![( ) [ ( ) ]
D D GS C TO
Q y WC V V y V
= − −
6/7/2021 24
Arpan Deyasi, RCCIIT
I-V Characteristics of MOSFET
Assume 1D carrier flow
Total mobile electron charge in surface
inversion layer (per unit length) is](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-24-2048.jpg)
![( )
D D n
I Q y v
= −
[( ( ) ]
D D GS C TO n
I WC V V y V v
=
− − −
6/7/2021 25
Arpan Deyasi, RCCIIT
I-V Characteristics of MOSFET
Current is given by
independent of dimension](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-25-2048.jpg)
![n n y
v E
µ
=
( )
n n C
d
v V y
dy
µ
= −
[( ( ) ] ( )
D D GS C TO n C
d
I WC V V y V V y
dy
µ
= − −
6/7/2021 26
Arpan Deyasi, RCCIIT
I-V Characteristics of MOSFET
Velocity of electron
Drain current becomes](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-26-2048.jpg)
![[( ( ) ] ( ( ))
D D GS C TO n C
I dy WC V V y V dV y
µ
= − −
0 0
[( ( ) ] ( ( ))
D
V
L
D D GS C TO n C
I dy WC V V y V dV y
µ
= − −
∫ ∫
6/7/2021 27
Arpan Deyasi, RCCIIT
I-V Characteristics of MOSFET](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-27-2048.jpg)
![2
1
( )
2
D n D GS TO D D
W
I C V V V V
L
µ
= − −
2
1
[2( ) ]
2
D n D GS TO D D
W
I C V V V V
L
µ − −
6/7/2021 28
Arpan Deyasi, RCCIIT
I-V Characteristics of MOSFET
I-V characteristics under active condition](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-28-2048.jpg)
![2
1
[2( ) ]
2
D n D GS TO D D
W
I C V V V V
L
µ
= − −
6/7/2021 29
Arpan Deyasi, RCCIIT
I-V Characteristics of MOSFET
β
Q: What is the significance of β?](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-29-2048.jpg)
![6/7/2021 Arpan Deyasi, RCCIIT 30
I-V Characteristics of MOSFET
For
( )
D GS TO
V V V
< −
1
[2( ) ]
2
D n D GS TO D
W
I C V V V
L
µ −
D D
I V
∝](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-30-2048.jpg)
![6/7/2021 33
Arpan Deyasi, RCCIIT
I-V Characteristics of MOSFET
At peak point
D GS TO
V V V
= −
2
1
[( ) ]
2
DP n D GS TO
W
I C V V
L
µ −](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-33-2048.jpg)
![6/7/2021 35
Arpan Deyasi, RCCIIT
I-V Characteristics of MOSFET
Effect of channel length modulation
2
1
[( ) ]
2 '
DS n D GS TO
W
I C V V
L
µ −
2
1
[( ) ]
2
DS n D GS TO
W
I C V V
L L
µ −
− ∆](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-35-2048.jpg)
![6/7/2021 36
Arpan Deyasi, RCCIIT
I-V Characteristics of MOSFET
Effect of channel length modulation
2
1
[( ) ]
2
DS n D GS TO
W L
I C V V
L L L
µ
−
− ∆
DS D
L
I I
L L
=
− ∆
](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-36-2048.jpg)
2
DS n D GS TO DS
W
I C V V V
L
µ λ
− +
I-V characteristics under saturation condition](https://image.slidesharecdn.com/electricalcharacteristicsofmosfet-210607174841/75/Electrical-characteristics-of-MOSFET-39-2048.jpg)
Uploaded byRCC Institute of Information Technology
Electrical characteristics of MOSFET
This document summarizes the electrical characteristics of n-channel MOSFETs. It describes the minority carrier concentration in the depletion region and how the depletion width changes with applied gate voltage. It then discusses the threshold voltage expression and how the threshold is affected by factors like bulk charge, fixed oxide charge and work function differences. Finally, it derives the drain current equation and shows how the I-V characteristics are affected by channel length modulation under different regions of operation.
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Electrical characteristics of MOSFET
- 1. Electrical Characteristics of MOSFET Part-I ArpanDeyasi Dept of ECE, RCCIIT, Kolkata, India 6/7/2021 1 Arpan Deyasi, RCCIIT
- 2. 6/7/2021 Arpan Deyasi,RCCIIT 2 Body (p) Channel (n) Insulator Gate S D n-channel MOSFET
- 3. 6/7/2021 3 Arpan Deyasi,RCCIIT ΨF ΨS p n Conductor Insulator VM>0 & large
- 4. 6/7/2021 4 Arpan Deyasi,RCCIIT ( ) ( ) z E z dz ρ ε = ∫ Minority Carrier Concentration We consider 1D analysis Charge density of depletion region A qN ρ = − majority carrier concentration at substrate Electric field
- 5. 6/7/2021 5 Arpan Deyasi,RCCIIT Minority Carrier Concentration Electric field ( ) A qN E z dz ε = −∫ 1 ( ) A qN E z z C ε = − + Boundary conditions at z=0, E=E0 at z=W, E=0
- 6. 6/7/2021 Arpan Deyasi,RCCIIT 6 Minority Carrier Concentration 1 A qN C W ε = ( ) ( ) A qN E z W z ε = − ( ) A d qN W z dz ψ ε = − −
- 7. 6/7/2021 Arpan Deyasi,RCCIIT 7 Minority Carrier Concentration ( ) A qN d W z dz ψ ε = − − ∫ ∫ Boundary conditions at z=0, ψ= ψS at z=W, ψ = ψF 2 2 A F S qN W ψ ψ ε − = −
- 8. 6/7/2021 Arpan Deyasi,RCCIIT 8 Minority Carrier Concentration 1/2 2 ( ) S F A W qN ε ψ ψ = − Expression of Depletion Region Width Under depletion condition, ψF > ψS Under inversion condition, ψS > ψF
- 9. 6/7/2021 Arpan Deyasi,RCCIIT 9 Minority Carrier Concentration Minority carrier concentration at depletion condition D A Q qN W = − 1/ 2 2 ( ) D A S F A Q qN qN ε ψ ψ = − − 1/ 2 2 D A S F Q qN ε ψ ψ = − −
- 10. 6/7/2021 Arpan Deyasi,RCCIIT 10 Minority Carrier Concentration At the onset of inversion S F ψ ψ = − 1/ 2 2 2 I A F Q qN ε ψ = − −
- 11. 6/7/2021 Arpan Deyasi,RCCIIT 11 Expression of Threshold Voltage Threshold voltage is defined as TO i MOS FB V V V − = + Vi-MOS: Threshold of ideal MOS capacitor VFB: Flatband voltage
- 12. 6/7/2021 Arpan Deyasi,RCCIIT 12 Expression of Threshold Voltage 2 b i MOS F D Q V C ψ − = − + Qb: bulk charge in the substrate CD: Dielectric constant
- 13. 6/7/2021 Arpan Deyasi,RCCIIT 13 Expression of Threshold Voltage fc FB MS D Q V C φ = − − Qfc: fixed charge due to surface states that arise due to imperfections at insulator-substrate interface φMS: conductor-substrate work function difference
- 14. 6/7/2021 Arpan Deyasi,RCCIIT 14 Expression of Threshold Voltage 2 g MS F E φ ψ = − − Eg: bandgap of semiconductor substrate
- 15. 6/7/2021 Arpan Deyasi,RCCIIT 15 Expression of Threshold Voltage 3 2 g fc b TO F D D E Q Q V C C ψ = − − − −
- 16. 6/7/2021 Arpan Deyasi,RCCIIT 16 Body Effect in n-channel MOSFET Body Channel Insulator Gate S (n+) D (n+) (p) (p)
- 17. 6/7/2021 Arpan Deyasi,RCCIIT 17 Role of Body Effect on Threshold Voltage at VSB = 0 1/ 2 2 2 I A F Q qN ε ψ = − − at VSB > 0 1/ 2 2 2 ISB A F SB Q qN V ε ψ = − − +
- 18. 6/7/2021 Arpan Deyasi,RCCIIT 18 Role of Body Effect on Threshold Voltage Change in space-charge density SB ISB I Q Q Q ∆ = − 1/2 1/2 2 2 2 SB A F SB F Q qN V ε ψ ψ ∆ = − × − + − −
- 19. 6/7/2021 Arpan Deyasi,RCCIIT 19 Role of Body Effect on Threshold Voltage Change in threshold voltage SB T D Q V C ∆ ∆ = 1/2 1/2 1 2 2 2 T A D F SB F V qN C V ε ψ ψ ∆ = − × − + − −
- 20. 6/7/2021 Arpan Deyasi,RCCIIT 20 Body Effect Coefficient 1 2 A D qN C γ ε = body effect coefficient
- 21. 6/7/2021 21 Arpan Deyasi,RCCIIT ΨF ΨS p n Conductor Insulator VM>0 & large Inversion Condition
- 22. 6/7/2021 22 Arpan Deyasi,RCCIIT Semiconductor (p-substrate) (n-channel) Insulator Conductor n+ n+ G B D S y z L Schematic Diagram
- 23. I-V Characteristics ofMOSFET 6/7/2021 23 Arpan Deyasi, RCCIIT Boundary conditions 1. VC(y = 0) = VS = 0 2. VC(y = L) = VDS 3. VGS ≥ VTO
- 24. ( ) [( ) ] D D GS C TO Q y WC V V y V = − − 6/7/2021 24 Arpan Deyasi, RCCIIT I-V Characteristics of MOSFET Assume 1D carrier flow Total mobile electron charge in surface inversion layer (per unit length) is
- 25. ( ) D Dn I Q y v = − [( ( ) ] D D GS C TO n I WC V V y V v = − − − 6/7/2021 25 Arpan Deyasi, RCCIIT I-V Characteristics of MOSFET Current is given by independent of dimension
- 26. n n y vE µ = ( ) n n C d v V y dy µ = − [( ( ) ] ( ) D D GS C TO n C d I WC V V y V V y dy µ = − − 6/7/2021 26 Arpan Deyasi, RCCIIT I-V Characteristics of MOSFET Velocity of electron Drain current becomes
- 27. [( ( )] ( ( )) D D GS C TO n C I dy WC V V y V dV y µ = − − 0 0 [( ( ) ] ( ( )) D V L D D GS C TO n C I dy WC V V y V dV y µ = − − ∫ ∫ 6/7/2021 27 Arpan Deyasi, RCCIIT I-V Characteristics of MOSFET
- 28. 2 1 ( ) 2 D nD GS TO D D W I C V V V V L µ = − − 2 1 [2( ) ] 2 D n D GS TO D D W I C V V V V L µ − − 6/7/2021 28 Arpan Deyasi, RCCIIT I-V Characteristics of MOSFET I-V characteristics under active condition
- 29. 2 1 [2( ) ] 2 Dn D GS TO D D W I C V V V V L µ = − − 6/7/2021 29 Arpan Deyasi, RCCIIT I-V Characteristics of MOSFET β Q: What is the significance of β?
- 30. 6/7/2021 Arpan Deyasi,RCCIIT 30 I-V Characteristics of MOSFET For ( ) D GS TO V V V < − 1 [2( ) ] 2 D n D GS TO D W I C V V V L µ − D D I V ∝
- 31. 6/7/2021 Arpan Deyasi,RCCIIT 31 I-V Characteristics of MOSFET For ( ) D GS TO V V V > − 2 D D I V ∝
- 32. 6/7/2021 32 Arpan Deyasi,RCCIIT I-V Characteristics of MOSFET graphical representation of the equation VGS1 VGS2 VGS3 VDS ID
- 33. 6/7/2021 33 Arpan Deyasi,RCCIIT I-V Characteristics of MOSFET At peak point D GS TO V V V = − 2 1 [( ) ] 2 DP n D GS TO W I C V V L µ −
- 34. 6/7/2021 34 Arpan Deyasi,RCCIIT I-V Characteristics of MOSFET Q: What happened after pinch-off? L ΔL L’ L ΔL L’ ' L L L = + ∆
- 35. 6/7/2021 35 Arpan Deyasi,RCCIIT I-V Characteristics of MOSFET Effect of channel length modulation 2 1 [( ) ] 2 ' DS n D GS TO W I C V V L µ − 2 1 [( ) ] 2 DS n D GS TO W I C V V L L µ − − ∆
- 36. 6/7/2021 36 Arpan Deyasi,RCCIIT I-V Characteristics of MOSFET Effect of channel length modulation 2 1 [( ) ] 2 DS n D GS TO W L I C V V L L L µ − − ∆ DS D L I I L L = − ∆
- 37. 6/7/2021 37 Arpan Deyasi,RCCIIT I-V Characteristics of MOSFET Effect of channel length modulation 1 1 DS D I I L L = ∆ − ( ) 1 DS D L I I L ∆ +
- 38. 6/7/2021 38 Arpan Deyasi,RCCIIT I-V Characteristics of MOSFET Effect of channel length modulation DS L V ∆ ∝ DS L V L ∆ ∝ DS L V L λ ∆ =
- 39. 6/7/2021 39 Arpan Deyasi,RCCIIT (1 ) DS D DS I I V λ + I-V Characteristics of MOSFET Effect of channel length modulation 2 1 [( ) ](1 ) 2 DS n D GS TO DS W I C V V V L µ λ − + I-V characteristics under saturation condition
- 40. 6/7/2021 40 Arpan Deyasi,RCCIIT I-V Characteristics of MOSFET VDS ID VGS1 VGS2 VGS3