Band pinning

Fig. 12a-c. Schematic representation of the effective potential Vejf and of different possibilities of localized and itinerant states for electrons of high 1 quantum number, a) The solid line d represents the periodic potential set-up by the cores R and R +i, which is a superimposition of central potential a dashed line). The dashed line b represents the centrifugal potential of kinetic origin 1(1 + l)/2 R in an atom, and c dashed line) the effective potential V f for an atom (compare Fig. 6) and full line) for a solid, b) Relative to two shapes of the effective potential Ve, two examples of localized state are given 1. resonant state 2. fully localized state. Notice that 1. is very near to Ep. h and t represent hopping and tunneling processes, c) A narrow band is formed (resonance band), pinning Ep 3. narrow band... 

In the preceding sections, we have rapidly reviewed the concepts that are involved in the band formation of actinide metals. We would like to point out what more is involved in the band formation of actinide compounds. This is very obvious the anion valence band. In fact, the hybridization with anion states which we presented as the main correction to the simple Hill scheme is indeed the central question involved in detailed band structure calculations in actinide compounds. We pointed out in the previous paragraph the case of UGea we would like here, as an example, to compare somewhat UO2 and NaCl compounds of uranium. As confirmed by recent photoemission studies " , UO2 has well localized 5 f states whereas NaCl compounds have a narrow 5 f band pinned at the Fermi level. Nevertheless the U-U spacing is the same in UO2, UP and US. This difference may be understood in terms of charge transfer versus f-p hybridization. 

Assume for simplicity that the potential drop in the Helmholtz layer does not change under illumination, so that the position of the band edges at the surface is fixed with respect to the system of energy levels in the solution ( band pinning at the surface see Section 3). At the same time, the position of the Fermi level F relative to the band edges Ec and Ey is strictly determined in the semiconductor bulk. Therefore, the bands unbend under illumination and pull the Fermi level, so the latter shifts with respect to its position in the nonilluminated semiconductor (Fig. 16b). This shift can be measured as the photopotential (ppb = —AF/e [cf. Eq. (8)]. 

The ideal behavior of cells presented here, is also of significance in view of prior reports according to which Fermi level pinning instead of band pinning occurs, as found with Schottky junctions (see Section 2.2) [43, 44]. It is surprising that it took more than 25 years until reliable results on majority carrier processes were published. Many issues, such as the influence of surface chemistry on the rate constants, are still open. 

Application of an external potential mainly changes the potential gradient in the space-charge layer while the surface potential and the band position at the surface remain nearly constant. This is called band pinning. The band bending changes with the potential. 

Schlieren /.pi. schlieren (regions of varying refraction, as in liquids) streaks, striae, schlieren (as in glass and igneous rocks). -ver-fahren n. (Photog.) schlieren process. schHerig a. streaked, striated, banded. Schliesse /. pin, peg, catch, anchor, clasp, schliessen, v.t. close shut, lock seal (tubes) bind embrace contract conclude. — v.r. close be related, be apropos. — v.i. close. 

Parker [55] studied the IN properties of MEH-PPV sandwiched between various low-and high work-function materials. He proposed a model for such photodiodes, where the charge carriers are transported in a rigid band model. Electrons and holes can tunnel into or leave the polymer when the applied field tilts the polymer bands so that the tunnel barriers can be overcome. It must be noted that a rigid band model is only appropriate for very low intrinsic carrier concentrations in MEH-PPV. Capacitance-voltage measurements for these devices indicated an upper limit for the dark carrier concentration of 1014 cm"3. Further measurements of the built in fields of MEH-PPV sandwiched between metal electrodes are in agreement with the results found by Parker. Electro absorption measurements [56, 57] showed that various metals did not introduce interface states in the single-particle gap of the polymer that pins the Schottky contact. Of course this does not imply that the metal and the polymer do not interact [58, 59] but these interactions do not pin the Schottky barrier. 

EB, a 48-year-old woman, presents to a new primary care clinic. EB s chief complaints are chronic pain of the knee and "pins and needles" and "numbness" in both hands. Over the past few years, she feels that her body has been changing. EB reports increased urinary frequency, excessive sweating, worsening headaches, an increase of two shoe sizes, and facial hair that she shaves once a week. She says that her hands have enlarged to the point that "my wedding band won t fit anymore."... 

Degeneracy can be introduced not only by heavy doping, but also by high density of surface states in a semiconductor electrode (pinning of the Fermi level by surface states) or by polarizing a semiconductor electrode to extreme potentials, when the bands are bent into the Fermi level region. 

My final recommendation to the customer was to put in a small RC snubber very close to the IC between its SW and GND pins. Typical values of this snubber are 470pF to 4.7nF and 10Q to 100Q. Note that since this Band-Aid fix is very layout and parasitic dependent, I usually ask the customer to try all the corner combinations first, such as 470pF/10Q, 470pF/100Q, and so on. The customer may also need to play with intermediate R and C values to optimize performance and not take too big a hit in efficiency in the process. I know the Japanese customer evaluated the snubber fix at his end and went into full production with it. 

A recent success in the detection of H species has been that of the molecular ion H3+. All of the models of ion-molecule chemistry in hydrogen-dominated regions are controlled by reactions of H3+ but until recently the H2+ molecular ion had not been detected. However, the modes of vibration of H3"1" provide for an allowed IR transition at 3.668 pin used for its detection. These ro-vibrational transitions have now been observed in a number of places, including the interstellar medium and in the aurorae of Jupiter. Not all astronomical detection and identification problems have been solved, however, and the most annoying and compelling of these is the problem of diffuse interstellar bands. 

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

Figure 12.24. PIN photodiode, (a) Fabrication, (b) Energy band diagram, (c) Absorption in the depletion layer.

Fig. 2-81. Surface degeneracy caused by Fermi level pinning at a surface state of high state density (a) in flat band state (Ep ep), G>) in electron equilibrium (cp = cp). cp = surface Fermi level = surface ccmduction band edge level.

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