Stable finite element method of eight-band k·p model without spurious solutions and numerical study of interfaces in heterostructures
A Lagrange-Hermite finite element method for the eight-band k·p model is developed. We demonstrate that besides the incompletion of k·p basis functions, the ill representation of first-order derivatives can also bend the conduction band structure down and lead to the highly oscillatory solutions. Ou...
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| Veröffentlicht in: | Journal of applied physics 2014-12, Vol.116 (23) |
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| container_title | Journal of applied physics |
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| creator | Ma, Xunpeng Li, Kangwen Zhang, Zuyin Jiang, Yu Xu, Yun Song, Guofeng |
| description | A Lagrange-Hermite finite element method for the eight-band k·p model is developed. We demonstrate that besides the incompletion of k·p basis functions, the ill representation of first-order derivatives can also bend the conduction band structure down and lead to the highly oscillatory solutions. Our method simultaneously solves these two problems and achieves robust stability and high accuracy in real-space numerical calculation. The more physical asymmetric operator ordering is employed and the connection problem in abrupt interface is resolved by using an approximately abrupt interface. The situation of smooth interface used to explain the discrepancies between experiment and simulation of abrupt interface is also calculated by our method, and the result suggests that the influence of the interface smoothing should be considered in the short period superlattices or quantum structures of the narrow well. |
| doi_str_mv | 10.1063/1.4904845 |
| format | Article |
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We demonstrate that besides the incompletion of k·p basis functions, the ill representation of first-order derivatives can also bend the conduction band structure down and lead to the highly oscillatory solutions. Our method simultaneously solves these two problems and achieves robust stability and high accuracy in real-space numerical calculation. The more physical asymmetric operator ordering is employed and the connection problem in abrupt interface is resolved by using an approximately abrupt interface. The situation of smooth interface used to explain the discrepancies between experiment and simulation of abrupt interface is also calculated by our method, and the result suggests that the influence of the interface smoothing should be considered in the short period superlattices or quantum structures of the narrow well.</description><identifier>ISSN: 0021-8979</identifier><identifier>EISSN: 1089-7550</identifier><identifier>DOI: 10.1063/1.4904845</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Applied physics ; ASYMMETRY ; Basis functions ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; Computer simulation ; Conduction bands ; Finite element analysis ; FINITE ELEMENT METHOD ; Heterostructures ; INTERFACES ; Mathematical models ; Nonlinear programming ; NUMERICAL ANALYSIS ; Quantum phenomena ; Robustness (mathematics) ; SIMULATION ; STABILITY ; SUPERLATTICES</subject><ispartof>Journal of applied physics, 2014-12, Vol.116 (23)</ispartof><rights>2014 AIP Publishing LLC.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c200t-a1aa0028f0ea8bdc035e69b4bade658aa1ce1eaab1b46d4748c27818dc9efa603</citedby><cites>FETCH-LOGICAL-c200t-a1aa0028f0ea8bdc035e69b4bade658aa1ce1eaab1b46d4748c27818dc9efa603</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,27903,27904</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/22402830$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Ma, Xunpeng</creatorcontrib><creatorcontrib>Li, Kangwen</creatorcontrib><creatorcontrib>Zhang, Zuyin</creatorcontrib><creatorcontrib>Jiang, Yu</creatorcontrib><creatorcontrib>Xu, Yun</creatorcontrib><creatorcontrib>Song, Guofeng</creatorcontrib><title>Stable finite element method of eight-band k·p model without spurious solutions and numerical study of interfaces in heterostructures</title><title>Journal of applied physics</title><description>A Lagrange-Hermite finite element method for the eight-band k·p model is developed. We demonstrate that besides the incompletion of k·p basis functions, the ill representation of first-order derivatives can also bend the conduction band structure down and lead to the highly oscillatory solutions. Our method simultaneously solves these two problems and achieves robust stability and high accuracy in real-space numerical calculation. The more physical asymmetric operator ordering is employed and the connection problem in abrupt interface is resolved by using an approximately abrupt interface. The situation of smooth interface used to explain the discrepancies between experiment and simulation of abrupt interface is also calculated by our method, and the result suggests that the influence of the interface smoothing should be considered in the short period superlattices or quantum structures of the narrow well.</description><subject>Applied physics</subject><subject>ASYMMETRY</subject><subject>Basis functions</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>Computer simulation</subject><subject>Conduction bands</subject><subject>Finite element analysis</subject><subject>FINITE ELEMENT METHOD</subject><subject>Heterostructures</subject><subject>INTERFACES</subject><subject>Mathematical models</subject><subject>Nonlinear programming</subject><subject>NUMERICAL ANALYSIS</subject><subject>Quantum phenomena</subject><subject>Robustness (mathematics)</subject><subject>SIMULATION</subject><subject>STABILITY</subject><subject>SUPERLATTICES</subject><issn>0021-8979</issn><issn>1089-7550</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNpNkU1OwzAQhS0EEqWw4AaWWLFIsRMncZao4k-qxAJYW44zIS6JXfwj1AtwJfacDFftgtXMaD69maeH0CUlC0qq4oYuWEMYZ-URmlHCm6wuS3KMZoTkNONN3ZyiM-_XhFDKi2aGvl-CbEfAvTY6AIYRJjABTxAG22HbY9DvQ8haaTr88fuzwZPtYMRfOu1jwH4TnbbRY2_HGLQ1Hu9IEydwWskR-xC77U5HmwCulwp8avEAabI-uKhCdODP0UkvRw8XhzpHb_d3r8vHbPX88LS8XWUqJyRkkkqZnPCegORtp0hRQtW0rJUdVCWXkiqgIGVLW1Z1rGZc5TWnvFMN9LIixRxd7XXTbS28Sp7VoKwxoILIc5a0i3_UxtnPCD6ItY3OpMdETvOKcZ5XNFHXe0olJ95BLzZOT9JtBSViF4ag4hBG8QfQeH_T</recordid><startdate>20141221</startdate><enddate>20141221</enddate><creator>Ma, Xunpeng</creator><creator>Li, Kangwen</creator><creator>Zhang, Zuyin</creator><creator>Jiang, Yu</creator><creator>Xu, Yun</creator><creator>Song, Guofeng</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>20141221</creationdate><title>Stable finite element method of eight-band k·p model without spurious solutions and numerical study of interfaces in heterostructures</title><author>Ma, Xunpeng ; Li, Kangwen ; Zhang, Zuyin ; Jiang, Yu ; Xu, Yun ; Song, Guofeng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-a1aa0028f0ea8bdc035e69b4bade658aa1ce1eaab1b46d4748c27818dc9efa603</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Applied physics</topic><topic>ASYMMETRY</topic><topic>Basis functions</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>Computer simulation</topic><topic>Conduction bands</topic><topic>Finite element analysis</topic><topic>FINITE ELEMENT METHOD</topic><topic>Heterostructures</topic><topic>INTERFACES</topic><topic>Mathematical models</topic><topic>Nonlinear programming</topic><topic>NUMERICAL ANALYSIS</topic><topic>Quantum phenomena</topic><topic>Robustness (mathematics)</topic><topic>SIMULATION</topic><topic>STABILITY</topic><topic>SUPERLATTICES</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ma, Xunpeng</creatorcontrib><creatorcontrib>Li, Kangwen</creatorcontrib><creatorcontrib>Zhang, Zuyin</creatorcontrib><creatorcontrib>Jiang, Yu</creatorcontrib><creatorcontrib>Xu, Yun</creatorcontrib><creatorcontrib>Song, Guofeng</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>Journal of applied physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ma, Xunpeng</au><au>Li, Kangwen</au><au>Zhang, Zuyin</au><au>Jiang, Yu</au><au>Xu, Yun</au><au>Song, Guofeng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stable finite element method of eight-band k·p model without spurious solutions and numerical study of interfaces in heterostructures</atitle><jtitle>Journal of applied physics</jtitle><date>2014-12-21</date><risdate>2014</risdate><volume>116</volume><issue>23</issue><issn>0021-8979</issn><eissn>1089-7550</eissn><abstract>A Lagrange-Hermite finite element method for the eight-band k·p model is developed. We demonstrate that besides the incompletion of k·p basis functions, the ill representation of first-order derivatives can also bend the conduction band structure down and lead to the highly oscillatory solutions. Our method simultaneously solves these two problems and achieves robust stability and high accuracy in real-space numerical calculation. The more physical asymmetric operator ordering is employed and the connection problem in abrupt interface is resolved by using an approximately abrupt interface. The situation of smooth interface used to explain the discrepancies between experiment and simulation of abrupt interface is also calculated by our method, and the result suggests that the influence of the interface smoothing should be considered in the short period superlattices or quantum structures of the narrow well.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/1.4904845</doi></addata></record> |
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| ispartof | Journal of applied physics, 2014-12, Vol.116 (23) |
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| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Applied physics ASYMMETRY Basis functions CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Computer simulation Conduction bands Finite element analysis FINITE ELEMENT METHOD Heterostructures INTERFACES Mathematical models Nonlinear programming NUMERICAL ANALYSIS Quantum phenomena Robustness (mathematics) SIMULATION STABILITY SUPERLATTICES |
| title | Stable finite element method of eight-band k·p model without spurious solutions and numerical study of interfaces in heterostructures |
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