nes ▁and ▁Sho ck ley ▁in ▁ 1 9 4 8 , ▁with ▁a ▁more ▁detailed ▁version ▁published ▁by ▁Sho ck ley , ▁Pear son , ▁and ▁Hay nes ▁in ▁ 1 9 4 9 . ▁▁ ▁The ▁experiment ▁can ▁be ▁used ▁to ▁measure ▁car rier ▁mob ility , ▁car rier ▁lifetime , ▁and ▁diffusion ▁coefficient . ▁ ▁In ▁the ▁experiment , ▁a ▁piece ▁of ▁sem icon duct or ▁gets ▁a ▁pul se ▁of ▁holes , ▁for ▁example , ▁as ▁induced ▁by ▁voltage ▁or ▁a ▁short ▁las er ▁pul se . ▁ ▁Equ ations ▁ ▁To ▁see ▁the ▁effect , ▁we ▁consider ▁a ▁n - type ▁sem icon duct or ▁with ▁the ▁length ▁d . ▁We ▁are ▁interested ▁in ▁determ ining ▁the ▁mob ility ▁of ▁the ▁carri ers , ▁diffusion ▁constant ▁and ▁relax ation ▁time . ▁In ▁the ▁following , ▁we ▁reduce ▁the ▁problem ▁to ▁one ▁dimension . ▁ ▁The ▁equations ▁for ▁electron ▁and ▁hole ▁curr ents ▁are : ▁ ▁where ▁the ▁js ▁are ▁the ▁current ▁dens ities ▁of ▁electrons ▁( e ) ▁and ▁holes ▁( p ), ▁the ▁ μ s ▁the ▁charge ▁car rier ▁mob ilities , ▁E ▁is ▁the ▁electric ▁field , ▁n ▁and ▁p ▁the ▁number ▁dens ities ▁of ▁charge ▁carri ers , ▁the ▁D s ▁are ▁diffusion ▁coefficients , ▁and ▁x ▁is ▁position . ▁The ▁first ▁term ▁of ▁the ▁equations ▁is ▁the ▁dr ift ▁current , ▁and ▁the ▁second ▁term ▁is ▁the ▁diffusion ▁current . ▁ ▁Der iv ation ▁ ▁We ▁consider ▁the ▁continu ity ▁equation : ▁