Nanoelectronics

1

1

Nanoengineering Overview

The next big thing in emerging technologies is going to be extremely small.

The typical scale of this smallness is a few nanometers (a nanometer, abbre-

viated as nm, is one-billionth of a meter). To appreciate the smallness of a

nm, let us assume that the diameter of the human hair is 100,000 nm. These

ultrasmall nanoelectronic devices are the subject of intensive research

directed toward system design for practical applications. Nanoengineering

is little known to the general public, but in the science and public policy

community its promise is exhilarating. Coming from the Stone Age of

5000 , we have made tremendous progress toward improving lifestyle

[1,2]. For about 200years after American independence, we followed Adam

Smith’s model of An Enquiry into Nature and Causes of the Wealth of Nations

(1776), which implied that the wealth is created by laissez-faire economy

and free trade. Over the next 50 years or so, the economy was dictated

by John Maynard Keynes as outlined in The General Theory of Employment,

Interest and Money. Keynes concluded that the wealth is created by care-

ful government planning and stimulation of the economy. In the 1990s,

according to Paul Romer, the wealth is created by innovations and inven-

tions, such as computer chips. The semiconductor industry is the heart of

this evolution and revolution. The eld is growing at a tremendous rate.

Carbon-based materials, for example, graphene, organic polymers, and

other smart meta materials, are appearing on the world stage for custom-

made nanoelectronic circuits in the future. Nanoengineering can be under-

stood only if we delve into the wave character of an electron.

1.1 Quantum Waves

Nanoengineering originated from the work of Louise de Broglie in 1926 who

postulated that an electron with its classical momentum p = m*v, where m*

is the effective mass and v is the velocity, is connected to its wave character

through the wavelength λ

D

, termed the de Broglie wavelength, given by [3]

λ

D

h

p

=

(1.1)

2 Nanoelectronics

The momentum is related to the kinetic energy E by

Emv

p

m

pm

E==⇒=

1

22

2

2

2

*

*

*

(1.2)

With the application of Equation 1.2, the thermal wavelength λ

Dth

for ther-

mal energy E = k

B

T is given by

λ

Dth

B

h

mkT

=

2*

(1.3)

Here, k

B

is the Boltzmann constant and T is the ambient temperature.

Equation 1.3 is suitably adapted to the numerical calculations as follows:

λ

Dth

o

mm T

=

×

763

300

.

(* )( )

nm

//

K

(1.4)

λ

Dth

for a free electron (m* = m

o

) is 7.63 nm at room temperature (T = 300 K).

However, in a semiconductor, for example, in GaAs (m* = 0.067m

o

), its value

is 29.5 nm. The wave character becomes more prominent as the temperature

is further reduced. The de Broglie wavelength for Si (m* = 0.26m

o

), GaAs

(m* = 0.067m

o

), and GaN (m* = 0.19m

o

) as a function of temperature is depicted

in Figure 1.1. Quantum effects are more pronounced at low temperatures

and for materials with low effective mass.

Figure 1.2 shows the spectrum going from macro- to nanoengineering

scale. The nanometer size of the de Broglie wavelength demonstrates why it

is important to consider the wave character of an electron. As body cells and

DNA are of nanometer size, nanoengineering is of special signicance for

applications in biosystems and hence the anticipated DNA or bioelectronics.

0 100 200 300

400

0

20

40

60

80

100

Temperature (K)

de Broglie wavelength (nm)

Si (m* = 0.26m

o

)

GaAs (

m

* = 0.067

m

o

)

GaN (m* = 0.19m

o

)

FIGURE 1.1

The de Broglie wavelength λ

D

as a function of temperature for Si, GaAs, and GaN.