Zeszyty Naukowe Wydziału Elektroniki i Informatyki Nr 5

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1 POLITECHNIKA KOSZALIŃSKA Zeszt Nakowe Wdział Elektroniki i Informatki Nr 5 KOSZALIN 03

2 Zeszt Nakowe Wdział Elektroniki i Informatki Nr 5 ISSN Przewodnicząc Uczelnianej Rad Wdawniczej Mirosław Maliński Przewodnicząc Komitet Redakcjnego Aleks Patrn Komitet Redakcjn Mirosław Maliński Darisz Gretkowski Krzsztof Bzdra Projekt okładki Tadesz Walczak Skład, łamanie Maciej Bączek Copright b Wdawnictwo Uczelniane Politechniki Koszalińskiej Koszalin 03 Wdawnictwo Uczelniane Politechniki Koszalińskiej Koszalin, l. Racławicka 5-7 Koszalin 03, wd. I, ark. wd. 7,, format B-5, nakład 00 egz. Drk: INTRO-DRUK, Koszalin

3 Spis treści Darisz Jakóbczak... 5 Active Object Modeling and Applications via the Method of Hrwitz-Radon Matrices Mirosław Andrzej Maliński, Łkasz Bartłomiej Chrobak, Leszek Bchto, Michał Pawlak... 7 Investigations of the Implanted Laer in Silicon Based on the Modlated Free Carrier Absorption Phenomenon Anna Witenberg, Maciej Walkowiak... 3 Odpowiedzi prądowe w kładzie dwóch anten liniowch ze szczególnm względnieniem redkcji późnoczasowch niestabilności Marcin Walczak Badania smlacjne charakterstk przetwornic bck i boost z względnieniem rezstancji pasożtniczch Michał Pawlak, Mirosław Andrzej Maliński Wznaczanie termodfzjności krształów CdMgSe z wkorzstaniem techniki radiometrii w podczerwieni Łkasz Przeniosło, Marcin Walków, Sonia Krzeszewska, Sandra Pisarek, Andrzej Biedka, Marek Jaskła, Daniel Matias, Krzsztof Penkala Integrated impedance scanner in selected biomeasrement applications control circit Slwester Wosiak... 7 Modelowanie 3D twarz w sstemach bezpieczeństwa pblicznego Przemslaw Makiewicz, Krzsztof Penkala Virtal magnetic resonance imaging as a didactic aid Konrad Jędrzejewski... 9 Porównanie metod filtracji obrazów z kamer monitorjącch

4 4 Spis treści Darisz Schel Redkcja czas wkonania algortm Cannego dzięki zastosowani połączenia OpenMP z technologią NVIDIA CUDA Piotr Ratszniak, Łkasz Gątnicki... 5 Aplikacja wszkiwania i wizalizacji tras dla przewoźników samochodowch Przemsław Plecka, Krzsztof Bzdra... 7 Wbór metod szacowania kosztów modfikacji na wstępnch etapach ckl żcia oprogramowania ERP

5 Darisz Jakóbczak Katedra Podstaw Informatki i Zarządzania Wdział Elektroniki i Informatki Politechnika Koszalińska Active Object Modeling and Applications via the Method of Hrwitz-Radon Matrices Kewords: Hrwitz-Radon Matrices, Active Object Modeling. Introdction Object description b its contor is a critical part in man applications of image processing. Ths compter vision and artificial intelligence have a problem: how to model the active shape [,] via discrete set of two-dimensional bondar points? Also sbject of shape representation and shape description is still opened [3,4]. The athor wants to approach a problem of image strctre representation b characteristic contor points and not limited to closed crves, bt also working on open crves (for example a signatre or handwriting). Proposed method relies on active fnctional modeling of bondar points sitated between the basic set of the nodes. The fnctions that are sed in calclations represent whole famil of elementar fnctions: trigonometric, cclometric, logarithmic, exponential and power fnction. Nowadas methods appl mainl polnomial fnctions, for example Bernstein polnomials in Bezier crves, splines and NURBS [5]. Nmerical methods for data interpolation are based on polnomial or trigonometric fnctions, for example Lagrange, Newton, Aitken and Hermite methods. These methods have some weak sides [6] and are not sfficient for object modeling in the sitations when the shape cannot be bild b polnomials or trigonometric fnctions. Also trigonometric basis fnctions in Forier Series Shape Models are not appropriate for describing all shapes. Model-based vision sch as Active Contor Models (called Snakes) or Active Shape Models se the training sets to fit the data and the are applied onl for closed crves. In this paper discssed approach is not limited to closed crves and it does not se a training set of some images, bt onl a set of two-dimensional nodes of the crve. Proposed Active Object Modeling is the fnctional modeling via an elementar fnctions and it helps s to fit the contor and to match the shape in object modeling or image analsis. The athor presents novel method of flexible modeling and bilding the image strctre for applications in signatre and handwriting modeling, crve fitting, object representation and shape geometr.

6 6 Darisz Jakóbczak This paper takes p new method of two-dimensional Active Object Modeling (AOM) b sing a famil of Hrwitz-Radon matrices. The method of Hrwitz-Radon Matrices (MHR) reqires minimal assmptions abot object. The onl information abot shape or crve is the set of at least five nodes. Proposed method of Hrwitz-Radon Matrices (MHR) is applied in crve modeling via different coefficients: sinsoidal, cosinsoidal, tangent, logarithmic, exponential, arc sin, arc cos, arc tan or power. Fnction for coefficient calclations is chosen individall at each Active Object Modeling and it depends on initial reqirements and shape specifications to fit and to match the object. MHR method ses two-dimensional vectors (x,) for data analsis and crve modeling. Shape of the object is represented b scceeding bondar points (x i, i) R as follows in MHR method:. At least five nodes (x, ), (x, ), (x 3, 3), (x 4, 4) and (x 5, 5) if MHR method is implemented with matrices of dimension N = ;. For better modeling nodes oght to be settled at ke points of the crve, for example local minimm or maximm and at least one point between two sccessive local extrema. Condition is connected with important featres of MHR method: MHR version with matrices of dimension N = (MHR-) needs at least five nodes, MHR version with matrices of dimension N = 4 (MHR-4) needs at least nine nodes and MHR version with matrices of dimension N = 8 (MHR-8) needs at least 7 nodes. Condition means for example the highest point of the object in a particlar orientation, convexit changing or crvatre extrema. So this paper wants to answer the qestion: how to model the active object for discrete set of points? Fig.. Nodes of the object before modelin Coefficients for Active Object Modeling are compted via individal featres of the object bondar sing power fnction, sins, cosine, tangent, logarithm, exponent or arc sin, arc cos, arc tan.

7 Active Object Modeling and Applications via the Method of Hrwitz-Radon Matrices 7. Active Object Modeling via MHR The method of Hrwitz Radon Matrices (MHR), described in this paper, is compting points between two sccessive nodes of the crve. Data of Active Object Modeling are interpolated and parameterized for real nmber α [0;] in the range of two sccessive nodes. MHR calclations are introdced with sqare matrices of dimension N =, 4 or 8. Matrices A i, i =, m satisfing A ja k+a ka j = 0, A j = -I for j k; j, k =,...m are called a famil of Hrwitz - Radon matrices, discssed b Adolf Hrwitz and Johann Radon separatel in 93. A famil of Hrwitz - Radon (HR) matrices [7] are skewsmmetric (A it = -A i), A i - = - A i and onl for dimension N=, 4 or 8 the famil of HR matrices consists of N- matrices. For N = :. 0 0 = A For N = 4 there are three HR matrices with integer entries:, = A, = A = A For N = 8 we have seven HR matrices with elements 0, ±. So far HR matrices have fond applications in Space-Time Block Coding (STBC) [8] and orthogonal design [9], in signal processing [0] and Hamiltonian Neral Nets []. How coordinates of crve points are applied in Active Object Modeling? If bondar points have the set of following nodes {(x i, i), i =,,, n} then HR matrices combined with the identit matrix I N are sed to bild the orthogonal Hrwitz - Radon Operator (OHR). For points p =(x, ) and p =(x, ) OHR of dimension N = is bild via matrix M : = ), ( x x x x x x x x x x p p M () For points p =(x, ), p =(x, ), p 3=(x 3, 3) and p 4=(x 4, 4) OHR M 4 of dimension N = 4 is introdced: = ),,, ( x x x x p p p p M ()

8 Darisz Jakóbczak 8 where x x x x =, x x x x + + =, x x x x + + =, x x x x + + =. For nodes p =(x, ), p =(x, ), and p 8=(x 8, 8) OHR M 8 of dimension N = 8 is constrcted [] similarl as () and (): = = )..., ( x p p p M i i (3) where = x x x x x x x x (4) and = ( 0,,, 7) T (4). OHR operators M N ()-(3) satisf the condition of interpolation M N x = (5) for x = (x,x,x N) T R N, x 0, = (,, N) T R N and N =, 4 or 8.. Fnctional coefficients in MHR Active Object Modeling Coordinates of points settled between the nodes are compted [3] sing described MHR method [4]. Each real nmber c [a;b] is calclated b a convex combination c = α a + ( - α) b for a b c b = α [0;]. (6)

9 Active Object Modeling and Applications via the Method of Hrwitz-Radon Matrices 9 The average OHR operator M of dimension N =, 4 or 8 is bild: M = γ A+ ( γ) B. (7) The OHR matrix A is constrcted ()-(3) b ever second point p =(x =a, ), p 3=(x 3, 3), and p N-=(x N-, N-): A = M N ( p, p 3,..., p N-). The OHR matrix B is compted ()-(3) b data p =(x =b, ), p 4=(x 4, 4), and p N=(x N, N): B = M N(p, p 4,..., p N). Vector of first coordinates C is defined for c i = α x i-+ (-α) x i, i =,,, N (8) and C = [c, c,, c N] T. The formla to calclate second coordinates (c i) is similar to the interpolation formla (5): Y( C) = M C (9) where Y(C) = [(c ), (c ),, (c N)] T. So modeled vale of (c i) depends on for, eight or sixteen (N) sccessive nodes, not onl two. Ke qestion is dealing with coefficient γ in (7). Coefficient γ is calclated sing different fnctions (power, sins, cosine, tangent, logarithm, exponent, arc sin, arc cos, arc tan) and choice of fnction is connected with initial reqirements and shape specifications dring fitting and matching of the object. Coefficients γ and α (6) are strongl related:. γ = 0 α =0;. γ = α =; 3. γ [0;]. Different vales of coefficient γ are connected with implemented fnctions and positive real nmber s: γ=α s, γ=sin(α s π/), γ=sin s (α π/), γ=-cos(α s π/), γ=-cos s (α π/), γ=tan(α s π/4), γ=tan s (α π/4), γ=log (α s +), γ=log s (α+), γ=( α ) s, γ=/π arcsin(α s ), γ=(/π arcsinα) s, γ=-/π arccos(α s ), γ=-(/π arccosα) s, γ=4/π arctan(α s ), γ=(4/π arctanα) s, γ=ctg(π/ α s π/4), γ=ctg s (π/-α π/4), γ=-4/π arcctg(α s ), γ=(-4/π arcctgα) s. For example if s = then: basic MHR γ = α, γ = sin(α π/), γ = -cos(α π/), γ = tan(α π/4), γ = log (α + ), γ = α, γ = /π arcsin(α), γ = -/π arccos(α), γ = 4/π arctan(α). What is ver important, above fnctions sed in γ calclations are strictl monotonic for α [0;], becase γ [0;] too. Choice of fnction and parameter s depends on object specifications and individal reqirements. Fixing of nknown coordinates for crve points sing (6)-(9) is called b athor the method of Hrwitz - Radon Matrices (MHR) [5]. Each strictl monotonic fnction between points (0;0) and (;) can be sed in Active Object Modeling not onl above fnctions.

10 0 Darisz Jakóbczak 3. Applications of AOM in Handwriting Modeling Bondar nodes: (0.;0), (0.;5), (0.4;.5), (;) and (;5) from Fig. are sed in some examples of MHR Active Object Modeling with different γ. These examples are connected with handwriting modeling for letter w. Points of the object are calclated with matrices of dimension N = and α = 0., 0.,,0.9. Example Sinsoidal modeling with γ = sin(α π/). Fig.. Sinsoidal modeling with nine reconstrcted points between nodes Example Tangent modeling for γ = tan(α π/4). Fig. 3. Tangent modeling with nine interpolated bondar points between nodes

11 Active Object Modeling and Applications via the Method of Hrwitz-Radon Matrices Example 3 Tangent modeling with γ = tan(α s π/4) and s =.5. Fig. 4. Tangent modeling with nine recovered crve points between nodes Example 4 Tangent modeling for γ = tan(α s π/4) and s =.797. Fig. 5. Tangent modeling with nine reconstrcted points between nodes

12 Darisz Jakóbczak Example 5 Sinsoidal modeling with γ = sin(α s π/) and s =.759. Fig. 6. Sinsoidal modeling with nine interpolated crve points between nodes Example 6 Power fnction modeling for γ = α s and s =.05. Fig. 7. Power fnction modeling with nine recovered object points between nodes

13 Active Object Modeling and Applications via the Method of Hrwitz-Radon Matrices 3 Example 7 Logarithmic modeling with γ = log (α s + ) and s =.533. Fig. 8. Logarithmic modeling with nine reconstrcted points between nodes These seven examples demonstrate possibilities of Active Object Modeling for bondar nodes. Reconstrcted vales and interpolated points, calclated b MHR method, are applied in the process of crve modeling for fitting and matching the object dring its analsis. Recovered points can be treated as a part of signatre or handwriting and sed dring different stages of image processing, for example signatre modeling, object representation, shape geometr and crve fitting. Ever individal signatre or handwriting, each letter or nmber can be modeled b some fnction for parameter γ. This parameter is treated as characteristic featre of letter or figre. 4. Conclsions The method of Hrwitz-Radon Matrices (MHR) enables active modeling of twodimensional shapes sing different coefficients γ: sinsoidal, cosinsoidal, tangent, logarithmic, exponential, arc sin, arc cos, arc tan or power fnction [6]. Fnction for γ calclations is chosen individall at each Active Object Modeling (AOM) and depends on initial reqirements and crve specifications. MHR method leads to shape modeling via discrete set of fixed points. So MHR makes possible the combination of two important problems: interpolation and modeling. Main featres of MHR method are: a) modeling of L points is connected with the comptational cost of rank O(L) ; b) MHR is well-conditioned method (orthogonal matrices) [7]; c) coefficient γ is crcial in the process of AOM and it is compted individall for each object (contor, letter or figre). Ftre works are going to: featres of coefficient γ, implementation of MHR and AOM in object recognition [8], shape representation, crve fitting, contor modeling and parameterization [9].

14 4 Darisz Jakóbczak References. Mahoor, M.H., Abdel-Mottaleb, M., Nasser Ansari, A.: Improved Active Shape Model for Facial Featre Extraction in Color Images. Jornal of Mltimedia (4), -8 (006). Cootes, T.F., Talor, C.J., Cooper, D.H., Graham, J.: Active Shape Models-Their Training and Application. Compter Vision and Image Understanding (6), (995) 3. Amanatiadis, A., Kabrlasos, V.G., Gasteratos, A., Papadakis, S.E.: Evalation of Shape Descriptors for Shape-Based Image Retrieval. IET Image Processing 5(5), (0) 4. Zhang, D., L, G.: Review of Shape Representation and Description Techniqes. Pattern Recognition (37), -9 (004) 5. Schmaker, L.L.: Spline Fnctions: Basic Theor. Cambridge Mathematical Librar (007) 6. Dahlqist, G., Bjoerck, A.: Nmerical Methods. Prentice Hall, New York (974) 7. Eckmann, B.: Topolog, Algebra, Analsis- Relations and Missing Links. Notices of the American Mathematical Societ 5(46), (999) 8. Citko, W., Jakóbczak, D., Sieńko, W.: On Hrwitz - Radon Matrices Based Signal Processing. Workshop Signal Processing at Poznan Universit of Technolog (005) 9. Tarokh, V., Jafarkhani, H., Calderbank, R.: Space-Time Block Codes from Orthogonal Designs. IEEE Transactions on Information Theor 5(45), (999) 0. Sieńko, W., Citko, W., Wilamowski, B.: Hamiltonian Neral Nets as a Universal Signal Processor. 8 th Annal Conference of the IEEE Indstrial Electronics Societ IECON (00). Sieńko, W., Citko, W.: Hamiltonian Neral Net Based Signal Processing. The International Conference on Signal and Electronic Sstem ICSES (00). Jakóbczak, D.: D and 3D Image Modeling Using Hrwitz-Radon Matrices. Polish Jornal of Environmental Stdies 4A(6), (007) 3. Jakóbczak, D.: Shape Representation and Shape Coefficients via Method of Hrwitz-Radon Matrices. Lectre Notes in Compter Science 6374 (Compter Vision and Graphics: Proc. ICCVG 00, Part I), Springer-Verlag Berlin Heidelberg, 4-49 (00) 4. Jakóbczak, D.: Crve Interpolation Using Hrwitz-Radon Matrices. Polish Jornal of Environmental Stdies 3B(8), 6-30 (009) 5. Jakóbczak, D.: Application of Hrwitz-Radon Matrices in Shape Representation. In: Banaszak, Z., Świć, A. (eds.) Applied Compter Science: Modelling of

15 Active Object Modeling and Applications via the Method of Hrwitz-Radon Matrices 5 Prodction Processes (6), pp Lblin Universit of Technolog Press, Lblin (00) 6. Jakóbczak, D.: Object Modeling Using Method of Hrwitz-Radon Matrices of Rank k. In: Wolski, W., Borawski, M. (eds.) Compter Graphics: Selected Isses, pp Universit of Szczecin Press, Szczecin (00) 7. Jakóbczak, D.: Implementation of Hrwitz-Radon Matrices in Shape Representation. In: Choraś, R.S. (ed.) Advances in Intelligent and Soft Compting 84, Image Processing and Commnications: Challenges, pp Springer- Verlag, Berlin Heidelberg (00) 8. Jakóbczak, D.: Object Recognition via Contor Points Reconstrction Using Hrwitz-Radon Matrices. In: Józefczk, J., Orski, D. (eds.) Knowledge-Based Intelligent Sstem Advancements: Sstemic and Cbernetic Approaches, pp IGI Global, Hershe PA, USA (0) 9. Jakóbczak, D.: Crve Parameterization and Crvatre via Method of Hrwitz- Radon Matrices. Image Processing & Commnications- An International Jornal - (6), (0) Abstract Artificial intelligence and compter vision need methods for object modeling having discrete set of bondar points. A novel method of Hrwitz-Radon Matrices (MHR) is sed in shape modeling. Proposed method is based on the famil of Hrwitz-Radon (HR) matrices which possess colmns composed of orthogonal vectors. Two-dimensional active crve is modeling via different fnctions: sins, cosine, tangent, logarithm, exponent, arc sin, arc cos, arc tan and power fnction. It is shown how to bild the orthogonal matrix OHR operator and how to se it in a process of object modeling. Streszczenie Matematka i jej zastosowania wmagają odpowiednich metod modelowania oraz interpolacji danch. Atorska metoda Macierz Hrwitza-Radona (MHR) jest sposobem modelowania krzwej D. Oparta jest ona na rodzinie macierz Hrwitza-Radona, którch klczową cechą jest ortogonalność kolmn. Dwwmiarowe dane są interpolowane z wkorzstaniem różnch fnkcji rozkład prawdopodobieństwa: potęgowch, wielomianowch, wkładniczch, logartmicznch, trgonometrcznch, cklometrcznch. W prac pokazano bdowę ortogonalnego operatora macierzowego i jego wkorzstanie w rekonstrkcji i modelowani danch. Słowa klczowe: macierze Hrwitza-Radona, aktwne modelowanie obiektów

16 6 Darisz Jakóbczak

17 Mirosław Andrzej Maliński Łkasz Barłomiej Chrobak Leszek Bchto Department of Electronics and Compter Science Technical Universit of Koszalin Śniadeckich St Koszalin Poland Michał Pawlak Faclt of Phsics, Astronom and Informatics Nicolas Copernics Universit 5 Grdziądzka St Torń Poland Investigations of the Implanted Laer in Silicon Based on the Modlated Free Carrier Absorption Phenomenon Kewords: semicondctors, ion implantation, nondestrctive testing techniqes Introdction Modlated free carrier absorption techniqe ses the effect of absorption of the infrared light b free electrons. In this method free electrons are generated b the modlated in intensit beam of light of the energ of photons bigger than the energ gap of the semicondctor. As a reslt a periodical concentration of electrons is observed in the condction band. At the same time the same spot of the sample is illminated b the constant in intensit infrared (IR) beam of light. Periodical changing concentration of electrons modlates transmission of the IR beam of light. These changes of the intensit of the transmitted light are detected b the photodiode. Voltage signal of the photodiode is amplified and measred b the lock-in amplifier. Tpicall amplitde and phase freqenc characteristics of this signal are measred and from the fitting of the theoretical characteristics to the experimental ones the lifetime of the opticall generated

18 8 Mirosław Andrzej Maliński, Łkasz Bartłomiej Chrobak, Leszek Bchto, Michał Pawlak carriers is measred. Sch a method was applied for example for investigations of the lifetime of carriers in silicon and the reslts pblished in papers [, 3]. Basics of the MFCA method are described in paper [4]. Different modifications of the MFCA method are described in papers [5-8]. The characteristic featre of these papers is that the deal with the measrements of the life time of carriers in silicon and the describe niform samples e.g. nonimplanted which can be analzed in the single laer model. The paper is the attempt of the application of the MFCA method for investigations of the implanted silicon samples. In this case the phsical model is a two laer one: a thin implanted laer of the thickness d on a sbstrate of the thickness L. Thickness of the implanted laer is mch smaller than the thickness of the sample. In this paper a comparison of the freqenc amplitde characteristics of the MFCA signal of the nonimplanted and O +6 and Ar +8 implanted samples is presented. The aim of the investigations was to check the inflence of the implantation on the freqenc characteristics of the MFCA signal. In this paper a possible explanation of the observed effect is given in the model of a damaged laer. Sample Preparation and Experimental Set Up The investigated samples of silicon were both of the n and p tpe nonimplanted and implanted. Si p tpe samples were nonimplanted and implanted b Ar +8 ions with the energ of 0 kev and implantation doses ions/cm, ions/cm and ions/cm. The thickness of the samples l=80 µm, resistivit ρ=5000 Ωcm. Si n tpe samples were nonimplanted and implanted b O +6 ions with the energ 90 kev and implantation doses ions/cm and ions/cm. The thickness of the samples l=40 µm, resistivit ρ=3-5 Ωcm. The experimental set p for investigations of the implanted silicon samples consisted of 50 W halogen lamp as a sorce of the probe light, 660 nm red laser diode as a sorce of the pmp light, beam splitter, adapter for the sample monting which was connected throgh the fiber with a detector, lock-in tpe amplifier and the compter which controlled the measring process. The schematic diagram of experimental set p is presented in Fig.. All measrements were performed in the room temperatre.

19 Investigations of the Implanted Laer in Silicon Based 9 Fig.. The experimental set p sed for investigations of the implanted laer in silicon samples Experimental reslts Experimental characteristics obtained for silicon samples: nonimplanted and O +6 implanted are shown in Fig.. 0. C7 C7 C8 C Amplitde [a..] C8 C Freqenc [Hz] Fig.. Experimental MFCA characteristics for n-tpe silicon samples implanted with O +6 ions. C7 - n-tpe silicon sample nonimplanted, C8 n-tpe silicon sample implanted with O +6 ions of the energ 90 kev and the dose ions/cm, C n-tpe silicon sample implanted with O +6 ions of the energ 90 kev and the dose ions/cm.

20 0 Mirosław Andrzej Maliński, Łkasz Bartłomiej Chrobak, Leszek Bchto, Michał Pawlak Experimental characteristics obtained for silicon samples: nonimplanted and Ar +8 implanted silicon are shown in Fig C09 C09 C0 C C Amplitde [a..] 0 3 C0 0 4 C C Freqenc [Hz] Fig. 3. Experimental MFCA characteristics for p-tpe silicon samples implanted with Ar +8 ions. C09 - p-tpe silicon sample nonimplanted, C0 p-tpe silicon sample implanted with Ar +8 ions of the energ 0 kev and the dose ions/cm, C p-tpe silicon sample implanted with Ar +8 ions of the energ 0 kev and the dose ions/cm and C p-tpe silicon sample implanted with Ar +8 ions of the energ 0 kev and the dose ions/cm Discssion For the pmping beam of light of the wavelength 660 nm the optical absorption coefficient for silicon is β=630 cm -. The lifetimes of carriers for n-tpe sample nonimplanted sample was τ=8 µs. The lifetime of carriers for p-tpe nonimplanted sample was τ=5 µs. When we assme that the lifetime of carriers in the damaged laer is mch shorter than in the sbstrate then the decrease of the amplitde of the MFCA signal is expected according to the formla given below: l S = β exp( β x) x () d When the parameter k is the ratio of the amplitde of the MFCA signal of implanted silicon for the freqenc in the range 0 3 Hz 0 4 Hz to that of the nonimplanted signal when the thickness of the damaged laer can be compted as:

21 Investigations of the Implanted Laer in Silicon Based ln( k) d = () β For n tpe silicon samples the following parameters k and d were obtained: k =0.059 d =0 µm, k =0.04 d = µm (see Fig.). For p-tpe silicon samples the following parameters k and d were obtained: k =0.07 d =5 µm, k =0.005 d =0 µm and k =0.003 d = µm (see Fig.3). Sch thicknesses of damaged laers were also measred with an argon laser of the wavelength 54 nm where the optical absorption coefficient was 6300 cm -. Obtained thicknesses for this wavelength of the pmping light was almost identical with these presented in this paper what confirmed the theoretical model taken for comptations of the thicknesses of damaged laers being the reslt of the high energ ion implantation. The decrease of the amplitde of the MFCA signal in the freqenc range from Hz to 0 3 Hz is cased b the diffsion of carriers from the damaged laer to the sbstrate. With the increase of the freqenc of modlation the diffsion length of carriers decreases and fewer carriers diffse to the region of the sbstrate. For high freqencies of modlation the MFCA signal comes onl from the sbstrate not from the implantation damaged laer. Conclsions The preliminar experimental reslts of the MFCA measrements of nonimplanted and implanted silicon samples, presented in the paper, indicate that the implantation process considerabl modifies the freqenc MFCA characteristics. The observed strong decrease of the amplitde of the MFCA signal was interpreted in a model of a damaged laer created in the reslt of a high energ implantation. Estimated thickness of damaged laers was in the range from 0 µm to µm. References. M. Maliński, Ł. Chrobak, Determination of the Life Time of Excess Carriers in Silicon With Photoacostic And Photocrrent Methods, Jornal of Phsics: Conference Series 4 (00), -5.. Ł. Chrobak, M. Maliński, Badania parametrów rekombinacjnch materiałów krzemowch z wkorzstaniem nieniszczącej techniki MFCA opartej na zjawisk modlacji absorpcji na nośnikach swobodnch, Zeszt Nakowe Wdział Elektroniki i Informatki 3 (0), WPK, Ł. Chrobak, M. Maliński, Zastosowanie zjawiska modlacji absorpcji na nośnikach swobodnch do nieniszczącch badań materiałów półprzewodnikowch, Elektronika - technologie, konstrkcje, zastosowania LIII () (0), 0-3.

22 Mirosław Andrzej Maliński, Łkasz Bartłomiej Chrobak, Leszek Bchto, Michał Pawlak 4. Dietzel D., Gibkes J., Chotikaprakhan S., Bein B. K., Pelz J., "Radiometric analsis of laser modlated IR properties of semicondctors", International Jornal of Thermophsics 4(3) (003), Li B., Li X., Li W., Hang Q., Zhang X., Accrate determination of electronic transport properties of semicondctor wafers with spatial resolved photo-carrier techniqes, Jornal of Phsics: Conference Series, 4 (00), Zhang X., Li B., Gao C., Analsis of free carrier absorption measrement of electronic transport properties of silicon wafers, Eropean Phsics Jornal Special Topics, 53 (008), Hang Q., Li B., Li X., Inflence of probe beam size on signal analsis of modlated free carrier absorption techniqe, Jornal of Phsics: Conference Series, 4 (00), Li W., Li B., Analsis of modlated free-carrier absorption measrement of electronic transport properties of silicon wafers, Jornal of Phsics: Conference Series, 4 (00), 06. Abstract This paper presents experimental amplitde MFCA characteristics of the implanted silicon samples. Inflence of the silicon implantation process for freqenc MFCA characteristics has been analzed. The idea and the experimental set-p of the proposed method have been presented and discssed. This paper proves that is possible to estimate depth of the implanted laer from MFCA experimental data. Streszczenie W artkle przedstawiono ekspermentalne charakterstki MFCA dla próbek implantowanego krzem. Przeanalizowano wpłw proces implantacji krzem na charakterstki MFCA. Przedstawiono i poddano dsksji ideę zaproponowanej metod oraz stanowisko ekspermentalne. Praca dowadnia, że możliwa jest estmacja głębokości warstw implantowanej na podstawie ekspermentalnch charakterstk MFCA.

23 Anna Witenberg Maciej Walkowiak Wdział Elektroniki i Informatki Politechnika Koszalińska l. Śniadeckich, Koszalin Odpowiedzi prądowe w kładzie dwóch anten liniowch ze szczególnm względnieniem redkcji późnoczasowch niestabilności Słowa klczowe: anten liniowe, całkowe równanie pola elektrcznego, metoda postęp w czasie (MOT), równanie Hallena w dziedzinie czas. Wprowadzenie Technologia szerokopasmowa (UWB) jest atrakcjnm rozwiązaniem w nowoczesnch sstemach komnikacji bezprzewodowej. Charakterzje ją, międz innmi, emisja i odbiór ciąg modlowanch ltrakrótkich implsów o czasie trwania rzęd kilk nanoseknd. Ma to bezpośrednie przełożenie na obniżenie kosztów w kładzie nadawanie - odbiór, zmniejsza prawdopodobieństwo zniekształceń transmitowanch informacji oraz ogranicza do minimm możliwość zakłócania proces przesłania danch. Jest wiele dziedzin z możliwością zastosowania tej form komnikacji: technika radiowa, telewizjna i radarowa, szeroko rozmiane obrazowanie w medcnie, sstem ochron i bezpieczeństwa, techniki sterowania i identfikacji [0, ]. Ze względ na bardzo szerokie pasmo częstotliwości transmitowanch sgnałów, prowadzone obecnie prace koncentrją się na modelowani i badani właściwości kładów antena nadawcza antena odbiorcza w dziedzinie czas. Taki stan rzecz jest natralną konsekwencją analiz i zachowania się pól elektromagnetcznch, które przecież są procesami, a więc natralnmi fnkcjami czas. Jest to szczególnie ważne prz projektowani i określani właściwości sstemów antenowch, a szerzej kanałów komnikacjnch []. W artkle przedstawiono wniki modelowania w dziedzinie czas kład dwóch anten liniowch oświetlonch implsem pola elektrcznego o kształcie krzwej Gassa.