Week12HWSolutions

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online