[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-665322-105":59,"doc-detail-665322-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","chapter-2-semiconductor-heterostructures-lecture-notes","Chapter 2 - Semiconductor Heterostructures - Lecture Notes","","Lecture notes on semiconductor heterostructures covering energy-band diagrams in real space, including how electrostatic potential and electric fields make band edges position dependent. The material defines electron affinity and work function, explains alignment of conduction and valence bands at hetero-interfaces via the electron affinity rule, and analyzes electron flow in N-N heterojunctions leading to depletion and accumulation regions. Equilibrium is treated through built-in voltage and Fermi-level alignment, then extended to P-N heterojunctions with electron and hole flows.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/chapter-2-semiconductor-heterostructures-lecture-notes/665322/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/chapter-2-semiconductor-heterostructures-lecture-notes/665322.png","ImageObject",300,407,{"name":92,"@type":93},"Aran","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the purpose of drawing band edges in real space?","Question",{"text":112,"@type":113},"It helps relate the conduction and valence band edges to real-space position, especially when electrostatic potential and electric fields are present.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do electron affinity and work function differ?",{"text":117,"@type":113},"Electron affinity is the energy to remove an electron from the bottom of the conduction band to the vacuum level, while work function is the energy to remove an electron from the Fermi level to the vacuum level.",{"name":119,"@type":110,"acceptedAnswer":120},"What determines the equilibrium condition in a heterojunction?",{"text":121,"@type":113},"Electron flow continues until the electric field created by depletion/accumulation regions makes the Fermi levels on both sides equal, producing a built-in voltage between the sides.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},665322,1793298200,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},137455076865,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Chapter 2  \nSemiconductor Heterostructures  \nIn this lecture you will learn:  \n• Energy band diagrams in real space  \n• Semiconductor heterostructures and heterojunctions  \n• Electron affinity and work function  \n• Heterojunctions in equilibrium  \n• Electrons at Heterojunctions  \n• Semiconductor Quantum wells  \nHerbert Kroemer (1920-)  \nNobel Prize 2000 for the Semiconductor Heterostructure Laser  \n University  \nBand Diagrams in Real Space- I  \nN-type semiconductor  \nn 􀀠 N e 􀀐 􀀋Ec 􀀐Ef 􀀌KT  \nc  \np 􀀠 Nv e 􀀐 􀀋Ef 􀀐Ev 􀀌KT  \nP-type semiconductor  \nFor devices, it is useful to draw the conduction and valence band edges in real space:  \nEc  \nEf  \nEv  \nx  \nEc  \nEf  \nEv  \nx  \n University  \nBand Diagrams in Real Space- II  \nElectrostatic potential and electric field:  \nAn electrostatic potential (and an electric field) can be present in a crystal:  \n􀁉􀀋􀀌 and 􀀋􀀌 􀀠 􀀐􀂒 􀁉􀀋􀀌  \nThdiseptotaersil eonnergE n􀀋yfbaunt  \nelectron in a crystal is then given not just by the energy band also includes the potential energy coming from the potential:  \nEn 􀀋􀀌 􀁯 En 􀀋􀀌 􀀐 e 􀁉􀀋􀀌  \nTherefore, the conduction and valence band edges also become position dependent:  \nE 􀁯 Ec 􀀐 e 􀁉􀀋􀀌  \nc  \nExample: Uniform x-directed electric field  \nEc  \n Ef  \n  􀀋􀀌 􀀠 Ex   \nEv  \nx  \nN-type semiconductor  \nE 􀁯 Ev 􀀐 e 􀁉􀀋􀀌  \nv  \n􀀋􀀌 􀀠 Ex   \n􀁉􀀋􀀌 􀀠 􀁉􀀋x 􀀠 0􀀌 􀀐 Ex x Ec 􀀋x 􀀌 􀀠 Ec 􀀋x 􀀠 0􀀌 􀀎 eExx  \n University  \nElectron Affinity and Work Function  \nElectron affinity “􀁆 ” is the energy required to remove an electron from the bottom of the conduction band to outside the crystal, i.e. to the vacuum level  \nWork function “W” is the energy required to remove an electron from the Fermi level to the vacuum level  \n• Work function changes with doping but affinity is a constant for a given material  \nV  \n􀁆  \nEc  \nEf  \nW  \n Ev  \n~~ ~~ x  \nECE 407 – Spring 2009 – Farhan Rana – Cornell University  \nSemiconductor N-N Heterostructure: Electron Affinity Rule  \nHeterostructure: A semiconductor structure in which more than one semiconductor material is used and the structure contains interfaces or junctions between two different semiconductors  \nConsider the following heterostructure interface between a wide bandgap and a narrow bandgap semiconductor (both n-type):  \n1 2 Eg 1 Eg2  \nV  \nEc1  \nEf 1  \nEv1  \nEc2  \nEf 2  \nEv 2  \nThe electron affinity rule tells how the energy band edges of the two semiconductors line up ata hetero-interface  \n University  \nSemiconductor N-N Heterojunction  \nV  \nEc1  \nEf 1  \nEv1  \n\n| \u003Cbr>􀁆 1\u003Cbr>Eg 1\u003Cbr>Electrons\u003Cbr>􀁆 2\u003Cbr>Eg2 | Ec2\u003Cbr>Ef 2\u003Cbr>Ev 2 |\n| --- | --- |\n\nSomething is wrong here:  \nthe Fermi level (the chemical potential) has to be the same everywhere in equilibrium (i.e. a flat line)  \n• Once a junction is made, electrons will flow from the side with higher Fermi level (1) to the side with lower Fermi level (2)  \n University  \nSemiconductor N-N Heterojunction: Equilibrium  \nV  \nEc1  \nDepletion region  \n􀁆 2  \nEc2  \n• Electrons will flow from the side with higher Fermi level (1) to the side with lower Fermi level (2)  \nEf 1  \nEv1  \n\n|  |  | |\n| --- | --- | --- |\n|  | Eg 1\u003Cbr>| Eg2 |\n|  |  | |\n|  |  |  |\n\nEf 2  \nEv 2  \nNote: the vacuum level follows the electrostatic  \npotential:  \nV 􀀋x 􀀌 􀀠 V 􀀋x 􀀠 0􀀌 􀀐 e 􀀾 􀁉􀀋x 􀀌 􀀐 􀁉􀀋x 􀀠 0􀀌 􀁀  \n• Electron flow away from semiconductor (1) will result in a region at the interface which is depleted of electrons (depletion region) . Because of positively charged donor atoms, the depletion region has net positive charge density  \n• Electron flow into semiconductor (2) will result in a region at the interface which hasan accumulation of electrons (accumulation region) . The accumulation region has net negative charge density  \n University  \nSemiconductor N-N Heterojunction: Equilibrium  \nV  \nEc1  \nEf 1  \nEv1  \n\n| 􀁆 1\u003Cbr>􀁆 2\u003Cbr>| Ec2\u003Cbr>Ef 2\u003Cbr>Ev 2 |\n| --- | --- |\n\n• Electron flow from semiconductor (1) to semiconductor (2) continues until the electric field due to the formation of depletion and accumulation regions becomes so large that the Fermi le","cbCaifljiIv2MEfC","https://ap.wps.com/l/cbCaifljiIv2MEfC","pdf",1161817,34,"English","# Chapter 2 Semiconductor Heterostructures\n## Band Diagrams in Real Space\n## Electron Affinity and Work Function\n## Semiconductor N-N Heterostructure and Heterojunctions\n## N-N Heterojunction: Equilibrium\n## Semiconductor P-N Heterojunction: Equilibrium","[{\"question\":\"What is the purpose of drawing band edges in real space?\",\"answer\":\"It helps relate the conduction and valence band edges to real-space position, especially when electrostatic potential and electric fields are present.\"},{\"question\":\"How do electron affinity and work function differ?\",\"answer\":\"Electron affinity is the energy to remove an electron from the bottom of the conduction band to the vacuum level, while work function is the energy to remove an electron from the Fermi level to the vacuum level.\"},{\"question\":\"What determines the equilibrium condition in a heterojunction?\",\"answer\":\"Electron flow continues until the electric field created by depletion/accumulation regions makes the Fermi levels on both sides equal, producing a built-in voltage between the sides.\"}]","Chapter 2 - Semiconductor Heterostructures - Lecture Notes | PDF",86]