Understanding the Electric Structure of Atoms

At one time, the atom was believed to be the smallest particle in the subdivision of matter; later, it has been found that the atom is made up of even smaller units. Currently, it is possible to subdivide the atom and explore its internal structure.

This article explores the atom’s general structure to develop a concept regarding the factors that govern the semiconductor’s electrical properties.

 

The Nuclear Model of the Atom

Lord Ernest Rutherford (1871 – 1937) started the experimental quest for the atom’s fine structure with scattering experiments. Joseph John “J.J.” Thomson (1856 – 1940) assumed negative and positive particles mixed uniformly throughout the atom’s volume.

During the period 1911 – 1913, experiments performed by Hans Geiger (1882 – 1945) and Ernest Marsden (1889 – 1970), under Rutherford’s direction, exposed that an atom is built of a positive nucleus – carrying practically all its mass – and negatively charged particles – electrons – circling the nucleus, resembling our planetary system. These experiments were the foundation for the nuclear model of the atom.

In 1913, Niels Bohr (1885 – 1962, Nobel laureate 1922) fused Rutherford’s model with Max Planck’s (1858 – 1947) quantum concept getting the first quantitative atomic model: The electrons orbit the nucleus at quantized distances. Electron’s orbital changes cause absorption and emission of radiation.

In 1932, James Chadwick (1891 – 1974, Nobel laureate 1935) discovered the neutron, another component of the atom. In the same year, Werner Heisenberg (1901 – 1976) and Dmitri Ivanenko (1904 – 1994) assumed an atomic nucleus built out of neutrons and protons.

Further theoretical developments led by Heisenberg, Erwin Schrödinger (1887 – 1961, Nobel laureate 1933), and Max Born (1882 – 1970, Nobel laureate 1954) refined the model.

 

The Bohr Model

Bohr’s atom model places an orderly arrangement of electrons in orbits around a nucleus of protons and neutrons. The theories developed from this model agreed well with experimental evidence during the early part of the 20th century. However, as the measuring instruments and techniques improved, it became evident that discrepancies existed between predicted and actual behavior.

The substantial support showing that light has a dual nature — it sometimes behaves like a particle and sometimes like a wave — and that the electrons in motion also have the properties of a wave, led to the development of a wave theory for all matter. This wave mechanics removes some inconsistencies inherent in the Bohr model.

The theory of quantum mechanics considers other principles used to analyze electron motion. One feature is the impossibility of defining electron orbits precisely, but regions where it is more likely to find the electron. This principle replaces the solid charged satellites of the Bohr model with probability densities dependent on boundary conditions.

Although the probabilistic quantum-mechanical theory has replaced Bohr’s model, the concepts of energy quantization and angular momentum quantization as applied to atomic-sized systems are successfully explained by Bohr’s model.

The number of protons in the nucleus of one atom of a chemical element is the atomic number designated by Z.

Since the atom appears neutral when observed from the outside, it must contain equal numbers of protons and electrons, with identical charges.

Figure 1 shows the Bohr model diagrams of some atoms of interest. The simplest atom is hydrogen which has one electron and one proton (Z = 1). 

Figure 1. Bohr model diagrams.

 

The Properties of an Electron

The electron is a fundamental particle in all models of the atomic structure thus far developed.

The electron’s properties are essential to electrical and electronic engineers. The electron’s behavior can be precisely predicted and controlled because it obeys specific basic laws. Indeed, man’s ability to predict and control the electron’s movements supports electricity and electronics’ fundamental science.

Certain electron’s properties are well known. Its rest mass me = 9.11 ✕ 10ˉ³¹ kg and the charge q = 1.60 ✕ 10ˉ¹⁹ C (computational rounded figures).

Other properties are somewhat inconsistent. It acts as a tiny particle in some experiments and as waves in others. The nature of the investigation decides which property will be more prominent.

There are two models of the electron used in semiconductor electronics: the classical and quantum-mechanical models. They diverge mainly in the way to predict electronic motion. The classical model is inaccurate but gives acceptable approximations to actual behavior in many cases. The quantum-mechanical model provides a precise representation of electronic behavior in any physical situation.

When studying the electrical characteristics of most semiconductor devices, an adjusted classical model is adequate. The quantum-mechanical model helps to understand the modified classical model’s basis and provides a physical foundation to comprehend the semiconductors’ structure.

 

The Electron Energy

There is plenty of experimental evidence indicating that the electron energy in an atom can have only discrete values E1,E2,E3,…,En,… – i.e., the energy of the electronic motion is quantized. This concept indicates that electrons travel only in orbits allowed by the laws of quantum mechanics.

The atom can be stable only when the electrons have these discrete energy levels. While in these energy levels, the electron does not emit radiation, and it is in a stationary or non radiating state.

The energy differences between the allowed levels designate the amounts of energy – or size of energy packets – that the atom can absorb or radiate. Absorption or emission of energy by an electron means that it jumps from one orbit into another one.

Max Planck, in 1900, showed that the relationship between the discrete energy packet and the frequency of the electromagnetic wave, either absorbed or radiated, is

E=h∙f

where

h = Planck’s constant = 6.62607 ∙10ˉ³⁴ J∙s

f = frequency of the electromagnetic wave

E = discrete energy packet

 

Unfortunately, the electron’s discovery happened after Planck’s findings, so he did not know at the time that the energy packets were the difference of permissible electron energy levels – the exchanged energy during the jump.

E = Ei - Ef

where

Ei = electron energy at initial orbit

Ef = electron energy at final orbit

Energy is absorbed if /Ef/>/Ei/ and emitted if /Ef/

 

About the Electronic Structure of Atoms

The electrons orbit the nucleus under the influence of electrostatic forces.

An atom has an equal number of protons and electrons, making it electrically neutral. The atomic number Z is the number of protons in the nucleus.

The electron models employed in semiconductor electronics are the classical model and the quantum-mechanical model.

The classical model gives satisfactory approximations to actual behavior.

Quantum theory postulates that electrons travel in allowable orbits – each electron’s kinetic energy is quantized. Therefore, electrons only emit or absorb discrete amounts of energy E = h ∙f = Ei - Ef

Electrons can make quantum jumps between their quantized energies, exchanging an energy amount h ∙ f when they jump between the initial orbit Ei and the final orbit Ef. This equation allows us to calculate the light’s frequency when a jump involves the absorption or emission of a photon.