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05_04_11 - 129 Approximation of tunneling T= |C |2 ~ | A| 2...

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[email protected] 129 Approximation of tunneling 04/11/2005 ( 29 2 4 2 2 2 ) sinh( ) ( ) cosh( 2 | ~ | | | 2 2 2 1 1 2 1 1 2 1 2 2 2 1 1 2 1 2 2 2 | | k k L k L k i L k L ik A C e e T + - - - + = = α α α α α α α α Φ Φ Φ Φ - = Φ = Φ - = Φ - - - - - - - + - - x N N N j j x d x x x x x x x N x x m j m x e x e e e x E V x E x V 0 1 1 2 2 0 1 1 1 2 2 2 2 ~ ) ~ ( ) ( ) ( ) ( 2 2 2 2 ) 0 ( ) ( ) 0 ( ) ( ] ) ( [ , ) ( ] ) ( [ α α α α α α ± 7KH±WUDQVPLVVLRQ±FRHIILFLHQW±RI±WXQQHOLQJ±LV±GRPLQDWHG±E\±WKH± H[SRQHQWLDO±GHFD\ ² V(x) x 0 x 3 x… x 2 ) (x 1 ) ) (x 2 ) ) (x 3 ) ) (x…) ( x 1 ) (x 0 ) &RQVLGHULQJ± RQO\±H[SRQHQWLDO±GHFD\ LQ± HYHU\±VWHS³
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[email protected] 130 Field emission of electrons 04/11/2005 / ( 9 ´ [ ´ eV 4 for 55 , ) exp( ) 0 ( ) ( ) ( m GV 3 2 3 4 1 2 ) 1 ( 2 ) ( 2 ) ( 2 2 0 2 1 3 2 2 3 4 1 0 2 2 0 2 2 0 0 2 2 0 - = - = = = = = = Φ Φ = - = - - - - - - - - - W W e e e e e L T L x e V x V m e W dx x W dx x W dx E x e V dx x e W m e e W m L W e m L m L E0 E field field E field E field E field field E E0 E E field α : 7KHUH±LV±YLUWXDOO\±QR±>H[Sµ¶··¸@±ILHOG±HPLVVLRQ±IRU± E field ¹º*9»P 9
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