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
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