{"id":103590,"date":"2024-07-26T12:02:04","date_gmt":"2024-07-26T10:02:04","guid":{"rendered":"https:\/\/www.linseis.com\/metodos-de-analise-termica\/medicao-de-van-der-pauw\/"},"modified":"2026-01-12T10:14:58","modified_gmt":"2026-01-12T09:14:58","slug":"medicao-de-van-der-pauw","status":"publish","type":"page","link":"https:\/\/www.linseis.com\/pt-pt\/metodos-de-analise-termica\/medicao-de-van-der-pauw\/","title":{"rendered":"Medi\u00e7\u00e3o de Van der Pauw"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"103590\" class=\"elementor elementor-103590 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 fetchpriority=\"high\" decoding=\"async\" width=\"800\" height=\"800\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/06\/linseis_scale-top-1.svg\" class=\"attachment-large size-large wp-image-29175\" alt=\"\" \/>\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\nMedi\u00e7\u00e3o de 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 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-36265\" 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\" width=\"800\" height=\"800\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/06\/linseis_scale-bottom-1.svg\" class=\"attachment-large size-large wp-image-29171\" alt=\"\" \/>\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=\"Go to Linseis.\" href=\"https:\/\/www.linseis.com\/pt-pt\/\" 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>Medi\u00e7\u00e3o de 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>O m\u00e9todo de medi\u00e7\u00e3o de Van der Pauw, que recebeu o nome do seu inventor Leo J. van der Pauw, \u00e9 um m\u00e9todo de medi\u00e7\u00e3o de 4 pontos amplamente utilizado para <strong>determinar a resist\u00eancia da folha e <a href=\"https:\/\/www.linseis.com\/pt-pt\/?page_id=103482\" data-auto-event-observed=\"true\">o coeficiente Hall<\/a><\/strong> dos materiais.<\/p><p>Em 1958, van der Pauw resolveu o problema geral da distribui\u00e7\u00e3o de potencial numa camada condutora fina e de forma arbitr\u00e1ria <strong><a href=\"https:\/\/www.linseis.com\/applikationen\/duennschichttechnik\/\" data-auto-event-observed=\"true\">numa camada condutora fina e de forma arbitr\u00e1ria<\/a> <\/strong>e tornou assim poss\u00edvel efetuar medi\u00e7\u00f5es de Hall e de resist\u00eancia.<\/p><p><strong>No entanto, para uma medi\u00e7\u00e3o correta, devem ser cumpridos alguns requisitos:<\/strong><\/p><ul><li>A espessura t da amostra deve ser homog\u00e9nea e pequena em rela\u00e7\u00e3o \u00e0 dist\u00e2ncia entre os contactos.<\/li><li>Em termos matem\u00e1ticos, deve consistir numa forma cont\u00ednua e, por conseguinte, n\u00e3o deve ter quaisquer buracos ou ilhas de material altamente condutor.<\/li><li>Os quatro contactos devem estar localizados no bordo da amostra e ser pequenos em rela\u00e7\u00e3o \u00e0 \u00e1rea da superf\u00edcie da amostra.<\/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 loading=\"lazy\" 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>Fig. 1) Instala\u00e7\u00e3o experimental para a medi\u00e7\u00e3o de 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 loading=\"lazy\" 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>Fig. 2a) Contacto de uma amostra para a medi\u00e7\u00e3o de Van der Pauw. 2b) Contacto da amostra no chip de medi\u00e7\u00e3o TFA, incluindo as suas dimens\u00f5es.  <\/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>Se todos os requisitos forem cumpridos, obt\u00e9m-se uma amostra preparada com os contactos laterais A, B, C e D, como se mostra na Fig. 2a-b. Para calcular a condutividade el\u00e9ctrica, devem medir-se as resist\u00eancias de Van der Pauw horizontal e vertical R<sub>(ij,kl)<\/sub>, aplicando-se o seguinte \u00e0 medi\u00e7\u00e3o da resist\u00eancia horizontal:  <\/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> \u00e9 a tens\u00e3o do contacto medida contra a terra e <sub>IAB<\/sub> \u00e9 a corrente aplicada entre os contactos A e B, come\u00e7ando em A e terminando em B. Se os contactos forem trocados ciclicamente, a resist\u00eancia vertical de Van der Pauw pode ser determinada. Se as resist\u00eancias horizontal e vertical tiverem sido medidas, a resist\u00eancia de superf\u00edcie ou, se a espessura da camada for conhecida, a <strong>resist\u00eancia espec\u00edfica<\/strong>, pode ser calculada resolvendo numericamente a f\u00f3rmula de Van der Pauw: <\/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>Como a <strong>condutividade el\u00e9ctrica<\/strong> \u00e9 o rec\u00edproco da resist\u00eancia espec\u00edfica, pode ser calculada utilizando a seguinte equa\u00e7\u00e3o.<\/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>Para determinar o <strong>coeficiente Hall<\/strong><sub>AH<\/sub> da amostra, aplica-se um campo magn\u00e9tico externo com densidade de fluxo <sub>BZ<\/sub> perpendicular \u00e0 superf\u00edcie da amostra e mede-se a varia\u00e7\u00e3o da resist\u00eancia diagonal de Van der Pauw (ver Fig. 3) em fun\u00e7\u00e3o da intensidade do campo magn\u00e9tico.<\/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>Fig. 3) Exemplo de configura\u00e7\u00e3o para medir o coeficiente Hall utilizando a t\u00e9cnica de medi\u00e7\u00e3o de Van der Pauw, com um campo magn\u00e9tico aplicado perpendicularmente \u00e0 superf\u00edcie da amostra. <\/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>Neste caso, aplica-se o seguinte:<\/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>com<\/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>Os efeitos de desvio na medi\u00e7\u00e3o da corrente e da tens\u00e3o podem ser suprimidos utilizando o princ\u00edpio da invers\u00e3o do sentido da medi\u00e7\u00e3o. Os efeitos de desvio resultantes da medi\u00e7\u00e3o da intensidade do campo magn\u00e9tico s\u00e3o suprimidos medindo a tens\u00e3o diagonal <g id=\"gid_0\">VHall<\/g> em diferentes intensidades de campo magn\u00e9tico e determinando o coeficiente Hall a partir do declive da tens\u00e3o Hall sobre a intensidade do campo magn\u00e9tico. O c\u00e1lculo final baseia-se na seguinte equa\u00e7\u00e3o:  <\/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>Se a constante Hall for medida utilizando o m\u00e9todo de medi\u00e7\u00e3o AC, \u00e9 aplicado um campo magn\u00e9tico alternado e a tens\u00e3o Hall resultante \u00e9 lida utilizando um amplificador lock-in. Isto permite a medi\u00e7\u00e3o de materiais com mobilidades particularmente baixas, uma vez que as tens\u00f5es Hall, que s\u00e3o normalmente comparativamente pequenas, j\u00e1 n\u00e3o s\u00e3o sobrepostas pelos chamados desvios de alinhamento. <\/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>Que propriedades s\u00e3o determinadas?<\/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>O m\u00e9todo de Van der Pauw \u00e9 utilizado para determinar as propriedades de transporte el\u00e9trico de amostras (desde materiais s\u00f3lidos a pel\u00edculas finas), tais como a condutividade el\u00e9ctrica, a resistividade, a constante de Hall, a concentra\u00e7\u00e3o de portadores de carga e a mobilidade dos portadores de carga.<\/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>Medi\u00e7\u00e3o de Van der Pauw Medi\u00e7\u00e3o de Van der Pauw O m\u00e9todo de medi\u00e7\u00e3o de Van der Pauw, que recebeu o nome do seu inventor Leo J. van der Pauw, \u00e9 um m\u00e9todo de medi\u00e7\u00e3o de 4 pontos amplamente utilizado para determinar a resist\u00eancia da folha e o coeficiente Hall dos materiais. Em 1958, van [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":103513,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-103590","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.linseis.com\/pt-pt\/wp-json\/wp\/v2\/pages\/103590","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.linseis.com\/pt-pt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.linseis.com\/pt-pt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pt-pt\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pt-pt\/wp-json\/wp\/v2\/comments?post=103590"}],"version-history":[{"count":0,"href":"https:\/\/www.linseis.com\/pt-pt\/wp-json\/wp\/v2\/pages\/103590\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/pt-pt\/wp-json\/wp\/v2\/pages\/103513"}],"wp:attachment":[{"href":"https:\/\/www.linseis.com\/pt-pt\/wp-json\/wp\/v2\/media?parent=103590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}