K-p method

Krasovskii E E and Sohattke W 1995 The extended-LAPW-based k p method for oompiex bandstruoture oaiouiations Solid State Commun. 93 775... 

The k p method provides analytic descriptions on electronic states of CNT. It shows, for example, that the band gap of a semiconducting CNT is inversely proportional to the diameter because of a linear dispersion of the bands. It is suitable also for descriptions of the electronic motion in external perturbations such as electric and magnetic fields. 

Franco Bassani, Methods of Band Calculations Applicable to III-V Compounds E.O. Kane, The k -p Method... 

The conduction-band minima and valence-band maxima are studied in terms of the k p method, which relates the effective masses to the oscillator strengths discussed in Chapter 4. Wannier excitons and impurity states are also understandable in this context. 

We do this by using the k p method, (called k-dol-p), which is based upon the perturbation theory of Eq. (1-14). In this method, energy is calculated near a band maximum or minimum by considering the wave number (measured from the extremum) as a perturbation. (The method is described in many solid state texts, such as Kittel, 1963, p. 186, or Harrison, 1970, p. 140.) The method was used for a study of effective masses by Cardona (1963, 1965). It was also usetl in the more extensive study by Lawaetz (1971) referred to in the discussion of heavy-hole bands. We shall discuss here only the conduction band and the light-hole band where the effects of interaction are great. 

We note now that the momentum operator is = hli)d/d, so the matrix elements that enter the k p method are exactly the same matrix elements that entered the calculations of optical absorption. This remarkable fact enables us to obtain parameters from the LCAO theory given in Chapter 4. 

From the experimental side, the band-structure parameters are mainly determined from the cyclotron resonance (CR) spectra of electron and holes (see for instance [4]). Some of these parameters can also be obtained from the Zeeman splitting of electronic transitions of shallow impurities involving levels for which the electronic masses can be taken as those of free electrons or holes, or from the magnetoreflectivity of free carriers. Average effective masses can also be deduced from the Hall-effect measurements or from other transport measurements. Calculation methods that have been used to obtain band-structure parameters free from experimental input are the ab-initio pseudopotential method, the k-p method and a combination of both. These theoretical methods are presented in Chap. 2 of [107]. VB parameters at k = 0 including k and q have been calculated for several semiconductors with diamond and zinc-blended structures by Lawaetz [55]. 

LCAO, from muffin-tin orbitals, 503-506 solid-state derivation, 408fl necessity of dropping some, 450 o(T-diagonal, 70 of p in k p method, 159 of r, evaluation, 112f of r and of p, relation, 99 solid state, 46fT transition-metal alloys, 505 transition-metal perovskites, 444 from transition-metal pseudopotentials, 516f Mechanical properties. See also Elasticity Lattice vibrations metals, 383-396... 

Although it had not been evaluated) the effective mass tensor can be ilated using the k p-method ( second-order perturbation theory) ... 

The k p method is much used in analyzing semiconductor nanostructures as it gives a good approximation of the states close to the F point (k = 0), which is the most relevant region for many device applications. The approximation is given with good accuracy, while in many... 

Chuang, S.L. and Chang, C.S. (1996) k.p method for strained wurtzite semiconductors. Physical Review B Condensed Matter, 54, 2491. 

---