Exam (elaborations) TEST BANK FOR Microelectronics Circuit Analysis and Design 4th Edition By Donald Neamen (Solution Manual)

1.1 3/ 2 Eg / 2kT in BT e− = (a) Silicon (i) ( )( ) ( )( ) [ ] 15 3/ 2 6 19 8 3 5.23 10 250 exp 1.1 2.067 10 exp 25.58 1.61 10 cm i i n n − − ⎡ − ⎤ = × ⎢ ⎥ ⎢⎣ × ⎥⎦ = × − = × (ii) ( )( ) ( )( ) [ ] 15 3/ 2 6 19 11 3 5.23 10 350 exp 1.1 3.425 10 exp 18.27 3.97 10 cm i i n n − − ⎡ − ⎤ = × ⎢ ⎥ ⎢⎣ × ⎥⎦ = × − = × (b) GaAs (i) ( )( ) ( )( ) ( ) [ ] 14 3/ 2 6 17 3 3 2.10 10 250 exp 1.4 8.301 10 exp 32.56 6.02 10 cm i i n n − − ⎡ − ⎤ = × ⎢ ⎥ ⎢⎣ × ⎥⎦ = × − = × (ii) ( )( ) ( )( ) ( ) [ ] 14 3/ 2 6 18 8 3 2.10 10 350 exp 1.4 1.375 10 exp 23.26 1.09 10 cm i i n n − − ⎡ − ⎤ = × ⎢ ⎥ ⎢⎣ × ⎥⎦ = × − = × ______________________________________________________________________________________ 1.2 a. 3/ 2 exp 2 i n BT Eg kT ⎛ − ⎞ = ⎜ ⎟ ⎝ ⎠ 12 15 3 / 2 6 10 5.23 10 exp 1.1 2(86 10 )( ) T − T ⎛ − ⎞ = × ⎜ ⎟ ⎝ × ⎠ 3 1.91 10 4 T 3/ 2 exp 6.40 10 T − ⎛ × ⎞ × = ⎜ − ⎟ ⎝ ⎠ By trial and error, T ≈ 368 K b. 109 cm 3 i n = − ( )( ) 9 15 3/ 2 6 10 5.23 10 exp 1.1 2 86 10 T − T ⎛ − ⎞ = × ⎜ ⎟ ⎜ × ⎟ ⎝ ⎠ 3 1.91 10 7 T3/ 2 exp 6.40 10 T − ⎛ × ⎞ × = ⎜ − ⎟ ⎝ ⎠ By trial and error, T ≈ 268° K ______________________________________________________________________________________ Microelectronics: Circuit Analysis and Design, 4th edition Chapter 1 By D. A. Neamen Problem Solutions ______________________________________________________________________________________ 1.3 Silicon (a) ( )( ) ( )( ) ( ) [ ] 15 3/ 2 6 18 10 3 5.23 10 100 exp 1.1 5.23 10 exp 63.95 8.79 10 cm i i n n − − − ⎡ − ⎤ = × ⎢ ⎥ ⎢⎣ × ⎥⎦ = × − = × (b) ( )( ) ( )( ) ( ) [ ] 15 3/ 2 6 19 10 3 5.23 10 300 exp 1.1 2.718 10 exp 21.32 1.5 10 cm i i n n − − ⎡ − ⎤ = × ⎢ ⎥ ⎢⎣ × ⎥⎦ = × − = × (c) ( )( ) ( )( ) ( ) [ ] 15 3/ 2 6 19 14 3 5.23 10 500 exp 1.1 5.847 10 exp 12.79 1.63 10 cm i i n n − − ⎡ − ⎤ = × ⎢ ⎥ ⎢⎣ × ⎥⎦ = × − = × Germanium. (a) ( )( ) ( )( ) 15 3/ 2 ( 18 ) [ ] 6 3 1.66 10 100 exp 0.66 1.66 10 exp 38.37 35.9 cm i i n n − − ⎡ − ⎤ = × ⎢ ⎥ = × − ⎢⎣ × ⎥⎦ = (b) ( )( ) ( )( ) 15 3/ 2 ( 18 ) [ ] 6 13 3 1.66 10 300 exp 0.66 8.626 10 exp 12.79 2.40 10 cm i i n n − − ⎡ − ⎤ = × ⎢ ⎥ = × − ⎢⎣ × ⎥⎦ = × (c) ( )( ) ( )( ) 15 3/ 2 ( 19 ) [ ] 6 15 3 1.66 10 500 exp 0.66 1.856 10 exp 7.674 8.62 10 cm i i n n − − ⎡ − ⎤ = × ⎢ ⎥ = × − ⎢⎣ × ⎥⎦ = × ______________________________________________________________________________________ 1.4 (a) n-type; = 1015 cm ; no −3 ( ) 11 15 2 13 2 5.76 10 10 2.4 10 = × × = = o i o n n p cm−3 (b) n-type; = 1015 cm ; no −3 ( ) 5 15 2 10 2 2.25 10 10 1.5 10 = × × = = o i o n n p cm−3 ______________________________________________________________________________________ Microelectronics: Circuit Analysis and Design, 4th edition Chapter 1 By D. A. Neamen Problem Solutions ______________________________________________________________________________________ 1.5 (a) p-type; = 1016 cm ; po −3 ( ) 4 16 2 6 2 3.24 10 10 1.8 10 = × − × = = o i o p n n cm−3 (b) p-type; = 1016 cm ; po −3 ( ) 10 16 2 13 2 5.76 10 10 2.4 10 = × × = = o i o p n n cm−3 ______________________________________________________________________________________ 1.6 (a) n-type (b) ( ) 16 3 10 2 2 3 3 16 5 10 cm 1.5 10 4.5 10 cm 5 10 o d i o o n N p n n − − = = × × = = = × × (c) 5 1016 cm 3 o d n = N = × − From Problem 1.1(a)(ii) 3.97 1011 cm 3 i n = × − ( )11 2 6 3 16 3.97 10 3.15 10 cm 5 10 o p − × = = × × ______________________________________________________________________________________ 1.7 (a) p-type; = 5×1016 cm ; po −3 ( ) 3 16 2 10 2 4.5 10 5 10 1.5 10 = × × × = = o i o p n n cm−3 (b) p-type; = 5×1016 cm ; po −3 ( ) 5 16 2 6 2 6.48 10 5 10 1.8 10 = × − × × = = o i o p n n cm−3 ______________________________________________________________________________________ 1.8 (a) Add boron atoms (b) = = 2×1017 cm Na po −3 (c) ( ) 3 17 2 10 2 1.125 10 2 10 1.5 10 = × × × = = o i o p n n cm−3 ______________________________________________________________________________________ 1.9 (a) ( ) 15 3 10 2 2 4 3 15 5 10 1.5 10 4.5 10 5 10 o i o o o n cm p n p n − cm− = × × = = ⇒ = × × (b) ⇒n-type no po (c) 5 1015 3 o d n ≅ N = × cm− ______________________________________________________________________________________ Microelectronics: Circuit Analysis and Design, 4th edition Chapter 1 By D. A. Neamen Problem Solutions ______________________________________________________________________________________