{"id":5145,"date":"2023-02-25T04:42:59","date_gmt":"2023-02-25T04:42:59","guid":{"rendered":"https:\/\/www.goodacademic.com\/blog\/questions\/quantum-mechanics\/"},"modified":"2023-02-25T04:42:59","modified_gmt":"2023-02-25T04:42:59","slug":"quantum-mechanics","status":"publish","type":"questions","link":"https:\/\/www.goodacademic.com\/blog\/questions\/quantum-mechanics\/","title":{"rendered":"Quantum mechanics"},"content":{"rendered":"<div class=\"col-sm-12 messageContent\">\n <b>Learning Goal: <\/b>I&#8217;m working on a electrical engineering multi-part question and need the explanation and answer to help me learn.<\/p>\n<p>2) Consider a heterostructure consisting of three layers \u00f0\ufffd\u2018\u2020\u00f0\ufffd\u2018\u2013\u00e2\u02c6\u2019\u00f0\ufffd\u2018\u2020\u00f0\ufffd\u2018\u2013\u00f0\ufffd\u2018\u201a2 \u00e2\u02c6\u2019\u00f0\ufffd\u2018\u2020\u00f0\ufffd\u2018\u2013 The central \u00f0\ufffd\u2018\u2020\u00f0\ufffd\u2018\u2013\u00f0\ufffd\u2018\u201a2 layer is<br \/>a barrier (insulator). Silicon which is a semiconductor is on the two sides of the central Silicon<br \/>dioxide layer. The barrier for electrons in the conduction band of Silicon that tunnel through<br \/>the Silicon dioxide to the Silicon on the other side is approximately 3.4 eV. The Silicon dioxide<br \/>region is 1.4 nm thick. Assume that the potential energy in both Silicon layers is the same. This<br \/>problem is representative of the device physics associated with tunneling through the insulator<br \/>in MOSFETs.<br \/>(a) Calculate the tunneling probability for electrons to tunnel through the Silicon dioxide as a<br \/>function of energy. In the plot, mark all the differences between a quantum barrier and a<br \/>classical barrier.<br \/>(b) Calculate the tunneling probability for a barrier that is 6 nm thick. All other parameters are<br \/>the same as part (a). In a single graph compare the tunneling probability of parts (a) and (b).<br \/>How does the tunneling probability change as a function of barrier thickness?<br \/>[In drawing plots for parts (a) and (b), focus on representing the data in an easy-to-read manner.<br \/>Use logarithmic scales when it is challenging to read values.]<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Learning Goal: I&#8217;m working on a electrical engineering multi-part question and need the explanation and answer to help me learn. 2) Consider a heterostructure consisting of three layers \u00f0\ufffd\u2018\u2020\u00f0\ufffd\u2018\u2013\u00e2\u02c6\u2019\u00f0\ufffd\u2018\u2020\u00f0\ufffd\u2018\u2013\u00f0\ufffd\u2018\u201a2 \u00e2\u02c6\u2019\u00f0\ufffd\u2018\u2020\u00f0\ufffd\u2018\u2013 The central \u00f0\ufffd\u2018\u2020\u00f0\ufffd\u2018\u2013\u00f0\ufffd\u2018\u201a2 layer isa barrier (insulator). Silicon which is a semiconductor is on the two sides of the central Silicondioxide layer. The barrier for [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":[],"disciplines":[704],"paper_types":[],"tagged":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/5145"}],"collection":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/comments?post=5145"}],"version-history":[{"count":0,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/5145\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/media?parent=5145"}],"wp:term":[{"taxonomy":"disciplines","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/disciplines?post=5145"},{"taxonomy":"paper_types","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/paper_types?post=5145"},{"taxonomy":"tagged","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/tagged?post=5145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}