{"id":102029,"date":"2024-07-26T12:02:04","date_gmt":"2024-07-26T10:02:04","guid":{"rendered":"https:\/\/www.linseis.com\/metody-analizy-termicznej\/pomiar-van-der-pauw\/"},"modified":"2026-01-16T10:20:16","modified_gmt":"2026-01-16T09:20:16","slug":"pomiar-van-der-pauw","status":"publish","type":"page","link":"https:\/\/www.linseis.com\/pl\/metody-analizy-termicznej\/pomiar-van-der-pauw\/","title":{"rendered":"Pomiar Van der Pauw"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"102029\" class=\"elementor elementor-102029 elementor-22670\" data-elementor-post-type=\"page\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a3549cf e-flex e-con-boxed e-con e-parent\" data-id=\"a3549cf\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ac41c94 elementor-widget elementor-widget-image\" data-id=\"ac41c94\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/\/linseis_scale-top-1.svg\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a7b7feb e-con-full e-flex e-con e-child\" data-id=\"a7b7feb\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-6100945 e-con-full e-flex e-con e-child\" data-id=\"6100945\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-cc1182c elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"cc1182c\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:250}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\"><b>\n\nPomiar Van der Pauw\n\n<\/b><\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6d91a43 e-con-full e-flex e-con e-child\" data-id=\"6d91a43\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9413374 elementor-widget elementor-widget-n-carousel\" data-id=\"9413374\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;carousel_items&quot;:[{&quot;slide_title&quot;:&quot;Produkt 1&quot;,&quot;_id&quot;:&quot;d6fbcdb&quot;}],&quot;slides_to_show&quot;:&quot;1&quot;,&quot;slides_to_scroll&quot;:&quot;2&quot;,&quot;autoplay_speed&quot;:2000,&quot;slides_to_show_tablet&quot;:&quot;1&quot;,&quot;slides_to_show_mobile&quot;:&quot;1&quot;,&quot;autoplay&quot;:&quot;yes&quot;,&quot;pause_on_hover&quot;:&quot;yes&quot;,&quot;pause_on_interaction&quot;:&quot;yes&quot;,&quot;infinite&quot;:&quot;yes&quot;,&quot;speed&quot;:500,&quot;offset_sides&quot;:&quot;none&quot;,&quot;image_spacing_custom&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:10,&quot;sizes&quot;:[]},&quot;image_spacing_custom_tablet&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;image_spacing_custom_mobile&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]}}\" data-widget_type=\"nested-carousel.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"e-n-carousel swiper\" role=\"region\" aria-roledescription=\"carousel\" aria-label=\"Karussell\" dir=\"ltr\">\n\t\t\t<div class=\"swiper-wrapper\" aria-live=\"off\">\n\t\t\t\t\t\t\t\t\t\t<div class=\"swiper-slide\" data-slide=\"1\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"1 of 1\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-44441f5 e-flex e-con-boxed e-con e-child\" data-id=\"44441f5\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4103051 elementor-widget__width-initial elementor-invisible elementor-widget elementor-widget-image\" data-id=\"4103051\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"800\" height=\"800\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Linseis-Icons_Linien-weiss_Zeichenflaeche-1-Kopie-88-1024x1024.png\" class=\"attachment-large size-large wp-image-36264\" alt=\"\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Linseis-Icons_Linien-weiss_Zeichenflaeche-1-Kopie-88-1024x1024.png 1024w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Linseis-Icons_Linien-weiss_Zeichenflaeche-1-Kopie-88-300x300.png 300w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Linseis-Icons_Linien-weiss_Zeichenflaeche-1-Kopie-88-150x150.png 150w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Linseis-Icons_Linien-weiss_Zeichenflaeche-1-Kopie-88-768x768.png 768w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Linseis-Icons_Linien-weiss_Zeichenflaeche-1-Kopie-88-1536x1536.png 1536w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Linseis-Icons_Linien-weiss_Zeichenflaeche-1-Kopie-88-2048x2048.png 2048w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b4a6800 elementor-widget elementor-widget-image\" data-id=\"b4a6800\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/\/linseis_scale-bottom-1.svg\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-7c8d6cc e-flex e-con-boxed e-con e-parent\" data-id=\"7c8d6cc\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d7b7522 e-flex e-con-boxed e-con e-parent\" data-id=\"d7b7522\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-449b6fd e-con-full e-flex e-con e-child\" data-id=\"449b6fd\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-031217d elementor-invisible elementor-widget elementor-widget-wp-widget-bcn_widget\" data-id=\"031217d\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;}\" data-widget_type=\"wp-widget-bcn_widget.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"breadcrumbs\" vocab=\"https:\/\/schema.org\/\" typeof=\"BreadcrumbList\"><span property=\"itemListElement\" typeof=\"ListItem\"><a property=\"item\" typeof=\"WebPage\" title=\"Przejd\u017a do Linseis.\" href=\"https:\/\/www.linseis.com\/pl\/\" class=\"home\" aria-current=\"page\"><span property=\"name\">Linseis<\/span><\/a><meta property=\"position\" content=\"1\"><\/span><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-ed98f58 e-flex e-con-boxed e-con e-parent\" data-id=\"ed98f58\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-bbc47b3 e-con-full e-flex e-con e-child\" data-id=\"bbc47b3\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-71a1ec4 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"71a1ec4\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>Pomiar Van der Pauw<\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-32d9053 elementor-widget elementor-widget-text-editor\" data-id=\"32d9053\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p>Metoda pomiarowa Van der Pauw, nazwana na cze\u015b\u0107 jej wynalazcy Leo J. van der Pauw, jest szeroko stosowan\u0105 4-punktow\u0105 metod\u0105 pomiarow\u0105 do <strong>okre\u015blania rezystancji powierzchniowej i <a href=\"https:\/\/www.linseis.com\/pl\/?page_id=101943\" data-auto-event-observed=\"true\">wsp\u00f3\u0142czynnika Halla<\/a><\/strong> materia\u0142\u00f3w.<\/p><p>W 1958 roku van der Pauw rozwi\u0105za\u0142 og\u00f3lny problem rozk\u0142adu potencja\u0142u w cienkiej, arbitralnie ukszta\u0142towanej warstwie przewodz\u0105cej. <strong><a href=\"https:\/\/www.linseis.com\/applikationen\/duennschichttechnik\/\" data-auto-event-observed=\"true\">w cienkiej, dowolnie ukszta\u0142towanej warstwie przewodz\u0105cej<\/a> <\/strong>i tym samym umo\u017cliwi\u0142 przeprowadzanie na nich pomiar\u00f3w Halla i rezystancji.<\/p><p><strong>Aby jednak pomiar by\u0142 prawid\u0142owy, nale\u017cy spe\u0142ni\u0107 szereg wymog\u00f3w:<\/strong><\/p><ul><li>Grubo\u015b\u0107 t pr\u00f3bki musi by\u0107 jednorodna i niewielka w stosunku do odleg\u0142o\u015bci mi\u0119dzy stykami.<\/li><li>Z matematycznego punktu widzenia musi on sk\u0142ada\u0107 si\u0119 z ci\u0105g\u0142ej formy, a zatem nie mo\u017ce mie\u0107 \u017cadnych otwor\u00f3w ani wysepek z materia\u0142u o wysokiej przewodno\u015bci.<\/li><li>Cztery styki musz\u0105 znajdowa\u0107 si\u0119 na kraw\u0119dzi pr\u00f3bki i by\u0107 ma\u0142e w stosunku do jej powierzchni.<\/li><\/ul><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fe4080d elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"fe4080d\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p><img decoding=\"async\" class=\"wp-image-22672 size-full aligncenter\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Van-der-Pauw-method-1.png\" alt=\"\" width=\"484\" height=\"343\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Van-der-Pauw-method-1.png 484w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Van-der-Pauw-method-1-300x213.png 300w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><\/p><p style=\"text-align: center;\"><em>Rys. 1) Uk\u0142ad eksperymentalny do pomiaru Van der Pauw <\/em><\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f06a3a0 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"f06a3a0\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p><img decoding=\"async\" class=\"aligncenter wp-image-22679 size-full\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Contacting-of-a-sample-for-the-Van-der-Pauw-measurement-1024x481-1.png\" alt=\"\" width=\"1024\" height=\"481\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Contacting-of-a-sample-for-the-Van-der-Pauw-measurement-1024x481-1.png 1024w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Contacting-of-a-sample-for-the-Van-der-Pauw-measurement-1024x481-1-300x141.png 300w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Contacting-of-a-sample-for-the-Van-der-Pauw-measurement-1024x481-1-768x361.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><p style=\"text-align: center;\"><em>Rys. 2a) Kontakt z pr\u00f3bk\u0105 do pomiaru Van der Pauw. 2b) Kontakt pr\u00f3bki z chipem pomiarowym TFA, w tym jego wymiary.  <\/em><\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-64ed86b elementor-widget elementor-widget-text-editor\" data-id=\"64ed86b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p>Je\u015bli wszystkie wymagania s\u0105 spe\u0142nione, otrzymuje si\u0119 pr\u00f3bk\u0119 przygotowan\u0105 ze stykami kraw\u0119dziowymi A, B, C i D, jak pokazano na rys. 2a-b. Aby obliczy\u0107 przewodno\u015b\u0107 elektryczn\u0105, nale\u017cy zmierzy\u0107 poziom\u0105 i pionow\u0105 rezystancj\u0119 Van der Pauwa R<sub>(ij,kl)<\/sub>, przy czym do pomiaru rezystancji poziomej stosuje si\u0119 nast\u0119puj\u0105ce zasady:  <\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-63cdf9f elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"63cdf9f\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-22686 size-full\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/horizontal-resistance.png\" alt=\"\" width=\"417\" height=\"129\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/horizontal-resistance.png 417w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/horizontal-resistance-300x93.png 300w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b0d0537 elementor-widget elementor-widget-text-editor\" data-id=\"b0d0537\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p><sub>VC<\/sub> jest napi\u0119ciem styku mierzonym wzgl\u0119dem ziemi, a <sub>IAB<\/sub> jest pr\u0105dem przy\u0142o\u017conym mi\u0119dzy stykami A i B, zaczynaj\u0105c od A i ko\u0144cz\u0105c na B. Je\u015bli styki s\u0105 wymieniane cyklicznie, mo\u017cna okre\u015bli\u0107 pionow\u0105 rezystancj\u0119 Van der Pauwa. Je\u015bli zmierzono rezystancj\u0119 poziom\u0105 i pionow\u0105, rezystancj\u0119 powierzchniow\u0105 lub, je\u015bli znana jest grubo\u015b\u0107 warstwy, <strong>rezystancj\u0119 w\u0142a\u015bciw\u0105<\/strong> mo\u017cna obliczy\u0107, rozwi\u0105zuj\u0105c numerycznie wz\u00f3r Van der Pauwa: <\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-771f150 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"771f150\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-22693 size-full\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/resistivity-formula-van-der-pauw.png\" alt=\"\" width=\"434\" height=\"147\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/resistivity-formula-van-der-pauw.png 434w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/resistivity-formula-van-der-pauw-300x102.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b4bb58a elementor-widget elementor-widget-text-editor\" data-id=\"b4bb58a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p>Poniewa\u017c <strong>przewodno\u015b\u0107 elektryczna<\/strong> jest odwrotno\u015bci\u0105 oporu w\u0142a\u015bciwego, mo\u017cna j\u0105 obliczy\u0107 za pomoc\u0105 nast\u0119puj\u0105cego r\u00f3wnania.<\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-26bec37 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"26bec37\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-22700 size-full\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/electrical-conductivity.png\" alt=\"\" width=\"153\" height=\"140\"><\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dba4700 elementor-widget elementor-widget-text-editor\" data-id=\"dba4700\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p>Aby okre\u015bli\u0107 <strong>wsp\u00f3\u0142czynnik Halla<\/strong><sub>AH<\/sub> pr\u00f3bki, zewn\u0119trzne pole magnetyczne o g\u0119sto\u015bci strumienia <sub>BZ<\/sub> jest przyk\u0142adane prostopadle do powierzchni pr\u00f3bki, a zmiana przek\u0105tnej rezystancji Van der Pauwa (patrz rys. 3) jest mierzona jako funkcja nat\u0119\u017cenia pola magnetycznego.<\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5d4d6e6 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"5d4d6e6\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-22707 size-full\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/sample-configuration-Hall-coefficient-measurement-using-Van-der-Pauw-technology.jpg\" alt=\"\" width=\"504\" height=\"452\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/sample-configuration-Hall-coefficient-measurement-using-Van-der-Pauw-technology.jpg 504w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/sample-configuration-Hall-coefficient-measurement-using-Van-der-Pauw-technology-300x269.jpg 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p><p style=\"text-align: center;\"><em>Rys. 3) Przyk\u0142adowa konfiguracja do pomiaru wsp\u00f3\u0142czynnika Halla przy u\u017cyciu techniki pomiarowej Van der Pauw, z przy\u0142o\u017conym polem magnetycznym prostopad\u0142ym do powierzchni pr\u00f3bki. <\/em><\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f10e311 elementor-widget elementor-widget-text-editor\" data-id=\"f10e311\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p>W takim przypadku obowi\u0105zuj\u0105 nast\u0119puj\u0105ce zasady:<\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b70a4ff elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"b70a4ff\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-22714 size-full\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Hall-formula.png\" alt=\"\" width=\"301\" height=\"136\"><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-90002f5 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"90002f5\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p>z<\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ecbdc27 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"ecbdc27\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-22721 size-full aligncenter\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Hall-formula-2.png\" alt=\"\" width=\"554\" height=\"112\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Hall-formula-2.png 554w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Hall-formula-2-300x61.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a2ae4fb elementor-widget elementor-widget-text-editor\" data-id=\"a2ae4fb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p>Efekty przesuni\u0119cia w pomiarach pr\u0105du i napi\u0119cia mog\u0105 by\u0107 t\u0142umione przy u\u017cyciu zasady odwr\u00f3cenia kierunku pomiaru. Efekty przesuni\u0119cia wynikaj\u0105ce z pomiaru nat\u0119\u017cenia pola magnetycznego s\u0105 t\u0142umione przez pomiar napi\u0119cia przek\u0105tnej <g id=\"gid_0\">VHall<\/g> przy r\u00f3\u017cnych nat\u0119\u017ceniach pola magnetycznego i okre\u015blenie wsp\u00f3\u0142czynnika Halla na podstawie nachylenia napi\u0119cia Halla w stosunku do nat\u0119\u017cenia pola magnetycznego. Ostateczne obliczenie opiera si\u0119 na nast\u0119puj\u0105cym r\u00f3wnaniu:  <\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fe61853 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"fe61853\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInUp&quot;,&quot;_animation_delay&quot;:500}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-22728 size-full\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Voltage-Hall-formula-300x123-1.png\" alt=\"\" width=\"300\" height=\"123\"><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-35b3714 elementor-widget elementor-widget-text-editor\" data-id=\"35b3714\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\"><div class=\"row\"><div class=\"spb_content_element col-sm-12 spb_text_column\"><div class=\"spb_wrapper clearfix\"><p>Je\u015bli sta\u0142a Halla jest mierzona przy u\u017cyciu metody pomiaru AC, stosowane jest zmienne pole magnetyczne, a wynikowe napi\u0119cie Halla jest odczytywane za pomoc\u0105 wzmacniacza lock-in. Pozwala to na pomiar materia\u0142\u00f3w o szczeg\u00f3lnie niskiej ruchliwo\u015bci, poniewa\u017c napi\u0119cia Halla, kt\u00f3re s\u0105 zwykle stosunkowo ma\u0142e, nie s\u0105 ju\u017c nak\u0142adane przez tak zwane przesuni\u0119cia niewsp\u00f3\u0142osiowo\u015bci. <\/p><\/div><\/div><\/div><\/section>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8801439 e-flex e-con-boxed elementor-invisible e-con e-parent\" data-id=\"8801439\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeInUp&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-4fda86f e-con-full e-flex e-con e-child\" data-id=\"4fda86f\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-a0a9aac e-con-full e-flex e-con e-child\" data-id=\"a0a9aac\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-53ea4ef elementor-widget elementor-widget-text-editor\" data-id=\"53ea4ef\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>Jakie w\u0142a\u015bciwo\u015bci s\u0105 okre\u015blane?<\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d38f832 elementor-widget elementor-widget-text-editor\" data-id=\"d38f832\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Metoda Van der Pauwa jest stosowana do okre\u015blania w\u0142a\u015bciwo\u015bci transportu elektrycznego pr\u00f3bek (od materia\u0142\u00f3w sta\u0142ych do cienkich warstw), takich jak przewodno\u015b\u0107 elektryczna, rezystywno\u015b\u0107, sta\u0142a Halla, koncentracja no\u015bnik\u00f3w \u0142adunku i ruchliwo\u015b\u0107 no\u015bnik\u00f3w \u0142adunku.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Pomiar Van der Pauw Pomiar Van der Pauw Metoda pomiarowa Van der Pauw, nazwana na cze\u015b\u0107 jej wynalazcy Leo J. van der Pauw, jest szeroko stosowan\u0105 4-punktow\u0105 metod\u0105 pomiarow\u0105 do okre\u015blania rezystancji powierzchniowej i wsp\u00f3\u0142czynnika Halla materia\u0142\u00f3w. W 1958 roku van der Pauw rozwi\u0105za\u0142 og\u00f3lny problem rozk\u0142adu potencja\u0142u w cienkiej, arbitralnie ukszta\u0142towanej warstwie przewodz\u0105cej. w [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":101974,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-102029","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/pages\/102029","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/comments?post=102029"}],"version-history":[{"count":0,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/pages\/102029\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/pages\/101974"}],"wp:attachment":[{"href":"https:\/\/www.linseis.com\/pl\/wp-json\/wp\/v2\/media?parent=102029"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}