MOS Transistors Yannis Tsividis

The Three-Terminal MOS Structure Part 1

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.

Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011 2

= 𝑁𝐴 𝑒 𝜓𝑠− 2𝜙𝐹+𝑉𝐶𝐵 𝜙𝑡

𝑛𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = 𝑛𝑜𝑒𝜓𝑠−𝑉𝐶𝐵 𝜙𝑡

q𝜙𝑏𝑖 a b

c d

q𝜓1

q𝑉𝐶𝐵 q𝑉𝐶𝐵

p

𝐸𝑐(𝑥)

𝑥

𝑉𝐺𝐵=𝑉𝐹𝐵 p (a)

𝜙𝑏𝑖

𝑉𝐺𝐵=𝑉𝐺𝐵1 > 𝑉𝐹𝐵

𝜓1

v p (b)

𝜙𝑏𝑖

𝑉𝐺𝐵=𝑉𝐺𝐵1

𝑉𝐶𝐵

𝜙𝑏𝑖+𝑉𝐶𝐵

p (c)

𝑉𝐺𝐵=𝑉𝐺𝐵2 > 𝑉𝐺𝐵1

𝑉𝐶𝐵 𝜓1+𝑉𝐶𝐵

p (d)

𝜙𝑏𝑖+𝑉𝐶𝐵

Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011 3

GENERAL ANALYSIS

As for the 2-terminal structure, only instead of

𝑛(𝑦) = 𝑛𝑜𝑒𝜓(𝑦) 𝜙𝑡

𝑛(𝑦) = 𝑛𝑜𝑒𝜓(𝑦)−𝑉𝐶𝐵 𝜙𝑡

we use:

This results in the same type of expressions as before, only

with the factor 𝑒−𝑉𝐶𝐵/𝜙𝑡 appearing at the right places. Example:

𝑄𝐶′ = −sgn 𝜓𝑠 2𝑞𝜖𝑠 𝑝𝑜𝜙𝑡 𝑒−𝜓𝑠 𝜙𝑡 − 1 + 𝑁𝐴 − 𝑁𝐷 𝜓𝑠 + 𝑛𝑜𝑒

−𝑉𝐶𝐵 𝜙𝑡 𝜙𝑡 𝑒𝜓𝑠 𝜙𝑡 − 1

Hole contribution

Electron contribution

Dopant ion contribution

Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011 4

Proceeding as for the 2-terminal structure, we obtain:

𝑄𝐶′ = −sgn 𝜓𝑠 2𝑞𝜖𝑠𝑁𝐴 𝜙𝑡𝑒

−𝜓𝑠 𝜙𝑡 + 𝜓𝑠 − 𝜙𝑡 + 𝑒− 2𝜙𝐹+𝑉𝐶𝐵 𝜙𝑡 𝜙𝑡𝑒𝜓𝑠 𝜙𝑡 − 𝜓𝑠 − 𝜙𝑡

𝑉𝐺𝐵 = 𝑉𝐹𝐵 + 𝜓𝑠 − sgn 𝜓𝑠 𝛾 𝜙𝑡𝑒−𝜓𝑠 𝜙𝑡 + 𝜓𝑠 − 𝜙𝑡 + 𝑒− 2𝜙𝐹+𝑉𝐶𝐵 𝜙𝑡 𝜙𝑡𝑒

𝜓𝑠 𝜙𝑡 − 𝜓𝑠 − 𝜙𝑡

As in the case of the 2-terminal structure, certain terms can be neglected in particular regions of inversion.

Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011 5

𝑄𝐵′ = − 2𝑞𝜖𝑠𝑁𝐴 𝜓𝑠

𝑄𝐺′ = 𝐶𝑜𝑥

′ 𝜓𝑜𝑥

𝑄𝐺′ + 𝑄𝑜

′ + 𝑄𝐼′ + 𝑄𝐵

′ = 0

𝑉𝐺𝐵 = 𝜓𝑜𝑥 + 𝜓𝑠+𝜙𝑀𝑆

= −𝛾𝐶′𝑜𝑥 𝜓𝑠

𝑉𝐺𝐵 = 𝑉𝐹𝐵 + 𝜓𝑠 + 𝛾 𝜓𝑠 + 𝜙𝑡𝑒𝜓𝑠− 2𝜙𝐹+𝑉𝐶𝐵 𝜙𝑡

𝑄𝐼′ = − 2𝑞𝜖𝑠𝑁𝐴 (𝜓𝑠 + 𝜙𝑡𝑒

𝜓𝑠− 2𝜙𝐹+𝑉𝐶𝐵 𝜙𝑡 − 𝜓𝑠

INVERSION

𝜓𝑠 𝑉𝐺𝐵

𝑉𝐶𝐵

Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011 6

𝜓𝑠 𝑉𝐺𝐵

𝑉𝐶𝐵

𝜓𝑠

𝐶𝑔′

𝑄𝐼′

2𝜙𝐹+𝑉𝐶𝐵

𝐶𝑜𝑥′

𝑉𝐹𝐵 𝑉𝐿𝐵 𝑉𝑀𝐵 𝑉𝑇𝐵 𝑉𝐻𝐵

𝑉𝐿 𝑉𝑀 𝑉𝑇 𝑉𝐻

ln 𝑄𝐼′

𝜙𝐹+𝑉𝐶𝐵

𝑉𝐺𝐵