Quiz #3 Practice Problem Set

Transcription

1 Name: Studet Number: ELEC 3908 Physical Electroics Quiz #3 Practice Problem Set? Miutes March 11, No aids excet a o-rogrammable calculator - ll questios must be aswered - ll questios have equal weight - swer questios o quiz sheets (use backs if ecessary) - Write your studet umber at the to of each age

2 Studet #: 1. Cosider a biolar juctio trasistor structure fabricated i silico with the cross-sectio show below. 2 + S a) How may imlat/diffusio stes would be eeded to fabricate this structure? b) Why is it imortat for the base to be thi i a biolar trasistor? c) What chages could be made to the collector to imrove this structure?

3 Studet #: 2. biolar trasistor with a very thi base regio havig a hysical searatio betwee metallurgical juctios of 0.25µm is biased to oerate i forward active mode as show below. N C =10 16 /cm 3 N B =10 17 /cm 3 N E =10 19 /cm 3 3? Usig the values for the doig levels of the regios of the trasistor ad V BE =0.8V, as show, calculate the value of collector-emitter voltage, V CE, required to comletely delete the base regio (i.e. = 0). (T = 300 K)

4 4 Studet #: 3. biolar trasistor is biased to oerate i forward active mode as show below. N C =10 16 /cm 3 N B =10 17 /cm 3 N E =10 19 /cm 3 5V V (a) ssume that the eutral regio widths are W C = 2µm, = 1µm ad W E = 0.5µm. Calculate the hole ad electro curret desities, J h ad J e, across the base-emitter juctio for the bias levels give. (T = 300 K). (b) How are the hole ad electro curret desities, J h ad J e, across the base-emitter juctio of a biolar trasistor related to the forward curret gai, β F?

5 5 Studet #: 4. biolar trasistor (BJT) has the arameters ad biases show i the diagram below. (T = 300 K) N C =10 16 /cm 3 N B =10 17 /cm 3 N E =10 19 /cm 3 W C = 5 µm = 1 µm W E = 0.5 µm 2V (a) Write simlified exressios for the collector curret, I C, ad the base curret, I B, for this biasig icludig oly the sigificat terms. (b) If the emitter of the BJT above is 2 µm wide ad 10 µm log, what are the values of the base ad collector currets? (c) What is beta for the trasistor show above?

6 Studet #: 5. I additio to the curret ijectio modellig of biolar juctio trasistors (BJTs), we have looked at two additioal effects the Early effect ad breakdow. (a) How does the Early effect chage the collector curret versus collector-emitter voltage characteristics (I C vs V CE ) for a BJT? 6 (b) What is the rimary hysical effect that causes the Early effect i a BJT? (c) For a BJT that has a Early voltage of V = 48 V, calculate the outut coductace, g 0, at a bias oit of I C = 10 m ad V CE = 2 V. (d) Briefly exlai the differece betwee BV CEO ad BV CBO for a BJT.

7 Studet #: 6. ackaged device with a device-to-ackage thermal resistace of 50 K/W is mouted o circuit board. The circuit board temerature is 60 C ad the thermal resistace betwee the ackage ad board is 90 K/W. The ackage also has a heat sik attached makig the ackage to ambiet air thermal resistace 120 K/W. The ambiet air temerature is 30 C. 7 (a) If the device above was dissiatig P o = 2 W durig oeratio what would the oeratig temerature, T o, of the device be? (b) t what oeratig ower, P o, is the device at the same temerature as the circuit board?

8 7. The small-sigal hybrid-i model for the biolar trasistor is show below. Studet #: 8 (a) I what trasistor oeratig rage is this model ormally used? (b) What restrictios aly to the use of this model? (c) What are the hysical origis of the extrisic base resistace, r bx, ad itrisic base resistace, r bb'? (i.e. What arts of the device structure do they corresod to?)

9 Studet #: 8. For most itegrated BJTs biased i forward active mode we ca assume to a good aroximatio that: C C π π >> C >> C debc debe (a) What is the hysical origi of the base diffusio caacitace C? π 9 (b) Fid a simlified exressio for the trasit frequecy, f, usig the aroximatio above. τ (c) If the eutral base width,, is 2.5 µm ad the trasistor collector curret, I C is 10 m, what is the value of the trasit frquecy, f, usig the above aroximatio? (T = 300 K) τ

10 Equatios Ideal iode: qv kt I = I S ( e 1) with both R s ad GR: ( ) ( ) q Vx I Rs kt I = I S e 1 where Vx = V + I Rs Eistei Relatios: iffusio Legth: Saturatio Curret esity: Resistivity: kt kt µ, µ q q L τ, L τ 0 0 J S = J Sh + J Se = q 0 + q 0, for thi ad w w = ( σ + σ ) = ( qµ + qµ ) ρ ρ ρ ρ x = q x x + N N kt N N V = l bi 2 q i Excess Charge esity i a iode: ( ) [ ( ) ( ) ] Built-I Voltage: eletio Width: Maximum Electric Field: valache Multilicatio Factor: Imact Ioizatio Probability: iode Juctio Coductace: iode Juctio Caacitace (/area): W = Charge Cotrol Equatio: ( ) Charge Storage Time: BJT Ijectio Model Currets: BJT Ebbers-Moll Model: 2ε Si q N N 2q N N E del max = ε Si N + N 1 M = 1 ii ν, 10 Studet #: ρ l R = N ( V ) = bi V, x = W, x W N + N N + N ( V V ) E del max ii =, 3 < ν < 6 E crit di q qv kt q g = = I Se I dv kt kt dqˆ del dqˆ del dw N N Cˆ del ( V ) = = = q dv dw dv N + N dq t Q( t) = i( t) dt τ 0 I V V I = I + I, I = I + I, I = I + I F F t s = τ 0 l 1 VF VR >> I τ 0 l 1 R V for, R C C B B C I C = q E C C0 W C e qv BC kt 1 I B = q E C C0 W C e qv BC kt 1 bi E E B ε Si N + N Wq N N ( ) + q E B B0 ( ) E e qv BE kt e qv BC kt ( ) + q E E E 0 ( ) I E = q E B B0 e qv BE kt e qv BC kt I ES q E B B0 + q E E E 0 W E W E e qv BE kt 1 ( ) + q E E E 0 ( ) W E e qv BE kt 1 I CS q E B B0 + q E C C0 W C N ε Si = W V ( ) Heat Flow: q α F E B B0 q α R E B B0 q E B B0 + q E E E 0 W E q E B B0 + q E C C0 W C ( ) α R I CS e qv BC ( kt 1) ( ) + ( 1 α R )I CS e qv BC ( kt 1) ( ) I CS e qv BC ( kt 1) I E = I ES e qv BE kt 1 I B = ( 1 α F )I ES e qv BE kt 1 I C = α F I ES e qv BE kt 1 dt Φ = κ, dx T rise = P R TH BJT Base iffusio Caacitace: C π = τ B g m, τ B = 2 2 B BJT Trasit Frequecy: f τ =1 2π " C debc + C debe! ( ) g m +τ B # $

11 Physical Costats ad Material Proerties 11 Studet #: Quatity Symbol Value Micro µm 10-4 cm = 10-6 m gstrom Uit Å 10-8 cm = m Boltzma s Costat k 8.62x10-5 ev/k 1.381x10-23 J/K Electroic Charge q 1.602x10-19 C Electro Volt ev 1.602x10-19 J Electro Rest Mass m o 9.11x10-31 kg Free Sace Permittivity ε o 8.854x10-14 F/cm Plak s Costat h 6.626x J-s 4.14x10-15 ev-s Thermal Voltage at 300K 1kT/q V Proerties of Silico at 300K Quatity Symbol Value Itrisic Carrier Cocetratio i 1.45x10 10 cm -3 Effective esities of States N v 1.08x10 19 cm -3 N c 2.8x10 19 cm -3 Electro ffiity χ Si 4.05 ev Eergy Ga E g 1.08 ev Bulk Electro Mobility µ 1350 cm 2 /V-s Bulk Hole Mobility µ 470 cm 2 /V-s Surface Electro Mobility µ 520 cm 2 /V-s Permittivity ε Si 11.7ε o Proerties of Silico ioxide Quatity Symbol Value Permittivity ε ox 3.9ε o