Fermi Level
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This document discusses the position of the Fermi level in intrinsic and extrinsic semiconductors. It begins by defining the intrinsic Fermi level position in an intrinsic semiconductor. It then describes how the Fermi level shifts in n-type and p-type extrinsic semiconductors due to the introduction of donor and acceptor dopants. Equations are provided for calculating the intrinsic carrier concentration and extrinsic carrier concentrations in n-type and p-type materials.
Fermi Level
- 1. Course: Electronic Devices paper code: EC301 Course Coordinator: Arpan Deyasi Department of Electronics and Communication Engineering RCC Institute of Information Technology Kolkata, India 8/4/2020 1Arpan Deyasi, RCCIIT Topic: Fermi Level (Intrinsic and Extrinsic)
- 2. 8/4/2020 Arpan Deyasi, RCCIIT 2 Position of Fermi level In intrinsic semiconductor 0 0n p= exp exp C FI C FI V V E E N kT E E N kT − − − − F FIE E=
- 3. 8/4/2020 Arpan Deyasi, RCCIIT 3 Position of Fermi level 2 expC C V FI V N E E E N kT + − = 1 1 ( ) ln 2 2 V FI C V C N E E E kT N = + +
- 4. 8/4/2020 Arpan Deyasi, RCCIIT 4 Position of Fermi level 3/2* * C e V h N m N m = 3/2 2 2 * 2 e C m kT N h π = 3/2 2 2 * 2 h V m kT N h π =
- 5. 8/4/2020 Arpan Deyasi, RCCIIT 5 Position of Fermi level * * 1 3 ( ) ln 2 4 h FI C V e m E E E kT m = + + 1 ( ) 2 FI C VE E E α= + + * * h em m>
- 6. 8/4/2020 Arpan Deyasi, RCCIIT 6 Position of Fermi level EC EV EFI EFI α Intrinsic Fermi level is not at the middle of forbidden region (EC+EV)/2 (EC+EV)/2 1 ( ) 2 FI C VE E E α= + +
- 7. 8/4/2020 Arpan Deyasi, RCCIIT 7 Intrinsic Carrier Concentration 2 0 0in n p= 2 exp exp C FI i C FI V V E E n N kT E E N kT − = − − × −
- 8. 8/4/2020 Arpan Deyasi, RCCIIT 8 Intrinsic Carrier Concentration 2 exp C V i C V E E n N N kT − − 2 exp g i C V E n N N kT = −
- 9. 8/4/2020 Arpan Deyasi, RCCIIT 9 Intrinsic Carrier Concentration exp 2 g i C V E n N N kT − * * ( , , )i e h gn f m m E=
- 10. 8/4/2020 Arpan Deyasi, RCCIIT 10 Extrinsic Carrier Concentration (n-type) Consider n-type semiconductor ND: Donor concentration 0exp C F C D E E N n N kT − − == exp C F C D E E N N kT − =
- 11. 8/4/2020 Arpan Deyasi, RCCIIT 11 exp C FI C i E E N n kT − − = Extrinsic Carrier Concentration (n-type) exp C FI C i E E N n kT − =
- 12. 8/4/2020 Arpan Deyasi, RCCIIT 12 Extrinsic Carrier Concentration (n-type) exp F FI i D E E n N kT − = exp expC FI C F i D E E E E n N kT kT − − =
- 13. 8/4/2020 Arpan Deyasi, RCCIIT 13 Extrinsic Carrier Concentration (n-type) ln D F FI i N E E kT n = + ND EF EFI ni=ND EC
- 14. 8/4/2020 Arpan Deyasi, RCCIIT 14 Extrinsic Carrier Concentration (p-type) Consider p-type semiconductor NA: Acceptor concentration 0exp F V V A E E N p N kT − − == exp F V V A E E N N kT − =
- 15. 8/4/2020 Arpan Deyasi, RCCIIT 15 Extrinsic Carrier Concentration (p-type) exp FI V V i E E N n kT − − = exp FI V V i E E N n kT − =
- 16. 8/4/2020 Arpan Deyasi, RCCIIT 16 Extrinsic Carrier Concentration (p-type) exp expFI V F V i A E E E E n N kT kT − − = exp FI F i A E E n N kT − =
- 17. 8/4/2020 Arpan Deyasi, RCCIIT 17 Extrinsic Carrier Concentration (p-type) ln A F FI i N E E kT n = − NA EF EFI ni=NA EV