Hole-states

Figure 9.2. Carbon Is photoelectron spectrum Is core-hole-state spectra for the 2-norbornyl cation of tert-butyl cation and Clark s simulated spectra for the classical and nonclassical ions.

The uncertainty principle, according to which either the position of a confined microscopic particle or its momentum, but not both, can be precisely measured, requires an increase in the carrier energy. In quantum wells having abmpt barriers (square wells) the carrier energy increases in inverse proportion to its effective mass (the mass of a carrier in a semiconductor is not the same as that of the free carrier) and the square of the well width. The confined carriers are allowed only a few discrete energy levels (confined states), each described by a quantum number, as is illustrated in Eigure 5. Stimulated emission is allowed to occur only as transitions between the confined electron and hole states described by the same quantum number. 

Another feature in PES spectra is the so-called shake-up structures, appearing as weak satellites on the high binding energy side of the main line. The shake-up structure reflects the spectrum of the 1 -electron-2-hole states generated in connection with pholoionization, and can give useful information about the valence n-electronic structure of a molecular ion. 

Again using the completeness of the particle-hole states (eq. 10), we find that the Bethe sum rule (eq. 6) is fulfilled. 

In the DC-biased structures considered here, the dynamics are dominated by electronic states in the conduction band [1]. A simplified version of the theory assumes that the excitation occurs only at zone center. This reduces the problem to an n-level system (where n is approximately equal to the number of wells in the structure), which can be solved using conventional first-order perturbation theory and wave-packet methods. A more advanced version of the theory includes all of the hole states and electron states subsumed by the bandwidth of the excitation laser, as well as the perpendicular k states. In this case, a density-matrix picture must be used, which requires a solution of the time-dependent Liouville equation. Substituting the Hamiltonian into the Liouville equation leads to a modified version of the optical Bloch equations [13,15]. These equations can be solved readily, if the k states are not coupled (i.e., in the absence of Coulomb interactions). 

As the number of eigenstates available for coherent coupling increases, the dynamical behavior of the system becomes considerably more complex, and issues such as Coulomb interactions become more important. For example, over how many wells can the wave packet survive, if the holes remain locked in place If the holes become mobile, how will that affect the wave packet and, correspondingly, its controllability The contribution of excitons to the experimental signal must also be included [34], as well as the effects of the superposition of hole states created during the excitation process. These questions are currently under active investigation. 

T ab.l - Energies (hartree) of ground and hole states of some small molecules. 

Tab.3 - Calculated energies (hartree) of ground and carbon hole states for fluorinated methanes and optimized scale factors.

The calculations were performed using a double-zeta basis set with addition of a polarization function and lead to the results reported in Table 5. The notation used for each state is of typical hole-particle form, an asterisc being added to an orbital (or shell) containing a hole, a number (1) to one into which an electron is promoted. In the same Table we show also the frequently used Tetter symbolism in which K indicates an inner-shell hole, L a hole in the valence shell, and e represents an excited electron. The more commonly observed ionization processes in the Auger spectra of N2 are of the type K—LL (a normal process, core-hole state <-> double-hole state ) ... 

The localization of the HOMO is also important for another reason. Since it describes the distribution of a hole in a radical cation, it relates to the hindrance that a positive charge will encounter as it propagates along the chain. There is indeed experimental evidence (9) that the hole states of the polysilane chain are localized and that they move by a hopping mechanism. 

The emission spectrum of some PT and PBD polymer bilayer devices cannot be explained by a linear combination of emissions of the components. Thus, white emission of the PLEDs ITO/422/PBD/A1 showed Hof 0.3% at 7 V, and consisted of blue (410 nm), green (530 nm), and red-orange (620 nm) bands. Whereas the first and the last EL peaks are due to the EL from the PBD and the PT layers, respectively, the green emission probably originates from a transition between electronic states in the PBD layer and hole states in the polymer... 

In the standard choice BHF the self-consistency requirement (5) is restricted to hole states (k < kF, the Fermi momentum) only, while the free spectrum is kept for particle states k > kF- The resulting gap in the s.p. spectrum at k = kF is avoided in the continuous-choice BHF (ccBHF), where Eq. (5) is used for both hole and particle states. The continuous choice for the s.p. spectrum is closer in spirit to many-body Green s function perturbation theory (see below). Moreover, recent results indicate [6, 7] that the contribution of higher-order terms in the hole-line expansion is considerably smaller if the continuous choice is used. 

Barsberg, S. and Thygesen, L.G. (1999). Spectroscopic properties of oxidation species generated in the lignin of wood fibres by a laccase catalysed treatment electronic hole state migration and stabilization in the lignin matrix. Biochimica et Biophysica Acta, 1472, 625-642. 

M. V. Mihailovic and M. Rosina, The particle-hole states in some light nuclei calculated with the two-body density matrix of the ground state. Nucl. Phys. A237, 229-234 (1975). 

---