ece3901_HW4_solutions

ece3901_HW4_solutions - CHAPTER 6 ELL (3) Majority carrier...

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Unformatted text preview: CHAPTER 6 ELL (3) Majority carrier injection (diffusion) to the opposite side of the junction. (b) Minority carriers wandering into the depletion region and being accelerated (drifting) to the opposite side of the junction. (c) The reverse bias current is expected to be small because it arises from minority carriers which are few in number. The reverse bias current saturates because a small voltage all but eliminates majority carrier injection across the junction, and the remaining current due to minority carriers is independent of the applied voltage. (d) generation and diffusion (e) The primary reason is that 8 qt 0. Also, low level injection conditions seldom apply; 3n/c9fithennar R-G it —Anp/Tn and 3P/3Ilmcnnar R-G it —Apn/Tp- (0 There is NO a priori justification. (g) A diode where the contacts are far removed (several minority carrier diffusion lengths) from the edges of the depletiou region. (h) np : rife-WM” ...—xp 3 x s xn (i) 10 is the extrapolated intercept of the straight-line region on the I (log scale) axis. (j) True 6._2_ The graphical ideal-device/Si-BOOK device comparison of [MV characteristics is presented on the next page. (Also see Fig. 6.6, Fig. 6.17, and Exercise 6.9.) The causes of the deviations noted in the sketches are: Causes Deviation #1...Breakd0wn is caused by avalanching in the depletion region or tunneling through the depletion region (the Zener process). The latter is important if VBR 5 4V. Deviation #2...Results from generation of carriers in the depletion region. (This was ignored in the ideal diode derivation.) Deviation #3...Results from recombination of carriers in the depletion region. Deviation #4...The slope—over on a log scale results from series resistance (bulk and/or contact resistance). An exp(qVA/2kT) region at large forward biases, if observed, is due to high-level injection. Graphical Comparimn an) 4—,— slop-c = q/kT Ideal ln([) #4 (slope~ovcr) #3 (forward-bias excess current) #2 (reverse— bias excess current) 1:“ \\\\\\\\\\\\\\.\\.\\.\ .‘l, 00 “‘\‘\\.“‘\\‘\“\\I 0—» 0-) 0—)- 0—)» VA>U m (a) Reverse biased — there is a deficit of minority carrier in the quasineutral region imm ate y a Jacent to the depletion region. (b) Low—level injection DOES prevail. As required for low-level injection lAn‘Jn-lax E npo << ... fOI'x S —xD LAanI-nax E pno I1“ ... 2 xn (0) Since we have low level injection, NA pp = 1014/cm3 Ill Ill ppO ND E 11.10 E nn =1015/em3 (d) Invoking the law of the junction, “(pr)[)(*xp) = ngquA/H VA 2 fll"{H(—Xp)P(—Xp)] q 2 “i As deduced from Fig. P610, 01‘ n(—xp) : 103/cm3 p(—xp) = 1014mm3 and n = w/Ztooiptoo) = w/ntwmt—oo) = 1/1076 = low/cm3 The foregoing manipulation to obtain ni was necessary because the semiCOnduCtor used in fabricating the diode was not specified in the problem statement. Lastly, substituting into the VA expression gives (103x10‘4) VA : (0.0259)1n[ ] = _ 0.18V 1020 CHAPTER 10 10,1 {3) Common base. (b) Common emitter. (e) Saturation active, inverted, and cutoff. (I) W in both cases, (g) The width of the base is 109‘? than‘ typically tnntth iess thtin, the t'tiinority carrier diffusion length in the bLtSC. (h) The narrow nature at the base couples the current flow across the BB and C78 junctions, a prerequisite for transistor action. _l_0_.3 (a) For the given doping concentrations, one computes Ep— Ei : 770.459eV, 0.298eV, and —0.239eV respectively in the emitter, base, and collector. Also, with NAB >> NDB, the EB depletion width will lie almost exclusively in the base. Likewise, the majority of the C-B depletion width will lie in the collector. The diagram produced by the BJ'I‘flEband program is displayed below. P+ N P I I I I I I I I I I r '. I. I l .. -....--.II..__ ___ _____________. . (b) (C) AVCE = (1/(1)[(Ei’EF)cmittcr*(Ei’EFkollcctod = (kT/CI)[1H(NAF,/nj) * 1H(NAC/ns)1 or AVCE= (kT/q)ln(NAE/NAC) 2 (0.0259)1n(5x1017/1014) = 0.221 V (6) As noted in the text (Eq. 10.3), W = WB — anB - XnCB 1/2 -14 , “2 XHEB 3 [2mm VbiEB : [(2)(11.8)(8.85X10 xenon] : 9_94X10_5cm qNDB (1.6x10-19x1015) 1 2 xnCB : [2mg NAC VbiCBJW = (2)(11.8)(8.85><10'14)(1014)((}.537) ’ qNDB NAC+NDB (1.6x10-19)(1015)(1.1x1015) = 2.52 X 10'5 cm and therefore w = 3 x1074 _ 9.94 ><10~5 ; 2.52 x1045 1.75 x1074 cm = 1.75 pm The emitter-base and collector-base built-in voltages (VbiEB and VbjCB) were deduced from the E1: 7 E vaiues computed in pan (3). (e) -19 15 -5 ldmagEAB) : qNDB anB = = 1.52 x 104 V/cm KS (11.8)(8.85x10-I4) -19 15 -5 gmax(c-B) 2 W93 xnCB = W = 336 x 103 wcm K880 (11.8)(885X10‘14) 10.6 The energy band diagram for a typically d0ped Si npn transistor under equilibrium conditions was sketched in Fig. E10.1(a). Under active mode biasing in the npn transistor VBE > 0 and VBC < 0. Appropriately modifying the Fig. E10.1(a) diagram to account for the applied biases, we conclude Following the usual procedures in interpreting the energy band diagram to deduce the electrostatic variables, we conclude V i032 . : [CiP = 0.98 mg 2 ((1) ar 1E? lmA 0.9800 (b) 7 [ED = —«~————1mA = 0.9901 : 15p + [En lmA + 0-01mA (c) [E : IEp+lEn = 1mA+0.01mA :— 1.01mA ' {C = rcp+1cfl = 0.98mA +0.10A = 0.9801 mA {3 = 1591c = 1.01mAu0.9801mA = 29.9 ,uA ((1) «Side = yaT = 0.9793 = adc = 0.9703 2323 fidc 1—0“C 190.9703 (e) As given by Eq. (10.12), [CBO :[Cn = O-IIJA Likewise, Eq. (10.17) states [C80 _ 0-1 #A __W= .7A Image 1—0.9703 33’” [CEO = (f) The [Cp increase while JED remains fixed indicates that the base transport factor has been improved. An increase in Ctr in turn leads to an increase in ordc = WT and therefore to an increase in fidc. (g) An increase in [En while [Ep remains fixed indicates that the emitter efficiency has been degraded. A decrease in y in turn leads to a decrease in adc : WT and therefore to a decrease in flat. CHAPTER 11 11.1 (a) The Ii, [3, and C dopings are asumed to be nondegenetate and constant throughout :1 given region. The quasineutml widths of the emitter and collector are assumed to be much greater than the minority carrier diffusion lengths in the respective regions. 0)) P130) p306) pm _ I I U w 0 w W/LB << 1 W/LB >> 1 11.7 Majority carriers...Assuming low-level injection, the majority carrier concentrations will be esentially unperturbed from their equilibrium values in all cases. Thus the majority carrier sketches will all be the same, with the solid carrier—distribution lines lying on top of the dashed equilibrium values in the three device regions. TM‘XP): PC E H C Majority Carrier Cuneanramms (all parts) M inorin carriers...With W << LB, the minority carrier concentration will vary linearly with position in the base under all biasing conditions. In the emitter and collector regions the carrier concentrations will decay exponentially with distance from the edges of the respective 13-8 and C-B depletion regions. The carrier concentrations will be greater than the equilibrium values when the applied biases are positive and less than the equilibrium values when the applied biaSes are negative. The distributions are concluded to be of the general form pictured below. Note that p300 in the base is approximately zero everywhere under cutoff biasing if IVEBE and IVCBI are greater than a few kT/q volts. Tnpupn 7 "co ‘ - ’ED 0 0 x L B ( (2:) Active mode (b) Inverted mode Tap own Tn P or pm Pm "C0 m 7 7 v V __ _ "Cu ' ___ n50 - ”FJ) 0 0 1 g f. 0 r_x. , i B C 13 B (c) Saturalion (d) CHM,” Anrmrumatly item if vaflvcfi >fcw kTr‘q ...
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ece3901_HW4_solutions - CHAPTER 6 ELL (3) Majority carrier...

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