Minimum energy gap

Figure 4.3 Glide activation energies for various covalent crystals versus their minimum energy gaps. The correlation coefficient is 0.95. Without the point for GaP, it would be much higher. 

Figure 1. Energy profile for a general endergonic photochemical reaction Ef, is the minimum energy gap between the lowest vibrational levels of the excited state R and the ground state R of the absorber. Er is the activation energy for the back reaction P R.

Figure 13 The CT adiabatic free energy surfaces in the CT inverted region Ae = 0.7, APIIX = -1.0, AEii/X = 3.0. The points Y and Y+ indicate the minima of the lower and upper adiabatic surfaces, respectively. The labels hv ],s/em are absorption and emission energies, and AEmin is the minimum energy gap between the free energy surfaces (Eq. [149]).

Ralio of the screening length to the zone-boundary wavelength, based upon the minimum energy gap and cITcctivc masses, and an experimental estimate of this ratio, based upon Weber s model of the vibration spectrum. 

Thus twice the chemical hardness is equal to the minimum energy gap, "g, an important property in solid-state physics. In the case of metals, y = = f-... 

The minimum energy gap is also the important factor for other properties of a solid which depend on the electrons in the conduction band. These include the Pauli spin paramagnetism, and the (small) contribution of the electrons to thermal conductivity. All of these properties are due to extremely small concentrations of free electrons. Thus for silicon, where El = 1.1 eV, the number of conduction electrons is only 2 x 10 /cm, compared with an atom concentration of 5 X 10 /cm. This is for a sample where impurity concentrations have been reduced to 1 part in 10 by zone refining. 

Substance Minimum Energy Gap, eV R.T. OK dEg dT xlO eV/°C dEg dP xlO eV cm /kg Density of States Electron Effective Mass (mo) Electron Mobility and Temperature Dependence cm /Vs —X Density of States Hole Effective Mass mdp, (mo) Hole Mobilit)r and Temperature Dependence cm lV s —X ... 

Minimum energy gap (eV) Electron effective Electron mobility and temperature dependence Hole effective Hole mobility and temperature dependence ... 

Solids can be classified as metals, semimetals, intrinsic semiconductors and insulators. The band structures of solids can be illustrated in Fig. 3. Monovalent metals, e.g., Na , have a partially filled valence band, the lower half of which is occupied. The Fermi level is in the valence band but at the top of the occupied orbitals. Furthermore, there is still an energy gap between the valence band and the conduction band (unoccupied MO). In some metals, such as the bivalent metals, the valence band is full but overlaps a higher unoccupied conduction band. In this case, the Fermi level is in the conduction band and the overlapped valence band. Thus, the electrons close to the Fermi level are still free to move as the extra bands supply the unoccupied states. In the latter case, there appears to be no minimum energy gap. Eg" y which is generally reported in the literature. However, it is not... 

In addition to metals, there are semimetals,such as graphite, whose valence band and conduction band can overlap. In general, their minimum energy gaps are very narrow. The third class of solids is the intrinsic semiconductor its minimum energy gap Eg is generally below 3 eV. Thus, thermal excitation alone can create an electron-hole pair to enhance conduction. The Fermi level of the intrinsic semiconductor lies between the valence band (HOMO) and the conduction band (LUMO). Hence,... 

Because in indirect-gap semiconductors generation and recombination of carriers are equally difficult, even in indirect-gap materials the distribution of electrons and holes is governed by the Fermi function. Because the Fermi energy can never be farther than half the energy gap from one band edge or the other, the density of carriers in an indirect-gap material is still determined by the minimum energy gap in spite of the difference in momenta of the band minima in indirect-gap materials. 

Figure 5.7 Shows the relationship of minimum energy gap to lattice constant for the common diamond-structure semiconductors.

Table 5.4 Pressure and Temperature Dependences of Selected Semiconductor Minimum Energy Gaps...

Suppose that a hypothetical homopolar semiconductor existed with a lattice constant of 0.4472 nm. Estimate its minimum energy gap. Explain briefly how you obtain this value. 

Binary and pseudobinary/ternary alloys allow tailoring of minimum energy gap without the ability to affect lattice constant independently. Pseudoternary, quaternary or higher order alloys - mixtures of three, four, or more compound semiconductors. 

These alloys are used to engineer minimum energy gap with independent control of lattice constant. 

Bowing results from symmetric or asymmetric changes to the effective atomic potentials that enter into the Schrodinger equation. These changes are reflected in the chemical and homopolar splittings or equivalentiy in the LCAO matrix elements. These, in turn, result in the observed changes in minimum energy gap. 

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