Nanoelectronic Devices

Byung-Gook Park, Sung Woo Hwang, Young June Park

• Publisher: Jenny Stanford Publishing
• Year: 2012
• Print ISBN: 9789814364003
• eBook ISBN: 9781439896570
• Topic: Physical Sciences
• Subtopic: Biology

This book provides readers with the knowledge in fundamentals of nanoelectronic devices. The authors build the principles of nanoelectronic devices based on those of microelectronic devices wherever possible and introduce the inherently nanoelectronic principles gradually. They briefly review quantum mechanics and solid-state physics that can form

Chapter 1

Quantum Mechanics for Nanoelectronic Devices

1.1 Fundamental Concepts of Quantum Mechanics

1.1.1 Wave Nature of Particles

In the late 19th century, scientists started to notice that there were phenomena that could not be explained by the classical theory of mechanics. One of them was the spectrum of absorption and emission by atoms. According to classical mechanics, the spectrum should be continuous, i.e., the emitted or absorbed light could have any frequency (wavelength). The experimental results, however, were surprising. The atoms emitted and absorbed light with discrete values of frequency only.

Let us examine the situation in more detail. Figure 1.1(a) shows an experimental setup to measure the emission spectrum of a hydrogen discharge lamp. If we pump out the air in a vacuum tube and fill it with a small amount of hydrogen (H₂) gas, an arc discharge can be initiated by supplying sufficient bias voltage to the electrodes in the tube. The electrons in the hydrogen atoms absorb energy from the arc discharge and emit light with various frequencies. One startling feature of this process is that the emitted light has certain discrete frequencies only, as shown in Fig. 1.1(b).

Figure 1.1. Spectrum of hydrogen discharge lamp: (a) experimental setup, (b) emission spectrum.

Many people studied this phenomenon and some came up with the following formula for the observed frequencies.

where n₁ and n₂ are integers (n₁ < n₂). Depending on the value of n₁, the discrete frequencies form distinctive groups, called Lyman (n₁ = 1), Balmer (n₁ = 2), and Paschen (n₁ = 3) series after their early investigators.

This phenomenon, however, cannot be understood at all in terms of classical mechanics. Maxwell’s theory of electromagnetic radiation predicts that there should be an emission of radiation since the electron is accelerated toward the positively charged nucleus. The electron loses its energy due to the emission of radiation and forms a continuously shrinking orbit. The continuous motion of the electron should generate a continuous emission spectrum as shown in Fig. 1.2(a). There is no way of explaining the discrete spectrum in the frame of classical mechanics. Furthermore, the electron should eventually settle down on the surface of nucleus (Fig. 1.2(b)). This conclusion again contradicts Rutherford’s well-known experiment that showed that there is a vast space between the electron and the nucleus.

Figure 1.2. Classical explanation of the emission spectrum of atoms: (a) emission intensity as a function of frequency, (b) mechanism of photo emission. Since the electron is accelerated toward the positively charged nucleus, it emits electromagnetic radiation and loses energy. The radius of electron orbit should shrink rapidly and the electron will eventually come in contact with the nucleus.

In order to explain the emission spectrum of atoms, Niels Bohr proposed a model for the hydrogen atom, based on the motion of the planetary system. His main hypothesis concerning the electron motion in an atom was the existence of quantized stable orbits. The condition for a stable orbit is that the phase integral of the electron angular momentum, Ρ_φ, should be an integer multiple of Planck’s constant, h.

In the case of a circular orbit with radius r, mass m_e, and velocity v, we can easily evaluate the phase integral, using the definition of angular momentum

.

For a circular motion, the Coulomb attraction between the electron and the nucleus should be balanced by the centrifugal force of the electron:

where e is the charge of an electron and ε₀ is the permittivity of vacuum. Combining Eqs. (1.3) and (1.4), we can obtain the velocity of the electron.

Thus, the velocity of the electron in a stable orbit is quantized and the corresponding energy is also quantized as

By the time Bohr proposed his model, it was well established that light is emitted as an energy quantum (E = hf) called the photon, and he postulated that a photon is emitted when an electron jumps from one stable orbit (with higher energy E_n2) to another (with lower energy En₁).

Now this equation is the same as Eq. (1.1) and the atomic spectrum is explained finally.

There was one major deficiency in Bohr’s theory, however, since he could not provide any reason why the angular momentum should be quantized....

Table of contents

• Cover
• Title Page
• Copyright Page
• Contents
• Preface
• 1 Quantum Mechanics for Nanoelectronic Devices
• 2 Electron Transport and Device Physics
• 3 MOS Structure and CMOS Devices
• 4 Quantum Well Devices
• 5 Quantum Wire Devices
• 6 Quantum Dot Devices
• 7 MOSFET as a Molecular Sensor
• Appendix I Physical Constants
• Appendix II Dirac Delta Function
• Appendix III Gamma Function
• Appendix IV Effective Mass Matrix
• Appendix V Density-Of-States (DOS) and Conductivity Effective Masses
• Index
• Color Insert