Degenerate and Non degenerate semiconductors. Nondegenerate semiconductor Degenerate and nondegenerate semiconductors
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1 4.3.4 Degeerte egeerte semicuctrs Degeerte egeerte semicuctrs Smll mut f t tms (imurity tms) itercti betwee t tms Discrete, iterctig eergy stte. F t the bg F F r ccetr egeerte semicuctr
2 4.3.4 Degeerte egeerte semicuctrs Lrge mut f t tms (~effective esity f sttes) Dt tms iterct with ech ther B f t sttes wies verl the llwe b vlece b) F lies withi vlece b
3 4.3.4 Degeerte egeerte semicuctrs
4 4.3.4 Degeerte egeerte semicuctrs
5 4.4 Sttistics f rs ccetrs Sttistic rs ccetrs Discrete r level r Ccetrti f electr ccuyig the r level 1 1 ex kt F Ccetrti f rs Ccetrti f iize rs
6 4.4.1 Prbbility fucti Discrete ccetr level ccetr Ccetrti f hles i the ccetr sttes 1 1 g ex F kt Ccetrti f ccetrs Ccetrti f iize ccetr g; egeercy fctr (Si; 4)
7 4.4. Cmlete iizti Freeze ut Cmlete iizti; The citi whe ll r tms re sitively chrge by givig u their r electrs ll ccetr tms re egtively chrge by ccetig electrs
8 4.4. Cmlete iizti Freeze ut At T=0 K, ll electr i their lwest ssible eergy stte + =0 - =0 Freeze-ut; The citi tht ccurs i semicuctr whe the temerture is lwere the rs ccetrs becme eutrlly chrge. The electr hle ccetrtis becme very smll.
9 4.5 Chrge eutrlity Chrge eutrlity Chrge-eutrlity citi I therml equilibrium, semicuctr crystl is electriclly eutrl egtive chrges = sitive chrge Determie the crrier ccetrtis s fucti f imurity ig ccetrti Cmeste semicuctr; A semicuctr tht ctis bth r ccetrs t the sme regi If > -tye cmeste semicuctr If > -tye cmeste semicuctr If = hs the chrcteristics f itrisic semicuctr
10 4.5.1 Cmeste semicuctrs Chrge-eutrlity citi egtive chrges Psitive chrges ( ) ( )
11 4.5. quilibrium electr hle ccetrtis ) ( ) ( If we ssume cmlete iizti ( =0, =0) Frm = i 0 i i lectr ccetrti is give s fucti f rs ccetrs ccetrtis
12 4.5. quilibrium electr hle ccetrtis xmle; Csier -tye silic semicuctr t T=300 K i which =10 16 cm -3 =0. The itrisic crrier ccetrti is ssume t be i =1.5x10 10 cm -3. Determie the therml equilibrium electr hle ccetrtis. lectr, i ( ) cm 3 10 ( ) hle, i cm
13 4.5. quilibrium electr hle ccetrtis Reistributi f electrs whe rs re e Whe rs re e, > i < i A few r electr will fll it the emty sttes i vlece b hle ccetrti will ecrese et electr ccetrti i cucti b itrisic electr + r ccetrti
14 4.5. quilibrium electr hle ccetrtis Temerture eeece f i Very strg fucti f temerture As temerture icreses, i term will mite. Shws itrisic chrcteristics
15 4.5. quilibrium electr hle ccetrtis Hle ccetrti Frm chrge-eutrlity citi ruct ) ( ) ( i i i
16 4.5. quilibrium electr hle ccetrtis xmle; Csier -tye silic semicuctr t T=300 K i which =10 16 cm -3 =3 x cm -3. The itrisic crrier ccetrti is ssume t be i =1.5x10 10 cm -3. Determie the therml equilibrium electr hle ccetrtis. Hle, cm i ( ) electr, i 10 ( ) cm rximti = -
17 4.6.1 Mthemticl erivti Psiti f Fermi ergy Level As fucti f ig ccetrti temerture qutis fr siti f Fermi level (-tye) C F C kt l C F C kt l Cmeste semicuctr, = - i Fi F kt l
18 4.6.1 Mthemticl erivti qutis fr siti f Fermi level (-tye) v v F kt l Cmeste semicuctr, = - v v F kt l i F Fi kt l
19 4.3.1 quilibrium istributi f electrs hles Chge f Fermi eergy cuses chge f crrier ccetrti. equti s fucti f the chge f Fermi eergy ( C F) F Fi C ex iex kt kt ( F v) ( F Fi) vex iex kt kt i ; itrisic crrier ccetrti fi ; itrisic Fermi eergy
20 4.6.1 Mthemticl erivti
21 4.6.1 Mthemticl erivti xmle; Silic t T=300 K ctis ccetr imurity ccetrti f =10 16 cm -3. Determie the ccetrti f r imurity tms tht must be e s tht the Silic is -tye Fermi eergy is 0.0 ev belw the cucti b ege. C F kt l C C ( C ex kt 0. ex F ) cm cm cm 3
22 4.6.Vriti f F with Dig ccetrti Temerture Psiti f F s fucti f r ccetrti (-tye) ccetr ccetrti (-tye)
23 4.6.3 Relevce f the Fermi ergy Psiti f F s fucti f temerture fr vrius ig ccetrti
24 4.7 Summry Imrtt terms Itrisic semicuctr; A ure semicuctr mteril with imurity tms lttice efects i the crystl xtrisic semicuctr; A semicuctr i which ctrlle muts f rs /r ccetrs hve bee e s tht the electr hle ccetrtis chge frm the itrisic crrier ccetrti reerce f either electr (-tye) r hle (-tye) is crete. Accetr tms; Imurity tms e t semicuctr t crete - tye mteril Dr tms; Imurity tms e t semicuctr t crete -tye mteril
25 4.7 Summry Cmlete iizti; The citi whe ll r tms re sitively chrge by givig u their r electrs ll ccetr tms re egtively chrge by ccetig electrs Freeze-ut; The citi tht ccurs i semicuctr whe the temerture is lwere the rs ccetrs becme eutrlly chrge. The electr hle ccetrtis becme very smll Fumetl reltishi i
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