SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

448 CHAPTER 9. FIELD EFFECT TRANSISTORS: MOSFET

Example 9.4Consider ann-MOSFET made from Si-dopedp-type at

Na=5× 1016 cm−^3 at 300 K. The other parameters for the device are the following:

φMS = − 0 .5V

μn = 600 cm^2 V−^1 s−^1

μp = 200 cm^2 V−^1 s−^1

The inversion condition isψs=2φF. Assume that the electrons induced under inversion

areinaregion200A wide near the Si/SiO ̊ 2 interface.

(i) Calculate the channel conductivity near the Si-SiO 2 interface under flat band condition

and at inversion.

(ii) Calculate the threshold voltage.

(i) Assuming that all of the acceptors are ionized, we have at flat band

p=Na=5× 1016 cm−^3

This gives

σ(fb)=(5× 1016 cm−^3 )(1. 6 × 10 −^19 C)(200 cm^2 /V·s) = 1.6(Ωcm)−^1

At inversion withψs=2φFwe have

n(interface) =p(bulk) = 5× 1016 cm−^3

This gives (near the interface)

σ(inv)=(5× 1016 cm−^3 )(1. 6 × 10 −^19 C)(600 cm^2 /V·s) = 4.8(Ωcm)−^1

(ii) To calculate the threshold voltage we needφF. This is given by

φF=

kBT

e

ln(

p

pi

)=+0.39 V

Using the parameters given and the equation for the threshold voltage we get

VT=− 0 .5+0.78 + 1.637 V = 1.93 V

9.4 CAPACITANCE-VOLTAGE CHARACTERISTICS

OF THE MOS STRUCTURE

The study of capacitance-voltage characteristics of a MOSFET provides valuable information
on threshold voltage, oxide thickness, trap density, etc. In the C-V measurement, a dc biasVis
applied to the gate, and a small ac signal (∼5-10 mV) is applied to obtain the capacitance at the
bias applied.