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Study of radiation damage in silicon detectors for high ... - F9

Study of radiation damage in silicon detectors for high ... - F9

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20 2. Operation and Radiation Damage <strong>of</strong> Silicon DetectorsThe generation current occurs via trapp<strong>in</strong>g centers <strong>in</strong> the depleted region. Thereare four processes that can change the occupancy <strong>of</strong> an energy level E T <strong>in</strong> the band gap(gure 2.3): electron capture from the conduction band electron emission to the conduction band hole capture from the valence band hole emission to the valence bandThe capture rates <strong>for</strong> electrons and holes are given byand the emission ratesr e c = T e nv e (1 ; f T )N T r h c = T h pv h f T N T (2.28)r e e = e e f T N T N C r h e = e h (1 ; f T )N T N V : (2.29)Here N T is trap concentration and f T =(1+e E T ;ET Fk B T) ;1 is the probability that the trapenergy level E T is occupied by an electron. eh T are capture cross sections <strong>for</strong> electronsand holes by atrapT,e eh are emission probabilities <strong>for</strong> electrons and holes, and v eh theirthermal velocitiesv eh =q3k B T=m eh : (2.30)From the condition that <strong>in</strong> thermal equilibrium emission and capture rates have to beequal followse e = T e v e e ;(E C ;E T )=k B Te h = T h v h e ;(E T ;E V )=k B T : (2.31)The change <strong>in</strong> concentration <strong>of</strong> occupied traps per time is the sum <strong>of</strong> the processes describeddn Tdt= r e c ; r e e ; r h c + r h e (2.32)where n T = f T N T is the concentration <strong>of</strong> occupied traps. But s<strong>in</strong>ce <strong>in</strong> the SCR almost n<strong>of</strong>ree charge carriers exist (n p 0) no capture will occur and only emission processestake placedn Tdt= r h e ; r e e : (2.33)

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