Mass parameters

Since shallow-level impurities have energy eigenvalues very near Arose of tire perfect crystal, tliey can be described using a perturbative approach first developed in tire 1950s and known as effective mass theoiy (EMT). The idea is to approximate tire band nearest to tire shallow level by a parabola, tire curvature of which is characterized by an effective mass parameter m. ... 

In this expression p is a mass parameter associated to the electronic fields, i.e. it is a parameter that fixes the time scale of the response of the classical electronic fields to a perturbation. The factor 2 in front of the classical kinetic energy term is for spin degeneracy. The functional f [ i , ] plays the role of potential energy in the extended parameter space of nuclear and electronic degrees of freedom. It is given by. 

The second term of Eq. (12) describes the fictitious kinetic energy of the electrons. The term contains an arbitrary parameter (fictitious mass parameter) p with appropriate units of energy times a squared time. 

The quantum number k takes positive and negative integer values, the appropriate electron mass parameter is given by /i, the energy parameter is W, and the central field potential energy is... 

According to Falicov and Stahowiak [12] the contribution of every segment of the cyclotron orbit to the cyclotron mass parameter is proportional to the subtended angle of this segment, and the total cyclotron mass parameter equals the sum of the partial cyclotron mass parameters. We have estimated the effective mass parameters from the temperature dependence of the SdH oscillation amplitude using the standard formula... 

The experimental IRSE data were analyzed assuming an isotropically-averaged effective electron mass parameter of m = 0.28me [135].6 Thereupon, the free-charge-carrier concentration N and the optical mobility parameters p,°pt (i =, L) were obtained [43]. The results of the IRSE-analysis of two sets of Ga-doped ZnO thin films are summarized in Fig. 3.18. 

Here Ai are inverse mass parameters in WZ structure, corresponding to Luttinger parameters in ZB structure, me11 and me1 are k-dependent electron effective masses. D , aic and a2c are Bir-Pikus deformation potentials. Ai and 3A2,3 correspond to the crystal-field and spin-orbit splitting energies, respectively. The definition of several operators is given as L+ = (U iLy)/V2, a+ = (ax iay)/2,... 

Figure 22. Powerspectrum obtained for Ari3 using Nose MD method with 7 = 20 K. Frequency is in units of 10 s" intensity has units of 10" s. (Data have been calculated for Nose bath-mass parameter Q = 100 amu but appear insensitive to changes in this parameter see Davis et al. )...

Three mass parameters are required to fully describe this characteristic, namely ... 

P. Tangney (2006) On the theory underlying the Car-Parrinello method and the role of the fictitious mass parameter. J. Chem. Phys. 124, 044111... 

Jalali-Heravi and coworkers used the three descriptors of their multivariable model, that is, Offord charge-to-mass parameter, corrected steric constant, and molar refractivity, as the input parameters for generating the network (Fig. 14.2). In fact, they proposed an MLR-ANN model for the prediction of the electrophoretic mobility of peptides. The purpose for choosing the MLR parameters as inputs for the ANN mode was to compare the abilities of linear and nonlinear models in predicting the electrophoretic mobilities of peptides (9). 

Fig. 7.8. Comparison of the calculated spectral dependence of the photoionization absorption for group-III acceptors in silicon (solid and dashed curves) with experiment (open circles). E is the ionization energy of the acceptor. The widths of the solid lines correspond to the use of different basic assumptions in the calculation (after [52]). The solid and dashed curves for boron correspond to different values of a mass parameter. The experimental results for B, AZ, and Ga are from [27], and those for In from [116]. Copyright 1977 by the American Physical Society...

The determination of SoC can be based on the measurement of internal parameters (electrolyte or active mass parameters) or external parameters (temperature, voltage, current). The possible measurement methods are shown in Fig. 8.8. 

Zq is the acoustic impedance of AT-cut quartz its value is 8.8 x 10 kg m s Strictly speaking, Zq is a complex quantity Z + iZ", where Z" accounts for internal friction. Zq is often considered to be real. When this happens, the fundamental frequency/f must also be a real number (see end of Sect. 2). The Sauerbrey equation fails to account for viscoelasticity and also, when applied in liquids, cannot distinguish between the adsorbed material itself and solvent trapped inside the adsorbed film. When a mass is derived by means of the Sauerbrey equation, the interpretation of this mass parameter is sometimes difficult. The terms Sauerbrey mass and Sauerbrey thickness are used in order to indicate that the respective parameters have been calculated by the simple Sauerbrey equation. 

The relativistic LMTO and LAPW methods were used to calculate [77-80] the Fermi surface of UPta. This is a heavy fermion compound, and its physical properties axe strongly influenced the presence of the narrow U-/ bands at the Fermi level. The shape of the Fermi surface is then sensitive to relativistic effects, in particular the SO-coupling. The results of the calculations [78] were surprising since they showed that the topology of the Fermi surface was well described by these band structures although they were obtained within the LDA. A similar precision was not found for the effective cyclotron masses which were off by up to a factor of 30 when compared to experiments. The crystal potential enters in the LMTO via the potential parameters [30,73] for each (or each j in the relativistic version [4]), including the mass parameters fi (eq.(49)). A convenient way... 

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