Longitudinal effective mass

This parameter is usually denoted by 7, but to avoid a confusion with the ratio of the transverse and longitudinal effective masses, it is denoted here by 7b. 

The quadratic shift of the Zeeman components has been calculated for silicon and germanium by a perturbation method [117]8, [139] and by a full calculation [108], The physical interpretation of this second-order effect in terms of the ratio 7 of the transverse and longitudinal effective masses of the donor electron is far from simple. 

Ratio of transverse and longitudinal effective masses, damping constant... 

More direct determination of electron effective masses was first performed by Kaplan et al [16] using electron cyclotron resonance (ECR) in n-type 3C-SiC epitaxially grown onto a silicon substrate. They obtained transverse effective mass m t = (0.247 0.011) n, and longitudinal effective mass m, = (0.667 0.015) m0. The effective masses derived from cyclotron resonance agree, within experimental error, with the values obtained from Zeeman luminescence studies [7] of small bulk crystals. An average effective mass of an electron, given by the equation me = (m t2m, )l/3, is 0.344m0. Recently, similar ECR measurements were made by Kono et al [17]. 

Our model operates with four parameters 1) longitudinal effective mass 2) azimuthal effective mass m 3) thickness of a conductive layer 2A 4) effective nanotube radius r . The agreement with experiments or with existing approximations can be obtained by a variation of these parameters. 

We have carried out calculations for armchair nanotubes in the range of indices n = 5-10. The longitudinal effective mass was taken to be equal to the TB effective mass m rrio. The azimuthal effective mass was chosen to adjust the Fermi level Ep in our model to the TB value. We use yo = 2.7 eV from [5], which gives Ep=8.l eV. For these conditions 1.3/ o for all nanotubes considered. 

Estimated from conduction band minimum and longitudinal effective mass. 

These weaknesses of the SDPC model stimulated Merunka and Rakvin [7, 63] to introduce some modifications to the model. Inspired by the basic ideas of the Fujii model [58,59], they decided to represent the PO4 dipole i in this modified SDPC model, or the MSDPC model, by the vector /Zj = (yu,f, yu, ). This vector has additional transverse components along the a- and fo-axes, beside the longitudinal component along the c-axis. The corresponding impulse is now pi = (pf.p. p ) and the value of the effective mass of the transverse dipole, Mj = Ma = Mb, differs from the value of the effective mass of longi-... 

Here k is the Fermi wave vector determined from the value of the hole concentration p assuming a spherical Fermi surface, m is the hole effective mass taken as 0.5/no (mo is the free electron mass), is the exchange integral between the holes and the Mn spins, and h is Planck s constant. The transverse and longitudinal magnetic susceptibilities are determined from the magnetotransport data according to x = 3M/dB and xh = M/B. 

The abbreviations mn and m L denote the longitudinal and transverse effective electron masses, respectively. m is the effective mass for isotropic conduction band minimum. 

In equation 3, ran is the effective mass of the electron, h is the Planck constant divided by 2/rr, and Eg is the band gap. Unlike the free electron mass, the effective mass takes into account the interaction of electrons with the periodic potential of the crystal lattice thus, the effective mass reflects the curvature of the conduction band (5). This curvature of the conduction band with momentum is apparent in Figure 7. Values of effective masses for selected semiconductors are listed in Table I. The different values for the longitudinal and transverse effective masses for the electrons reflect the variation in the curvature of the conduction band minimum with crystal direction. Similarly, the light- and heavy-hole mobilities are due to the different curvatures of the valence band maximum (5, 7). 

TABLE 2 Electron effective masses (mo) of zincblende GaN and AIN. m e (0 denotes the density of states electron mass at the T point, and m e(X) and m e(X) denote the longitudinal and transverse electron masses at the X point, respectively. For ZB AIN, the conduction band minimum occurs at the X point. 

In general, good agreement is found for the longitudinal and transverse effective masses, when measured by several techniques, within the various polytypes. There is a wider variability for the values of the overall electron effective mass. Theoretical studies yield values for electron effective masses which are in good agreement with measured values. Data on hole effective masses is scarce and much of what is available is from theoretical studies. 

Band Curvature Effective Mass Longitudinal Transverse... 

A minimum sum of all three dispersion processes yields the "optimum velocity" at this velocity the column has maximum efficiency. The B term decreases with increasing flow rate and the C term increases with increasing flow rate. The A term is Independent on flow rate variation. Band broadening in SEC separation is mainly controlled by the mass transfer terms. The longitudinal effect (B term) is insignificant except for small molecules, and a minimum HETP is not usually observed in SEC. 

GaAs 1.35 InP 1.27 InAs 0.36 InSb 0.165 CdTe 1.44 Energy Substance Gap 0.067 8500 3 (or 6 ) equivalent [100] valleys 0.36 eV above this maximum with a mobility of 50 0.067 5000 3 (or 6 ) equivalent [100] valleys 0.4 eV above this minimum 0.022 33,000 Equivalent valleys 1.0 eV above this minimum 0.014 78,000 0.11 1000 4 (or 8 ) equivalent [111] valleys 0.51 eV above this minimum Multivalley Semiconductors Band Curvature Effective Mass Number of Equivalent Longitudinal Transverse Anisotropy Valleys and Direction nii mj K = mi/ mj ... 

Number of equivalent Band curvature effective masses Anistrophy Measured (light) hole Substance valleys and direction Longitudinal Transverse K = mjm mobility (cm /V-s)... 

The dispersion of a solute band in a packed column was originally treated comprehensively by Van Deemter et al. [4] who postulated that there were four first-order effect, spreading processes that were responsible for peak dispersion. These the authors designated as multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase. Van Deemter derived an expression for the variance contribution of each dispersion process to the overall variance per unit length of the column. Consequently, as the individual dispersion processes can be assumed to be random and non-interacting, the total variance per unit length of the column was obtained from a sum of the individual variance contributions. 

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