Lecture #8Generation and RecombinationGeneration ProcessesRecombination ProcessesDirect vs. Indirect Band Gap MaterialsExcess Carrier Concentrations“Low-Level Injection”Indirect Recombination RateSlide 9Relaxation to Equilibrium StateMinority Carrier (Recombination) LifetimeExample: PhotoconductorSlide 13Net Recombination Rate (General Case)SummaryLecture #8OUTLINE• Generation and recombination• Excess carrier concentrations• Minority carrier lifetimeRead: Section 3.3EE130 Lecture 8, Slide 2Spring 2007Generation and Recombination•Generation:•Recombination:•Generation and recombination processes act to change the carrier concentrations, and thereby indirectly affect current flowEE130 Lecture 8, Slide 3Spring 2007 Generation ProcessesBand-to-Band R-G Center Impact IonizationEE130 Lecture 8, Slide 4Spring 2007 Recombination ProcessesDirect R-G Center AugerRecombination in Si is primarily via R-G centersEE130 Lecture 8, Slide 5Spring 2007Direct vs. Indirect Band Gap MaterialsLittle change in momentum is required for recombination momentum is conserved by photon emissionLarge change in momentum is required for recombination momentum is conserved by phonon + photon emissionE-k DiagramsEE130 Lecture 8, Slide 6Spring 20070nnn 0ppp Excess Carrier ConcentrationsCharge neutrality condition:pn equilibrium valuesEE130 Lecture 8, Slide 7Spring 2007“Low-Level Injection”•Often the disturbance from equilibrium is small, such that the majority-carrier concentration is not affected significantly:–For an n-type material:–For a p-type material:•However, the minority carrier concentration can be significantly affected so ||||00nnnpn so ||||00ppppn EE130 Lecture 8, Slide 8Spring 2007Indirect Recombination RateSuppose excess carriers are introduced into an n-type Si sample (e.g. by temporarily shining light onto it) at time t = 0. How does p vary with time t > 0?1. Consider the rate of hole recombination via traps:2. Under low-level injection conditions, the hole generation rate is not significantly affected:pNcTpRtp0pNcTpmequilibriuRtpmequilibriuGtpGtpEE130 Lecture 8, Slide 9Spring 20073. The net rate of change in p is therefore0pNcpNcTpTpGtpRtpGRtpTppNcppTpGRtpppNc10 where)(EE130 Lecture 8, Slide 10Spring 2007nntnpptpRelaxation to Equilibrium Statefor electrons in p-type materialfor holes in n-type materialConsider a semiconductor with no current flow in which thermal equilibrium is disturbed by the sudden creation of excess holes and electrons. The system will relax back to the equilibrium state via the R-G mechanism:EE130 Lecture 8, Slide 11Spring 2007The minority carrier lifetime is the average time an excess minority carrier “survives” in a sea of majority carriers ranges from 1 ns to 1 ms in Si and depends on the density of metallic impurities (contaminants) such as Au and Pt, and the density of crystalline defects. These deep traps capture electrons or holes to facilitate recombination and are called recombination-generation centers. Minority Carrier (Recombination) LifetimeTnTpNcnNcp11 EE130 Lecture 8, Slide 12Spring 2007Consider a sample of Si doped with 1016 cm-3 boron, with recombination lifetime 1 s. It is exposed continuously to light, such that electron-hole pairs are generated throughout the sample at the rate of 1020 per cm3 per second, i.e. the generation rate GL = 1020/cm3/sExample: PhotoconductorWhat are p0 and n0 ?What are n and p ?(Note: In steady-state, generation rate equals recombination rate.)EE130 Lecture 8, Slide 13Spring 2007What are p and n ?What is the np product ? Note: The np product can be very different from ni2.EE130 Lecture 8, Slide 14Spring 2007Net Recombination Rate (General Case)•For arbitrary injection levels and both carrier types in a non-degenerate semiconductor, the net rate of carrier recombination is:kTEEikTEEinpiTiiTenpennppnnnp ntptn/)(1/)(1112 and where)()(EE130 Lecture 8, Slide 15Spring 2007Summary•Generation and recombination (R-G) processes affect carrier concentrations as a function of time, and thereby current flow–Generation rate is enhanced by deep (near midgap) states associated with defects or impurities, and also by high electric field–Recombination in Si is primarily via R-G centers•The characteristic constant for (indirect) R-G is the minority carrier lifetime:•Generally, the net recombination rate is proportional tomaterial) type-(p material) type-(n 11TnTpNcnNcp2innp
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