484 CHAPTER 9. FIELD EFFECT TRANSISTORS: MOSFET
Problem 9.16Consider ap-channel MOSFET with oxide thickness of 500A, and ̊
Nd=10^16 cm−^3. Calculate the body-to-source voltage needed to shift the threshold
voltage from theVBS= 0 results by− 1 .0 V.
Problem 9.17A NMOS withVTof 1.5 V is operated atVGS=5VandIDS= 100μA.
Determine if the device is in linear or saturation regime.
k=
μZCox
L
=20μA/V^2
Problem 9.18In the text we considered a criterion for inversionVs=2φF. Consider
another criterion that asserts that inversion occurs when the channel conductivity near the
interface is 0.1(Ωcm)−^1. Calculate the surface potential bending needed to satisfy this
criterion when the channel has ap-type doping of: (a) 1014 cm−^3 ;(b) 1015 cm−^3 ;(c)
1016 cm−^3. Compare the surface band bending arising from this new criterion to be a
value ofVsgiven by the criterion used in the text (μn= 600 cm^2 /V·s).
Problem 9.19Threshold bias for ann-channel MOSFET: In the text we used a criterion
that the inversion of the MOSFET channel occurs whenVs=ψs=2φFwhere
eφF=(EFi−EF). Consider another criterion in which we say that inversion occurs
when the electron density at the Si/SiO 2 interface becomes 1016 cm−^3. Calculate the gate
threshold voltage needed for an MOS device with the following parameters for the two
different criteria:
dox = 500A ̊
φms =1.0V
Na =10^13 cm−^3
Problem 9.20A frequently needed quantity in experimental studies of MOS transistors is
ψS, the surface potential.
(a) Show that when the gate voltage VGis changed in a MOS capacitor biased in the
depletion region, it is possible to find the corresponding change inψS,byusingthe
measured capacitance of the MOS system. The change is calculated from the relation
ψS(VG 2 )−ψS(VG 1 )=
∫VG 2
VG 1
(1−
C
Cox
)dVG (9.8.1)
(b)IfVG 1 is taken as VFB(flat-band voltage), sketch a low frequency MOS capacitance
curve for p-type silicon bulk. Normalize it to C∞and indicate by shading an area of the
curve equal toΔφS.
Problem 9.21Consider the Si MOSFET structure in figure 9.33. Calculate the threshold
voltage when the p-type region is doped at 10^17 cm−^3 uniformly as shown in Fig. 9.26b.
Because of problems during processing, I lose Boron atoms from 50 nm of the Si and it
gets magically incorporated uniformly in the oxide and provides unit negative charge per
atom there. The resultant doping in the Si is shown below in Fig. 9.26c. Calculate the new
threshold voltage VTHof the structure. AssumeφMS=0eV.
