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**Unformatted text preview: **E13 306 804 MIDTERM EXAM #1 Braun CLOSED BOOK + 1/2 Cheat Sheet
Part 1 (18 Points) State any assumptions and show all work.
Part 2 (29 Pomts)
(1 point) Print Your Name: 5&4 “7/ Total (49 Points) No unauthorized help given or received. I will not discuss this exam with another human being until after
11:00 am Friday. (1 point) Signature: For today’s exam you may assume for Silicon at room temperature that the intrinsic carrier concentration,
n,- = 1010 cm'3, with B=l.08 x 103' cm'6 K'3. 1. Semiconductor Fundamentals A piece of Silicon has a uniform donor concentration of 1018 cm‘3 and a uniform acceptor concentration of
2x1017 cm'3. An applied electric ﬁeld of +10 kV/cm exists in the piece of Silicon. Please determine the
following quantities at room temperature with VT = 0.025 V. You may use the mobility approximations from p. 61 of Jaeger & Blalock. ﬁgﬁzﬁ} {2%} CmZ/y.5 m1
. . . 3'1” "' 3 71 3; am
(3 pomts) A) Determine the electron concentration)? 3 4/ W)”: E + ‘ T
i -3 ' _ ‘ 0 ‘ I _/ M
Mg : Wig”, )% ,Qx/a (m .5 L3 X m3? 011—3
._ ’7 x3 /7 -g
n z A? ~44 : m'gcm 3 “2"” M : 3M9 6’” 6% da‘kmﬂ/s
>72»; 5a yaw/7 #27” r0 ‘(55 ﬂMﬂ/WV 15/ “if mégﬁwm
$0LI/77 . ~ ‘
(3 points) B) Determine the hole concentration. v g 4. 3
m2 [fife _5 .63 x10“? 0;
’72:“: [75:12ch
I") gx/p [M
(3 points) C) Determine the electron mobilitng 3
M: Wye/£6 :/,.2X/t7 (M
;2 70 i y a J [1% 5’” 2
» ‘22 + $0" =- 1 7* : “WSW; ‘r’ : .
ﬂ” — A]? ’+//.31/a"7(»” V} V 5 * “5
(3 points) D) Determine the electron diffusivity cm a W2 .
Dy, awn ; > » Vr :(2w ‘5 X29110: (.9 S V. (3 points) E) Determine the electron drift current density Jr”,sz : ﬂu” mg : ﬂgw‘lzjkéfﬂégijmlim'y/MJ : 3077 f1; (3 points) E) Determine the electron diffusion current density d]
I? . [(17 -
r dyFF ‘— n . C 0 ﬂ ‘5 , -.z a 2. Silicon PN Junction Diode The solid line plots the electric ﬁeld as a function of position in a PN—junction at VD = VR = 0 V. The P-side
is x<0 pm, and the N-side is x>0 pm. Please analyze this problem at room temperature with VT = 0.025 V. 50 (3 points) A) The solid line plots the electric ﬁeld as a function of position
in a PN—junction at VD = VR = 0 V (zero bias), and the dashed line plots the electric ﬁeld in the same PN— a O
junction at: o
1.VD<0V(VR>0V), S
2.VD=VR=OV, ﬂ 3.VD>OV(VR<OV),or U "
4. Insufﬁcient information '5
1» ﬁve/F55 6%; “r —100
Explain m
,sz Y/A/é army 49/5 1 O
W/pws 7M5 MgT/Mt/ 4055/5” ' 5 _O 1 O 0 1
zM/ﬂ //1/C'/17./:WS£S 7/505 £255 toe/é X [Hm] '
/ é/ﬂ/C . . . . .
£752” ﬂW 7 " Fig. 2A — E—ﬁeld vs. Posrtion 1n PN—Junction
(4 points) B) On the lower plot, graph the charge density normalized to q, p/q, as a function of position for the
junction at zero bias. cpl—i
Hint: complete subsequent sections of a _ [7, V3
problem 2 ﬁrst. Label y-axis. ﬂl ’9 0"”
\Z +- s'x/o'ﬂm'i
CD
30 0
CG
I c
6 C 3300 [rim ;
‘D -
g __ I. 0}?” 3
Q
m Fig. 2B — Space Charge vs. Position in PN-Junction
(3 points) C) Calculate the total depletion layer width of the junction at zero bias. W6!” : ‘Xfm + X”; I 0,0521)» ~l— ﬂay/w I ﬂ/fj/Iw (3 points) D) Calculate the built-in potential, ¢j. (1/
/ -
qﬂ» : ~ [MM 2 ;’ Wﬂvgw : 3/a/52MMWM — 4 WV J
(3 points) E) Calculate the doping concentration on the P-type side of the junction. , , ~ , . x: 5!)
w 6' . ,¥x§,3€4x/D ’5’va .m I; w
is,” = 3L” X’” r? M = "m" = Wm 0" __..._¢ : mm a, 5 65“ (’23, Xpo Géx lD§qu)[0, 057"”) (3 points) F) Calculate the doping concentration on the N-type side of the junction. "" x ‘A .lg—[f - ,_,.
M) ___ 0.5”” :01} 3.35;: m m){/0z>cm : alga/0 am 3 5,. Km; (Aéx/c? 'HC ,) {ﬁx/ﬂ”) (3 points) G) Determine the voltage applied to the diode that produces the electric ﬁeld distribution indicated by the
dashed line in Fig. 2A. Cl); rl/K 1 ~/z€§<)/>l< : “fa/£51m 3321/0,pw+a/5;W)//5'0kV/cw) : [.5525'1/
Vk - «My name? :A9775'V wisy: ~ny ﬁzz/£435 3/2125 (7 points) H) For each region in the PN—junction, determine if the description in the left applies to it at zero bias. Place an “X” in the appropriate cell, if the description ﬁts the region. Your instructor ﬁlled out the ﬁrst
row as an example. I II 7—111 IV R M instructor loves this region X X X X J
Space Charge—Region _r X X 4
Neutral Region X4 _J X l N—Type Region X X I P-Type Regio_n X X
Doped with Donors [—7— >4 X ' Doped with Acceptors X X
Depletion Region I—X Kﬂ— ...

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