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MOS Transistors
Yannis Tsividis
The Two-Terminal MOS Structure
Surface Condition
These slides are based on Y. Tsividis and C.
McAndrew, “Operation and Modeling of the
MOS Transistor”, Copyright © Oxford University
Press, 2011. They are meant to be part of a
lecture, and may be incomplete or may not even
make sense without the accompanying
narration.
With general externally applied bias:
𝑉𝐺𝐡
πœ“π‘œπ‘₯
πœ“π‘ 
πœ“(𝑦)
𝑉𝐺𝐡
πœ“(𝑦)
πœ“π‘ 
πœ™π‘€π‘†
πœ“π‘œπ‘₯
y
𝑄𝐺′ + 𝑄0′ + 𝑄𝐢′ = 0
𝑉𝐺𝐡 = πœ“π‘œπ‘₯ + πœ“π‘  + πœ™π‘€π‘†
(Charge balance)
(Potential balance)
Δ𝑄𝐺′ + Δ𝑄𝐢′ = 0
Δ𝑉𝐺𝐡 = Δπœ“π‘œπ‘₯ + Δπœ“π‘ 
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
2
EFFECT OF 𝑉𝐺𝐡 ON SURFACE CONDITION
Accumulation
𝑉𝐺𝐡
𝑝 type
𝑉𝐹𝐡
Depletion
𝑉𝐺𝐡
𝑉𝐹𝐡
𝑉𝐺𝐡 < 𝑉𝐹𝐡
𝑄𝐢′ > 0
πœ“π‘  < 0
Holes
𝑑𝐡
πœ“π‘ 
𝑝 type
𝑉𝐺𝐡 > 𝑉𝐹𝐡
𝑄𝐢′ < 0
πœ“π‘  > 0
π‘›π‘ π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ is negligible
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
3
Inversion
𝑉𝐺𝐡
𝑉𝐹𝐡
πœ“π‘ 
𝑝0 , 𝑛0
p type
𝑉𝐺𝐡 > 𝑉𝐹𝐡
′
ΰ’€π‘¦ 𝑄𝐢 < 0
𝑦𝑐
πœ“π‘  > 0
π‘›π‘ π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ is significant
π‘›π‘ π‘’π‘Ÿπ‘“π‘Žπ‘π‘’
𝑛𝑖2
𝑁𝐴
π‘π‘œ ≈ 𝑁𝐴
π‘›π‘ π‘’π‘Ÿπ‘“π‘Žπ‘π‘’
= 𝑒 πœ“π‘  πœ™π‘‘
𝑛0
𝑁𝐴
πœ™πΉ = πœ™π‘‘ ln
𝑛𝑖
π‘›π‘ π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ = 𝑁𝐴 𝑒 πœ“π‘  −2πœ™πΉ
πœ™π‘‘
π‘›π‘ π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ =
π‘π‘ π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ =
𝑛𝑖
πœ™πΉ
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
2πœ™πΉ
πœ“π‘ 
4
Energy band picture:
(Assume for simplicity
πœ™π‘€π‘† = 0, 𝑄0′ =0)
𝐸𝐹𝑀
𝐸𝐹𝑀
q𝑉𝐺𝐡 < 0
q𝑉𝐺𝐡 > 0
𝐸𝐹𝑀
q𝑉𝐺𝐡 > 0
qπœ™πΉ
qπœ™πΉ
𝐸𝑐
𝐸𝑖
𝐸𝐹
𝐸𝑣
Flatband
𝐸𝑐
𝐸𝑖
𝐸𝐹
𝐸𝑣
Accumulation
𝐸𝑐
𝐸𝑖
𝐸𝐹
𝐸𝑣
Depletion
𝐸𝑐
𝐸𝑖
𝐸𝐹
𝐸𝑣
Inversion
𝐸𝐹𝑀
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
5
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