SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

9.8. PROBLEMS 481

Discrete dopants fluctuations

Low gate leakage

Enhanced gate control

Drain to source and Band to Band

tunneling

High current density

Electron velocity and mobility

Source/Drain resistances

Challenges

Discrete dopants fluctuations

Low gate leakage

Enhanced gate control

Drain to source and Band to Band

tunneling

High current density

Electron velocity and mobility

Source/Drain resistances

Challenges

Increase in current

Low power dissipation

Good channel control

Figure 9.32: Challenges to the future of MOSFETs.

all electronic components. As devices continue to be scaled new challenges continue to be faced
as is summarized in figure 9.32. The solutions will come in the form of highKdielectrics,
structures with enhanced gate control such as the FINFET or Tri-gate structures, and probably
new semiconductors such as GaAs, InGaAs, and InSb based MOSFETs. The future direction is
truly unpredictable and therefore very exciting for research.

9.8 PROBLEMS ....................................

Assume a temperature of 300 K unless explicitly stated otherwise.

• Section 9.3

Problem 9.1Calculate the maximum space charge widthWmaxinp-type silicon doped at

Na=10^16 cm−^3 and at 101 7cm−^3.

Problem 9.2Ap-type silicon has a uniform doping ofNa=10^16 cm−^3. Calculate the

surface potential needed to cause strong inversion.

Problem 9.3A50A oxide is grown on ̊ p-type silicon withNa=5× 1015 cm−^3.

Assume that the oxide charge is negligible and calculate the surface potential and gate

voltage to create inversion at the surface. Calculate the value ofWmaxfor the device. The

flat band voltage is -1.0 V.