半导体物理学半导体 (25).pdf

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1、Ambipolar TransportSince the internal E-field creates a force attracting the electrons and holes,this E-field will hold the pulses of excess electrons and excess holes together.The negatively charged electrons and positively charged holes then will drift or diffuse together with a single effective m

2、obility or diffusion coefficient.This phenomenon is called ambipolar diffusion or ambipolar transport.Derivation of the Ambipolar Transport EquationThe excess electron and hole concentrations to the internal electric field is related by Poissons equation,which may be written as:assume that6.3 双极输运(A

3、mbipolar Transport)Ambipolar TransportThe condition of charge neutrality：We will assume that the excess electron concentration is just balanced by an equal excess hole concentration at any point in space and time.nnppMultiply byMultiply byAdd the two equations,the term will be eliminated.xE6.3 双极输运(

4、Ambipolar Transport)Derivation of the Ambipolar Transport Equation?=?Ambipolar Transport:ambipolar mobilityD：ambipolar diffusion coefficientSince both n and p contain the excess carrier concentration n,the coefficient in the ambipolar transport equation D and are not constants.The ambipolar transpor

5、t equation is a nonlinear differential equation.6.3 双极输运(Ambipolar Transport)Derivation of the Ambipolar Transport EquationAmbipolar TransportLimits of Extrinsic Doping and Low InjectionLow Injection：the excess carrier concentration is much smaller than the thermal-equilibrium majority carrier conce

6、ntration；For the p-type semiconductor，0Ptn 0ntpFor the n-type semiconductor，n-type semiconductor under low injection，It is important to note that for an extrinsic p-type semiconductor under low injection,the ambipolar diffusion coefficient and the ambipolar mobility coefficient reduce to the minorit

7、y carrier electron parameter values,which are constants.The ambipolar transport equation reduces to a linear differential equation with constant coefficients.Ambipolar Transport)()(00nnnnnnRRgGRgRgFor electronsFor holes6.3 双极输运(Ambipolar Transport)Limits of Extrinsic Doping and Low InjectionThe gene

8、ration rate for excess electrons must equal the generation rate for excess holes.We may then define a generation rate for excess carriers as g,so that gn gp g.We also determined that the minority carrier lifetime is essentially a constant for low injection.Then,the term g-R in the ambipolar transpor

9、t equation may be written in terms of the minority carrier parameters.The ambipolar transport equation,given by Equation(6.39),for a p-type semiconductor under low injection then becomes:n-type semiconductor under low injectionAmbipolar TransportApplications of the Ambipolar Transport Equation6.3 双极

10、输运(Ambipolar Transport)Ambipolar TransportApplications of the Ambipolar Transport EquationExcess hole concentration versus distance at various times for zero applied electric field.Excess hole concentration versus distance at various times for a constant applied electric field.Ambipolar TransportDie

11、lectric Relaxation Time ConstantThe injection of a concentration of holes into a small region at the surface of an n-type semiconductor.EJtJEJdtdtPoissons equation Continuity equation Ohms law)/()0()(dtetd0dtdAmbipolar TransportHaynes-Shockley Experiment（海恩斯海恩斯-肖克莱实验肖克莱实验）(a)The idealized excess car

12、rier pulse at terminal A at t 0.(b)The excess carrier pulse versus time at terminal B for a given applied electric field.(c)The excess carrier pulse versus time at terminal B for a smaller applied electric field.Ambipolar Transport6.3 双极输运(Ambipolar Transport)Haynes-Shockley Experiment（海恩斯海恩斯-肖克莱实验肖

13、克莱实验）The minority carrier mobility,lifetime,and diffusion coefficient can be determined from this single experiment.As a good first approximation,the peak of the minority carrier pulse will arrive at contact B when the exponent involving distance and time is zero：Ambipolar Transport6.3 双极输运(Ambipola

14、r Transport)In this case x d,where d is the distance between contacts A and B,and t t0,where t0 is the time at which the peak of the pulse reaches contact B.The mobility may be calculated asAmbipolar TransportHaynes-Shockley Experiment（海恩斯海恩斯-肖克莱实验肖克莱实验）6.3 双极输运(Ambipolar Transport)At times t1 and t

15、2,the magnitude of the excess concentration is e1 of its peak value.If the time difference between t1 and t2 is not too large,e t/p 0 and(4 Dp t)12 do not change appreciably during this time;then the equationAmbipolar TransportHaynes-Shockley Experiment（海恩斯海恩斯-肖克莱实验肖克莱实验）6.3 双极输运(Ambipolar Transport

16、)If we set t1 and t2 as t1=t2.add the two resulting equations,we may show that the diffusion coefficient is given byAmbipolar TransportHaynes-Shockley Experiment（海恩斯海恩斯-肖克莱实验肖克莱实验）6.3 双极输运(Ambipolar Transport)The area S under the curve shown in Figure 6.13 is proportional to the number of excess hol

17、es that have not recombined with majority carrier electrons.We may writewhere K is a constant.By varying the electric field,the area under the curve will change.A plot of ln(S)as a function of(dp E0)will yield a straight line whose slope is(1/p 0),so the minority carrier lifetime can also be determined from this experiment.Ambipolar TransportHaynes-Shockley Experiment（海恩斯海恩斯-肖克莱实验肖克莱实验）