{"id":218377,"date":"2025-05-23T17:23:19","date_gmt":"2025-05-23T17:23:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=218377"},"modified":"2025-05-23T17:23:21","modified_gmt":"2025-05-23T17:23:21","slug":"the-intrinsic-carrier-concentration-of-silicon-sample-of-300-k-is-1-5-x1016-m3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/23\/the-intrinsic-carrier-concentration-of-silicon-sample-of-300-k-is-1-5-x1016-m3\/","title":{"rendered":"The intrinsic carrier concentration of silicon sample of 300 K is 1.5 \u00d71016\/m3"},"content":{"rendered":"\n<p>The intrinsic carrier concentration of silicon sample of 300 K is 1.5 \u00d71016\/m3 . If after doping, the number of majority carriers is 5 \u00d7 1020\/m3 , the minority carrier density is (a) 4.50 \u00d7 1011\/m3 (b) 3.33 \u00d7 104 \/m3 (c) 5.00 \u00d7 1020\/m3 (d) 3.00 \u00d7 10-5\/m3<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this, we use the <strong>mass action law<\/strong> in semiconductors: ni2=n\u22c5pn_i^2 = n \\cdot p<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>nin_i is the <strong>intrinsic carrier concentration<\/strong><\/li>\n\n\n\n<li>nn is the <strong>concentration of electrons (majority carriers in n-type)<\/strong><\/li>\n\n\n\n<li>pp is the <strong>concentration of holes (minority carriers in n-type)<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>ni=1.5\u00d71016\u2009m\u22123n_i = 1.5 \\times 10^{16} \\, \\text{m}^{-3}<\/li>\n\n\n\n<li>n=5\u00d71020\u2009m\u22123n = 5 \\times 10^{20} \\, \\text{m}^{-3} (majority carriers after doping)<\/li>\n<\/ul>\n\n\n\n<p>We are to find pp, the minority carrier concentration.<\/p>\n\n\n\n<p>Using the mass action law: p=ni2np = \\frac{n_i^2}{n}<\/p>\n\n\n\n<p>Substitute values: p=(1.5\u00d71016)25\u00d71020=2.25\u00d710325\u00d71020=0.45\u00d71012=4.5\u00d71011\u2009m\u22123p = \\frac{(1.5 \\times 10^{16})^2}{5 \\times 10^{20}} = \\frac{2.25 \\times 10^{32}}{5 \\times 10^{20}} = 0.45 \\times 10^{12} = 4.5 \\times 10^{11} \\, \\text{m}^{-3}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Correct Answer: <strong>(a) 4.50 \u00d7 10\u00b9\u00b9\/m\u00b3<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 Explanation:<\/h3>\n\n\n\n<p>In intrinsic (pure) silicon at 300 K, the concentration of electrons and holes is equal and given by the intrinsic carrier concentration nin_i. When a semiconductor is doped (with donor atoms to make it n-type), the majority carrier concentration (electrons) increases significantly.<\/p>\n\n\n\n<p>However, the product of electron and hole concentrations must still satisfy the mass action law n\u22c5p=ni2n \\cdot p = n_i^2. This means if one carrier type increases, the other must decrease to maintain this equilibrium.<\/p>\n\n\n\n<p>Here, after doping, n=5\u00d71020\u2009m\u22123n = 5 \\times 10^{20} \\, \\text{m}^{-3}, much larger than nin_i. So, the minority carrier concentration (holes in n-type) must decrease.<\/p>\n\n\n\n<p>Using the mass action law, we find the hole concentration pp drops to 4.5\u00d71011\u2009m\u221234.5 \\times 10^{11} \\, \\text{m}^{-3}, which is logical: heavily doped semiconductors have very few minority carriers.<\/p>\n\n\n\n<p>This principle is critical in designing diodes and transistors, where control over minority and majority carrier populations determines electrical behavior.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/image-227.png\" alt=\"\" class=\"wp-image-218378\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The intrinsic carrier concentration of silicon sample of 300 K is 1.5 \u00d71016\/m3 . If after doping, the number of majority carriers is 5 \u00d7 1020\/m3 , the minority carrier density is (a) 4.50 \u00d7 1011\/m3 (b) 3.33 \u00d7 104 \/m3 (c) 5.00 \u00d7 1020\/m3 (d) 3.00 \u00d7 10-5\/m3 The Correct Answer and Explanation is: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-218377","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218377","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=218377"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218377\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=218377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=218377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=218377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}