Kinetic equations for a modeling system with type-I radical-mediated and type-II oxygen-mediated pathways are derived and numerically solved for the photopolymerization efficacy and curing depth, under the quasi-steady state assumption, and bimolecular termination. We show that photopolymerization efficacy is an increasing function of photosensitizer (PS) concentration (C₀) and the light dose at transient state, but it is a decreasing function of the light intensity, scaled by [C₀/I₀]^0.5 at steady state. The curing (or cross-link) depth is an increasing function of C₀ and light dose (time × intensity), but it is a decreasing function of the oxygen concentration, viscosity effect, and oxygen external supply rate. Higher intensity results in a faster depletion of PS and oxygen. For optically thick polymers (>100 um), light intensity is an increasing function of time due to PS depletion, which cannot be neglected. With oxygen inhibition effect, the efficacy temporal profile has an induction time defined by the oxygen depletion rate. Efficacy is also an increasing function of the effective rate constant, K = k′/$k_{\text{T}}^{0.5}$, defined by the radical producing rate (k′) and the bimolecular termination rate (k_T). In conclusion, the curing depth has a non-linear dependence on the PS concentration, light intensity, and dose and a decreasing function of the oxygen inhibition effect. Efficacy is scaled by [C₀/I₀]^0.5 at steady state. Analytic formulas for the efficacy and curing depth are derived, for the first time, and utilized to analyze the measured pillar height in microfabrication. Finally, various strategies for improved efficacy and curing depth are discussed.

A quantum–stochastic treatment is presented for multiphoton processes of chemisorbed species on solid surfaces. The average excitation is evaluated for different stochastic processes. In the Markovian fast modulation limit, the average excitation takes a Lorentzian form, while taking Gaussian in the slow modulation limit. The addition of the memory effects is calculated by Mori’s projection operator technique and is found to be a function of the correlation time and the frequency modulation of the stochastic processes. For low excitations, the average excitation is found to be linearly proportional to the laser intensity, and is saturated by the red shift of the anharmonicity for high excitations. The overall broadening of the infrared line shape is caused by the fluctuation of the adspecies‐field interaction energy, the excitation‐induced surface migration, the phonon‐dispersion‐induced dephasing, and the energy relaxation due to the adspecies–phonon coupling. The population distributions for the slow T₁ relaxation rate are characterized by a Poisson‐type distribution (governed by the average excitation), and are characterized by a Boltzmann thermal distribution for the fast T₁ relaxation rate (governed by both the average excitation and the vibrational degrees of freedom of the adspecies). A comparison of laser‐stimulated desorption and the effective thermal desorption is quantitatively shown by introducing an effective temperature. Finally, a chemisorbed–physisorbed state–state transition channel with lower desorption energy (and hence enhancing the desorption probability) is proposed.

Surface temperatures generated by gaussian, rectangular, and triangular laser pulses are determined by solving a heat diffusion equation. The dependence of the temperature on the pulse shape and, in turn, the dependence of the thermal diffusivity and absorptance on the temperature are investigated. The lifetime of an adspecies on a laser-heated solid (e.g., Cs on W) is estimated in terms of the temperature, the desorption energy, and the coverage. The mechanism of laser-generated electron emission from the adspecies is analyzed by means of the Richardson equation. A condition for generating an intense electron beam is that the laser pulse duration and the rise time of the temperature must be less than the lifetime of the adspecies.

Analysis of the crosslink time, depth and efficacy profiles of UV-light-activated corneal collagen crosslinking (CXL). A modeling system described by a coupled dynamic equations are numerically solved and analytic formulas are derived for the crosslinking time (T*) and crosslinking depth (z*). The z-dependence of the CXL efficacy is numerically produced to show the factors characterizing the profiles. Optimal crosslink depth (z*) and maximal CXL efficacy (Ceff) have opposite trend with respective to the UV light intensity and RF concentration, where z* is a decreasing function of the riboflavin concentration (C₀). In comparison, Ceff is an increasing function of C₀ and the UV exposure time (for a fixed UV dose), but it is a decreasing function of the UV light intensity. CXL efficacy is a nonlinear increasing function of [C₀/I₀]^-0.5 and more accurate than that of the linear theory of Bunsen Roscoe law. Depending on the UV exposure time and depth, the optimal intensity ranges from 3 to 30 mW/cm² for maximal CXL efficacy. For steady state (with long exposure time), low intensity always achieves high efficacy than that of high intensity, when same dose is applied on the cornea. The crosslinking depth (z*) and the crosslinking time (T*) have nonlinear dependence on the UV light dose and the efficacy of corneal collagen crosslinking should be characterized by both z* and the efficacy profiles. A nonlinear scaling law is needed for more accurate protocol.