Chapter 1: Background on Microelectronics

Published:2021
"Background on Microelectronics", Magnetic Field Effects on Quantum Wells, Sujaul Chowdhury, Chowdhury Shadman Awsaf, Ponkog Kumar Das
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This chapter is titled “Background on Microelectronics.” Material processing, mainly semiconductor and metal, and related physics to fabricate (make) nanostructures and electronic devices, such as transistors, are the subject matter of microelectronics. Before proceeding with nanostructure physics, it is imperative to get acquainted with some basics of microelectronics. This chapter introduces readers to the basics and some essentials of microelectronics. Topics covered are intrinsic, elemental, binary, ternary, and quaternary semiconductors; bandgap engineering; and semiconductor heterojunctions and heterostructures.
1.1 Introduction
Material processing, mainly semiconductor and metal, and related physics to fabricate (make) nanostructures and electronic devices, such as transistors, are the subject matter of microelectronics. As such, before proceeding with nanostructure physics in Chap. 2, it is imperative to get acquainted with some basics of microelectronics in this chapter. This chapter begins with elemental, binary, ternary, and quaternary semiconductors, then concludes with a discussion on bandgap engineering, semiconductor heterojunctions and heterostructures, and the idea of effective mass. For a coherent text on microelectronics, see Chowdhury (2014).
1.2 Intrinsic Semiconductors
The energy bands of intrinsic semiconductors are broad and the gaps are narrow. For intrinsic semiconductors, Fermi energy is given by
at 0 K. At 0 K, the valence band (VB) is completely filled, and the conduction band (CB) is completely empty. Above 0 K, the VB is partially empty, and the CB is partially filled. See Fig. 1.1. Appreciable electrical conduction is then possible by electrons in the CB and by holes in the VB. The conduction increases with increasing temperature. Above 0 K, the Fermi energy is given by
So $EF\u2248Eg2$ and rises above $Eg2$ as the temperature is raised.
For semiconductors (intrinsic or extrinsic), electron concentration in the CB is given by
or
n_{e} ∼ 10^{10}/cm^{3} for intrinsic Si crystal at 300 K. There are ∼10^{22} atoms/cm^{3} in Si crystal.
The hole concentration in the VB is given by
or
Equations (1.3) to (1.6) hold if E_{c} − E_{F} ≫ k_{B}T and E_{F} − E_{v} ≫ k_{B}T, or, taken together, E_{g} ≫ k_{B}T. At 300 K, k_{B}T ≈ 25 meV. E_{g} = 1.12 eV for Si and 0.66 eV for Ge. So E_{g} ≫ k_{B}T for both Si and Ge.
1.3 Semiconductors: Elemental and Binary
The most widely used elemental semiconductors are Si and Ge. Their notable properties (at 300 K) are given in Table 1.1.
Property .  Si .  Ge . 

Energy gap (eV)  1.12  0.66 
Electron mobility (cm^{2}V^{−1}s^{−1})  1500  3900 
Hole mobility (cm^{2}V^{−1}s^{−1})  450  1900 
Transition  Indirect  Indirect 
Lattice structure  Diamond  Diamond 
Lattice constant (Å)  5.43  5.66 
Dielectric constant  11.9  16.2 
Density (gm/cm^{3})  2.33  5.32 
Melting point (°C)  1415  936 
Property .  Si .  Ge . 

Energy gap (eV)  1.12  0.66 
Electron mobility (cm^{2}V^{−1}s^{−1})  1500  3900 
Hole mobility (cm^{2}V^{−1}s^{−1})  450  1900 
Transition  Indirect  Indirect 
Lattice structure  Diamond  Diamond 
Lattice constant (Å)  5.43  5.66 
Dielectric constant  11.9  16.2 
Density (gm/cm^{3})  2.33  5.32 
Melting point (°C)  1415  936 
Si and Ge have some important drawbacks:
Energy gaps are indirect.
Energy gaps are small.
Si, considered by many as a universal semiconductor material, cannot perform many important functions. It was natural to turn to other materials, notably compound semiconductor materials, which offer many desired properties and can be synthesized without much difficulty.
Compound semiconductors are made from elements of different columns of the periodic table. Examples are III–V and II–VI compounds. Group III–V compounds are most widely used. Table 1.2 shows a list of elements of group III and V of the periodic table generally used to obtain III–V compound semiconductors.
Group III elements .  Group V elements . 

B  N 
Al  P 
Ga  As 
In  Sb 
Te  Bi 
Group III elements .  Group V elements . 

B  N 
Al  P 
Ga  As 
In  Sb 
Te  Bi 
Examples of III–V compound semiconductors are GaAs and InP. InSb was the first III–V compound semiconductor discovered in 1950. Compound semiconductors have some particular features that attracted interest:
Ease with which these can be synthesized.
High mobility of electrons.
Compared to Si and Ge, GaAs and InP have a high mobility of electrons and a high velocity of electrons. These properties are extremely important for development of highspeed electronic devices. Their (GaAs and InP) bandgaps are direct, which is also useful. Table 1.3 provides a comparison of properties of elemental and binary semiconductors (at 300 K).
Property .  Si .  GaAs .  InP . 

Energy gap (eV)  1.12  1.42  1.34 
Electron mobility (cm^{2}V^{−1}s^{−1})  1500  9000  5000 
Hole mobility (cm^{2}V^{−1}s^{−1})  450  400  100 
Transition  Indirect  Direct  Direct 
Lattice structure  Diamond  Zinc blende  Zinc blende 
Lattice constant (Å)  5.43  5.65  5.87 
Dielectric constant  11.9  13.2  12.6 
Atoms/cm^{3}  5 × 10^{22}  4.42 × 10^{22}  − 
Density (gm/cm^{3})  2.33  5.32  4.8 
Atomic weight  28  144  145 
Melting point (°C)  1415  1238  − 
Breakdown field (V/cm)  ≈3 × 10^{5}  ≈4 × 10^{5}  − 
Effective mass of electron (m*/m_{e})  −  0.067  0.077 
Intrinsic carrier concentration (cm^{−3})  1.45 × 10^{10}  1.8 × 10^{6}  10^{6} 
Intrinsic resistivity (Ωcm)  2.3 × 10^{5}  10^{8}  − 
Property .  Si .  GaAs .  InP . 

Energy gap (eV)  1.12  1.42  1.34 
Electron mobility (cm^{2}V^{−1}s^{−1})  1500  9000  5000 
Hole mobility (cm^{2}V^{−1}s^{−1})  450  400  100 
Transition  Indirect  Direct  Direct 
Lattice structure  Diamond  Zinc blende  Zinc blende 
Lattice constant (Å)  5.43  5.65  5.87 
Dielectric constant  11.9  13.2  12.6 
Atoms/cm^{3}  5 × 10^{22}  4.42 × 10^{22}  − 
Density (gm/cm^{3})  2.33  5.32  4.8 
Atomic weight  28  144  145 
Melting point (°C)  1415  1238  − 
Breakdown field (V/cm)  ≈3 × 10^{5}  ≈4 × 10^{5}  − 
Effective mass of electron (m*/m_{e})  −  0.067  0.077 
Intrinsic carrier concentration (cm^{−3})  1.45 × 10^{10}  1.8 × 10^{6}  10^{6} 
Intrinsic resistivity (Ωcm)  2.3 × 10^{5}  10^{8}  − 
1.4 Alloy Semiconductors (Ternary and Quaternary)
An attractive feature of binary compounds is that they can be combined or alloyed to form ternary or quaternary compounds, or mixedcrystal or alloy semiconductors. The “solid solution” of binary compounds can form ternary or quaternary alloys. For example, a ternary III–V semiconductor A_{x}B_{1−x}C is made of binary compounds AC and BC in a solid solution.
A_{x}B_{1−x}C consists of 100x atoms of element A and 100(1 − x) atoms of element B randomly distributed in every 100 sites of group III sublattice. Atoms of element C occupy all sites of group V sublattice. x can be varied continuously between 0 and 1.
A typical example is Al_{x}Ga_{1−x}As, a ternary alloy semiconductor of great technological importance. In Al_{x}Ga_{1−x}As, atoms of Al and Ga are randomly distributed in a group III sublattice, and atoms of As occupy all sites of the group V sublattice.
Another form of ternary alloy is AB_{1−y}C_{y}, where all group III sublattice sites are occupied by atoms of element A, and sites of group V are randomly occupied by atoms of element B and C. An example of this type of ternary compound is GaAs_{1−x}P_{x}, which is also technologically important and made of GaAs and GaP in a solid solution.
In a similar manner, quaternary alloy semiconductors are formed by mixing atoms of four different elements. Such a compound can consist of atoms of two group III elements A and B randomly distributed in group III sublattice sites and atoms of two group V elements C and D randomly distributed in group V sublattice sites to give the compound A_{x}B_{1−x}C_{y}D_{1−y}. An example is In_{x}Ga_{1−x}As_{y}P_{1−y}.
If atoms of three group III elements A, B, C randomly occupy group III sublattice sites and atoms of only one group V element are present in group V sublattice sites, a quaternary compound A_{x}B_{y}C_{z}D is formed. The composition is more conveniently expressed as (A_{x}B_{1−x})_{y}C_{1−y}D, where x and y can be varied from 0 to 1. An example is (In_{x}Ga_{1−x})_{y}Al_{1−y}As or In_{x}Ga_{y}Al_{z}As.
Alloy semiconductors are formed by mixing in group III sublattice or group V sublattice or both. But mixing in group V sublattice with accurate control of alloy composition is more difficult to achieve than mixing in group III sublattice.
1.5 Bandgap Engineering
Ternary alloy semiconductors are made of two binary semiconductors. Alloy semiconductors lie on the lines joining binary compounds (see Fig. 1.2). For example, In_{x}Ga_{1−x}As lies on the tie line between InAs and GaAs.
By choosing different binary compounds, it is possible to get ternary compounds of desired bandgaps.
By alloying, it is possible to vary the bandgap continuously and monotonically by varying the composition. As an example, the bandgap of the ternary alloy Al_{x}Ga_{1−x}As (0 ≤ x ≤ 1) depends on x. The (minimum) bandgap can be varied continuously from 1.43 eV (GaAs, x = 0) to 2.17 eV (AlAs, x = 1); see Eqs. (1.8) and (1.9). (See Fig. 1.3.) Among the common ternary and quaternary alloys, properties of Al_{x}Ga_{1−x}As have been most thoroughly investigated. See Fig. 1.4 for the case with In_{x}Ga_{1−x}As.
An empirical relation usually gives bandgap E_{g} for the ternary alloy A_{x}B_{1−x}C semiconductor as a function of x:
where E_{g}_{0} is the bandgap of BC, the lower bandgap binary; E_{g}_{0} + b + c is the bandgap of AC, the upper bandgap binary; b is a fitting parameter; and c is called the bowing parameter, which may be calculated theoretically or determined experimentally.
Variation of direct and indirect bandgaps of Al_{x}Ga_{1−x}As with the composition are approximately given (in eV) by
1.6 Semiconductor Heterojunctions and Heterostructures
A semiconductor heterojunction is a junction of two different semiconductors of unequal bandgap, and this combination of semiconductors is called a heterostructure. See Fig. 1.5. Figure 1.6 shows a band model of the (undoped) GaAs–AlGaAs heterostructure having an abrupt (sharp) junction. The discontinuity in the valence band edge ΔE_{v} and in the conduction band edge ΔE_{c} are not equal.
1.7 Effective Mass
The velocity of an electron (in a periodic potential) is defined as the group velocity of the associated matter wave packet:
Otherwise, the electron will soon be at a location where there is no matter wave. Here, E is the energy of the electron, and k is the momentum of the electron in the unit of $\u210f$. If we have E as a function of k, we can find the velocity as a function of k using Eq. (1.11).
Newton's law gives
or
Using Eq. (1.11), we can write $dvdt=a=1\u210fddt(dEdk)$ for acceleration.
Thus,
Effective mass m* is the ratio of the force F and the acceleration a. Hence,
or
Equation (1.14) is used to calculate the effective mass of an electron in a periodic potential. If we have E as a function of k, we can find the effective mass m* as a function of k using Eq. (1.14). This value of m* depends on the value of k. Usually, we use values of m* for values of k at the extrema of the E vs k curve, because carriers usually reside there. Electrons reside at the minimum of the E vs k curve for the conduction band to stay at lower energy.