{"id":100477,"date":"2024-07-26T12:02:04","date_gmt":"2024-07-26T10:02:04","guid":{"rendered":"https:\/\/www.linseis.com\/metodi-di-analisi-termica\/misura-van-der-pauw\/"},"modified":"2026-01-13T08:52:19","modified_gmt":"2026-01-13T07:52:19","slug":"misura-van-der-pauw","status":"publish","type":"page","link":"https:\/\/www.linseis.com\/it\/metodi-di-analisi-termica\/misura-van-der-pauw\/","title":{"rendered":"Misura Van der Pauw"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"100477\" class=\"elementor elementor-100477 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\nMisura 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 di 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-36263\" 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=\"Vai a Linseis.\" href=\"https:\/\/www.linseis.com\/it\/\" 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>Misura 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>Il metodo di misurazione Van der Pauw, che prende il nome dal suo inventore Leo J. van der Pauw, \u00e8 un metodo di misurazione a 4 punti ampiamente utilizzato per <strong>determinare la resistenza di strato ed il <a href=\"https:\/\/www.linseis.com\/it\/?page_id=100290\" data-auto-event-observed=\"true\">coefficiente di Hall<\/a><\/strong> dei materiali.<\/p><p>Nel 1958, van der Pauw risolse il problema generale della distribuzione del potenziale <strong><a href=\"https:\/\/www.linseis.com\/applikationen\/duennschichttechnik\/\" data-auto-event-observed=\"true\">in uno strato conduttivo sottile e di forma arbitraria<\/a> <\/strong>e rese cos\u00ec possibile effettuare misure di Hall e di resistenza su di essi.<\/p><p><strong>Tuttavia, per una misurazione corretta \u00e8 necessario soddisfare una serie di requisiti:<\/strong><\/p><ul><li>Lo spessore t del campione deve essere omogeneo e piccolo rispetto alla distanza tra i contatti.<\/li><li>In termini matematici, deve essere costituito da una forma continua e quindi non deve presentare buchi o isole di materiale altamente conduttivo.<\/li><li>I quattro contatti devono essere situati sul bordo del campione e devono essere piccoli rispetto alla superficie del campione.<\/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>Fig. 1) Configurazione sperimentale per la misurazione di 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>Fig. 2a) Contatto con un campione per la misurazione Van der Pauw. 2b) Contatto del campione sul chip di misurazione TFA, comprese le sue dimensioni.  <\/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 tutti i requisiti sono soddisfatti, si ottiene un campione preparato con i contatti di bordo A, B, C e D, come mostrato nella Fig. 2a-b. Per calcolare la conduttivit\u00e0 elettrica, \u00e8 necessario misurare le resistenze di Van der Pauw orizzontali e verticali R<sub>(ij,kl)<\/sub>; per la misurazione della resistenza orizzontale vale quanto segue:<\/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> \u00e8 la tensione del contatto misurata verso terra e <sub>IAB<\/sub> \u00e8 la corrente applicata tra i contatti A e B, partendo da A e arrivando a B. Se i contatti vengono scambiati ciclicamente, \u00e8 possibile determinare la resistenza verticale di Van der Pauw. Se le resistenze orizzontali e verticali sono state misurate, la resistenza superficiale o, se lo spessore dello strato \u00e8 noto, la <strong>resistenza specifica<\/strong> pu\u00f2 essere calcolata risolvendo numericamente la formula di 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>Poich\u00e9 la <strong>conduttivit\u00e0 elettrica<\/strong> \u00e8 il reciproco della resistenza specifica, pu\u00f2 essere calcolata utilizzando la seguente equazione.<\/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>Per determinare il <strong>coefficiente di Hall<\/strong><sub>AH<\/sub> del campione, si applica un campo magnetico esterno con densit\u00e0 di flusso <sub>BZ<\/sub> perpendicolare alla superficie del campione e si misura la variazione della resistenza diagonale di Van der Pauw (vedi Fig. 3) in funzione dell&#8217;intensit\u00e0 del campo magnetico.<\/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) Esempio di configurazione per la misurazione del coefficiente di Hall con la tecnica di misurazione di Van der Pauw, con un campo magnetico applicato perpendicolare alla superficie del campione. <\/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>In questo caso, si applica quanto segue:<\/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>con<\/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>Gli effetti di offset nella misurazione della corrente e della tensione possono essere eliminati utilizzando il principio dell&#8217;inversione della direzione di misurazione. Gli effetti di offset derivanti dalla misurazione dell&#8217;intensit\u00e0 del campo magnetico vengono eliminati misurando la tensione diagonale <g id=\"gid_0\">VHall<\/g> a diverse intensit\u00e0 di campo magnetico e determinando il coefficiente di Hall dalla pendenza della tensione di Hall rispetto all&#8217;intensit\u00e0 del campo magnetico. Il calcolo finale si basa sulla seguente equazione:  <\/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 la costante di Hall viene misurata con il metodo di misurazione CA, viene applicato un campo magnetico alternato e la tensione di Hall risultante viene letta con un amplificatore lock-in. In questo modo \u00e8 possibile misurare materiali con mobilit\u00e0 particolarmente bassa, poich\u00e9 le tensioni di Hall, che di solito sono relativamente piccole, non vengono pi\u00f9 sovrastate dai cosiddetti offset di disallineamento.<\/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>Quali propriet\u00e0 vengono determinate?<\/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>Il metodo Van der Pauw viene utilizzato per determinare le propriet\u00e0 di trasporto elettrico dei campioni (dai materiali solidi ai film sottili) come la conduttivit\u00e0 elettrica, la resistivit\u00e0, la costante di Hall, la concentrazione dei portatori di carica e la mobilit\u00e0 dei portatori di carica.<\/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>Misura Van der Pauw Misura Van der Pauw Il metodo di misurazione Van der Pauw, che prende il nome dal suo inventore Leo J. van der Pauw, \u00e8 un metodo di misurazione a 4 punti ampiamente utilizzato per determinare la resistenza di strato ed il coefficiente di Hall dei materiali. Nel 1958, van der Pauw [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":100333,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-100477","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.linseis.com\/it\/wp-json\/wp\/v2\/pages\/100477","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.linseis.com\/it\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.linseis.com\/it\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/it\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/it\/wp-json\/wp\/v2\/comments?post=100477"}],"version-history":[{"count":0,"href":"https:\/\/www.linseis.com\/it\/wp-json\/wp\/v2\/pages\/100477\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/it\/wp-json\/wp\/v2\/pages\/100333"}],"wp:attachment":[{"href":"https:\/\/www.linseis.com\/it\/wp-json\/wp\/v2\/media?parent=100477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}