Presentation on theme: "• A look at current models for m-s junctions (old business)"— Presentation transcript:
1 6.772/SMA5111 - Compound Semiconductors Lecture 4 - Carrier flow in heterojunctions - Outline • A look at current models for m-s junctions (old business)Thermionic emission vs. drift-diffusion vs. p-n junction• Conduction normal to heterojunctions (current across HJs)Current flow:1. Drift-diffusion2. Ballistic injectionInjection tailoring:decoupling injection from dopingBand-edge spikes:1. Impact on conduction and evolution with bias:a. Forward flow: i. Barriers to carrier flow; ii. Division of applied bias; iii. Evolution with biasb. Reverse flow: i. impact on collection; ii. evolution with bias2. Elimination of spikes by composition grading (quasi-Fermi level discussion)• Conduction parallel to heterojunctions (in-plane action)Modulation doped structures:Mobility vs. structureInterface roughness
2 Applying bias to a metal-semiconductor junction, review • CurrentsNote: the barrier seen by electrons in the metal does not change with bias, whereas the barrier seen by those in the semiconductor does.Thus the carrier flux (current) we focus on is that of majority carriers from the semiconductor flowing into the metal. Metal-semiconductor junctions are primarily majority carrier devices.(Minority carrier injection into the semiconductor canusually be neglected; more about this later)
3 M-S JUNCTION CURRENT MODELS: General form of net barrier current: comparing modelsid = A q R ND e [-qΦb / kT]( e [qvAB/ kT]-1)Thermionic emission model - ballistic injection over barrierid / A= A*Td / A = ( e [qvAB/ kT]-1)A*: Thermionic emission coefficientΦbm : Barrier in metal, =Φb + (kT /q) ln(NC / ND )Substituting for Φbm and rearranging :id / A=q(A*T/qNC) ND e [-qΦb / kT]( e [qvAB/ kT]-1)from which we see RTE = A*T/qNC
4 id/A= qμe EpkND e [-qΦb / kT]( e [qvAB/ kT]-1) Where : Drift-diffusion model - drift to and over barrierid/A= qμe EpkND e [-qΦb / kT]( e [qvAB/ kT]-1)Where :Epk : Peak electric field, =E(0) =√ 2q(Φb -vAB )ND /εComparing this to the stan dard form we see :RDD =μe Epk ,which is the drift velocity at x =0!Before comparing the thermionic emission and drift-diffusion expressions, we will look at the current through a p-n+ junction diode.
6 Comparing the results RTE= A*T2/qNC , modeling from metal side RTE Thermionic emissionRTE= A*T2/qNC , modeling from metal side RTEDrift-diffusionRDD =μe Epk , the drift velocity at x =0.p-n+ diodeR p-n += De / wp , the diffusion velocity.
7 Conduction normal to heterojunctions Emitter efficiency expressions with and without spike, and comparison with homojunction resultGrading composition to eliminate spikes:WHITE BOARDQuasi-Fermi levels and built-in effective fields due to band-edge slopes ∂Ec/∂x for electrons, ∂Ev/∂x for holes
8 Homojunctions - band picture, depletion approximation • Electrically connected:i. Charge shifts between sides ii. Fermi levels shift until equal iii. Vacuum ref. is now-qf(x) where f(x) = (q/e)∫∫r(x) dx dxiv. Ec(x) is -qf(x) -c(x) and Ev(x) = -qf(x) - [c(x) +Eg(x)] v. Depletion approximation is a
9 Conduction parallel to heterojunctions Modulation doped structuresN-n heterojunctions and accumulated electrons Modulation doped structure with surface pinning and HJWHITE BOARDBack to foilsCarrier scattering and mobilities in accumulated two-dimensional electron gas
10 Modulation doping - two-dimensional electron gases • Components of mobilityGaAs(Image deleted)See Fig in: Shur, M.S. Physics of Semiconductor DevicesEnglewood Cliffs, N.J., Prentice-Hall, 1990.
11 Modulation doping - two-dimensional electron gases • Bulk mobilities in GaAs as a function of doping level(at room temperature)(Image deleted)See Ch2 Fig19 in: Sze, S.M. Physics of Semiconductor Device2nd ed. New York: Wiley, 1981.
12 Modulation doping - two-dimensional electron gases • Improvementof TEG mobilitywith time(Image deleted)See Fig 60 in: Weisbuch, C. and Vinter, B., Quantum Semiconductor Structures: Fundamentals and ApplicationsBoston: Academic Press, 1991.