Electronics I - Physics of Bipolar Transistors

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1 Chapter 5 Electronics I - Physics of Bipolar Transistors B E N+ P N- C B E C Fall 2017 claudio talarico 1

2 source: Sedra & Smith Thin Base Types of Bipolar Transistors n+ p n- Figure - A simplified structure of the npn transistor Figure Symbol of the npn transistor Thin Base p+ n p- Figure Symbol of the pnp transistor Figure - A simplified structure of the pnp transistor. 2

3 Physical structure of an npn BJT source: Sedra & Smith + Figure - npn BJT symbol - Figure - Simplified Cross-section of an npn BJT. source: Gray & Meyer Claudio Talarico 3

4 NPN BJT operating in Forward Active Mode source: B. Murmann Conceptual View: Device acts as a voltage controlled current source V BE controls I C I & exp V -. V / B V "# V "# V $ C I - I & Forward Biased - + C B E Reverse Biased I. = I & + I - I & The BE junction is forward biased (V BE > 0) and the BC junction is reverse biased (V BC < 0 V CB > 0) E V &- = V &. V -. The device is built such that: The BASE region is very thin The EMITTER doping is much higher than the BASE doping ( N E (donors) >> N B (acceptors) ) The COLLECTOR doping is much lower than the BASE doping ( N B (acceptors) >> N C (donors) ) 4

5 Outline of discussion for NPN BJT in Active mode source: B. Murmann To understand the operation of the NPN BJT in active mode, we will to look at: Properties of forward biased PN + junction (BE) Properties of reverse biased PN - junction (BC) The idea of combining the two junctions by a very thin P-type region (B) source: Razavi Although the device contains two PN junctions it cannot be modeled as two back to back diodes. Reverse Biased Forward Biased B C E D BC D BE + - The doping levels and dimensions of E and C are quite different (N E >> N C and A C >> A E ). The device is not symmetric: E and C cannot be interchanged 5

6 Main idea Make the P-region (B) of the PN+ junction (BE junction) very thin and forward bias it This way the electrons injected from the N + side (E) into the P side (B) cannot recombine much Attach an N - region (C) to the P-region (B) and reverse bias the resulting PN - junction (BC junction) This way most of the electrons injected into the P-region (B) are swept into the N - region (C) before there is any significant amount of recombination occurring Final Result: most of the electrons emitted in E will make it through B and get collected in C Claudio Talarico 6

7 Voltage polarities for BJTs in active mode source: Razavi I C V BE I B NPN I E NPN V -. ³ V -.,:; V &. > V &.,<=/ I B I C PNP V.- ³ V.-,:; V.& > V.&,<=/ I E Figure Voltage polarities and current flow in bipolar transistors biased in the active mode 7

8 Currents for NPN BJT in active mode source: Sedra & Smith + - & holes source: B. Murmann Primary current is due to electrons captured by the collector Two (undesired) base current components Hole injection into emitter (à 0 for infinite emitter doping) Recombination in base (à 0 for base width approaching 0) 8

9 Currents for NPN BJT in active mode source: Razavi holes & electrons recombining Electrons diffusing in P region C N- E B C injected holes P B - E N+ injected electrons 0 W B x There a lot of electrons injected into the P region, not that many holes injected in N+ region (N E >> N B ) The electrons injected in the P region causes a diffusion current decaying in the x direction due to recombination (recombination necessitate a flow of holes to balance out the flow of electrons) Claudio Talarico 9

10 source: Gray & Meyer Carrier Concentrations N + P N - carrier concentration n?. N. n?& N & N - N & p?. n B C /N. p?& n B C /N & Claudio Talarico

11 BE (PN + ) junction Built-in Potential (PN+ junction at equilibrium: V BE =0) (E) N + -X n0 x=0 +X p0 Electrostatic force and diffusion balance out: (B) P x dp drift qμ G pe = qd G (diffusion) dx `a(b cd ) _ dv = D G _ μ G a(eb fg ) G cd G fd dp p n?f N. p GF N - Φ F V / p?f n B C /N. E J u L n GF n B C /N - p GF p?f = exp Φ F V / = n?f n GF electrons want to diffuse electrostatic force prevents e - from diffusing Φ F holes want to diffuse electrostatic force prevents h + from diffusing Φ F = V / J ln n?f n GF V / J ln N.N - n B C = V / J ln p GF p?f 11

12 BE (PN + ) junction with forward bias The depletion region narrows and diffusion processes are no longer balanced by electrostatic forces (E) N + X + + V BE Φ k = Φ F V (B) P X With a forward bias applied some electrons can now diffuse from the N+ side (where they are majority carriers) to the P side (where they become minority carriers). Similarly, some holes diffuse from the P side into the N+ side This migration of carriers from one side to another is called INJECTION As a result of injections the concentration of minority carriers at the edges of the depletion region (x =0 and x =0) is significantly increased Claudio Talarico 12

13 BE (PN + ) junction with forward bias (E) N + X 0 0 (B) P QNR-1 QNR-2 n? N. p G N - Depletion n G (0) p Region? (0) p?f Important result to remember Forward Bias increases the concentration of electrons at the P side s edge of depletion region by a factor exp(v BE /V T ) (Law of the Junction) X n GF n?f n G 0 = exp Φ = F V -. V / n?f = exp V -. exp Φ F /V / V / n GF J exp V -. V / n B C N - exp V -. V / Since outside the depletion region there must be charge neutrality, the concentrations of the majority carriers at the edges of the depletion region must also increase of the same amount the minority carriers increased However if we assume low level of injection the increase in majority carriers in not significant and can be neglected The carriers injected would like to diffuse into the neutral regions, but quickly fall victim of recombination The number of minority carriers decay exponentially and drops to 1/e at the so called diffusion length (L p and L n are on the order of microns) Claudio Talarico 13

14 Reverse Biased BC (PN - ) junction Reverse bias increases the width of the depletion region and increases the electric field Depletion region extends mostly in N - side Any electron that somehow make it into the depletion region is swept through by the electric field, into the N- region P (B) ρ(x) N - (C) qn e E L E qn & x x 14

15 Collector Current for an NPN BJT in active mode source: Razavi Electrons diffusing in P region I. I - E B C - First order expression: I & 0 W B x The electrons injected from the emitter into base diffuse through base and then get swept into collector: J? = qd? dn G dx o F Δn G qd? Δx = qd n G 0 n GF? = 0 W - C n B W - = qd? W - n GF e a rs/a t 1 qd? N - e a rs/a t Multiplying by the emitter area and changing the sign to obtain the conventional current C qd? n B I & A. e W - N - a rs a t a rs = I < J e a t I <. to be picky The device operates as a voltage controlled current source (it performs voltage-current conversion) Claudio Talarico 15

16 source: Razavi Relation between collector current and emitter area When two transistors are put in parallel and experience the same potential across all three terminals, they can be thought of as a single transistor with twice the emitter area. Parallel combination of two transistors I C V BE V CE V BE V CE I C I & 2A. qd C? n B e W - N - a rs a t Claudio Talarico 16

17 Characteristics of NPN BJT in active mode source: Razavi V BE,ON CH4 Physics of Bipolar Transistors 17

18 NPN BJT in active mode behaves as a constant current source Ideally, the collector current does not depend on the collector to emitter voltage. This property allows the transistor to behave as a constant current source when its base-emitter voltage is fixed. source: Razavi V BE V BE V BE V BE NOTE: don t forget the BC (PN - ) junction must be reverse biased V &- = V &. V -. V -& = V -. V &. so V CE must not go below V BE (V -& 0): 18

19 Effect of temperature on I C vs. V BE characteristics for NPN BJT in active mode source: Sedra and Smith I & V -. Figure - Effect of temperature on the I C -V BE characteristics. At constant I C the V BE changes by about -2mV/Celsius 19

20 Base current for NPN BJT in active mode (1) source: Sedra & Smith Primary current is due to electrons captured by the + - collector holes injected in emitter I - = I - + I -C I - 0 n p (0) Base W B recombination in base In modern narrow-base transistors I B1 >> I B2 n p0 I -C = Q,-=<. x & holes τ -=<. life time electrons Charge of minority carriers (electrons) in BASE Two (undesired) base current components 1 2 n G(0)qA. W - 1 qa. W - τ? 2 τ? n G 0 n GF n G 0 Hole injection into emitter (à 0 for infinite emitter doping) Recombination in base (à 0 for base width approaching 0) C n B e a rs/a t N - 20

21 Base current for NPN BJT in active mode (2) source: Sedra & Smith Primary current is due to electrons captured by the + - collector holes injected in emitter recombination in base I - = I - + I -C I - =p n0 0 x & holes In modern narrow-base transistors I B1 >> I B2 current due to holes diffusing in emitter dp? (x) I - = qa. D G dx o F = qa. c ˆ? c ; s e rs t Two (undesired) base current components Hole injection into emitter (à 0 for infinite emitter doping) Recombination in base (à 0 for base width approaching 0) qa. D G d dx C n a rs B e N. el a t e c F 21 =

22 Base current for NPN BJT in active mode (3) holes injected in emitter recombination in base I - = I - + I -C I - current due to holes diffusing in emitter I - = I - + I -C = qa. c C qd? n B I & A. e W - N - a rs a t recombination current in base ˆ? + c ; s C a rs = I < J e a t In modern narrow-base transistors I B1 >> I B2 ˆ Š= s r? e Œ f ; r rs t Primary current is due to electrons captured by the collector Two (undesired) base current components Hole injection into emitter (à 0 for infinite emitter doping) Recombination in base (à 0 for base width approaching 0) β Ž = I & I - = 1 W - C 2τ? D? + D G D? W - L G N - N. As expected: b F is maximized by minimizing W B and maximizing N E /N B Important result: I B is a constant fraction of I C (----> b F = I C /I B ) 22

23 Large signal (DC) model of NPN BJT in active region source: Gray and Meyer I C I C E E I E a rs I - = I & = I a <e t β Ž β Ž I E Figure - Simplified model; very useful for bias point calculations (assuming e.g. VBE(on) = 0.8V) β Ž I & I - α Ž I & I. = (ideally infinite: I B =0) I & I - + I & = β Ž β Ž + 1 (ideally one) The subscript F indicates that the device is assumed to operate in the forward active region (BE junction forward biased, BC reverse biased, as assumed so far) More on other operating regions soon

24 Small signal (AC) model of NPN BJT in active mode source: Razavi I CQ Q V BEQ ΔI C g m ΔV BE The transconductance g m expresses the strength of the device (how well the controlling voltage is converted in a current) g = di & dv -. = d dv -. a rs I < e a t = I & V / g = di - dv -. = d I &/β Ž dv -. = g β š Common notations: ΔV -. v œ v ΔI & i ΔI - i œ ΔV BE ΔV &. v r = 1/g h B β š h š β Ž h Ž. i b i e i c 24

25 Flavors of b (with BJT in forward active mode) I C I B β F h FE DC beta ΔI C ΔI B β f h fe AC beta ln(i) To first order we assume β DC β AC ln(b F ) In other words we assume b F is constant (we ll see later that is not always accurate) V BE (linear scale) 25

26 Let s finally build an amplifier! I < = 3 10 e A β = 100 source: Razavi v B? V Ÿ = V Ÿ + v Ÿ v B? v Ÿ V -. = a rs I & = I < e a t 6.92 ma g = I & V / 266 ms r = β g 376 Ω A a = v Ÿ v B? = g R 26.6 It looks like by increasing R C we can get whatever gain we want. This sounds too good to be true! There must be limitations we are missing! Claudio Talarico 26

27 Practical Limitations First of all for the device to behave as a voltage controlled current source we must operate in forward active mode (BE must be forward biased and BC reverse biased) As R C increases, V CE drops and eventually forward biases the collector-base junction. This will force the transistor out of forward active region. Therefore, there exists a maximum tolerable collector resistance V &. = V && R & I & V -. R & V && V -. I & Second, I am very skeptical we can build anything that behave exactly as an ideal current source source: Razavi R &, =b V -. V -. V -. V CE (V) V -. Claudio Talarico 27

28 I & A. qd? W B µ C n a rs B e a t N - a rs = I < J e a t J 1 + V &. V = Early Effect (1) source: Razavi n - n - W B 0 W B 0 The claim that collector current does not depend on V CE is not accurate As V CE increases, the depletion region between base and collector increases. Therefore, the effective base width decreases, which leads to an increase in the collector current. 28

29 Early Effect (2) source: Razavi V &. V &. V -. V -. V &. Claudio Talarico 29

30 Small-signal model including Early effect source: Razavi ΔI - ΔI & ΔV -. ΔV ΔV &. ΔI. V &. V = g Ÿ = 1 r Ÿ = di & dv &. = d dv &. a rs I < J e a t J 1 + V &. V = a rs = I < J e a t J 1 = V = I & 1 + V &. V = J 1 V = I & V = g = di & dv -. I & V / g = di - = d(i &/β Ž ) I & β š dv -. dv -. V / = g β š r = 1/g h B g Ÿ = 1/r Ÿ h Ÿ β š h š β Ž h Ž. intrinsic gain g r F V = V / max gain the device can provide Claudio Talarico 30

31 Base modulation and Early voltage source: Gray & Meyer I C = diffusion current of electrons in base µ gradient of electrons in base = Dn p (x)/dx NOTE: the slope changes very little, so it is reasonable to assume it» constant) slope ΔV &. ΔI & ΔW - V = I & = I & V &. W - dw - dv &. const. since DW B is negative we need a minus sign in the equation 31

32 Dependence of I C on V CE source: Sedra & Smith I & I & V A = Early Voltage V &. In Forward active region: I & A. qd? W B µ C n a rs B e a t N - a rs = I < J e a t J 1 + V &. V = Claudio Talarico 32

33 Model Extensions Complete picture of BJT operating regions Dependence of b F on operating conditions Claudio Talarico 33

34 NPN BJT operating regions source: Gray & Meyer Discussed so far: BE = forward biased BC = reverse biased BV CE0 ½ BV CB0 BV EB0 << BV CB0 β R << B F BE = reverse biased, BC = forward biased the collector injects electrons in base and Claudio the emitter Talarico collect them 34

35 source: Gray & Meyer Dependence of b F on operating conditions (and temperature) A typical temperature coefficient for b F is about ppm/ Claudio Talarico 35

36 Gummel Plot (I C and I B vs. V BE ) source: Gray & Meyer b F stays about const. excess of undesired recombination in base L = low current density M = medium current density H = high current density High level of electrons injected in base (near to The doping level of the base: N B ) Claudio Talarico 36

37 b F fall-off source: B. Murmann Region II (medium current density) b F is about constant (as desired) Region I (low current density) there is an excess of undesired recombination in base Region III (high current density) the level of electrons injected in base is extremely high near the level of doping of the base (N B ). It can be shown that for this case: I & I < ec a rs a t Claudio Talarico 37

38 NPN BJT in saturation mode source: Razavi saturation mode: V -. ³ V -.,:; V &. V &.,<=/ The term saturation is used because increasing the base current in this region of operation leads to little change in collector current (there is a significant drop in b compared to active mode) V CE,SAT In active mode I C is almost independent of V CE (and V CB «V CB = V CE V BE V CE 0.8) In saturation not only the BE junction is forward biased, but also the BC junction is forward biased As a result, I C must also strongly depends on V CB (and V CE «V BC = V BE (on) V CE = 0.8 V CE Claudio Talarico 38

39 NPN BJT in Saturation mode source: Razavi Add the BC forward diode to the previous model I SC exp(v BC /V T ) I SC = saturation current of the BC (PN ) diode I SE º I S = saturation current of the BE (PN + ) diode I B I E I C I SE exp(v BE /V T ) r½ rs I. = I - I <& e t + I <. e t = = I - + I & A E < A C «I SC > I SE The BC junction area is larger than the BE junction area therefore the ON voltage of the BC diode is smaller than the ON voltage of the BE diode (typically V BC,on < V BE,on by 0.4 V) In saturation the collector current is reduced by I SC exp(v BC /V T ): a rs I & = I <. e a t a r½ I <& e a t while the base current is increased by I SC exp(v BC /V T ): I - = I <. β ¾ B e a rs a t + I <& e a r½ a t Claudio Talarico 39

40 NPN BJT in Saturation mode Since in saturation I C decreases and I B increases the beta of the transistor decreases significantly: β sat β forced = I C I B sat β β active By adjusting V BC (i.e. V CE ) the beta of a transistor in saturation (β forced ) can be set to any value lower than β active source: Razavi I B =I B3 I B =I B2 I B =I B1 V CE,SAT Claudio Talarico

41 source: Razavi Soft Saturation For V CE =V BE, the BC junction sustain a zero voltage difference (V BC =V BE -V CE =0), and its depletion region still absorbs most of the electrons injected by the emitter into the base We consider this condition as the edge between active mode and saturation mode What happens if V CE < V BE, i.e. V BC > 0? Not much until V BC ³ V BC,ON. Up to V BC,ON the current carried by the BC forward biased diode is still extremely small, so assume the behavior of I the device still acceptable: C As a rule of thumb we permit soft saturation: V BC < 400 mv «V CB > -400 mv (V CB = V CE V BE > 400 mv ««V CE > V BE 400 mv «V CE > 400 mv) soft source: Sedra & Smith for I B = I B1 Typically assume: V CE (edge) = 800mV V CE,SAT (soft) = V CB,ON + V 400 mv V CE,SAT (deep) º V 200 mv edge between active region and saturation region: V CB = 0 «V CE = V BE edge 41 V CB

42 Deep Saturation source: Razavi In deep saturation the BC diode carries a significant amount of current, so the transistor bear no longer any resemblance to a controlled current source. The collector-emitter voltage approaches a constant value called V CE, SAT and the transistor can be modeled as follows: almost a short Claudio Talarico 42

43 NPN BJT in Saturation mode source: Sedra & Smith In saturation the I C vs. V CE curves are rather steep indicating that the saturated BJT exhibits a low resistance (R CE,SAT ranges from a few ohms to a few tens of ohms). This result was to be expected from the fact that between C and E we have two forward biased diodes source: Razavi large b (=b active ) small b (=b sat ) slope = 1/R CE, SAT I B =I B3 I B =I B2 I B =I B1 V CE,SAT Claudio Talarico 43

44 Example source: Sedra & Smith b active = 50 Find V BB to set the transistor in: (a) Active mode with V CE = 5V (b) Edge of saturation (c) Deep in saturation with β forced = 10 a) V &. =V && R & I & I & = a ½½ea ½s Á ½ = 5mA I - = b) I & = a ½½ea ½s ( ËÌ ) Á ½ c) I & = a ½½ea ½s (Ë G) Á ½ = FeF.Í FFF = 9.2mA I - = = FeF.C FFF = 9.8mA I - = Ã ½ Ä ÅÆÇ ÈÉ = 100μA V -- = V -. + R - I - = k 100μ = 1.8V Ã ½ Ä ÅÆÇ ÈÉ = 184μA V -- = V -. + R - I - = K 184μ 2.64V Ã ½ Ä ÐgÑÆÉÒ = 980μA V -- = V -. + R - I - = K 980μ 10.6V Claudio Talarico 44

45 PNP transistor All the principles that applied to NPN also apply to PNP, with the exception that emitter is at a higher potential than base and base at a higher potential than collector. source: Razavi I. I - E B C I & I - I & P+ N 0 W B P- I. NOTE: Use the currents directions shown in figure and VEB and VEC to get all positive values Claudio Talarico 45

46 PNP transistor Equations for PNP in active mode source: Razavi I - I & I. I I I I C B E C = I = S b + 1 = I b æ = ç I è V exp V S S EB T I S V exp b V EB T V exp V V exp V EB T EB T ç øæ ö V 1 + è V EC A ö ø A comparison between NPN (a) and PNP (b) Claudio Talarico 46

47 PNP BJT in active mode: large signal (DC) model source: Razavi Claudio Talarico 47

48 PNP BJT in active mode: small signal (AC) model source: Razavi The small signal model for the PNP transistor is exactly IDENTICAL to that of the NPN. This is not a mistake! Claudio Talarico 48

49 PNP BJT is deep saturation source: Gray & Meyer I B I C I B I C 800 mv 200 mv mv mv I E IE Claudio Talarico 49

50 Summary of operating regions NPN Bipolar Transistor Region V BE V BC Cutoff Forward Active Reverse Active Saturation < V BE(on) ³ V BE(on) < V BE (on) ³ V BE(on) < V BC(on) < V BC(on) ³ V BC(on) ³ V BC(on) PNP Bipolar Transistor Region V EB V CB Cutoff Forward Active Reverse Active Saturation < V EB(on) ³ V EB(on) < V EB (on) ³ V EB(on) < V CB(on) < V CB(on) ³ V CB(on) ³ V CB(on) Claudio Talarico 50

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