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:
𝑉𝐺𝐵
𝜓𝑜𝑥
𝜓𝑠
𝜓(𝑦)
𝑉𝐺𝐵
𝜓(𝑦)
𝜓𝑠
𝜙𝑀𝑆
𝜓𝑜𝑥
y
𝑄𝐺′ + 𝑄0′ + 𝑄𝐶′ = 0
𝑉𝐺𝐵 = 𝜓𝑜𝑥 + 𝜓𝑠 + 𝜙𝑀𝑆
(Charge balance)
(Potential balance)
Δ𝑄𝐺′ + Δ𝑄𝐶′ = 0
Δ𝑉𝐺𝐵 = Δ𝜓𝑜𝑥 + Δ𝜓𝑠
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
2
EFFECT OF 𝑉𝐺𝐵 ON SURFACE CONDITION
Accumulation
𝑉𝐺𝐵
𝑝 type
𝑉𝐹𝐵
Depletion
𝑉𝐺𝐵
𝑉𝐹𝐵
𝑉𝐺𝐵 < 𝑉𝐹𝐵
𝑄𝐶′ > 0
𝜓𝑠 < 0
Holes
𝑑𝐵
𝜓𝑠
𝑝 type
𝑉𝐺𝐵 > 𝑉𝐹𝐵
𝑄𝐶′ < 0
𝜓𝑠 > 0
𝑛𝑠𝑢𝑟𝑓𝑎𝑐𝑒 is negligible
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
3
Inversion
𝑉𝐺𝐵
𝑉𝐹𝐵
𝜓𝑠
𝑝0 , 𝑛0
p type
𝑉𝐺𝐵 > 𝑉𝐹𝐵
′
ࢤ𝑦 𝑄𝐶 < 0
𝑦𝑐
𝜓𝑠 > 0
𝑛𝑠𝑢𝑟𝑓𝑎𝑐𝑒 is significant
𝑛𝑠𝑢𝑟𝑓𝑎𝑐𝑒
𝑛𝑖2
𝑁𝐴
𝑝𝑜 ≈ 𝑁𝐴
𝑛𝑠𝑢𝑟𝑓𝑎𝑐𝑒
= 𝑒 𝜓𝑠 𝜙𝑡
𝑛0
𝑁𝐴
𝜙𝐹 = 𝜙𝑡 ln
𝑛𝑖
𝑛𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = 𝑁𝐴 𝑒 𝜓𝑠 −2𝜙𝐹
𝜙𝑡
𝑛𝑠𝑢𝑟𝑓𝑎𝑐𝑒 =
𝑝𝑠𝑢𝑟𝑓𝑎𝑐𝑒 =
𝑛𝑖
𝜙𝐹
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
2𝜙𝐹
𝜓𝑠
4
Energy band picture:
(Assume for simplicity
𝜙𝑀𝑆 = 0, 𝑄0′ =0)
𝐸𝐹𝑀
𝐸𝐹𝑀
q𝑉𝐺𝐵 < 0
q𝑉𝐺𝐵 > 0
𝐸𝐹𝑀
q𝑉𝐺𝐵 > 0
q𝜙𝐹
q𝜙𝐹
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