Optical threshold

For p-type Mg-doped GaN, DLTS measurements [15,19] have detected three deep levels with activation energies for hole emission to the valence band of -0.21 (DLPi), -0.32 (DLP2) and -0.42 eV (DLP3). The concentrations ranged from -4 x 1014 to -9 x 1014 cm 3. For the same Mg-doped GaN sample the ODLTS spectrum exhibited a dominant deep level near midgap (OLPt) with an optical threshold energy for hole emission to the valence band of -1.8 eV (180 K) its concentration was estimated to be -2.4 x 1015 cm 3. 

Using this approximate form in Eq. (3-39), we may write the optical threshold Eq... 

Table 2 Electronic conductivity, activation energy, and optical threshold. Eg, of pristine polyaer.

The maximum energy in the valence band is the lower degenerate level given in Eq. (3-27), and ordinarily, the minimum energy in the conduction band occurs at the upper nondegenerate level of Eq. (3-27). (This is discussed in Chapter 6.) We may subtract one from the other, and writing e, — s = 4F, (the metallic energy) for each of the atom types, as in Eq. (3-5), we obtain a difference known as atJ optical threshold (discussed in Chapter 4). It is... 

In the normal band structure, at F the nondegenerate level (F, in Ge) lies below the triply degenerate level (Fg and Fg in Ge) in the conduction band, just as it does in the valence band. We see that silicon is not normal in this sense. In Section 3-E we identified the energy difference between the nondegenerate level in the conduction band and the degenerate level in the valence band as the optical threshold, g. (That identification only applies to normal band structures.) We lound q to be given approximately by 3.6F2(am 1)/(1 Both the... 

Fig. 1. Calculated capacitance C and optical transmission of a nematic liquid-crystal cell of thickness d and area A between parallel polarizers set parallel or perpendicular to the rubbing directions (solid curve) or at 45 to these directions (dashed curve) as a function of the applied RMS voltage V. Definition of Freederlksz threshold optical threshold Vthr> 50 80...

The optical threshold voltage Vthr is obtained by extrapolating the linear portion of the transmission/voltage curve (with the polarizers parallel or perpendicular to the rubbing directions) as shown in Fig. 1. 

The dependence of the merit figure on the dielectric anisotropy is a rather sensitive function of the choice of the threshold voltage. Had we selected the Freedericksz transition (capacitance) threshold voltage Instead of an optical threshold V9o(40 ), we would observe a decrease in figure of merit with increasing such as reported elsewhere.15 However, for an optical reponse, the latter seems more relevant. 

Temperature dependence of the optical threshold voltage Vth is a dominant factor in the figure of merit (M), It is worth analyzing the relations between AV, or and LC material properties, or molecular structures. Concerning physical constants, viz, dielectric anisotropy and elastic constant, both of which govern the threshold voltage of LC, we made some investigation of temperature dependence of V h for each LC in relation to that of ECH ... 

This optical threshold voltage (V p) can be derived by assuming that the rise lime is approaching infinity at V= V p. Thus, the denominator in Equation (8.9) should vanish ... 

From Equation (8.11), the optical threshold voltage is derived as... 

From Equation (8.8), when = 0 and x —> 0, the optical threshold is reduced to the Fr dericksz threshold. As the mbbing angle is increased, the optical threshold voltage is gradually decreased. At d> = 45°, the optical threshold voltage reaches a minimum however, the on-state voltage is also increased. 

P. A. Breddels and H. A. van Sprang, An analytical expression for the optical threshold in highly twisted nematic systems with nonzero tilt angles at the boundaries, J. Appl. Phys., 58, 2162 (1985). 

The threshold intensity for the laser induced deformation of nematic liquid crystals is calculated as a function of the spot size of the illuminating beam. It is shown, that due to the small size of the light spot, the optical threshold is higher than that expected from the Fredericks threshold formula for static electric fields of infinite large dimension in the cell plane. Experimental data measured on a homeotrop OCB (octyl-cyano-byphenyl) sample fit well the theoretical curve. Results obtained on the temperature and wavelength dependence of the threshold can be interpreted on the basis of the given theory. 

The typical transmission-voltage curve (TVC) of the twist effect for normal light incidence is shown in Fig. 4.12 for the twist cell placed between parallel polaroids. As mentioned above, the deformation of the director, measured by birefringence [66] or capacity [73], begins for smaller voltages U = C/tw then visible variations of the twist cell transmission. In view of the Mauguin requirement (4.53), the optical threshold of the twist effect decreases for the smaller values of the cell thickness [74] and the optical anisotropy of the liquid crystal as well as for director pretilt on the boundaries [76]... 

This voltage is very close to the optical threshold for the supertwist transition, and for 0 we have... 

For a finite director pretilt at the boundaries a sharp threshold disappears however, it is possible to find a voltage at which the director angle at the center of the layer becomes equal to the boundary pretilt angle 6s [116]. This voltage is very close to the optical threshold for the supertwist transition. 

The formula presented in Eq. 3 indicates the threshold voltage at which the director starts to reorient. Gerritsma, DeJeu, and Van Zan-ten 4 have measured the magnetic threshold by both capacitive and optical techniques and found that the capacitive threshold is lower than the optical one. Van Doorn has shown that this difference is to be expected, since the fluid starts to reorient by the tilting of the director toward the applied magnetic field before the twist has appreciably changed. Consequently the capacitive threshold, which occurs when the director starts to tilt toward the applied field, is lower than the optical threshold, which occurs when the twist becomes sufficiently nonuniform that the optical vector of the light does not Tol-low the twist. A similar difference has been observed in twisted nematic devices excited with electric fields. Berreman s explanation of the static characteristics of electric-field-excited devices is similar to that of Van Doorn. ... 

---