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CALIFORNIA POLYTECHNIC STATE UNIVERSITY Solid State Physics Laboratory Experiment 17: LIFETIME OF MINORITY CARRIERS SCOPE: Minority charge carriers will be produced in both n-type and p-type germanium by optical stimulation using a pulsed light source. The average "lifetime" of the resulting electron=hole pairs will be determined by observing the time- dependence of the electrical conductivity. INTRODUCTION: In a semiconductor in thermal equilibrium, there is a continual process of electron-hole pair generation and recombination with a resulting thermal equili- brium concentration of carriers. The recombination rate can be determined by generating an excess concentration of electron-hole pais (a non-equilibrium condition) and observing the return to the equilibrium concentration by moni- toring the cnange in electrical conductivity. 7 ena The non-equilibrium excess concentra— pepe ere oan tion of charge carriers is generated ~~; optically using a pulsed strobe light. t E, . 5 Electrons are optically stimulated — across the band gap with a correspond- ok ° | Vo leace ead ing increase in electrical conductivity @ due to both electrons and holes. Genrration — Recom binatren The electron-hole recombination occurs in order to restore the thermal equili+~ brium carrier concentration when the light is off. The rate at which .recombina~ tion oceurs is proportional to the concentration of excess carrlers—-a situation that produces the usual exponential decay equation. That is, (dn/dt) = -(l& ynct) yields the time dependent excess carrier concentration u(t) = n,exp(-t/), where n_ is the excess concentration when t=0 (the time the strobe light shuts off) and y fs the mean lifetime of excess electron-hole pairs--or recombination “time. In extrinsic semiconductors, the recombination time is the lifetime of the - minority carriers. By diffusion, the minority carriers drift an average distance of L = @ + )%, where D = (kT/e)M* is the diffusion constant, before recombining. In an n-type semiconductor, the minority carriers are holes, so the hole mobility is uséd in determining the diffusion constant. THE EXPERIMENT: The apparatus consists of a small box containing three extrinsic semiconducting crystals each of which can be selected by a switch to be in series with a resistor, very large compared to the specimen's resistance, and a battery. The voltage across the specimen is then monitored on an oscilloscope. . Because the specimen resistance is small compared to the large series resistor, the current through the semiconductor is essentially constant. The voltage drop due to the change in electrical conductivity is therefore proportional to the e sample resistance, or inversely proportional to the conductivity of the material. 
