Semiconductor Crystal Structure and Fundamentals

Course Curriculum and Thematic Scope

• The study of semiconductor physics encompasses ten foundational subject areas:

  • Semiconductor crystal structure

  • Semiconductor band structure

  • Bandgap engineering

  • Manufacturing of semiconductors

  • Carrier distributions in semiconductors

  • Electrical properties of semiconductors

  • Recombination processes in semiconductors

  • Absorption of light in semiconductors

  • The $pn$-junction

  • Semiconductor devices

Fundamental Properties and Taxonomy of Semiconductors

• Dual Charge Carrier Mechanisms:

  • Unlike metals, which conduct current exclusively via electrons, semiconductors possess two distinct classes of mobile charge carriers:

  • Negative charge carriers: conduction-band electrons ($e^-$).

  • Positive charge carriers: valence-band vacancies termed holes ($h^+$).

• Chemical Doping and Carrier Concentration Control:

  • Introducing extrinsic impurity atoms (dopants) into an intrinsic crystal lattice modulates and increases the concentration of specific carrier types by orders of magnitude:

  • $n$-type (or $n$-doped) semiconductors: contain donor impurities yielding a majority carrier population of electrons.

  • $p$-type (or $p$-doped) semiconductors: contain acceptor impurities yielding a majority carrier population of holes.

• Structural and Chemical Classes of Semiconductor Materials:

  • Elemental semiconductors: Group IV elements of the periodic table, specifically silicon ($Si$) and germanium ($Ge$).

  • Compound semiconductors:

  • III-V binary compounds: formed between Group 13 and Group 15 elements, including gallium nitride ($GaN$), gallium arsenide ($GaAs$), aluminum nitride ($AlN$), and indium antimonide ($InSb$).

  • II-VI binary compounds: formed between Group 12 and Group 16 elements, including cadmium sulfide ($CdS$), zinc oxide ($ZnO$), and mercury telluride ($HgTe$).

  • I-III-VI$_2$ chalcopyrite compounds: such as copper indium diselenide ($CuInSe_2$).

  • Alloy semiconductors (solid solutions):

  • Group IV alloys: binary mixtures such as $Si_xGe_{1-x}$.

  • Group III-V ternary alloys: such as $Ga_xIn_{1-x}N$.

  • Group III-V quaternary alloys: such as $Ga_xIn_{1-x}As_yP_{1-y}$.

• Commercial, Economic, and Technological Considerations:

  • Silicon ($Si$) dominance in microelectronics:

  • Economic advantage: standard $8\text{-inch}$ ($8''$) silicon wafers cost approximately $40\,€$, whereas $2\text{-inch}$ ($2''$) compound semiconductor wafers ($GaAs$ or $InP$) cost approximately $200\,€$.

  • Material perfection: high crystalline purity and atomic flatness are achievable on large wafer diameters.

  • Fabrication maturity: supported by an advanced manufacturing and lithographic infrastructure.

  • High-speed electronics (operating at high frequencies up to $600\,\text{GHz}$):

  • Dominated by materials exhibiting high carrier mobilities, specifically $GaAs$, $InP$, and $SiGe$, alongside emerging $GaN$ technologies.

  • High-voltage power applications:

  • Dominated by wide-bandgap semiconductors with high breakdown fields, primarily gallium nitride ($GaN$) and silicon carbide ($SiC$).

  • Optoelectronic systems (lasers, LEDs, photodetectors):

  • Compound semiconductors such as $GaAs$, $InP$, and $GaN$ are utilized due to their direct electronic bandgaps, which allow efficient radiative recombination.

Electronic Shell Structures and Valence Configurations

• Aufbau Orbital Filling Sequence:

  • Electrons fill atomic subshells according to increasing energy levels in the standard progression:     $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p$

  • Subshell electron capacities governed by the Pauli exclusion principle:

  • $s$-orbital: maximum of $2$ electrons.

  • $p$-orbital: maximum of $6$ electrons.

  • $d$-orbital: maximum of $10$ electrons.

  • $f$-orbital: maximum of $14$ electrons.

• Electronic Configurations of Key Semiconductor Elements:

  • Silicon ($Si$, atomic number $Z = 14$):

  • Electron configuration: $1s^2 2s^2 2p^6 3s^2 3p^2$.

  • Features $4$ valence electrons in the outermost $n=3$ principal shell, leaving $4$ vacancies to achieve octet completion ($3s^2 3p^6$).

  • Gallium ($Ga$, atomic number $Z = 31$):

  • Electron configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^1$.

  • Features $3$ valence electrons in the outermost shell, requiring $5$ electrons to achieve a closed shell configuration.

  • Arsenic ($As$, atomic number $Z = 33$):

  • Electron configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^3$.

  • Features $5$ valence electrons in the outermost shell, requiring $3$ electrons to complete its valence octet.

Interatomic Bonding Mechanisms in Solids

• Primary Classes of Interatomic Chemical Bonds:

  • Ionic bond:

  • Formation mechanism: complete transfer of one or more electrons from an electropositive atom to an electronegative atom, forming opposing ions bound by electrostatic attraction.

  • Physical properties: high melting point, hard and brittle mechanical nature, electrically nonconducting in the solid crystal phase.

  • Examples: sodium chloride ($NaCl$), cesium chloride ($CsCl$), zinc sulfide ($ZnS$).

  • Covalent bond:

  • Formation mechanism: mutual sharing of localized valence electron pairs between neighboring atomic orbitals.

  • Physical properties: very high melting point, high hardness, brittle mechanical behavior, generally nonconducting at low temperatures.

  • Examples: diamond ($C$), crystalline silicon ($Si$), planar sheets of graphite.

  • Metallic bond:

  • Formation mechanism: positively charged ion cores held within a delocalized, collective gas of valence conduction electrons.

  • Physical properties: variable melting points, variable hardness, ductile and malleable mechanical behavior, high electrical and thermal conductivity.

  • Examples: iron ($Fe$), copper ($Cu$), silver ($Ag$).

  • Van der Waals bond:

  • Formation mechanism: weak, non-directional electrostatic attraction resulting from fluctuating or induced electric dipole moments.

  • Physical properties: low melting point, soft and mechanically brittle, electrically nonconducting.

  • Examples: solidified noble gases ($Ne$, $Ar$, $Kr$, $Xe$), interlayer stacking cohesion in graphite.

  • Hydrogen bond:

  • Formation mechanism: dipolar interaction between a covalently bonded hydrogen atom and an adjacent electronegative atom ($O$, $N$, or $F$).

  • Physical properties: low melting point, hard and brittle, generally nonconducting.

  • Examples: solid ice ($H_2O$), molecular organic crystals.

• Covalent Bonding in Elemental and Compound Semiconductors:

  • Covalent network in pure silicon ($Si$):

  • Each silicon atom shares its $4$ outer electrons with $4$ neighboring atoms in a tetrahedral arrangement, saturating the outer valence shell with $8$ shared electrons.

  • In pure, undoped silicon at low temperatures, valence electrons remain localized within these bonding states and cannot participate in electrical conduction, making intrinsic silicon an insulator.

  • Thermal generation or donor/acceptor impurity doping supplies mobile carriers into unbonded states.

  • Covalent network in gallium arsenide ($GaAs$):

  • Alternating Gallium (Group III, $3$ valence electrons) and Arsenic (Group V, $5$ valence electrons) atoms contribute a combined total of $8$ valence electrons per atomic pair.

  • All valence electrons participate in localized interatomic bonds, satisfying tetrahedral bonding coordination.

• Heteropolar Bonding and Fractional Ionic Character:

  • Bonds within semiconductor crystal lattices frequently exhibit a hybrid character between purely covalent and purely ionic states.

  • Quantitative fractional ionic character across semiconductor materials:

  • Group IV-IV materials:

    • Silicon ($Si$): $0.00$

    • Germanium ($Ge$): $0.00$

    • Silicon carbide ($SiC$): $0.18$

  • Group III-V compound materials:

    • Indium phosphide ($InP$): $0.42$

    • Indium arsenide ($InAs$): $0.36$

    • Indium antimonide ($InSb$): $0.32$

    • Gallium arsenide ($GaAs$): $0.31$

    • Gallium antimonide ($GaSb$): $0.26$

  • Group II-VI compound materials (strong ionic component):

    • Zinc oxide ($ZnO$): $0.62$

    • Zinc sulfide ($ZnS$): $0.62$

    • Zinc selenide ($ZnSe$): $0.63$

    • Zinc telluride ($ZnTe$): $0.61$

    • Cadmium oxide ($CdO$): $0.79$

    • Cadmium sulfide ($CdS$): $0.69$

    • Cadmium selenide ($CdSe$): $0.70$

    • Cadmium telluride ($CdTe$): $0.67$

Ordering Regimes in Solid-State Materials

• Degrees of Structural Order in Condensed Matter:

  • Single crystals:

  • Atoms are ordered across the entire volume in a periodic, repeating spatial lattice.

  • Exhibits long-range translational symmetry; the crystal environment is identical when displaced by any integer lattice vector.

  • Macroscopic examples include naturally formed quartz crystals.

  • Polycrystals:

  • Aggregates composed of multiple individual single-crystal grains with random spatial orientations, separated by crystallographic grain boundaries.

  • Periodic ordering exists locally within each distinct grain, but long-range crystallographic orientation is broken at the grain boundaries.

  • Technologically exemplified by multicrystalline silicon solar cell wafers.

  • Quasicrystals:

  • Solids characterized by ordered, deterministic atomic arrangements possessing rotational symmetries (such as 5-fold or 10-fold symmetry) that lack translational invariance.

  • Amorphous solids:

  • Materials devoid of long-range periodic crystal structure.

  • Exhibit short-range atomic coordination (such as fixed bond lengths and nearest-neighbor coordination numbers), but lack long-range spatial periodicity.

  • Technologically exemplified by vitreous silica (amorphous $SiO_2$).

• The Crystalline-Amorphous Semiconductor Heterointerface:

• Transmission electron microscopy (TEM) of the amorphous silicon dioxide ($SiO_2$) on crystalline silicon ($Si$) system demonstrates the structural juxtaposition:

  • The underlying crystalline silicon exhibits periodic lattice fringes with a measured interplanar spacing of $3.14\,\text{\AA}$ along the $[001]$ and $[110]$ crystallographic orientations.

  • The interface plane defines a structural boundary between the single-crystal substrate and the disordered glass overlay.

  • A perturbed interface region (marked by positions A, B, and P) contains localized bond straining, broken bonds, and sub-stoichiometric transition oxide species.

Mathematical Formalism of Crystal Lattices

• Lattice and Basis Composition:

  • A physical crystal structure is constructed by attaching a basis of one or more atoms to each point of an infinite Bravais lattice:     $\text{Crystal Structure} = \text{Bravais Lattice} + \text{Basis}$

  • The basis represents the fundamental assembly of atoms repeated periodically at every lattice site with the symmetry of the underlying Bravais lattice.

  • Invariance under translation: displacing by any real-space lattice translation vector yields an identical atomic environment.

  • Additional spatial symmetries: crystals can display point-group operations including rotation, mirror plane reflection, and spatial inversion.

• Real-Space Translation Vectors and Unit Cells:

  • Conventional unit cell: a repeated spatial region (area in 2D, volume in 3D) that tiles the crystal, selected to highlight the symmetry of the lattice system.

  • Primitive unit cell: the unit cell containing the minimum possible area or volume that tiles space without voids or overlapping regions.

  • Primitive vectors: linearly independent vectors (denoted $\{a, b\}$ in 2D or $\{a, b, c\}$ in 3D) that define the boundaries of the primitive unit cell.

  • General two-dimensional translation vector:     $\mathbf{R} = n\mathbf{a} + m\mathbf{b}, \quad n, m \in \mathbb{Z}$

  • Multiplicity of primitive vector choices: primitive translation vectors are not unique; multiple distinct sets of vectors can enclose the identical minimum primitive area while defining the same physical lattice.

• The Wigner-Seitz Primitive Cell:

• Algorithmic construction sequence:

  • Select an arbitrary lattice point as the origin.

  • Construct line segments connecting this origin point to all adjacent neighboring lattice points.

  • Draw perpendicular bisecting lines (normals in 2D) or planes (in 3D) through the exact midpoints of these line segments.

  • The smallest geometric area or volume enclosing the origin point within these bisecting planes forms the Wigner-Seitz primitive cell.

• Inherent symmetry: the Wigner-Seitz cell displays the full point-group symmetry of the crystal lattice.

Two-Dimensional and Three-Dimensional Bravais Lattices

• The Five 2D Bravais Lattices:

• Square lattice: edge lengths satisfy $|\mathbf{a}_1| = |\mathbf{a}_2|$, with an inter-axis angle of $\phi = 90^\circ$.

• Rectangular lattice: edge lengths satisfy $|\mathbf{a}_1| \neq |\mathbf{a}_2|$, with an inter-axis angle of $\phi = 90^\circ$.

• Centred rectangular lattice: conventional rectangular cell with $|\mathbf{a}_1| \neq |\mathbf{a}_2|$ and $\phi = 90^\circ$, containing an additional lattice point at the center of the rectangle.

• Hexagonal lattice: edge lengths satisfy $|\mathbf{a}_1| = |\mathbf{a}_2|$, with an inter-axis angle of $\phi = 120^\circ$ (or $\phi = 60^\circ$ depending on vector choice).

• Oblique lattice: edge lengths satisfy $|\mathbf{a}_1| \neq |\mathbf{a}_2|$, with an arbitrary inter-axis angle $\phi \neq 90^\circ, 120^\circ$.

  • Three-Dimensional Unit Cell Geometry and Metrics:

• A 3D unit cell forms a parallelepiped defined by three axial vector lengths ($a, b, c$) and three inter-axial angles:

  • $\alpha$: the angle enclosed between axial vectors $\mathbf{b}$ and $\mathbf{c}$.

  • $\beta$: the angle enclosed between axial vectors $\mathbf{a}$ and $\mathbf{c}$.

  • $\gamma$: the angle enclosed between axial vectors $\mathbf{a}$ and $\mathbf{b}$.

• Four unit-cell centering types:

  • Primitive ($P$): lattice points reside strictly at the unit cell vertices ($1$ net lattice point per cell).

  • Body-Centred ($I$): points at vertices plus a single point at the unit cell body center ($2$ net lattice points per cell).

  • Face-Centred ($F$): points at vertices plus points at the centers of all six bounding faces ($4$ net lattice points per cell).

  • Side-Centred / Base-Centred ($C$): points at vertices plus points centered on two parallel opposite faces ($2$ net lattice points per cell).

  • The Seven 3D Crystal Classes and Fourteen Bravais Lattices:

• Cubic System ($a = b = c$; $\alpha = \beta = \gamma = 90^\circ$):

  • Simple Cubic ($P$)

  • Body-Centered Cubic ($I$)

  • Face-Centered Cubic ($F$)

• Tetragonal System ($a = b \neq c$; $\alpha = \beta = \gamma = 90^\circ$):

  • Primitive Tetragonal ($P$)

  • Body-Centered Tetragonal ($I$)

• Orthorhombic System ($a \neq b \neq c$; $\alpha = \beta = \gamma = 90^\circ$):

  • Primitive Orthorhombic ($P$)

  • Body-Centered Orthorhombic ($I$)

  • Face-Centered Orthorhombic ($F$)

  • Side-Centered Orthorhombic ($C$)

• Hexagonal System ($a = b \neq c$; $\alpha = \beta = 90^\circ$, $\gamma = 120^\circ$):

  • Primitive Hexagonal ($P$)

• Trigonal System / Rhombohedral ($a = b = c$; $\alpha = \beta = \gamma \neq 90^\circ$):

  • Primitive Trigonal ($P$)

• Monoclinic System ($a \neq b \neq c$; $\alpha = \gamma = 90^\circ$, $\beta \neq 120^\circ$):

  • Primitive Monoclinic ($P$)

  • Side-Centered Monoclinic ($C$)

• Triclinic System ($a \neq b \neq c$; $\alpha \neq \beta \neq \gamma \neq 90^\circ$):

  • Primitive Triclinic ($P$)

Mathematical Vector Basis and Cell Volumes of Cubic Lattices

• Simple Cubic (SC) Lattice:

  • Conventional cell length parameter: $d$.

  • Primitive translation vectors along Cartesian axes:     $\mathbf{a} = d\,\hat{\mathbf{i}}$     $\mathbf{b} = d\,\hat{\mathbf{j}}$     $\mathbf{c} = d\,\hat{\mathbf{k}}$

  • Volume of the primitive cell:     $V = \mathbf{a} \cdot (\mathbf{b} \times \mathbf{c}) = d^3$

• Body-Centered Cubic (BCC) Lattice:

  • Conventional cubic edge length: $d$.

  • Symmetric primitive translation vectors directed from a corner to the body centers:     $\mathbf{a} = \frac{d}{2}(\hat{\mathbf{i}} + \hat{\mathbf{j}} - \hat{\mathbf{k}})$     $\mathbf{b} = \frac{d}{2}(-\hat{\mathbf{i}} + \hat{\mathbf{j}} + \hat{\mathbf{k}})$     $\mathbf{c} = \frac{d}{2}(\hat{\mathbf{i}} - \hat{\mathbf{j}} + \hat{\mathbf{k}})$

  • Volume of the primitive cell:     $V = |\mathbf{a} \cdot (\mathbf{b} \times \mathbf{c})| = \frac{d^3}{2}$

  • Coordination number: $8$.

• Face-Centered Cubic (FCC) Lattice:

  • Conventional cubic edge length: $d$.

  • Symmetric primitive translation vectors directed from a corner to adjacent face centers:     $\mathbf{a} = \frac{d}{2}(\hat{\mathbf{i}} + \hat{\mathbf{j}})$     $\mathbf{b} = \frac{d}{2}(\hat{\mathbf{j}} + \hat{\mathbf{k}})$     $\mathbf{c} = \frac{d}{2}(\hat{\mathbf{k}} + \hat{\mathbf{i}})$

  • Volume of the primitive cell:     $V = |\mathbf{a} \cdot (\mathbf{b} \times \mathbf{c})| = \frac{d^3}{4}$

  • Coordination number: $12$.

  • Nearest-neighbor interatomic distance: $\frac{d}{\sqrt{2}} = \frac{d\sqrt{2}}{2}$.

Principal Semiconductor Crystal Geometries

• The Diamond Structure:

• Space lattice: Face-Centered Cubic (FCC) Bravais lattice.

• Basis composition: two identical atoms associated with each primitive lattice point, positioned at fractional coordinates:     $(0, 0, 0) \quad \text{and} \quad \left(\frac{a}{4}, \frac{a}{4}, \frac{a}{4}\right)$

• Geometry: formed by two interpenetrating FCC sublattices displaced along the body diagonal by one-fourth of the cubic body diagonal length:     $\frac{a\sqrt{3}}{4}$

• Atomic coordination: each atom is tetrahedrally coordinated to $4$ nearest neighbors through $sp^3$-hybridized covalent bonds.

• Representative elemental materials: carbon (diamond), silicon ($Si$), and germanium ($Ge$).

  • The Zinc-Blende (Sphalerite) Structure:

• Space lattice: Face-Centered Cubic (FCC) Bravais lattice.

• Basis composition: two distinct chemical elements (a cation and an anion) positioned at:     $\text{Cation site: } (0, 0, 0)$     $\text{Anion site: } \left(\frac{a}{4}, \frac{a}{4}, \frac{a}{4}\right)$

• Geometry: identical to the diamond lattice, but composed of alternating sublattices of differing atomic species.

• Coordination: each atom possesses $4$ tetrahedrally positioned nearest neighbors of the opposing chemical species.

• Representative compound materials: gallium arsenide ($GaAs$), indium phosphide ($InP$), gallium phosphide ($GaP$), gallium antimonide ($GaSb$), indium antimonide ($InSb$), zinc sulfide ($ZnS$), and zinc selenide ($ZnSe$).

• Phase stability note: gallium nitride ($GaN$), silicon carbide ($SiC$), and zinc oxide ($ZnO$) are difficult to synthesize in the zinc-blende phase because they form the hexagonal wurtzite phase under equilibrium conditions.

  • Simple Hexagonal and Hexagonal Close-Packed (HCP) Structures:

• Primitive vectors defining the simple hexagonal Bravais lattice:     $\mathbf{a} = a\,\hat{\mathbf{i}}$     $\mathbf{b} = \frac{a}{2}\hat{\mathbf{i}} + \frac{a\sqrt{3}}{2}\hat{\mathbf{j}}$     $\mathbf{c} = c\,\hat{\mathbf{k}}$

• Hexagonal Close-Packed (HCP) structure:

  • Formed from two interpenetrating simple hexagonal sublattices displaced relative to one another by the vector:       $\mathbf{T} = \frac{1}{3}\mathbf{a} + \frac{1}{3}\mathbf{b} + \frac{1}{2}\mathbf{c}$

  • The Wurtzite Structure:

• Space structure: two interpenetrating hexagonal close-packed (HCP) sublattices, each occupied by a distinct atomic species (cation and anion), mutually displaced along the $c$-axis.

• Coordination: preserves local tetrahedral coordination, with each atom bonded to four nearest neighbors of the opposite species.

• Representative compound materials: gallium nitride ($GaN$), silicon carbide ($SiC$), zinc oxide ($ZnO$), and aluminum nitride ($AlN$).

  • Tetrahedral Orientation in Wurtzite versus Zinc-Blende:

• Microscopic differences in atomic tetrahedra:

  • In the wurtzite structure, adjacent atomic tetrahedra along the hexagonal $c$-axis exhibit an eclipsed conformation (possessing mirror symmetry across the basal plane).

  • In the zinc-blende structure, adjacent atomic tetrahedra along the cubic $[1,1,1]$ axis exhibit a staggered conformation (rotated by $60^\circ$, possessing inversion symmetry).

  • Stacking Sequences of Close-Packed Spheres:

• Layering of hard spheres on a planar hexagonal array:

  • The initial layer of packed spheres is designated as layer $A$.

  • The second layer of spheres nests in the triangular interstitial hollows of layer $A$, designated as positions $B$.

  • Placement of the third layer determines the overall crystal symmetry:

    • Placing the third layer directly aligned above layer $A$ produces the two-layer repeating sequence:         $\dots ABABAB\dots$         This sequence generates the Hexagonal Close-Packed (HCP) and Wurtzite structures.

    • Placing the third layer in the remaining interstitial sites $C$ produces the three-layer repeating sequence:         $\dots ABCABCABC\dots$         This sequence generates the Face-Centered Cubic (FCC) and Zinc-Blende structures.

  • Polytypism: the existence of varied repeating stacking orders of chemically identical layers gives rise to distinct crystal polytypes, as observed in silicon carbide ($SiC$) polytypes (such as $3C\text{-}SiC$, $4H\text{-}SiC$, and $6H\text{-}SiC$).

Quantitative Metrics of Semiconductor Crystal Lattices

• Parameter Definitions:

  • Lattice constant ($a$): the physical edge length of the conventional unit cell.

  • Coordination number: the total count of nearest-neighbor atomic sites surrounding a central lattice atom:

  • Body-Centered Cubic ($BCC$): coordination number = $8$.

  • Face-Centered Cubic ($FCC$): coordination number = $12$.

  • Diamond and Zinc-Blende structures: coordination number = $4$.

  • Nearest-neighbor distance ($d_{\text{nn}}$) in cubic semiconductors:

  • For standard Face-Centered Cubic ($FCC$) lattices:       $d_{\text{nn}} = \frac{a}{\sqrt{2}} = \frac{a\sqrt{2}}{2}$

  • For Diamond and Zinc-Blende lattices:       $d_{\text{nn}} = \frac{a\sqrt{3}}{4}$

  • Atomic Packing Fraction ($APF$):     \text{APF} = \frac{\text{Total Volume of Spheres in Unit Cell}}{\text{Total Volume of Unit Cell}} = \frac{N_{\text{atoms}} \times \left(\frac{4}{3}\pi r^3\right)}{V_{\text{cell}}}}

• Measured Lattice Constants, Nearest-Neighbor Distances, and Covalent Radii:

  • Structural parameters for elemental and compound semiconductors at $25\,^\circ\text{C}$ (adapted from M. Shur, Physics of Semiconductor Devices, Prentice Hall, 1990):

  • Group IV Elemental Semiconductors:

    • Silicon ($Si$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.4309\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.353\,\text{\AA}$

    • Sum of covalent radii: $2.34\,\text{\AA}$

    • Germanium ($Ge$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.6461\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.450\,\text{\AA}$

    • Sum of covalent radii: $2.44\,\text{\AA}$

  • Group III-V Compound Semiconductors ($A^{\text{III}}B^{\text{V}}$):

    • Aluminum arsenide ($AlAs$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.6611\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.430\,\text{\AA}$

    • Sum of covalent radii: $2.44\,\text{\AA}$

    • Aluminum phosphide ($AlP$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.451\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.360\,\text{\AA}$

    • Sum of covalent radii: $2.36\,\text{\AA}$

    • Aluminum antimonide ($AlSb$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.136\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.224\,\text{\AA}$

    • Sum of covalent radii: $2.52\,\text{\AA}$

    • Boron arsenide ($BAs$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $4.776\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.068\,\text{\AA}$

    • Sum of covalent radii: $2.06\,\text{\AA}$

    • Boron nitride ($BN$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $3.615\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $1.565\,\text{\AA}$

    • Sum of covalent radii: $1.58\,\text{\AA}$

    • Boron phosphide ($BP$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $4.538\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $1.965\,\text{\AA}$

    • Sum of covalent radii: $1.98\,\text{\AA}$

    • Boron antimonide ($BSb$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.170\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.239\,\text{\AA}$

    • Sum of covalent radii: $2.24\,\text{\AA}$

    • Gallium arsenide ($GaAs$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.6532\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.448\,\text{\AA}$

    • Sum of covalent radii: $2.44\,\text{\AA}$

    • Gallium phosphide ($GaP$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.4495\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.360\,\text{\AA}$

    • Sum of covalent radii: $2.36\,\text{\AA}$

    • Gallium antimonide ($GaSb$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $6.095\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.639\,\text{\AA}$

    • Sum of covalent radii: $2.62\,\text{\AA}$

    • Indium arsenide ($InAs$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $6.0584\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.623\,\text{\AA}$

    • Sum of covalent radii: $2.62\,\text{\AA}$

    • Indium phosphide ($InP$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.8687\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.540\,\text{\AA}$

    • Sum of covalent radii: $2.54\,\text{\AA}$

    • Indium antimonide ($InSb$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $6.479\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.805\,\text{\AA}$

    • Sum of covalent radii: $2.80\,\text{\AA}$

  • Group II-VI Compound Semiconductors ($C^{\text{II}}D^{\text{VI}}$):

    • Cadmium telluride ($CdTe$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $6.482\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.807\,\text{\AA}$

    • Sum of covalent radii: $2.95\,\text{\AA}$

    • Mercury sulfide ($HgS$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.841\,\text{\AA}$

    • Mercury selenide ($HgSe$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $6.084\,\text{\AA}$

    • Mercury telluride ($HgTe$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $6.462\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.798\,\text{\AA}$

    • Sum of covalent radii: $2.95\,\text{\AA}$

    • Zinc sulfide ($ZnS$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.415\,\text{\AA}$

    • Zinc selenide ($ZnSe$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $5.653\,\text{\AA}$

    • Zinc telluride ($ZnTe$):

    • Lattice constant $a$ at $25\,^\circ\text{C}$: $6.101\,\text{\AA}$

    • Nearest-neighbor distance $\frac{a\sqrt{3}}{4}$: $2.642\,\text{\AA}$

    • Sum of covalent radii: $2.78\,\text{\AA}$