5.2 Silicon Nanowire MOSFETs

The approach of Chapter 3 can be used to establish some general features of semiconductor nanowire MOSFETs. We assume a very simple geometry as shown in Fig. 5.1 - a nanowire that is coaxially gated. Instead of C _ins = K _ins ? ₀/ t _ins F/cm ² as for a MOSFET, we have an insulator capacitance of

(5.1)

where t _wire is the diameter of the wire.

Figure 5.1: The geometry of a simple, idealized coaxial gate nanowire MOSFET.

We first need to evaluate some directed moments analogous to Eqns. (3.5). Specifically, we must evaluate

(5.2a)

(5.2b)

(5.2c)

(5.2d)

We will work within the effective mass approximation and assume a simple, parabolic bandstructure,

(5.3)

where ? ₁(0) is the minimum of the first subband at the top of the barrier. We assume that only one subband is occupied, so the directed moments can be evaluated to find

(5.4a)

(5.4b)

(5.4c)

(5.4d)

(5.4e)

(5.4f)

where ? _F = ( E _F- ?(0))/ k _BT _L, U _D = qV _D/ k _BT _L, and as before. The one-dimensional effective density of states is

(5.4g)

It is important to note that the expressions for the directed currents are independent of the bandstructure, because when converting the sum over k-states to an integral over energy, the density of states cancels with the velocity in Eqns. (5.2c) and (5.2d).