Nanoelectronics

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5

Charge Transport

Information processing by transporting carriers in nanoelectronic devices

and circuits is severely affected by the breakdown of Ohm’s law when the

applied voltage V in a nanoscale (L < 1000 nm) device exceeds the critical volt-

age V

c

= V

t

L/∙

o∞

(V > V

c

). Here V

t

is the thermal voltage with a value 0.0259 V

at room temperature and ∙

o∞

(typically 100 nm) is the mfp. This nonohmic

behavior is the cause of the current saturation leading to the resistance surge.

The saturation arises due to realignment of randomly oriented velocity vec-

tors to the unidirectional streamlined ones in a high electric eld when volt-

age applied across a resistor exceeds the critical value. The surge accelerates

for signal propagation as dc voltage is increased. Both the digital and analog

signal processing will be affected by the presence of nonohmic nonlinear

behavior. This surge changes the RC time constants, power consumption,

and voltage and current division laws. Ballistic processes overpower the

scattering-limited transport in a high electric eld and in channels where

length is smaller than the scattering-limited mfp. The transient switching

delay in a micro-/nanoscale circuit containing resistive and reactive elements

is sternly affected by the surge in the resistance arising out of sublinear cur-

rent–voltage (I–V) characteristics limited to the drift velocity leading to cur-

rent saturation. The frequency response f = 1/2πτ

t

, where τ

t

is the transit time

through the conducting channel and is lower than that predicted from the

application of Ohm’s law. The resistance surge boosts the RC time constant

and attenuates the

L/R

time constant dramatically. These results are neces-

sary for extraction of transport parameters and assessing the limitations of

parasitic elements in a micro-/nanoscale circuit.

5.1 Primer

The ever-decreasing length of a conducting channel has now entered the

decananometer regime with a typical length in the order in 10–100 nm. Many

unexpected effects that are normally negligible in the long channels demon-

strate their prowess in nanoscale channels. One such effect is the surge in

the resistance of a signal due to saturated current [1]. This increase in resis-

tance affects all timing delays that are normally based on Ohm’s law where

resistance is constant due to current rising linearly with the applied voltage.