AUTEX Research Journal, Vol. 14, No 2, June 2014, DOI: 10.2478/v10304-012-0050-4 © AUTEX DETERMINATION OF FABRIC SURFACE RESISTANCE BY VAN DER PAUW METHOD IN CASE OF CONTACTS DISTANT FROM THE SAMPLE EDGE Magdalena Tokarska Department of Architecture of Textiles, Lodz University of Technology, 116 Zeromskiego St., 90-924 Lodz Poland E-mail: [email protected] Abstract: The van der Pauw method can be used to determine the electroconductive properties of textile materials. However, the sample surface resistance can be determined provided that the sample has characteristics typical for the van der Pauw structure. In the paper, a method of evaluating the sample structure is shown. The selected electroconductive woven fabrics are used as an example of van der Pauw structure. An analysis of impact of electrodes placement on the resistance measurements was conducted. Knowing how the resistance of the sample varies with the electrodes distance from the edge, the samples’ surface resistances were calculated in cases when the electrodes are placed at the sample edge. An uncertainty analysis of the samples’ surface resistances was conducted based on the Monte Carlo method. Keywords: Electroconductive properties, woven fabric, van der Pauw structure, van der Pauw method, surface resistance, electrodes placement, Monte Carlo method 1. Introduction of the sample. The effect of electrode placement on resistance measurement was investigated [8,10,14]. In the case of the The van der Pauw method was developed to determine the woven fabrics, the contacts should not be too close to the properties of thin semiconductors [1,2]. This method is currently boundaries of the sample because errors can be introduced used to evaluate the conductivity of thin layers deposited on [3,15]. In this paper, a solution for the problem is proposed. different substrates [3-6] or thin electroconductive materials Knowing how the resistance of the sample varies with the [7-10]. The van der Pauw method can be applied to small electrodes distance from the edges, the sample surface samples contrary to the four electrode method [11] where resistance can be calculated in cases when the electrodes electrodes are located collinearly on the tested material placement is consistent with the van der Pauw notion. surface. The surface resistance can be determined using the van der Pauw equation [1] provided that the electroconductive sample has the structure typical for that used by van der Pauw. 2. Materials An evaluation of the fibrous structure from this point of view is difficult and requires a detailed analysis of its structure. The Two electroconductive woven fabrics were selected for testing. complexity of a textile sample, for example woven fabric, shows The first fabric, labelled as S1, is an antioxidant silver fibre the number of different parameters describing the structure shielding rip-stop fabric. The rip-stop fabric is resistant to [12,13]. In order to verify whether the conditions described in tearing and ripping. The second sample, signed as S2, is a the van der Pauw method are represented in the woven fabric silver fibre shielding canvas fabric. The canvas is a tight fabric structure, a special criterion was developed [7]. The criterion is and very durable. The chosen fabrics parameters and their useful in selecting appropriate fabric sample for testing. standard deviation are juxtaposed in Table 1. The van der Pauw method requires that the point contacts The samples with a measuring area in the shape of a 70 mm used for the resistance measurements be placed at the edges side square were prepared from the electroconductive woven Table 1. Parameters of the electroconductive woven fabrics. Standard Standard Volumetric Thickness deviation of Areal density deviation of areal density Sample thickness density mm mm g/m2 g/m2 kg/m3 S1 0.15 1.4×10-3 76 0.12 507 S2 0.35 1.4×10-3 149 0.31 426 http://www.autexrj.com 55 Brought to you by | University of Technology Lódz Authenticated Download Date | 1/21/16 1:43 PM h V h av 100% 1% (2) V h avs100% 1% (2) h s h h h V av 100% 1% (2) h sL G L h 15 (3) AUTEX Research Journal, Vol. 14, No 2, June 2014, DOI: 10.2478/v10304-012-0050-4 © AUTEXG h15 (3) h fabrics. The direction of cut lines was perpendicular to warp B) The measureL of the structure compactness: G 15 (3) and weft yarns. h Awedwa Awadwe dwedwa C A d A d d d 100 95 (4) (4) C we wa waA weA we wa 100 95 (4) The structure of the selected fabrics was analysed in detail. wa we Awa Awe It was examined if the fabrics possess characteristics typical where Awa is the spacing of the warp yarns, Awe is the spacing of for the van der Pauw structure [1]. A special criterion was the weft yarns,A d d is Athe ddiameter d dof warp yarns and d is the C we wawa wa we we wa 100 95 we (4) developed by Tokarska [7] based on [11,12,16] to assess the diameter of weft yarns. Awa Awe following characteristics: • geometry of the sample (A), C) The measure of the structure homogeneity: R A R A • compactness of the structure (B), wa wa we we H Rwa AwaRwe Awe 0.001 (5) • homogeneity of the structure (C), H S 0.001 (5) (5) S • isotropy of the sample (D). where Rwa and Rwe are the warp and weft repeats, respectively, Rwa AwaRwe Awe H min{R1, R2 ,...,R0n.}001 (5) Accordingly, the measures given below were used. and S is theIz surfacemin{ R of, Rthe tested,..., R sample.} 0.95 (6) Iz max{R1S , R2 ,..., Rn }0.95 (6) 1 2 n A) The measures of the sample geometry: D) The measuremax{ ofR the1, Rsample2 ,..., Risotropy:n} min{R , R ,..., R } h ≤ 1 mm (1) Iz 1 2 n 0 . 95 (6) (6) max{R1, R2 ,..., Rn} where h is the sample thickness; where Ra , Ra, …, RRa are resistances R measured in the 1 exp 2 R v n exp R h 1 0 (7) selected nexp directions v using exp four electrodes h 1 located0 collinearly (7) hav Rs Rs Vh 100% 1% (2) on the sample (2) [11]. Rs Rs hav sh Vh 100% 1% (2) sh R R v h where hav is the average sample thickness, sh is the standard Analysis expof the fabrics structureexp was conducted1 0 based on (7) R R deviation and Vh is the coefficient of variation of the sample microscopic images s of the sampless taken with Olympus thickness; L microscope. The Rimages were R captured atR 7.5´ magnification R G 15 (3) R R A D,B C R D A,C B R B C, A D R C B,D A (8) L (Figure 1). v AD,BC D A,CB BC, AD CB,D A G h 15 (3) Rv 4 (8) h (3) 4 The designated parameters are juxtaposed in Table 2. where L is the peripheral length of the sample. RAD,BC RD A,CB RBC, AD RCB,D A Rv (8) A d A d d d 4 C we wa wa we we wa 100 95 (4) Awedwa Awadwe dwedwa Awa Awe (4) C 100 95 Awa Awe R R R R AB,DC B A,CD DC, AB CD,B A Rh RAB,DC RB A,CD RDC, AB RCD,B A (9) R 4 (9) h 4 RAB,DC RB A,CD RDC, AB RCD,B A R A R A R (9) wa wa we we h H R A R A 0.001 (5) 4 H wa waS we we 0.001 (5) S min{R , R ,..., R } Iz 1 2 n 0.95 (6) min{R1, R2 ,..., Rn} max{R1, R2 ,..., Rn} Iz 0.95 (6) max{R1, R2 ,..., Rn} Sample S1 Sample S2 Rv Rh Figure 1. Microscopic imagesexp of the samples. exp 1 0 (7) Rv Rh exp s exp s 1 0 (7) Rs Rs Table 2. Parameters of the fabrics for the analysis of the fabric structure. Sample L Rwa dwa Awa Rwe dwe Awe Nwa Nwe RAD,BC RD A,CB RBC, AD RCB,D A Rv (8) yarns per yarns per R R R R - mm R AunitsD,B C D mmA,C B 4 B Cmm, A D C Bunits,D A mm (8)mm v 4 1 cm 1 cm S1 280 2 0.21 0.24 2 0.28 0.32 41 31 S2 280 6 0.14 0.14 6 0.27 0.30 71 33 http://www.autexrj.com/ 56 Brought to you by | University of Technology Lódz RAB,DC RB A,CD RDC, AAuthenticatedB RCD,B A Rh (9) RAB,DC RB A,CD Download RDC, A DateB R| 1/21/16CD,B A1:43 PM R 4 (9) h 4 AUTEX Research Journal, Vol. 14, No 2, June 2014, DOI: 10.2478/v10304-012-0050-4 © AUTEX The designated parameters, Awa and Awe, allowed calculating external contacts and by measuring the voltage drop on the two the number of warp yarns, Nwa, and the number of weft yarns, internal ones. The received results are presented in Table 3. Nwe, per 1 cm [12]. The received results are summarised in Table 2. All the received results are summarised in Table 4. The characteristics typical for a van der Pauw structure It was finally confirmed that the selected electroconductive have been determined by the implemented measures, i.e.: h woven fabrics had all the characteristics typical for a van der calculated from formula (1), Vh from (2), G from (3), C from (4) Pauw structure.