EECS130 Integrated Circuit DevicesAnnouncementsSlide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Excess Carriers and Charge NeutralitySlide Number 15Recombination LifetimeRate of recombination (s-1cm-3)EXAMPLE: Photoconductors EXAMPLE: PhotoconductorsEXAMPLE: Photoconductors Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25EECS130 Integrated Circuit DevicesProfessor Ali Javey9/11/2007Semiconductor FundamentalsLecture 5Reading: Chapter 3Announcements• 1st HW due….. right now….• 2nd HW due next Tuesday• Professor Javey’s OH for tomorrow is cancelled. He will have an extra OH next week.EreferenceEc and Ev vary in the oppositedirection from the voltage. Thatis, Ec and Ev are higher where the voltage is lower.Ec -Ereference = -qVxxEVEcEvVariation in Ec with position is called band bendingEinstein Relationship between D and μdxdEekTNdxdnckT/)EE(cfc−−−=dxdEkTnc−=kT/)EE(cfceNn−−=Consider a piece of non-uniformly doped semiconductor.Ev (x)Ec (x)Ef n-type semiconductorDecreasing donor concentration N-type semiconductorqkTn−=Einstein Relationship between D and μqkTndxdn−=0=+=dxdnqDqnJnnnμat equilibrium.kTqDqnqnnn−=μ0nnqkTDμ=These are known as the Einstein relationship.ppqkTDμ=Similarly,EXAMPLE: Diffusion ConstantWhat is the hole diffusion constant in a piece of silicon with μp = 410 cm2 V-1s-1 ?Solution:Remember: kT/q = 26 mV at room temperature./scm 11sVcm 410)mV 26(2112=⋅=⎟⎟⎠⎞⎜⎜⎝⎛=−−ppqkTDμnnnΔ+≡0pppΔ+≡0Excess Carriers and Charge NeutralityCharge neutrality:pnΔ=ΔEquilibrium ExcessIf not neutral, then built in field causes drift until neutrality is achievedRecombination LifetimeAssume light generates Δn and Δp. If the light is suddenly turned off, Δn and Δp decay with time until they become zero. The process of decay is called recombination. The time constant of decay is the recombination time or carrier lifetime, τ. Recombination is nature’s way of restoring equilibrium (Δn= Δp= 0).τranges from 1ns to 1ms in Si and depends on the density of metal impurities (contaminants) such as Au and Pt. These deep traps capture electrons or holes to facilitate recombination and are called recombination centers.EcEvRecombination LifetimeτndtdnΔ−=dtdppndtdn=Δ−=Δ−=ττpnΔ=ΔConsider recombination only.Rate of recombination (s-1cm-3)A bar of Si is doped with boron at 1015cm-3. It is exposed to light such that electron-hole pairs are generated throughout the volume of the bar at the rate of 1020/s·cm3. The recombination lifetime is 10μs. What are (a) p0 , (b) n0 , (c) Δp, (d) Δn, (e) p , (f) n, and (g) the np product? EXAMPLE: PhotoconductorsSolution:(a) What is p0 ?p0 = Na = 1015 cm-3(b) What is n0 ?n0 = ni2/p0 = 105 cm-3(c) What is Δp?In steady-state, the rate of generation is equal to the rate of recombination.1020/s-cm3 = Δp/τ∴Δp = 1020/s-cm3 ·10-5s = 1015 cm-3EXAMPLE: Photoconductors(d) What is Δn?Δn = Δp= 1015 cm-3(e) What is p?p= p0 + Δp= 1015cm-3 + 1015cm-3 = 2×1015cm-3(f) What is n?n = n0 + Δn = 105cm-3 + 1015cm-3 ~ 1015cm-3 since n0 << Δn (g) What is np?np ~ 2×1015cm-3 ·1015cm-3 = 2×1030cm-6 >> ni2 = 1020cm-6. The np product can be very different from ni2.EXAMPLE: PhotoconductorsQuasi-equilibrium and Quasi-Fermi LevelsWhenever Δn = Δp ≠0, np ≠ni2. However, we would like to preserve and use the relations:But these equations lead to np = ni2. The solution is to introduce two quasi-Fermi levels Efn and Efp such thatkTEEcfceNn/)( −−=kTEEvvfeNp/)( −−=kTEEcfnceNn/)( −−=kTEEvvfpeNp/)( −−=Even when electrons and holes are not at equilibrium, within each group the carriers are usually at equilibrium. Electrons are closely linked to other electrons but only loosely to holes.Chapter SummarydxdnqDJndiffusionn=,dxdpqDJpdiffusionp−=,nnqkTDμ=ppqkTDμ=ppvμ=nnvμ=pdriftpqpJμ=,ndriftnqnJμ=,-Chapter Summaryτis the recombination lifetime.n´ and p´ are the excess carrier concentrations.n = n0 + Δnp = p0 + ΔpCharge neutrality requires Δn= Δp.rate of recombination = Δn/τ= Δp/τEfn and Efp are the quasi-Fermi levels of electrons and holes.kTEEvvfpeNp/)( −−=kTEEcfnceNn/)(
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