Bipolar junction transistor operation and modeling

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1 Electronic Devices and Circuits Lecture 8 - Bipolar Junction Transistor Basics - Outline Announcements Handout - Lecture Outline and Summary; Old eam 1's on Stellar First Hour Eam - Oct. 8, 7:30-9:30 pm; thru p-n diodes, PS #4 Review/Diode model wrap-up Eponential diode: i D (v AB = I S (e qvab/kt -1 (holes (electrons with I S A q n i [(D h / w n* + (D e /N Ap w p* ] Short- vs. long-base diodes: effective diode lengths and consequences Observations: Saturation current, I S, goes down as doping levels go up Injection is predominantly into more lightly doped side Junctions as injecting and etracting contacts. Diffusion charge stores; diffusion capacitance: Quasi-neutral region ecess carriers as charge store Total charge vs. voltage and current; incremental capacitance Bipolar junction transistor operation and modeling Bipolar junction transistor structure Qualitative description of operation: 1. Visualizing the carrier flues (using npn as the eample. The control function 3. Design objectives Operation in forward active region, v BE > 0, v BC < 0: d E, d B, a F, I ES Clif Fonstad, 9/03 Lecture 8 - Slide 1

2 Biased p-n junctions: ecess minority carrier (diffusion charge stores Ecess minority carrier charge stores; Diffusion capacitance: Using eample of asymmetrically doped p+-n diode Note: Assuming negligible charge stored on p-side p ( n Diffusion charge store, n-side: Notice that the stored positive charge (the ecess holes and the stored negative charge (the ecess electrons occupy the same volume in space (between = n and = w n! [ [ ] w n - n ] q A,DF (v AB = Aq p'( n - p'(w n p (, n ( -w p - p n w n Clif Fonstad, 9/03 Lecture 8 - Slide Charge stored on n-side (holes and electrons ª Aq n i e qv AB / [ kt -1] w n,eff The charge stored depends non-linearly on v AB. As we did in the case of the depletion charge store, we define an incremental linear equivalent diffusion capacitance, C df, as: n (- p C df q A,DF v AB v AB =V AB ª A q kt w n,eff n i e qv AB / kt

3 Diffusion capacitance, cont.: p ( n p (, n ( Ecess holes and electrons stored on n-side n (- p -w p - p n w n A very useful way to write the diffusion capacitance is in terms of the bias current, I D : I D ª Aqn i D h e qv AB / kt D [ -1] ª Aqn h i e qv AB / kt w n,eff w n,eff for V AB >> kt Comparing this to C dff we find: C df ª A q kt w n,eff n i e qv AB / kt ª w n,eff q I D D h kt ** Notice that the cross-sectional area of the device, A, does not appear eplicitly in this epression. Only the total current! Clif Fonstad, 9/03 Lecture 8 - Slide 3

4 Comparing charge stores and small-signal linear equivalent capacitors: Parallel plate capacitor q A r( q A,PP = A e d v AB -d/ d/ q B ( = -q A C pp q A,PP = Ae v AB d v AB =V AB Depletion region charge store - p qa q r( q B ( = -Q A -qn Ap QNR region diffusion charge store p ( n n p (, n ( n (- p -w p - p n w n q A, q B (=-q A q A,DP (v AB = -A qe Si [ f b - v AB ] C dp = A q AB,DF (v AB ª Aqn i C df ª w n,eff q I D D h kt N Ap [ N Ap + ] D h e qv AB / [ kt -1] w n,eff = w n,eff i D (v AB D h Clif Fonstad, 9/03 Lecture 8 - Slide 4 qe Si [ ] f b -V AB Note: Approimate because we are only accounting for the charge store on the lightly doped side. Note: Valid in forward bias where v AB >> kt/q N Ap [ N Ap + ] = A e Si w

5 Bipolar Junction Transistors: basic operation and modeling how the base-emitter voltage, v BE, controls the collector current, i C E C i C E - - i E n N DE v CE p N AB n N DC + i C C + vbe- E v BE + B i B -w E 0 w B w B + w C Forward biased v BE, the bias on the emitter-base junction, controls the injection of electrons across the E-B junction into the base and toward the collector. Reverse biased v CB, the reverse bias on the collectorbase junction, insures collection of those electrons injected across the E-B junction that reach the C-B junction as the collector current, i C Our net task is to determine: Given a structure, what are i E (v BE,v CE, i C (v BE,v CE, and i B (v BE,v CE? Clif Fonstad, 9/03 Lecture 8 - Slide 5

6 npn BJT: Forward active region operation, v EB > 0 and v CB 0 Ecess Carriers: (n i /N DE (eqvbe/kt - 1 p, n (n i /N AB (eqvbe/kt (ohmic ~ 0 (vbc < 0 0 (ohmic -we 0 wb wb + wc Currents: i e, i h -we 0 wb wb + wc Clif Fonstad, 9/03 i he [= d E i ee ] i ee i E [= i ee + i ee = i ee (1 + d E ] } i C [= i ee (1 d B ] i B [= i he + d B i ee = i ee (d E + d B ] Lecture 8 - Slide 6

7 npn BJT: Well designed structure in FAR N DE >> N AB, w E << L he, w B <<L eb Ecess Carriers: (n i /N DE (eqvbe/kt - 1 p, n (n i /N AB (eqvbe/kt (ohmic 0 (vbc = 0 0 (ohmic -we 0 wb wb + wc Currents: i e, i h -we 0 wb wb + wc i he [= d E i ee ] i ee i C [= i ee (1 d B i ee ] Clif Fonstad, 9/03 i E [= i ee (1 + d E ] i B [= i E ( i C = i ee (d E + d B i ee d E ] Lecture 8 - Slide 7

8 B + ib vbe Electronic Devices and Circuits Lecture 8 - Bipolar Junction Transistor Basics - Summary Review/Junction diode model wrap-up Refer to "Lecture 7- Summary" for a good overview Diffusion capacitance: adds to depletion capacitance In asym., short-base diodes: C df (qi D /kt[(w n - n /D h ] (area doesn't enter epression! (p + -n eample Bipolar junction transistor operation and modeling Hole Flu n n p C E ie ic Electron Flu wb 0 -we wb + wc Currents (forward active: (npn eample i E (v BE,0 = I ES (e qvbe/kt 1 i C (v BE,0 = a F i E (v BE,0 with a F [(1 d B /(1 + d E ] Emitter defect, d E (D h N AB w B* /D e N DE w E* (ratio of hole to electron current across E-B junction Base defect, d B (w B /L e (fraction of injected electrons recombining in base n, p Also, i B (v BE,0 = [(d E + d B /(1 + d E ] i E (v BE,0 and, i C (v BE,0 = b F i B (v BE,0, with b F a F /(1 a F = [(1 d B /(d E + d B ] Clif Fonstad, 9/03 Lecture 8 - Slide 8

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