Chapter 1: Background on Microelectronics
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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 and rises above as the temperature is raised.
For semiconductors (intrinsic or extrinsic), electron concentration in the CB is given by
or
ne ∼ 1010/cm3 for intrinsic Si crystal at 300 K. There are ∼1022 atoms/cm3 in Si crystal.
The hole concentration in the VB is given by
or
Equations (1.3) to (1.6) hold if Ec − EF ≫ kBT and EF − Ev ≫ kBT, or, taken together, Eg ≫ kBT. At 300 K, kBT ≈ 25 meV. Eg = 1.12 eV for Si and 0.66 eV for Ge. So Eg ≫ kBT 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 (cm2V−1s−1) | 1500 | 3900 |
Hole mobility (cm2V−1s−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/cm3) | 2.33 | 5.32 |
Melting point (°C) | 1415 | 936 |
Property . | Si . | Ge . |
---|---|---|
Energy gap (eV) | 1.12 | 0.66 |
Electron mobility (cm2V−1s−1) | 1500 | 3900 |
Hole mobility (cm2V−1s−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/cm3) | 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 high-speed 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 (cm2V−1s−1) | 1500 | 9000 | 5000 |
Hole mobility (cm2V−1s−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/cm3 | 5 × 1022 | 4.42 × 1022 | − |
Density (gm/cm3) | 2.33 | 5.32 | 4.8 |
Atomic weight | 28 | 144 | 145 |
Melting point (°C) | 1415 | 1238 | − |
Breakdown field (V/cm) | ≈3 × 105 | ≈4 × 105 | − |
Effective mass of electron (m*/me) | − | 0.067 | 0.077 |
Intrinsic carrier concentration (cm−3) | 1.45 × 1010 | 1.8 × 106 | 106 |
Intrinsic resistivity (Ω-cm) | 2.3 × 105 | 108 | − |
Property . | Si . | GaAs . | InP . |
---|---|---|---|
Energy gap (eV) | 1.12 | 1.42 | 1.34 |
Electron mobility (cm2V−1s−1) | 1500 | 9000 | 5000 |
Hole mobility (cm2V−1s−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/cm3 | 5 × 1022 | 4.42 × 1022 | − |
Density (gm/cm3) | 2.33 | 5.32 | 4.8 |
Atomic weight | 28 | 144 | 145 |
Melting point (°C) | 1415 | 1238 | − |
Breakdown field (V/cm) | ≈3 × 105 | ≈4 × 105 | − |
Effective mass of electron (m*/me) | − | 0.067 | 0.077 |
Intrinsic carrier concentration (cm−3) | 1.45 × 1010 | 1.8 × 106 | 106 |
Intrinsic resistivity (Ω-cm) | 2.3 × 105 | 108 | − |
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 mixed-crystal or alloy semiconductors. The “solid solution” of binary compounds can form ternary or quaternary alloys. For example, a ternary III–V semiconductor AxB1−xC is made of binary compounds AC and BC in a solid solution.
AxB1−xC 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 AlxGa1−xAs, a ternary alloy semiconductor of great technological importance. In AlxGa1−xAs, 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 AB1−yCy, 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 GaAs1−xPx, 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 AxB1−xCyD1−y. An example is InxGa1−xAsyP1−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 AxByCzD is formed. The composition is more conveniently expressed as (AxB1−x)yC1−yD, where x and y can be varied from 0 to 1. An example is (InxGa1−x)yAl1−yAs or InxGayAlzAs.
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, InxGa1−xAs 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 AlxGa1−xAs (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 AlxGa1−xAs have been most thoroughly investigated. See Fig. 1.4 for the case with InxGa1−xAs.
An empirical relation usually gives bandgap Eg for the ternary alloy AxB1−xC semiconductor as a function of x:
where Eg0 is the bandgap of BC, the lower bandgap binary; Eg0 + 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 AlxGa1−xAs 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 ΔEv and in the conduction band edge ΔEc 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 . 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 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.