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CHAPTER 1
Semiconductor Fundamentals and Background
1.1.Tetrahedral Semiconductors
The material most widely associated with photovoltaics is silicon (Si), and its well-established properties are often the reference from which those of other PV materials are drawn. Silicon is a group-IV, tetravalent metalloid, inert, grey solid, with a high melting point (1400°C), a chemical analog to carbon. The four valence electrons of both Si and carbon (C) make these elements compatible with tetrahedral coordination. Building from the core of a neon (Ne) atom, a pair of spin-opposite electrons are first added to the 3s level, followed by two electrons in the 3p levels, which are spin aligned, according to Hund’s rule. The energy levels are shown in Fig. 1.1. Hybridization by linear combination of the 3s and 3p atomic orbitals can be used to form four molecular orbitals with minimal overlap. Whereas the hybridized levels have higher energy for isolated atoms, they result in an overall reduction in energy in the solid by forming tetrahedral bonds.
The molecular-orbital wave functions are constructed from linear combinations of these four, equally weighted orbitals:
Fig. 1.1.3sp3 hybridization.
Fig. 1.2.Atomic orbitals that contribute to 3sp3 molecular orbitals.
Fig. 1.3.The tetrahedron formed of nearest neighbors in Si can be inscribed within a cube of dimension a/2, where a is the cubic lattice parameter.
From the eight distinct possibilities generated by the various sign combinations, four can be selected with a tetrahedral arrangement. These functions are illustrated in Fig. 1.2.
Pure Si has the diamond crystal structure, most associated with carbon, which is comprised of two interpenetrating face-centered cubic lattices, both occupied by Si atoms, but separated by
the cube diagonal. The structures are shown in
Fig. 1.3. Tetrahedral bonds associate each atom in either sublattice to the four nearest
neighbors in the other sublattice. The tetrahedron formed among each atom and its four nearest neighbors can be inscribed within a cube of dimension
a/2. Four such tetrahedra arranged with edges touching can be assembled into the full cubic unit cell.
The electronic properties of crystals are influenced by the available states supported by the material and the distribution of electrons within these states. Continuous bands form that dictate the variation of energy with wave vector. The occupation of these bands depends on the numbers of electrons and temperature. Thus, the electrical-conduction properties of materials are closely linked to the band structure, carrier density, and temperature. Of utmost importance is the bandgap Eg — the energy between the highest occupied state and the lowest unoccupied state, which are derived from the highest-occupied and lowest-unoccupied molecular orbitals, [HOMO and LUMO, respectively] of isolated molecules. A schematic of these energy levels are shown in Fig. 1.4.
Semiconductor bandgaps are either direct or indirect, which refers to the alignment in crystal momentum space of the VB maximum and the CB minimum. For a direct-gap semiconductor, these are aligned in wave vector; for an indirect-gap semiconductor they are not aligned. The implication is that no change in crystal momentum is required for electronic transitions between the VB and CB. Thus, the transition may represent only a change in energy of an electron. That change in energy can occur by the absorption or emission of a photon which, as a massless particle, has negligible momentum. An indirect transition, on the other hand, requires concomitant momentum change, generally by the emission or absorption of a phonon.
Fig. 1.4.The semiconductor bandgap can be related back to the HOMO-LUMO energy difference of isolated molecules.
Bandgap is only one parameter describing the rather complex electronic structure of semiconductors. For example, the electronic bands of a three-dimensional crystal potential will not be spatially isotropic. The conductive properties of a semiconductor are dramatically influenced by doping, temperature, and illumination. These variations are exploited to enable control of electrical conduction for...
