半导体物理学半导体 (65).pdf

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1、E-M(Ebers-Moll)model In order to analyze a transistor circuit either by hand calculations or using computer codes,one needs a mathematical model,or equivalent circuit of the transistor.Here,we consider three equivalent circuit models.Each of these follows directly from the work we have done on the p

2、n junction diode and on the bipolar transistor.Equivalent Circuit Models E-M(Ebers-Moll)Model G-P(Gummel-Poon)Model H-P(Hybrid-Pi)Model Two categoriesswitching and amplificationdefined by their use in electronic circuits.Switching usually involves turning a transistor from its“off”state,or cutoff,to

3、 its“on”state,either forward-active or saturation,and then back to its“off”state.Amplification usually involves superimposing sinusoidal signals on dc values so that bias voltages and currents are only perturbed.E-M(Ebers-Moll)model：used in switching applications G-P(Gummel-Poon)model：used in nonuni

4、form doping concentration in the base H-P(Hybrid-Pi)model：used in amplification applications.Equivalent Circuit ModelsGummel-Poon Modelwhere p(x)is the majority carrier hole concentration in the base.Under low injection,the hole concentration is just the acceptor impurity concentration.The direction

5、 of this electric field aids the flow of electrons across the base.The GummelPoon model of the BJT considers more physics of the transistor than the EbersMoll model.This model can be used for nonuniform doping concentration in the base and emitter.An electric field will occur in the base if nonunifo

6、rm doping exists in the base.This is discussed before.The electric field can be written in the formEThe electron current density in the base of an npn transistor can be written as Substituting into ,we obtainUsing Einsteins relation:Dn/n=Dp/p=kT/e,we can write Equation in the formIntegrating this eq

7、uation through the base region while assuming that the electron current density is essentially a constant and the diffusion coefficient is a constant,we findThis can be written in the formGummel-Poon ModelThe integral in the denominator is the total majority carrier charge in the base and is known a

8、s the base Gummel number,defined as QB.If we perform the same analysis in the emitter,we find that the hole current density in the emitter of an npn transistor can be expressed asThe integral in the denominator is the total majority carrier charge in the emitter and is known as the emitter Gummel nu

9、mber,defined as QE.Assuming that the BE junction is forward biased and the BC junction is reverse biased,we have n(0)=nB0exp(VBE/Vt)and n(xB)0.We may note that nB0pni2，so that electron current density in the base isGummel-Poon ModelSince the currents in the GummelPoon model are functions of the tota

10、l integrated charges in the base and emitter,these currents can easily be determined for nonuniformly doped transistors.The GummelPoon model can also take into account nonideal effects,such as the Early effect and high-level injection Early effect：As the BC voltage changes,the neutral base width cha

11、nges so that the base Gummel number Q B changes.The change in QB with BC voltage then makes the electron current density given by a function of the BC voltage.This is the base width modulation effect or Early effect.Gummel-Poon ModelHigh-level injection effect：If the BE voltage becomes too large,low

12、 injection no longer applies,which leads to high-level injection.In this case,the total hole concentration in the base increases because of the increased excess hole concentration.This means that the base Gummel number will increase.The change in base Gummel number implies,from Equation that the ele

13、ctron current density will also change.High-level injection has also been previously discussed.The GummelPoon model can then be used to describe the basic operation of the transistor as well as to describe nonideal effects.Gummel-Poon ModelBipolar transistors are commonly used in circuits that ampli

14、fy time-varying or sinusoidal signals.In the analysis of small signal amplification current,the Hybrid-Pi Model equivalent circuit is the most commonly used model.In these linear amplifier circuits,the transistor is biased in the forward-active region and small sinusoidal voltages and currents are s

15、uperimposed on dc voltages and currents.Hybrid-Pi ModelAn npn bipolar transistor in a common-emitter configuration with the small-signal terminal voltages and currents.The C,B,and E terminals are the external connections to the transistor,while the C，B，E points are the idealized internal collector,b

16、ase,and emitter regions.Cross section an npn bipolar transistor for the hybrid-pi modelHybrid-Pi Model1.The equivalent circuit between the external input base terminal and the external emitter terminalConstructing the equivalent circuit of the transistor.Resistance rbis the series resistance in the

17、base between the external base terminal B and the internal base region B.Cis the junction diffusion capacitance,ris the junction diffusion resistance.The diffusion capacitance C,diffusion resistance rrexis the series resistance between the external emitter terminal and the internal emitter region.Hy

18、brid-Pi Modelrcresistance is the series resistance between the external and internal collector connections and the capacitance Csis the junction capacitance of the reverse-biased collector substrate junction.The dependent current source gmVbe,is the collector current in the transistor,which is contr

19、olled by the internal baseemitter voltage.The resistance r0is the inverse of the output conductance g0and is primarily due to the Early effect.2.The equivalent circuit looking into the collector terminalHybrid-Pi ModelThe Cparameter is the reverse-biased junction capacitance and ris the reverse-bias

20、ed diffusion resistance.Normally,ris on the order of megaohms and can be neglected.The value of Cis usually much smaller than Cbut,because of the feedback effect that leads to the Miller effect and Miller capacitance，Ccannot be ignored in most cases.Miller capacitance：equivalent capacitance between

21、B and E due to Cand the feedback effect,which includes the gain of the transistor.The Miller effect also reflects Cbetween the C and Bterminals at the output.However,the effect on the output characteristics can usually be ignored.3.The equivalent circuit of the reverse-biased B-C junctionHybrid-Pi M

22、odelA computer simulation is usually required for this complete model because of the large number of elements.However,some simplifications can be made in order to gain an appreciation for the frequency effects of the bipolar transistor.Thecapacitancesleadtofrequencyeffectsinthetransistor,which means that thegain,forexample,isafunctionoftheinputsignalfrequency.4.Hybrid-Pi ModelHybrid-Pi Model circuitHybrid-Pi Model