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Unformatted text preview: 5.1 Chapter 5 solutions 5.2 Intrinsic Ge Using the values of the density of states effective masses m e * and m h * in Table 5.1, calculate the intrinsic concentration in Ge. What is n i if you use N c and N v from Table 5.1? Calculate the intrinsic resistivity of Ge at 300 K. Solution From Table 5.1, we get and e e m m 56 . = e h m m 4 . = Now, 2 / 3 2 34 1 23 31 2 / 3 2 ) s J 10 626 . 6 ( ) K 300 )( K J 10 38 . 1 )( kg 10 1 . 9 56 . ( 2 2 2 2 = = h kT m N e c = 1.0510 25 m3 or 1.05 10 19 cm3 2 / 3 2 34 1 23 31 2 / 3 2 ) s J 10 626 . 6 ( ) K 300 )( K J 10 38 . 1 )( kg 10 1 . 9 4 . ( 2 2 2 2 = = h kT m N v v = 6.3510 24 m3 or 6.35 10 18 cm3 The intrinsic concentration is = kT E N N n g v c i 2 exp ) ( 2 / 1 [ ] = ) K 300 )( K eV 10 62 . 8 ( 2 eV 66 . exp ) cm 10 33 . 6 )( cm 10 049 . 1 ( 1 5 2 / 1 3 18 3 19 i n = 2.33 10 13 cm3 2.3 10 13 cm3 From Table 5.1, we get N c = 1.0410 19 cm3 and N v = 6.010 18 cm3 [ ] = ) K 300 )( K eV 10 62 . 8 ( 2 eV 66 . exp ) cm 10 . 6 )( cm 10 04 . 1 ( 1 5 2 / 1 3 18 3 19 i n = 2.26 10 13 cm3 2.3 10 13 cm3 The intrinsic conductivity is ) ( h e i h e en ep en + = + = = 0.022 1 1 2 3 13 19 s V cm ) 1900 3900 )( cm 10 34 . 2 )( C 10 6 . 1 ( + = 1 cm1 And the intrinsic resistivity is = 1/ = 45.45 cm 5.2 5.3 Fermi level in intrinsic semiconductors Using the values of the density of states effective masses m e * and m h * in Table 5.1, find the position of the Fermi energy in intrinsic Si, Ge and GaAs with respect to the middle of the bandgap ( E g /2). Solution + = h e g v Fi m m kT E E E ln 4 3 2 1 For Si, and e e m m 08 . 1 = e h m m 6 . = + = e e g v Fi m m E E E 6 . 08 . 1 ln ) K 300 )( eVK 10 62 . 8 ( 4 3 2 1 1 5 eV 011 . 2 1 + = g v Fi E E E So intrinsic Fermi level of Si is 0.011 eV below the middle of the bandgap ( E g /2). For Ge, and e e m m 56 . = e h m m 4 . = + = e e g v Fi m m E E E 4 . 56 . ln ) K 300 )( eVK 10 62 . 8 ( 4 3 2 1 1 5 eV 0065 . 2 1 + = g v Fi E E E So intrinsic Fermi level of Ge is 0.0065 eV below the middle of the bandgap ( E g /2). For GaAs, and e e m m 067 . = e h m m 5 . = + = e e g v Fi m m E E E 5 ....
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This note was uploaded on 04/24/2008 for the course MSE MSE 350 taught by Professor Morelli during the Spring '08 term at Michigan State University.
 Spring '08
 Morelli

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