Introduction to Electronic Devices

Transcription

1 troductio to lectroic Devices, Fall 2006, Dr. D. Ki troductio to lectroic Devices (ourse Number ) Fall 2006 s Dr. Dietmar Ki Assistat Professor of lectrical gieerig formatio: htt:// Source: Ale Ref.: Ale Ref.: M ritical dimesio (m) Ref.: Palo Alto Research eter 1

2 troductio to lectroic Devices, Fall 2006, Dr. D. Ki troductio to lectroic Devices 5 s 5.1 troductio 5.2 asic trasistor oeratio 5.3 Trasistor uder zero bias 5.4 Trasistor uder bias coditios Shockley Assumtios The ideal trasistor equatio The trasistor equatio i its geeral form Modes of Oeratio The active mode The Saturatio mode The cutoff mode The iversio mode 5.5 Trasort ad gai factors The mitter efficiecy The Trasort factor The ommo-base curret gai The summary of the trasort ad gai factors 2

3 troductio to lectroic Devices, Fall 2006, Dr. D. Ki Refereces 5.6 Trasistor Desig The trasort factor The mitter fficiecy 5.7 s as Amlifiers ommo base circuit ommo emitter circuit The arly ffect 5.8 Trasfer characteristic ad gai 5.9 Device arameters 5.10 quivalet circuit of a biolar juctio trasistor 3

4 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.1 troductio The trasistor (Germaium oit cotact trasistor) was ivited by arttai, ardee ad Shockley i As the ame already imlies it is a biolar device (like a diode), which meas that both electros ad holes (miority ad majority carriers) cotribute to the overall curret flow. The biolar juctio trasistor (JT) is oe of the most imortat semicoductor devices. The trasistor is used for high seed circuits, aalog circuits ad ower alicatios. The uderlyig electroic trasort mechaisms of biolar juctio trasistors (JT) ad diodes are similar. oth devices are diffusio cotrolled devices. Therefore, the ifluece of the drift curret o the total curret is egligible. The oeratig ricile of biolar devices is differet from the behavior of uiolar device like a Field ffect Trasistors (FTs), where the curret is either cotrolled by electros or holes. Furthermore, a field effect trasistor is a drift cotrolled electroic device. 4

5 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.1 troductio A biolar trasistor (like all other trasistors) is a three (four) termial device. The device cosists of a iut ad a outut loo. The device is desiged i such a ways that small iut chages of a curret or/ad a voltage result i large chages of the outut curret or/ad voltage. The JT device structure cosists of two juctios. The device ca be imlemeted as a or a structure. ach of the doed regios is coected with oe of the termials: ase, mitter or ollector. The three regios of a JT are formed by the diffusio of a doig rofiles i a substrate. Schematic cross sectio of a trasistor. The trasistor is imlemeted i a -tye substrate. The -tye ad the + - tye regios are formed by diffusio of doats i the -tye substrate. The electrodes are formed by metal cotacts. Ref.: M.S. Sze, Semicoductor Devices 5

6 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.1 troductio The oeratio ricile of a biolar trasistor relies o the fact that the base regio of the trasistor is a very thi regio, so that the two diodes affect each other. The thickess of the base i cotrolled by the maufacturig (diffusio) rocess. terms of alicatios ure aalog itegrated circuits are gettig less imortat. Nowadays the techology shifts towards imos techology. imos is a combiatio of biolar techology ad metal oxide semicoductor techology (techology required to maufacture field effect trasistors). t allows the realizatio of aalog ad digital circuits o a sigle chi. 5.2 asic trasistor oeratio The two ossible device structures of a biolar trasistor or P- ad a structures. iolar trasistors ca oerate i four modes of oeratio, deedig o the voltage alied to the base-emitter ad the base-collector juctio. The four modes of oeratio are: Active mode, iversio mode, cutoff mode, Saturatio mode. 6

7 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.2 asic trasistor oeratio order to realize a amlifier the JT will be oerated i the active mode. the followig the basic oeratig ricile of a biolar trasistor i the active mode will be reseted. The + ad sigs idicate the olarities of the voltages alied to the termials uder ormal oeratig coditios (active mode). -trasistor the active mode the emitter base diode is forward biased (V >0) ad the base collector diode is reverse biased (V <0). -trasistor Ref.: M.S. Sze, Semicoductor Devices 7

8 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.2 asic trasistor oeratio O this slide the + ad sigs idicate the directio of the curret flow. = The -structure is comlemetary to the structure. As a cosequece the curret flow ad the voltage olarities are reversed. the followig we will discuss the electroic trasort of a trasistor. -trasistor Ref.: M.S. Sze, Semicoductor Devices -trasistor 8

9 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.3 iolar Juctio Trasistors uder zero bais At first the JT will be studied i thermal equilibrium. All three termials of the device are grouded. Uder thermal equilibrium the Fermi level is costat throughout the etire device structure. As a cosequece the derivative of the Fermi level is zero, so that the overall curret flowig through the device is zero. The followig device structure is used for the discussio: The emitter is (much) heavier doed tha the base ad the base is agai heavier doed tha the collector. The base regio is much shorter tha the emitter ad the collector regio. The base width of the base regio is much shorter tha the diffusio legth of the miority carriers. Therefore, the two -juctios affect each other. f the base-regio would be much loger tha the diffusio legth of the miority carriers i the base regio of the two -juctios would behave like two searate diodes. The oeratio of the diodes would be ideedet of each other. The electric field distributio i the JT ca be calculated by solvig the Poisso equatio. As a cosequece of the doig rofile i the idividual regios of the device the maximum electric field ad the built-i voltage for the base/emitter juctios is higher tha the maximum electric field ad the built-i voltage for the base/collector juctio (uder thermal equilibrium). 9

10 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.3 iolar Juctio Trasistor uder zero bias Throughout the followig discussio it is assumed that two abrut juctios are formed. As a cosequece the electric field distributio outside of the deletio regios is zero. The formatio of the sace charge regio for a JT is comarable with the formatio of the sace charge regio of a diode. -trasistor (a) -trasistor uder thermal equilibrium (all termials grouded). (b) Doig rofile of a abrut structure, (c) lectric field rofile, (d) ergy bad diagram Ref.: M.S. Sze, Semicoductor Devices 10

11 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.3 iolar Juctio Trasistor uder zero bias There are techological ad a hysical reasos for the differet doig rofiles i the idividual regios of the device: Techological: The fabricatio of a JT requires two diffusio stes to form three regios with differet doig cocetratios. the first diffusio ste the base has to be formed ad the already existig doats i the material (i the substrate) have to be comesated or over comesated. the secod diffusio ste the doig cocetratio has to be icreased agai to comesate the icororated doats of the first diffusio ste. Physical: The goal of the trasistor desig is the realizatio of trasistors with high curret ad/or voltage gai. High curret ad voltages gais ca be achieved if the doig cocetratio i the base is lower tha the doig cocetratio i the emitter. The uderlyig hysical reasos for this articular behavior will be discussed i the chater o trasort ad gai factors. 11

12 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.4 Trasistor uder bias coditios efore derivig the ideal biolar juctio trasistor equatios the basic oeratig ricile of JT uder biasig coditios will be described. Here we will cocetrate o a commo base biolar trasistor i active mode as this is the most imortat mode of oeratio. this case the base/emitter juctio is i forward bias ad the base/collector juctio oerates uder reverse bias coditios. The iut ad the outut loo share the base termial. Therefore, the circuit is called a commo base circuit. As a cosequece of the alied bias voltages the width of the deletio regios is chaged. Sice the base emitter juctios is uder forward bias holes are ijected via the emitter ad electros are ijected via the base. At the same time the base collector juctio is reverse biased ad the curret flow should be small. However, as the width of the base regio is very short the holes ijected i the emitter diffuse through the base so that they reach the base collector deletio regio, where the holes float u ito the collector regio. Therefore, the collector collects the holes floatig u. The emitter is called emitter because holes are emitted, which are collected by the collector (JT i the active mode). Most of the emitted holes reach the collector regio. 12

13 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.4 Trasistor uder bias coditios Due to the forward bias alied to the base/emitter juctio the exteral electric field lowers the electric field caused by the built-i voltage. The width of the sace charge regio ad the electric field is reduced. The oosite behavior is observed for the reverse biased diode. Here the exteral electric field ehaces the iteral electric field, so that the width of the sace charge regio is exteded. (a) -trasistor uder bias coditios. The trasistor oerates i the active mode. (b) Doig rofile of a abrut structure, (c) lectric field rofile, (d) ergy bad diagram Ref.: M.S. Sze, Semicoductor Devices 13

14 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.4 Trasistor uder bias coditios Due to the alied bias voltages the Fermi level slit u ito quasi Fermi levels. For the juctio uder forward bias the quasi Fermi levels shift closer to the corresodig bads. This meas that the quasi Fermi level for the electros shift closer to the coductio bad, whereas the quasi Fermi level for the holes shifts closer to the valece bad. For the reverse bias diode the oosite behavior is observed. The Quasi Fermi levels shift away from the corresodig bads, because the roduct of the carrier cocetratio is below the square of the itrisic carrier cocetratio. 14

15 troductio to lectroic Devices, Fall 2006, Dr. D. Ki Shockley Assumtios order to derive the ideal trasistor equatio the Shockley assumtios have to be fulfilled. The assumtios for derivig the ideal trasistor equatios are comarable with the assumtios used for derivig the ideal diode equatio. Uiform doig throughout the idividual regios of the device, so that abrut juctios are formed at the emitter/base ad the collector/base iterface. The hole drift curret i the base regio ad the collector saturatio curret are egligible. Low-level ijectio for the forward biased diodes No losses due to geeratio ad recombiatio i the deletio regios of the base/emitter juctio ad the base/collector juctio No series resistace i the device (No voltage dro across the eutral regios.) 15

16 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The ideal trasistor equatio the active mode the base/emitter juctio is forward biased ad the base/collector juctio is reverse biased. Uder forward bias coditios of the base emitter diode holes are ijected from the emitter regio ito the base regio. Subsequetly the holes diffuse across the base regio ad reach the collector juctio. order to determie the ideal trasistor equatio the Diffusio equatio has to be solved. t ca be assumed that the curret flow i the base is determied by the diffusio rather tha the drift of carriers. As a cosequece the electric field i the base ca be igored. The Diffusio equatio has to be solved for the forward biased base/emitter juctio which ca be described by a asymmetric -juctio. D 2 x 2 τ l 0 = 0 Diffusio equatio for holes 16

17 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The ideal trasistor equatio Firstly we determie the miority carrier distributio (i.e. hole cocetratio i the -tye base regio). a secod ste the curret flow ca be obtaied from the miority-carrier gradiet. The geeral solutio of the Diffusio equatio is give by ( x) = ex 2 ex L L x where L ad L are the hole ad the electro diffusio legth of the miority carriers. x L L = D = D τ τ l l Hole diffusio legth lectro diffusio legth 17

18 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The ideal trasistor equatio The followig boudary coditios are used to determie the costats 1 ad 2 : qv kt ( x = 0) = ex ( x = W ) = 0 0 where 0 is the equilibrium miority carrier cocetratio i the base. t is imortat to ote that the miority carrier cocetratio has to be zero for x=w. The miority carrier cocetratio i thermal equilibrium ca be calculated by 0 = N 2 i where N is the door cocetratio i the base. Solvig the Diffusio equatio leads to the followig exressio for the miority carrier cocetratio. ( x) = 0 ad W x W x sih sih qv L L ex kt W W sih sih L L 18

19 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The ideal trasistor equatio The sih(x) fuctio ca be aroximated by x for x << 1, so that the electro cocetratio results to qv kt ( x) = ex x W Miority carrier cocetratio i the base regio The aroximatio is valid because the Diffusio legth is large i comariso to the width of the base. The miority carrier cocetratio (holes) is aroximatio by a straight lie because the width of the base is much smaller tha the diffusio legth for the holes. Ref.: M.S. Sze, Semicoductor Devices 19

20 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The ideal trasistor equatio The miority carrier cocetratio i the emitter ad the collector regio ca be obtaied i a very similar way. qv x x ( x) = x x kt L ex 1 ex x x ( x) = x x L 0 0 ex where 0 ad 0 are the equilibrium electro cocetratio. At the boudaries betwee the eutral regio ad the sace charge regio the carrier cocetratio ca be simlifies to qv 0 kt qv = kt ( x = x ) = ex ( ) = x x ex 0 0 = We assume that the emitter deth ad the collector deth are much larger tha the diffusio legth L ad L for the miority carriers. 20

21 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The ideal trasistor equatio Kowig the miority carrier cocetratio the various curret comoets ca be determied by solvig the curret desity equatio. j d = qµ F qd urret desity for holes dx t is assumed that the overall curret is determied by the diffusio curret. The ifluece of the drift curret is egligible. 21

22 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The ideal trasistor equatio Further it is assumed that the hole ad the electro diffusio curret desities remai early costat throughout the deletio regio. L >> x L >> x W This is a valid aroximatio because the diffusio legth of the emitter ad collector is much larger tha the width of the deletio regios. qv 1 ( x) = ex 1 Miority carrier cocetratio i 0 kt W the base regio The curret desities ca be determied assumig a costat curret desity i the deletio regio by d qad = 0 qv A qd ex dx = W kt x 0 The collector curret ca be calculated i very similar way: x mitter hole curret i the base d qad = 0 qv A qd ex dx = W kt x W ollector hole curret i the base 22

23 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The ideal trasistor equatio is equal to if W/L << 1. The electro curret corresods to A qd d = dx x= x qv ex kt The collector curret ca be calculated i a similar way: = qad L 0 1 mitter electro curret d = A qd dx x= x = qad L 0 ollector electro curret where D ad D are the miority carrier diffusio costats i the emitter ad the collector regio. The overall emitter ca be calculated by the sum of the electro ad the hole curret. = + = qa D W 0 D + L 0 qv ex 1 + qa kt D W 0 mitter curret 23

24 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The ideal trasistor equatio The collector ca be calculate accordigly. D 0 qv D 0 = + = + D qa ex 1 qa + W kt W L 0 ollector curret The base curret is the differece betwee the emitter ad the collector curret: D 0 V D = = qa ex 1 + L Vth L 0 The curret flow through the trasistor is maily determied by the miority carrier distributio i the base. ase curret 24

25 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The trasistor equatio i its geeral form The curret voltage characteristic ca be exressed i geeral terms which facilitates the discussio of the differet modes of oeratio. The curretvoltage characteristic ca be described by the followig set of equatios: qv qv = a11 ex 1 a12 ex 1 kt kt qv qv = a21 ex 1 a22 ex 1 kt kt mitter curret ollector curret D = qa W D 0 0 a11 + L a qa 21 = D 0 W a 12 = D = qa W D qa W 0 D 0 0 a22 + L oefficiets 25

26 troductio to lectroic Devices, Fall 2006, Dr. D. Ki Modes of Oeratio iolar trasistors ca be oerated i four modes of oeratio, deedig o the voltages alied to the base-emitter ad the basecollector juctio. So far we have cosidered the active mode, where the base-emitter juctio is forward biased ad the base collector juctio is reverse biased. Modes of oeratio: Active mode, Saturatio mode, utoff mode ad verted mode. Miority carrier distributio of a trasistor uder the four modes of oeratio: Active, Saturatio, utoff ad verted mode. Ref.: M.S. Sze, Semicoductor Devices 26

27 troductio to lectroic Devices, Fall 2006, Dr. D. Ki Active Mode the active mode the base/emitter juctio is forward biased ad the base/collector juctio is reverse biased. The device behavior i the active mode was discussed i the chater deal trasistor equatio. The derived ideal trasistor equatios idicate that all three currets, base, emitter ad collector curret are ideedet of the base/collector voltage. Therefore, the currets are oly cotrolled by the base/emitter voltage, the device desig ad the material roerties Saturatio Mode the saturatio mode both juctios are forward biased. The miority carrier cocetratio for x=w is ozero. The carrier cocetratio is: qv kt ( x = W ) = ex 0 The trasistor oerates as a switch. 27

28 troductio to lectroic Devices, Fall 2006, Dr. D. Ki utoff Mode the cutoff mode both diodes are uder reverse bias coditios. Uder such coditios ( x = 0 ) = ( x = W ) = 0 The cutoff mode corresods to the off mode of a trasistor which is used as a switch verted Mode the iverted mode the base-emitter juctio is reverse biased, whereas the base-collector juctio is forward biased. the iverted mode the emitter behaves like the collector i the active mode ad vice versa (The collector behaves like the emitter i the active mode). As the doig cocetratio tyically decreases from the emitter to the collector the emitter efficiecy of the trasistor is lower i the iverted mode. Therefore, the curret gai is reduced i comariso to the active mode. 28

29 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.5 Trasort ad gai factors The schematic sketch illustrates the differet iteral curret comoets of a trasistor. The red arrows idicate a hole currets, whereas the blue arrows corresod to the electro currets. = + ase () mitter urret rec 0 = + = + 0 ollector urret mitter () ollector () = ase urret urret comoets of a trasistor i the active mode. 29

30 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.5 Trasort ad gai factors corresods to the electros ijected via the base that recombie with holes (which reach the base) from the emitter. is the electro curret beig ijected from the base to the emitter. should be as low as ossible. t ca be miimized by usig heavy doig of the emitter or usig a heterostructure. 0 is a thermally geerated curret i the deletio regio of the base ad the collector. the active mode the base collector diode is uder reverse bias coditios. Therefore, the electros are flowig from the - to the -regio. The curret 0 corresods to the leakage curret of the base collector diode. 30

31 troductio to lectroic Devices, Fall 2006, Dr. D. Ki ommo base curret gai the first se the commo base ad the commo emitter curret gai is itroduced. The commo base circuit is the most basic trasistor circuit. The base is used as a termial for the iut ad the outut loo. Therefore, the circuit is called the commo base circuit. The commo base curret gai is defied as the curret reachig the collector versus the ijected emitter curret. The curret gai for a commo base circuit is very close to 1. Therefore, the commo base is ot used as a curret amlifier. The commo base circuit is tyically used as a voltage amlifier (the commo base circuit has a large voltage gai). The commo-base curret gai is give by α 0 = ommo-base curret gai The electro collector curret for a trasistor is tyically small i comariso to the emitter hole curret, so that ifluece of the electro curret ca be igored. 31

32 troductio to lectroic Devices, Fall 2006, Dr. D. Ki ommo-emitter curret gai The commo emitter gai is defied as the curret reachig the collector versus the base curret. The curret gai for a commo base circuit is tyically much larger tha 1. β 0 = ommo-emitter curret gai The commo emitter curret gai ca be exressed i terms of the base curret gai. The commo-emitter curret gai is give by β 0 = = β α 0 0 = ommo-emitter curret gai 1 α0 32

33 troductio to lectroic Devices, Fall 2006, Dr. D. Ki ommo-emitter curret gai The commo base factor ca be described as the roduct of the emitter efficiecy ad base trasort factor. α 0 = = = γαt

34 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The mitter efficiecy The emitter efficiecy γ is defied as the ratio of the emitter holes (for a trasistor) curret versus the total emitter curret. γ + mitter efficiecy As the emitter electro curret does ot cotribute to the curret flowig from the emitter to the collector the emitter electro curret should be miimized. With other word: The emitter efficiecy should be maximized. The emitter efficiecy allows the descritio of the electro ad hole emitter currets i terms of the overall emitter curret. = + = γ ( 1 ) = γ mitter efficiecy Later o the emitter efficiecy will be correlated with the material roerties ad the device desig. 34

35 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The Trasort Factor ase trasort factor is the ratio of the holes reachig the collector versus the holes ijected from the emitter. Therefore, the trasort factor α T is defied as the ratio of emitter miority curret ad the collector miority curret. α T = ( x = W ) ( x ) = 0 <1 ase trasort factor The trasort factor should be close to 1. With icreasig trasort factor more holes are trasorted from the emitter to the collector. 35

36 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.5 Trasort ad gai factors The commo-base curret gai is the roduct of the emitter efficiecy ad the trasort factor. oth of these arameters have to be maximized to achieve a high curret gai. The commo-base curret gai should be close to 1. α 0 = γα T ommo-base curret gai For well-desiged trasistors is small comared to ad is close to. oth γ ad α T are aroachig uity. Therefore, α 0 is very close to 1. = + = αt + = γαt + = α + γ 0 0 The imortace of maximizig the commo-base curret gai gets clear whe cosiderig the equatio of the commo-emitter gai. creasig the commobase curret gai from 90% to 99% leads to a icrease of the commo-emitter gai from 9 to 99. α0 β0 = 1 α 0 36

37 troductio to lectroic Devices, Fall 2006, Dr. D. Ki Summary of the trasort ad gai factors ase () =α = γ rec ( 1 αt ) = γ = 0 α = γα 0 T ( 1 0) 0 = α ollector curret ( 1 ) = γ mitter curret mitter () ( 1 α0 ) ollector () = + ase curret 37

38 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.6 Trasistor Desig the followig the ifluece of the material roerties ad the device desig o the trasort ad the gai factors will be discussed The trasort factor orrelatio betwee the trasort factor ad the material arameters ad the device desig. α T = ( x = W ) ( x ) = 0 <1 The currets ca be substituted by the diffusio curret j D qd d dx Leadig to the followig exressio for the base trasort factor ase trasort factor = urret desity for holes 38

39 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The trasort factor Leadig to the followig exressio for the base trasort factor α T = d dx d dx ( x) ( x) x= W x= o <1 Usig the assumtio that W/L <<1 leads to : ase trasort factor α T cosh 1 ( W L ) < 1 ase trasort factor ased o the equatio for the trasort factor the trasistor ca be otimized: To get a large trasort factor the width of the base should be small ad the Diffusio legth should be large! The trasort factor should be high to achieve a high curret gai! The Diffusio legth is gettig large for low levels of doig i the base. 39

40 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The mitter fficiecy orrelatio betwee the emitter efficiecy ad the material arameters ad the device desig. The emitter efficiecy should be high to achieve a high curret gai. The emitter efficiecy ca be rewritte i the followig form. γ = + = ( x = 0) ( x = 0) + ( x = x ) < 1 The emitter efficiecy ca be rewritte i the followig from γ D D L W 0 0 > 1 The carrier cocetratio uder thermal equilibrium are give by 0 = N 2 i 0 = N 2 i mitter efficiecy mitter efficiecy 40

41 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The mitter fficiecy Fially the emitter efficiecy is give by γ = 1 + D D 1 W L N N < 1 mitter efficiecy ased o the equatio for the emitter efficiecy the trasistor ca be otimized: To get a large emitter efficiecy ad therefore a high curret gai the ratio N /N has to be as small as ossible, which meas that the doig cocetratio i the emitter should be much higher tha the doig cocetratio i the base. To get a large trasort factor ad therefore a high curret gai the width of the base should be small! α 0 = γα T ommo base curret gai 41

42 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.7 s as Amlifiers Trasistors ca be imlemeted as commo base, commo emitter ad commo collector circuit. the followig the /V characteristic of the idividual circuits will be discussed. deedet of the circuit imlemetatio the circuit ca be described by ut curves (iut curret) as a fuctio of the iut voltage. The outut voltage is tyically used as a arameter for the lot. Outut curves (outut curret) as a fuctio of the outut voltage. The iut curret or the iut voltage is tyically used as a arameter for the lot. V V V V i Rg Q1 Rout R V out V i Rg Rout R Q1 V out V i Rg Q1 R Rout V out ommo ase circuits ommo mitter circuits ommo ollector circuits (emitter follower) 42

43 troductio to lectroic Devices, Fall 2006, Dr. D. Ki ommo base circuit ut curret: mitter curret Outut curret: ollector curret ut voltage: ase/mitter voltage Outut voltage: ase/ollector voltage ommo ase circuits ut curret: ( V V ) f ( V ) = f, qv 0 ex 1 kt The base/collector voltage has oly a mior effect o the iut curve. Therefore, the ifluece of the base/collector voltage o the emitter curret ca be eglected. ollector urret Ref.: M.S. Sze, Semicoductor Devices 43

44 troductio to lectroic Devices, Fall 2006, Dr. D. Ki ommo base circuit Outut curret Voltage cotrolled amlificatio: = α ( V V ) = f, qv qv = α0 0 ex ex 1 kt kt urret cotrolled amlificatio: ( V ) = f, = α qv = α0 + 0 ex 1 kt 44

45 troductio to lectroic Devices, Fall 2006, Dr. D. Ki ommo emitter circuit ut curret: ase curret Outut curret: ollector curret ut voltage: ase/mitter voltage Outut voltage: ollector/mitter voltage ommo mitter ircuits ad collector curret as a fuctio of the emitter/collector voltage. Ref.: M.S. Sze, Semicoductor Devices 45

46 troductio to lectroic Devices, Fall 2006, Dr. D. Ki ommo emitter circuit ut curret: ( V V ) = f, V ( 1 0 ) 0 = α qv qv = kt kt ( α ) ex 1 ex = V V qv q = kt kt ( α ) ex 1 ex ( V V ) 46

47 troductio to lectroic Devices, Fall 2006, Dr. D. Ki ommo emitter circuit Outut currret Voltage cotrolled amlificatio: = f ( V, V ) V qv qv = α0 0 ex 1 0 ex 1 kt kt = V V qv q = α0 0 ex 1 0 ex 1 kt kt ( V V ) 47

48 troductio to lectroic Devices, Fall 2006, Dr. D. Ki ommo emitter circuit Outut curret urret cotrolled amlificatio: = f ( V, ) = = + α α 0 0 α = + = β0 + 1 α0 α0 1 α0 ( α ) 0 0 β0 q = β0 0 ex 1 α kt 0 ( V V ) 48

49 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The arly effect the commo emitter (commo collector) cofiguratio the collector curret (emitter curret) should be ideedet of V. This is oly the case for a ideal trasistor, where the width of the base regio is assumed to be costat for differet alied voltages V. Sice the width of the deletio regio is modulated by the alied voltage V, the base width is a fuctio of the alied bias voltage. With icreasig reverse bias alied o the outut side of the commo emitter or commo collector circuit the width of the base is reduce. We seak about base width modulatio. Due to the reduced width of the base the collector curret ad the commo emitter gai is icreased. The deviatio from the model of a ideal biolar trasistor is described by the arly effect. The arly effect ca be characterized by the arly voltage. The early voltage corresods to the itersectio of the extraolated outut curves with the voltage axis. 49

50 troductio to lectroic Devices, Fall 2006, Dr. D. Ki The arly effect hage of the width of the base collector diode i the active mode: w Mod = w l l w l w Mod w 2ε 0 ε Si q ( V + V V ) bi N D N A ( N + N ) D A ( 0) V 1 + V = A Outut curves icludig the arly effect. The arly voltage ca be extracted from the outut curves. Ref.: M.S. Sze, Semicoductor Devices 50

51 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.8 Trasfer characteristic ad gai The ommo emitter circuit is the most imortat JT based circuit. The circuit exhibits a high curret gai so that it ca be used as a curret amlifier. The relatioshi betwee the iut curret (base curret) ad the outut curret (collector curret) is liear over several orders if magitude, which assumes that the curret gai is costat. However, for low ad high curret levels the curret gai dros. Trasfer urve: ollector curret as a fuctio of the base curret. Ref.:M. öhm, Microeletrocis 51

52 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.8 Trasfer characteristic ad gai the followig we will discuss the ifluece of the oeratig oit o the D ad the differetial curret gai for differet circuits. So far we cocetrated i our discussio o the D curret gais α 0 ad β 0. As art of a amlifier the differetial curret gai of the trasistor might be of more iterest. The D ad differetial commo base curret gai ca be defied by: α 0 = = γ α T α 0 α T γ D curret gai α = = T α γ Differetial curret gai 52

53 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.8 Trasfer characteristic ad gai The commo base D ad differetial curret gai is more ore less equal. Furthermore, the commo base curret gai ca be assumed to be costat for differet curret levels. For the commo emitter circuit the situatio is differet. Here the D ad the differetial curret gai is calculated to be: β0 D curret gai β = Differetial curret gai Furthermore, the commo emitter curret gai deeds o the curret level flowig through the trasistor. 53

54 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.8 Trasfer characteristic ad gai For medium curret levels the curret gai ca be cosidered to be costat or slightly icreasig. The slight icrease is caused by the arly effect. The ifluece of the arly effect o the curret gai has already be discussed. The wideig of the deletio regio of the reverse biased base/collector juctio leads to a slow icrease of the curret gai with icreasig collector curret levels. β, β 0 β 0 β β 0 β = urret gai curves: D ad differetial gai as a fuctio of the collector curret level. Ref.:M. öhm, Microeletrocis 54

55 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.8 Trasfer characteristic ad gai For low curret levels oe of the assumtios of the Shockley model caot be alied. The recombiatio curret i the deletio regios caot be igored. γ = + de rec < + For high curret levels aother assumtios of the Shockley model is ot fulfilled. The assumtio of weak ijectio is ot fulfilled aymore. The strog ijectio of carriers via the emitter ito the base leads to a icrease of the miority carrier cocetratio. As a cosequece the hole diffusio curret i the emitter is icreased ad the emitter efficiecy is reduced. γ = + mitter efficiecy mitter efficiecy 55

56 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.9 Device arameters additio to the gai factors several other arameters are of major imortace. articular whe it comes to the desig of JT based circuits. Therefore, the most imortat device arameters will be itroduced i the followig. r V = Differetial ut resistace V = cost. V qv 0 ex 1 kt r kt q Differetial iut resistace Rout R Rg Q1 V out V i ommo mitter circuits 56

57 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.9 Device arameters The differetial collector emitter resistace ca be calculated by usig the arly voltage. r = V = cost. Differetial outut resistace r V A Ouut curves icludig the arly effect. The arly voltage ca be extracted from the outut curves. 57

58 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.9 Device arameters The reverse voltage ratio ad the sloe ca be calculated by: v r = V V = cost. v r kt qv A Reverse voltage ratio S = V V = cost. S q kt Sloe 58

59 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.10 quivalet circuit of a biolar juctio trasistor So far we discussed /V characteristic of JTs. the followig a rocedure will be described, which allows to derive a equivalet circuit for the JT. order to imlemet a JT i a circuit simulator like SP the trasistor has to be described by a equivalet circuit. We will start the descritio by usig a 2-ort theory. We assume that the iut ad the outut loo of the trasistor is described by: v 1 = h11 i1 + h12 v2 2-ort i 2 = h21 i1 + h22 v2 v 1 v 2 The roerties of the 2-ort are give by the h-arameters (hybrid arameters). 59

60 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.10 quivalet circuit of a biolar juctio trasistor The JT arameters V ad ca be described as a fuctio of the arameters ad V leadig to V =f(,v ) ad (,V ). the ext ste the base emitter voltage ad the collector curret ca be liearized aroud the oeratig oit. dv d = d = d V V V + dv V V = cost. = cost. = cost + dv V. = cost. Liearize aroud the oeratig oit. dv d = d r = d β + + dv dv 1 r v r Liearize aroud the oeratig oit. 60

61 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.10 quivalet circuit of a biolar juctio trasistor Due to the correlatio betwee the commo emitter circuit ad the 2-ort the h- arameters ca be derived. ommo emitter circuit 2-ort dv dv v 1 v 2 dv d = r β v 1 r r d dv v i 1 2 = h h h h i v 1 2 h 11 h 21 = r = β h h = v = 1 r r Ref.: M. öhm, Microeletrocis 61

62 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.10 quivalet circuit of a biolar juctio trasistor The three basic biolar trasistor circuits ca be described by a 2-ort circuit. The equivalet circuit of a commo emitter circuit is show o the slides. The equivalet circuit reresets the D or low frequecy equivalet circuit. Due to the correlatio betwee the commo emitter circuit ad the 2-ort the h-arameters ca be derived. i 1 i 2 v 1 h 11 h 12 v 2 h 21 i 1 1/h 22 v 2 D or low frequecy equivalet circuit of a commo emitter circuit. 62

63 troductio to lectroic Devices, Fall 2006, Dr. D. Ki 5.10 quivalet circuit of a biolar juctio trasistor High frequecy equivalet circuit of a commo emitter circuit. Full hybrid π equivalet circuit model (Giacoletto model) Rerf.: M. Shur, troductio to lectroic Devices 63

64 troductio to lectroic Devices, Fall 2006, Dr. D. Ki Refereces Michael Shur, troductio to lectroic Devices, Joh Wiley & Sos; (Jauary 1996). (Price: US$100), Audiece: uder graduate studets Simo M. Sze, Semicoductor Devices, Physics ad Techology, Joh Wiley & Sos; 2 d ditio (2001). (Price: US$115), Audiece: uder graduate studets R.F. Pierret, G.W. Neudeck, Modular Series o Solid State Devices, Volumes i the Series: Semicodcutor Fudametals, The juctio diode, The biolar juctio trasistor, Field effect devices, (Price: US$25 er book), Audiece: uder graduate studets 64