Free electron density

Measurements of mobility in PS suffer from the fact that the number of free charge carriers is usually small and very sensitive to illumination, temperature and PS surface condition. Hall measurements of meso PS formed on a highly doped substrate (1018 cm3, bulk electron mobility 310 cm2 V-1 s-1) indicated an electron mobility of 30 cm2 V 1 s 1 and a free electron density of about 1013 cm-3 [Si2]. Values reported for effective mobility of electron and hole space charges in micro PS are about five orders of magnitude smaller (10-3 to 10 4 cm2 V 1 s ) [PelO]. The latter values are much smaller than expected from theoretical investigations of square silicon nanowires [Sa9]. For in-depth information about carrier mobility in PS see [Si6]. 

In the previous example, we have calculated the plasma frequency for metallic Na from the free electron density N. In Table 4.1, the measnred cutoff wavelengths, Xp, for different alkali metals are listed together with their free electron densities. The relatively good agreement between the experimental values of Xp and those calculated from Equation (4.20), within the ideal metal model, should be noted. It can also be observed that the N values range from abont 10 to about 10 cm leading to... 

An electron donating substituent such as phenyl and methoxy will polarise electron density on the radical-anion of an alkene in favour of more positive charge density on the carbon atom bearing this substituent with more free electron density on the other carbon atom. This promotes dimer formation by linkage through atoms with free electron density. Styrene is oxidised at a graphite anode in methanol... 

Although the existence of charged particles in the deton waves of solid expls has been known for some time, it was Lewis and then Bone et al who indirectly demonstrated the existance of electrons as well as positive ions in condensed and gaseous deton flames. However, it was not until 1956 that measurements of electron densities in the detonation waves of solids were carried out by Cook et al (Ref 6). They found free-electron densities in excess of 10 7/cc in the de ton reaction zone dropping slharply outside the reaction zone (Ref pl44)... 

Table 9.2 Plasma Frequencies and Corresponding Wavelengths for a Range of Free-Electron Densities...

Plasma frequencies and the corresponding wavelengths for a range of free-electron densities are given in Table 9.2 the plasma effects mentioned in this section are noted beside the wavelengths (electron-hole droplets will be discussed in Chapter 12). 

The free-electron density of states n( ) may be obtained directly from eqn (2.39) by writing it in the form... 

These measurements cannot be used to quantify the electron transfer from the semiconductor to the metal deposit, but an estimate has been drawn from studies of oxygen photoadsorption on Pt/Ti(>2 samples in a pressure range such that nearly all of the free electrons are captured to form adsorbed 05 ion-radicals. Increasing Pt contents corresponded to decreasing amounts of photoadsorbed oxygen, which corroborates the effect of deposited Pt on the Ti(>2 free electron density. For Ti(>2 samples evacuated at 423 K and... 

Figure 5.11 Charge density after the XUV-pump pulse, at small (top row) and large (bottom row) radii. At each breathing cycle, the metastable wave packet, formed by a coherent superposition of doubly excited states, ejects a burst of electrons. The peak of the free electron density originating close to the nucleus results in a wave front, which propagates outward at almost constant speed, up to very large distances.

Eq. (1) is used to find the d-band width (6.5 eV) once the other parameters of the band shape are determined. Similarly, Eq. (2) is used to determine the s-band width (12.9 eV) of a free-electron density of states symmetric in energy about the middle of the band. The d-band density of states, Nj(E). rises sharply at the lower band edge to about 1.5 states/eV atom then falls off to 0.47 states/eV atom near the middle. With the general shape of Nj. (E) and Ns(E) given, the critical magnitude of Nd( q ), the chemical potential in d-orbital, is determined from the observed linear part of the low-temperature specific heat as follows ... 

The fact that LME can take place only when there is a good contact between the metal and the liquid metal — observation.4.1.5 - means free electrons must be free to move from solid metal to liquid metal and vice versa. This logically means the phenomenon of LME is due to the change in the free electron density in the solid metal under the influence of the free-electron density in liquid metal. Our task is to characterize a) the type of change, b) the type of mechanical effects (based on the theory proposed here) that can come from such a change and c) comparison between these theoretical intuitions against the experimental evidence to see how they fit together. 

Because of the potentially high intensities occuring in femtosecond pulses, free electrons are generated by MPI and avalanche mechanisms. Then it is necessary to account for the response of the optical field to the presence of a dilute plasma. Since the relevant times scales are so short, plasma diffusion and ion motion are neglected, and the free-electron density p is usually obtained as a solution to an equation of the following form [7,12,13]... 

Possibility to prepare highly-doped films with free electron density n > 1020cm-3 and low resistivity (<10 3Ocm)... 

If the two materials were then electrically connected, electrons from the side with more free electrons would tend to diffuse toward the material with fewer free electrons.2 This tendency would occur on both the hot and cold end, generating electron flows which oppose. However, the electrons on the high temperature side, propagating and impacting more forcefully, would overcome the opposing electron flow from the other side, and a net current would result. Note that if both materials were the same, one side would have the same free electron density as the other, producing no diffusion tendency and therefore no current. Further, if the temperatures were the same at both junctions of the dissimilar materials, then the diffusion currents would exactly cancel and there would also be... 

Infrared active modes couple to the free carrier plasma and the energy of the coupled phonon-plasmon mode is sensitive to the electron density [3,20-22], In the range 1 x 1017 cm 3 < n < 1019 cm 3 the following approximation can be used for the free electron density as a function of the Ai(LO) mode frequency vmax [21] ... 

FIGURE 1 Phonon, plasmon and phonon-plasmon coupled modes in Raman and infrared reflection spectroscopy as a function of free electron density (+ data from [25], see also [3]) [24],... 

Introducing the quasi-free electron density of states... 

A detailed derivation was described elsewhere (Kishida et al., 1983). On the other hand, the free electron density nc in the conduction band is also given... 

We consider a metallic phase of volume V, with N free electrons, and hence a free electron density n given by n = NjV. The charge of the core ions is smeared out and leads to a potential energy well keeping the free electrons in the metallic phase (Figure 3). Since in the Sommerfeld model the electrons do not interact with each other, we can describe the electron energy levels by one-electron wave functions. An independent electron can be described by a single-electron wave function ij/ x,y,z) which satisfies... 

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