466 CHAPTER 9. FIELD EFFECT TRANSISTORS: MOSFET
orNa^2 D =ΔVTCox
e=
(0.5)(3. 9 × 8. 85 × 1014 )
(1. 6 × 10 −^19 )(5× 10 −^6 )
=2. 16 × 1011 cm−^2The dopants are distributed over a thickness of 0.1μm. The dopant density is thenNa=2. 16 × 1011
10 −^5
=2. 16 × 1016 cm−^3The use of controlled implantation can be very effective in shifting the threshold voltage.9.6 IMPORTANT ISSUES AND FUTURE CHALLENGES IN REAL MOSFETS
In the discussions above, we have made a number of simplifying assumptions. These assump-
tions allowed us to obtain simple analytical expressions for the I-V relationships for the device.
However, in real devices a number of important effects cause the device behavior to differ from
our simple results. In this section we will briefly examine the important issues that control the
performance of real MOSFETs and discuss future challenges. A summary of these challenges is
shown in figure 9.32.
9.6.1 Subthreshold Conduction..........................
As device dimensions are shrunk below 50 nm the behavior of the device below threshold or
in the sub-threshold regime becomes critical. The analysis up to now has assumed that the device
turns on abruptly at a gate voltage above threshold or
Vg−Vth>
∼0 ∗
that no current flows at gate voltages belowVth. As shown in figure 9.20, this assumption does
not account for current that flows through the channel in the region below strong inversion or in
the weak inversion regime which is defined as the region where the surface band bendingψsis
in the range,
φF<ψs< 2 φF
Note that in strong inversion as we move from the source to the drain, the voltage across the
oxide,Voxdecreases and the band bending in the semiconductor,ψSincreases by a magnitude
equal toVc(x). Now, let us compare this to the weak-inversion case: Figure 9.21 and illustrate
the fundamental difference between current flow and the evolution of the band diagram between
∗This is equivalent to a band bending ofψs=2φFwhereφFis the bulk potential=EiB−EFPandψSis the
band bending measured from the bulk