Week12HWSolutions

# 3 ef d e de 3d ec n0 2 e ec m 3

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Unformatted text preview: in !-cm 2 . A very good value is !C " 10#8 \$-cm 2 . Consider n+ Si at room temperature and doped to N D = 1020 cm -3 . What is the lower limit to !C ? (Assume a fully degenerate semiconductor and use appropriate effective masses for the conduction band of Si.) ECE ­656 8 Fall 2013 Mark Lundstrom 10/30/13 Solution: The lower limit resistance must be the ballistic contact resistance: RB = 1 1 = 2 GB 2q h T ( ) M Assuming that one ­half of the ballistic resistance is associated with each of the two contacts: !C = RB A h =2 2 4q T 1 MA Assume a strongly degenerate semiconductor: !C = h 1 2 4q T ( E F ) M ( E F ) A The lower limit occurs when the transmission is one m !C in = h 1 2 4q M ( E F ) A Need to find the Fermi level. Recall that at 0 K, n0 = EF ! D ( E ) dE 3D EC D3 D n0 = (m ) ( E) = * DOS 3/ 2 EF " 2!3 EF ! D ( E ) dE = ! 3D EC n0 = 2 ( E ! EC ) (m ) ( 3! ! 23 ) (E 2 ( E " EC ) 3/ 2 * DOS #! 23 EC 2 2 m* OS D dE = ( 2 m* OS D #! 23 ) 3/ 2 EF ! (E " E ) 1/ 2 C dE EC 3/ 2 " EC ) 3/ 2 F 1 # 3" 2 ! 3 & E F ! EC ) = * % ( mDOS \$ 2 2 ( ' 2/ 3 (n ) 0 2/ 3 m* OM M 3D ( E F ) = D 2 ( E F " EC ) 2! ! ECE ­656 9 Fall 2013 Mark Lundstrom m* 1 " 3! 2 ! 3 % M 3D ( E F ) = DOM m* OS 2! ! 2 \$ 2 2 ' # & D 2/ 3 (n ) 10/30/13 2/ 3 0 m* " 3 ! % = DOM \$ ' m* OS # 8 & D 2/ 3 2 n0 /3 For Si, we have to consider the ellipsoida...
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