Chapter 2
Bonds
Protons give an atom its identity, electrons its personality.
B. Bryson [168]
Abstract A little bit of solid state physics... The schemes of covalent, ionic and mixed bonds are
explained which are the basis for the atomic arrangement and crystal structures of semiconductors.
2.1 Introduction
The positively charged atomic nuclei and the electrons in the atomic shells of the atoms making up
the semiconductor (or any other solid) are in a binding state. Several mechanisms can lead to such
cohesiveness. First, we will discuss the homopolar, electron-pair or covalent bond, then the ionic bond
and subsequently the mixed bond. We will only briefly touch on the metallic bond and the van-der-Waals
bond. A classical book on bonds in semiconductors is [169, 170].
2.2 Covalent Bonds
Covalent bonds are formed due to quantum-mechanical forces. The prototype covalent bond is the
bonding of the hydrogen molecule due to overlapping of the atomic shells. If several electron pairs are
involved, directional bonds can be formed in various spatial directions, eventually making up a solid.
2.2.1 Electron-Pair Bond
The covalent bond of two hydrogen atoms in a H 2 molecule can lead to a reduction of the total energy
of the system, compared to two single (distant) atoms (Fig. 2.1). For fermions (electrons have spin
1/2) the two-particle wavefunction of the two (indistinguishable) electrons A and B must be antisymmetric, i.e. (A, B) = −(B, A) (Pauli principle). The wavefunction of each electron has degrees
of freedom in real space (r) and spin (σ ), (A) = r (A) ) σ (A). The two-particle wavefunction
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_2
21
Bonds
Protons give an atom its identity, electrons its personality.
B. Bryson [168]
Abstract A little bit of solid state physics... The schemes of covalent, ionic and mixed bonds are
explained which are the basis for the atomic arrangement and crystal structures of semiconductors.
2.1 Introduction
The positively charged atomic nuclei and the electrons in the atomic shells of the atoms making up
the semiconductor (or any other solid) are in a binding state. Several mechanisms can lead to such
cohesiveness. First, we will discuss the homopolar, electron-pair or covalent bond, then the ionic bond
and subsequently the mixed bond. We will only briefly touch on the metallic bond and the van-der-Waals
bond. A classical book on bonds in semiconductors is [169, 170].
2.2 Covalent Bonds
Covalent bonds are formed due to quantum-mechanical forces. The prototype covalent bond is the
bonding of the hydrogen molecule due to overlapping of the atomic shells. If several electron pairs are
involved, directional bonds can be formed in various spatial directions, eventually making up a solid.
2.2.1 Electron-Pair Bond
The covalent bond of two hydrogen atoms in a H 2 molecule can lead to a reduction of the total energy
of the system, compared to two single (distant) atoms (Fig. 2.1). For fermions (electrons have spin
1/2) the two-particle wavefunction of the two (indistinguishable) electrons A and B must be antisymmetric, i.e. (A, B) = −(B, A) (Pauli principle). The wavefunction of each electron has degrees
of freedom in real space (r) and spin (σ ), (A) = r (A) ) σ (A). The two-particle wavefunction
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_2
21