EE 105 - Fall 2009 - Salahuddin - Midterm 1 (solution)

EE 105 - Fall 2009 - Salahuddin - Midterm 1 (solution) -...

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Unformatted text preview: UNEVERSETY 0F CALIFORNEAS BERKELEY College of Engineering Department oi" Electrical Engineering and Computer Sciences ER 105: Microelectronic Devices and Circuits Fall 2009 MIDTERM EXAMINATION #1 Time allotted: 45 minutes NAME: STUDENT ID#: INSTRUCTIONS: 1. SHOW YOUR WORK. (Make your methods clear to the grader!) Specially, While using chart, make sure that you indicate how you have got your numbers. For example, if reading off mobility, clearly write down what doping density that corresponds to. 2. Clearly mark (underline or box) your answers. 3. Specify the units on answers whenever appropriate. SCORE: 1 / 15 2 [15 3 /20 Total I 50 PHYSICAL CONST ANTS Description Symbol Value Electronic charge .2] 1.6x‘10'19 C Boltzmann’s constant k 8.62><10'5 eV/K Thermal voltage at VT = 0.026 V 300K kT/q USEFUL NUMBERS VTin(10) = 0.060 V at T2300}: exp( 30) ~ 1013 A MOU- '- 1200 l 1000 #- mobllity (cnlst) m ._ 3 V n 600 2m o‘- l - a 10121 101-1 “31!: __ __________ M,“ _________ "W holes ~ ln'“ ' PROPERTIES OF SILICON AT 300K Descrigtlon Symbol Value Band gap energy E0 1.12 eV Intrinsic carrier m 1010 cm'3 concentration Dielectric permittivity eSi 1.0x10'12 F/cm t'elmztronfi .:5 10” 10‘“ 10‘” to?“ 303+ JVRIUHH dopant concentration (Cilia) Prob 1.115 pts] Let us assume that we have a Si sample of Eength 16 pm and a cross sectional area of 10 pm2 at room temperature. Also assume that we apply 1V across this sample. (a) If it is desired to have an electron density that is 105 times the intrinsic density, [4 pt} (i) What kind of dopant atoms is needed? Can you give an example? (ii) What doping density will be required? , \x‘ _ i l y [I rm} f ‘ {b} Estimate the drift velocity of this sample. \I [5 pt] .. i ‘ l." .7 fit; if; 2-: {Ni ‘2’; y ‘ I, I, H: x‘ (1.. "'l \. H») l l (c) Now let us assume that we countendope the sample with opposite type of doparli‘s with a density that is 3 times more than the previous dopant density. Estimate the resistance and current flowing in this sample under these conditions. [6 Pt} } i 4 ifciixli 2 {Kg [if “ti-iii" ) ;[:}’le )"u i x“! i l I. . K. ‘4‘.- .i /\ (W) A r . ELI: 3 { 5,( fl 1‘ 3" l \ | \ ‘\: I! i ( ’t ‘ 1" ‘“" ‘\ r" “"5 i E i ii ’ i i “r in I f i M” g -“ A i 1' '3 . I“ ~ . . i if v . 'r‘ y’ \ i n I ’ RI: 1 v _\' h x )(m; x n\ i“ i z ’ ’ ' i. 3 ‘ y a! , f._\ .1 ‘i i x I; i l \ A F: l. f ,‘L r J» . i, f,‘ S: 7 'i T4 Prob 2E15 pts]. Consider a p—n junction diode of Si as shown below: (a) Find out the built in potential and the depletion width at T=300K. [4 pt] ,5 .rx“ ju f ( I ‘ i g iv 1*; i‘ . ‘ -_ 1 ‘ _ ‘ ‘ «3 ‘ ’i , i ' 'l l J ‘J' y\ f" /\ It i I; I I t. t \F l lsz - x ml, ‘ i 3‘; l "j y . I f < I. a} “u: * l i J i A F N“ 1' I t l i g} ‘l c e f \ . i if \ i ii 3“ ll " X it: ) Cm. _, (b) Assume that at T=300K a voltage of 0.9 volt is applied across the diode such that the diode is forward biased. How much should the voltage have to be changed if at T=400 K one needs to ensure that the same current is flowing as in Tz300K? Assume no change in bandgap due to change in temperature. [5 pt] \ a 3 in élt \ X h it," i r, i z , _ r A. E i . “x \3 « 1 ; i . l \- I 1 l l i I ‘ \v ; l x 7-» -"'~ i l . E L ‘ -l . x, \, i— :4 g \V i c’ l L PK) ’1'}, (c) in this probiem we shall design a diode to meet certain requirements. We want a total current of 40 A/cm2 at a vottage of 0.8 V at T=300¥<. Half of the current will have to be supplied by holes and half by electrons. Assume the mobility of electrons to be 500 cmZ/V-sec and that of holes to be 250 cmZ/V-sec. Also assume that the diffusion length for electrons and holes are the same and equal to 10 pm. Find out how you will design your diode, i.e., how you will dope your p and n sides so that the aforementioned requirements are met. {5 Pt} V. D r» V i .7 f ‘ K .V i r, ,4 x ,2‘ r, . ._. ‘ “Xi; H l}; z<= .r’\ #623!“ w e \f: ’7) r ( X i a “t x \ l i7 r" l ' r, r '7 ' "x" l “ix \ ! vie ‘ l a V \l. f I, ‘ . ly' \ L V . l" 1"" 4 f if. l l « rm. i 5 3 (t ‘in QM \ ‘3" "x l t in; i '2 "’3: 1 1’ m r E 1 =t 3 f W“: J ; .~, ‘4, I w. W " E . ‘v * c ..... {a l I {v.15} Prob 3. {20 pts}Bipolar junction transistors. (a) Design Fundamentals [4 pts]. {i) Why is the base region doped more lightly than the emitter? {2 pt] {Mat '1": L215) taxi: ‘t. 'i'i'iii l ‘1. '2 l i: " l H i sit Hosea imiii it. Nomi“: *lw “\iitt iiir‘iiixi tiliw’i (ii) Why is the width of the base region narrower than emitter and coilector regions? [2 pt} if i‘Z); i' 13f {Niki I ii Jr (b) Write down the condition for active mode operation and saturation mode operation for a NESN bipolar junction transistor. Consider the following transistor that has 5:100‘ if it is desired that 1 mA current must be flowing in the collector at Vcc=1 V, what is the maximum value for RL that can be used before the transistor goes from active to saturation mode? [Sptl t'_ i ‘ ‘1, i. ‘ g r to m. €756 £53100 ’ x \i L i' av ' ~ V -. i - 1 c (“it i , V > ‘i: i .i ‘\ 2 is r/ w s \ \ "E 5 ~ _ i I} 1 a s v w is} i n: .‘ 1 i ': NM.“ ‘\ ' : k ‘ y i/ \J i-\ ‘th \‘ { 3‘54 'y‘ i f i . l _ . .' s n"- \ l ‘, \ 2 i2 if A M“ \§ 73 {2.\r ; a I“; / L ‘ i .2 Q t i ' 1‘” K. I | ~. (c) Draw the small signal model for the BJT descried in part (b) assuming no Early effect. indicate the numerical values and units for all the components of this small signal model. [5 pt] $6.2. l" , " x \ l I?“ x t L / 1% £ ‘ I’ ~ ‘l- (flu-"p is - l a g ‘ E I ' l j h‘\: V, t z . , la: n: ‘ x ‘v I > i l l: l, i. I ‘ I l ‘ < ,. . :13 5 r s t .2 3 ((1) Early effect/ base width modulation causes the collector current to increase with collectorw emitter voltage, VCE. Normally it is assumed that the base current remains independent of m. However, if the depletion region spreads a long distance into the base, it can reduce the base current by recombination of injected holes with the negative immobile charges in the base region (for a NPN transistor}. This is shown in the following figure. Considering this decrease of £8 with VCE, derive and draw complete (including conventional early effect and the new phenomenon) the small-signal model of a NPN transistor. [6 pt] a i , ,, . "i'l'll" r! (ll “(ll we: ;_- ,« ~.= LI: ‘ L, _ V I ~ 3 f , 5(4):" " r , r i i. i ., l v ‘-., '3” ~, l, {i {p} s V_ ., w a g l . E ‘l . V K r; r \E. ' .r A r y f y I] \ .x i ’9 ‘ i li ~~ l. lr'\ ' is \‘l’ l l" l i: l.. 1 l ’ l 1 l... l t it i; I l \ 7'7 ...
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This note was uploaded on 08/30/2011 for the course EE 105 taught by Professor King-liu during the Fall '07 term at Berkeley.

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EE 105 - Fall 2009 - Salahuddin - Midterm 1 (solution) -...

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