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Semiconductor Physics

1.1 Introduction

The definition of semiconductors is somewhat broad. For instance, semiconductors may be defined as materials possessing a bandgap (a fundamental concept to be explained later, signifying the minimum electronic excitation energy) ranging between 0 and 4 eV. Materials characterized by a zero bandgap are classified as metals or semimetals, whereas those featuring energy gaps exceeding 4 eV are termed insulators. Alternatively, semiconductors can be defined by their electrical conductivity, which lies between that of conductors and insulators, typically within the range of approximately 10-2-109 O cm. Unlike metals, the conductivity of semiconductors generally increases with elevated temperature. However, these definitions are not absolute. The conductivity of semiconductors, for example, can be drastically modified via doping-a technique involving the deliberate introduction of specific foreign atoms into the semiconductor lattice to modulate its conductive properties. Consequently, crystalline diamond, exhibiting a bandgap near 6 eV and typically considered an insulator, can be engineered into a functional semiconductor suitable for potential power electronic devices.

Common examples of semiconductors include silicon, germanium, and gallium arsenide, among others. Undoubtedly, silicon remains the most extensively studied and widely recognized semiconductor. It serves as the primary functional material in numerous electronic applications, including solar cells, analog circuits, and large-scale integrated circuits. The prominence of silicon stems from several key factors: its natural abundance, moderate energy bandgap, established doping techniques, and the exceptional stability of both silicon and its native oxide, silicon dioxide. Semiconductor properties critically depend on their chemical compositions and crystal structures, which fundamentally govern respective band structures, doping characteristics, and carrier transport mechanisms. As silicon-based electronic devices approach material performance limits while semiconductor markets demand enhanced device performance, research focus increasingly shifts toward alternative materials such as wide-bandgap semiconductors and oxide semiconductors. The fundamental physics of these semiconductors is comprehensively addressed within this chapter.

1.2 Properties of Semiconductors

The importance of semiconductors in electronics stems from their unique physical properties, determined by their atomic structure and governed by the physics of semiconductor materials. An intrinsic semiconductor exhibits very low conductivity. However, introducing a relatively small concentration of impurity atoms, known as doping, enables modulation of the material's conductivity over a large dynamic range. Crucially, depending on the type of dopant employed-such as phosphorus or boron in silicon-semiconductors are categorized as n-type or p-type, dictating whether electrical current conduction is mediated primarily by electrons or holes, respectively. Moreover, semiconductor conductivity can be significantly modulated by applied electric fields. Collectively, these properties render semiconductor materials exceptionally valuable for constructing electronic devices, enabling the realization of critical functionalities including unidirectional current flow, variable resistance, variable capacitance, photosensitivity, voltage-controlled conductivity, signal amplification, switching operations, and energy conversion.

1.2.1 Atomic Bonding of Semiconductors

The properties of semiconductors are predominantly governed by their chemical compositions and structures, which, in accordance with semiconductor physics, subsequently dictate their overall characteristics. Generally, atomic bonds can be classified into ionic, covalent, metallic, van der Waals, and hydrogen bonding, as illustrated in Figure 1.1, contingent upon electron transfers and the charge states of the constituent atoms. Certain atoms exhibit a strong proclivity to attain a completed outer electron shell by either gaining or losing a limited number of valence electrons, thereby forming charged ions. Ionic bonding-exemplified by the NaCl crystal structure shown in Figure 1.1a-arises from Coulombic attraction between positively and negatively charged ions. Ionic bonding also plays a significant role within semiconductors. For instance, in perovskite CsPbBr3, ionic bonding occurs between Cs+ ions and the surrounding PbBr3- network, while it has been established that the bonding character between Pb and Br is metavalent, intermediate between covalent and metallic [1].

Figure 1.1 (a) Schematic of NaCl crystal with ionic bonding. (b) Schematic of Si crystal with covalent bonding. (c) Schematic of GaAs crystal with covalent bonding. (d) Hydrogen bonding between water molecules. (e) Pentacene and (f) MoS2 with van der Waals bonding.

Covalent bonding is formed through the sharing of electrons between atoms, rather than through the gain or loss of electrons. The shared electrons create a bond that holds the atoms together. This bonding mechanism is essential for many important elemental and compound semiconductors (Figure 1.1b,c). Examples of elemental semiconductors involving covalent bonding include silicon (Si), germanium (Ge), and semiconducting single-walled carbon nanotubes (SWCNTs). In compound semiconductors, covalent bonding produces numerous critical materials. For instance, III-V semiconductors result from covalent bonding between Group III and Group V elements, such as gallium nitride (GaN), gallium phosphide (GaP), gallium arsenide (GaAs), and indium phosphide (InP). Similarly, II-VI semiconductors are formed by covalent bonding between Group II and Group VI elements, including zinc oxide (ZnO), zinc sulfide (ZnS), mercury telluride (HgTe), and cadmium telluride (CdTe). The bonding in these semiconductors typically exhibits a coordination number of 4, meaning each atom has four nearest neighbors, forming a tetrahedral structure.

When all atoms release their valence electrons, metallic bonding is formed, with the free electron fluid acting as the bonding agent. Although typically characteristic of metals, metallic bonding can also contribute to the lattice mechanical strength of semiconductors with a very high density of free carriers. Hydrogen bonding resembles ionic bonding and results from the attraction between a positively charged proton involved in a covalent bond and a nearby negatively charged atom (Figure 1.1d). This bonding type is highly localized due to the small size of the proton.

For atoms or molecules characterized by saturated covalent bonds, bonding can still arise via van der Waals interactions, including permanent dipole-dipole attractions and induced dipole interactions (Figure 1.1e,f). Many organic semiconductors, such as pentacene and polyacetylene, whose constituent building blocks are organic molecules, are primarily held together by van der Waals forces [2]. van der Waals forces are also responsible for the stacking of two-dimensional materials, such as transition metal dichalcogenides [3].

1.2.2 External Modulation Effects

Semiconductors possess a medium-sized bandgap, distinguishing them from metals and insulators. A precise understanding of the bandgap concept necessitates quantum physics, which describes electron motion within a crystal lattice. Broadly defined, the bandgap represents the minimum energy required for electronic excitation. Due to the presence of this bandgap, the intrinsic conductivity of a pure semiconductor is markedly low, as the excitation of free carriers necessitates overcoming the bandgap energy. This energy is typically substantial relative to thermal fluctuation energy at room temperature. Nevertheless, the conductivity of semiconductors can be profoundly modulated through the controlled introduction of foreign impurity atoms, known as dopants. Dopants significantly enhance the concentration of free charge carriers within the crystal lattice. Semiconductors accommodate two types of charge carriers, namely electrons and holes; doping processes associated with generating these carriers are designated as n-type and p-type, respectively. This versatility in controlling carrier type and concentration enables the fabrication of diverse semiconductor junctions. These junctions form the foundation for realizing electronic devices exhibiting specific functionalities, such as the rectifying properties characteristic of a PN junction.

Besides doping, the properties of semiconductors, particularly their electrical conductivity, can be modulated by various external forces, including temperature, applied voltage, magnetic field, light, mechanical stress, and chemical adsorption. These factors enhance the capability of semiconductors to serve as functional devices, as demonstrated in Figure 1.2. For example, numerous semiconductor properties can be significantly influenced by temperature. Elevated temperatures lead to lattice expansion, typically reducing the bandgap. Furthermore, high temperatures facilitate intrinsic carrier excitation and dopant activation, while diminishing the effect of Coulomb scattering. Consequently, semiconductors generally exhibit increased conductivity at heightened temperatures. However, excessively high temperatures induce more pronounced lattice oscillations, manifesting as heightened phonon excitation; this scatters carriers, reducing carrier mobility...