05_04_11 - [email protected] 129 Approximation...

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Unformatted text preview: [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 1 1 2 2 1 1 1 2 2 2 2 ~ ) ~ ( ) ( ) ( ) ( 2 2 2 2 ) ( ) ( ) ( ) ( ] ) ( [ , ) ( ] ) ( [ α α α α α α 7KH WUDQVPLVVLRQ FRHIILFLHQW RI WXQQHOLQJ LV GRPLQDWHG E\ WKH H[SRQHQWLDO GHFD\ V(x) x x 3 x… x 2 ) (x 1 ) ) (x 2 ) ) (x 3 ) ) (x…) ( x 1 ) (x ) &RQVLGHULQJ RQO\ H[SRQHQWLDO GHFD\ LQ HYHU\ VWHS [email protected] 130 Field emission of electrons 04/11/2005 / ( 9 [ eV 4 for 55 , ) exp( ) ( ) ( ) ( m GV 3 2 3 4 1 2 ) 1 ( 2 ) ( 2 ) ( 2 2 2 1 3 2 2 3 4 1 2 2 2 2 2 2 ≈ ≈- =- = = ∫ = ∫ = ∫ = ∫ = 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...
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This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell.

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05_04_11 - [email protected] 129 Approximation...

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