Applying GA method, we have optimized filling factors (f1 and f2) of Wiener model.

First, we identify the GA parameters such as upper and lower limits, the fitness function, number of variable crossover, mutation, and selection [10].

Figure 3. GA-based estimation of the glottal flow parameters IV. RESULTS AND DISCUSSION

Table I illustrates the filling factors optimized for Wiener model using GA method.

Initial Population

Selection Crossover

Mutation

Evaluation of Fitness function

Stopping criteria

Best Solution End

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TABLE I. FILLING FACTORS OPTIMIZED

h1 (µm) 10 50 100 150 200 250

f1 0.980 0.950 0.892 0.844 0.7909 0.745

f2 0.019 0.051 0.104 0.147 0.1969 0.2361

Figure 4. Equivalent permittivity of the multi-layer substrate according to the thickness of the thin layer (h1)

Figure 5. Comparisons effective permittivity between GA model and Mosallaie

Fig. 4 shows the evolution of the equivalent permittivity of a multilayer composite in accordance with the thickness of the thin layer and for different values of the relative permittivity.

We note that the change in the equivalent permittivity is a little large relative to the variance in thickness. This change becomes almost zero when the thickness is less than 10 µm.

In order to validate the obtained results, we compared the equivalent permittivity acquired using our proposed model with those obtained by GA model and Mosallaie model. The comparison is illustrated in Fig. 5, in which the results are quite similar.

Filling factors of GA model and Mosallaei models are very close, especially for f2 in Fig. 6, this approach shows that the

filling factors are influenced only by the thickness of the composite material.

Figure 6. Comparisons filling factors between GA model and Mosallaie V. MODELS VALIDATION

In the latter case, the performance of the filling factors of Mosallaie model compared to the filling factors of Wiener model is evaluated using various statistical indices [8] such as:

Mean-squared error (MSE,), Mean Absolute Bias Error (MABE), Root Mean Square Error (RMSE), and Relative Square Error (RRMSE):

The MSE gives the mean squared error. Its expression is given by:

MSE =1

n |H − H | ^{^} (12) The mean absolute value of bias error is referred by MABE. Its expression is given by:

MABE =1

n |H − H | (13) Where Hm ̀is the filling factor of Mosallaie model value and HGA is the filling factor of GA model value.

The RMSE represents the difference between the predicted values (Mosallaie model value) and the measured values (the filling factor of GA model value). In fact, RMSE identifies the model's accuracy. It is calculated by:

RMSE = 1

n H − H ^{^} (14) The RRMSE is calculated by dividing RMSE to the average of measured data as:

0 50 100 150 200 250

9 9.5 10 10.5 11 11.5 12 12.5

thickness of thin film in µm

effective permittivity

eps_GA =100 eps_GA =200 eps_GA =300 eps_GA =400 eps_HfSS =100 eps_HfSS =200 eps_HfSS =300 eps_HfSS =400

0 50 100 150 200 250

9 9.5 10 10.5 11 11.5 12 12.5

effective permittivity

eps Mosallaei=100 eps Mosallaei=200 eps Mosallaei=300 eps Mosallaei=400 eps_GA =100 eps_GA =200 eps_GA =300 epsGA =400

0 50 100 150 200 250

0.7 0.8 0.9 1

Filing factor

= f1 Mosallaei

= f1 GA model

0 50 100 150 200 250

0 0.1 0.2 0.3 0.4

Filing factor

= f2 Mosallaei

= f2 GA model

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1n ∑ H − H ^{^}

∑ × 100 (15) The performance of the model is defined by the RMSE range as follows: Excellent: RMSE <10%; Good:

10%<RMSE<20% ;Fair: 20%<RMSE<30%; Poor:

RMSE>30%.

TABLE II. PERFORMANCE OF THE MODEL ACCORDING TO RMSE

h1 (µm) 10 50 100 150 200 250

f1 1.01% 2.00% 1.96% 2.84% 3.22% 2.89%

f2 0.91% 0.18% 0.55% 0.06% 0.05% 0.037%

Table. III and the curves in Fig. 7 illustrate that the error of the filling factors depends on the thickness of the thin layer which│f1m-f1GA│tends to zero if h2 decreases and │f2m-f2GA│ tends to zero if h2 increases.

TABLEIII. THE VARIOUS ERRORS BETWEEN THE FILLING FACTORS

Error MSE MABE RMSE RRMSE

f1 5.942e-004 0.0232 0.0244 2.86%

f2 1.975e-005 0.0029 0.0044 3.49%

Figure 7. The variation of the differences between the filling factors (f1 and f2) as a function of the thickness of the thin film

VI. C^ONCLUSION

In this paper a new model using the high frequency electromagnetic simulator for several binary mixtures is proposed. The Nicolson-Ross-Weir method is used as a numerical tool to estimate the value of relative complex permittivity of (MUT) over the X band. We estimate the dielectric composite behavior using simulation and GA approach. It should be noted that in this case the error of the filling factors depends on the thickness of the thin layer.

The obtained results are in a good agreement with the theoretical models, which ensure the validity of the algorithm for characterizing thin film dielectric media. The proposed model operates in a variety of frequencies from 8.2 GHz to 12.4 GHz.

VII. R^EFERENCES

[1] Z. Qin, W. Chen, X. Wang, et al. "Microwave dielectric characterisation of SiO 2 thin films through a single MIM test structure", In : Microwave and Millimeter Wave Technology (ICMMT), 2016 IEEE International Conference on. IEEE, p. 204-206, 2016.

[2] C. Yildizl, K. Guney, M. Turkmen, et al. "Neural models for quasi-static analysis of conventional and supported coplanar waveguides". AEU- International Journal of Electronics and Communications, vol. 61, no. 8, p. 521-527, 2007.

[3] H. Kassem, and V. Vigneras. "Non-destructive measurements of dielectric constant of thin dielectric films with metallic backing using coplanar transmission line", In : Advances in Computational Tools for Engineering Applications (ACTEA), 3rd International Conference on.

IEEE, 2016. p. 58-61, 2016.

[4] S. Kim, and J. Baker-Jarvis, "An approximate approach to determining the permittivity and permeability near λ/2 resonances in transmission/reflection measurements", Progress In Electromagnetics Research B, vol. no.58, 95–109, 2014.

[5] G. Antonini, and D. Romano. "Quasi-static partial element equivalent circuit models of magneto-dielectric materials", IET Microwaves, Antennas & Propagation, 2017.

[6] Luo, Bingcheng, et al. "Synthesis, characterization and dielectric properties of surface functionalized ferroelectric ceramic/epoxy resin composites with high dielectric permittivity." Composites Science and Technology 112 .1-7.2015.

[7] A. Boultif, A. Kabouche, and S. Ladjel. "Application of Genetic Algorithms (GA) and Threshold Acceptance (TA) to a Ternary Liquid- Liquid Equilibrium System", International Review on Modelling and Simulations (IREMOS), vol. 9, no 1, p. 29-36, 2016.

[8] K. Ferroudji, N. Benoudjit, and A. Bouakaz. "An automated microemboli detection and classification system using backscatter RF signals and differential evolution", Australasian Physical & Engineering Sciences in Medicine, vol. 40, no 1, p.85-99, 2017.

[9] I. Bouchachi, J. Mateu, and M.L. Riabi. "Waveguide Filter Modeling and Simulation using Mode-matching, Fullwave Network Analysis and Swarm Optimization", Applied Computational Electromagnetics Society Journal, Vol. 32, No. 2, pp 169-177, 2017.

[10] M. Boudjerda and A. Kacha, "Assessment of disordered voices based on an optimized glottal source model", Turk. J. Elec. Eng. & Comp. Sci., vol. 25, no. 4, pp. 3201-3214, 2017.

0 50 100 150 200 250

0.01 0.02 0.03 0.04

error

Error(f1)

0 50 100 150 200 250

0 0.005 0.01

error

Error(f2)