Threshold fluences

Here, L total is the depth of the etched hole per pulse and is assumed to be the sum of photochemical and photothermal contributions, Tphoto and Thermal, respectively 0Ceff is the effective photon absorption coefficient of the medium and can vary with laser emission characteristics, e g., photon density Fis the incident laser fluence Fth is the medium s threshold fluence A and F are the effective frequency factor with units of pm/pulse and the effective activation energy with units of J/cm2, respectively, for the zeroth-order thermal rate constant F0, comparable in magnitude to Fth, is important only at low fluences.64 Equation (5) is obtained after assuming that the polymer temperature T in the laser-exposed region of mass mp and the thermal rate constant k are given, respectively, as... 

From a knowledge of the absorption coefficient aeff and the threshold fluence Fth, the value of the photochemical contribution to the etch rate, Fph0to> can calculated and subtracted from the measured hole depth for any given fluence. The difference, which according to this model is the thermal etch rate Fthermai will be modeled by Eq. (5) by rewriting it as... 

The threshold fluence decreases with increasing dopant concentration and for the lowest concentration where ablation is observed (0.2% polyimide) the threshold fluence is about 0.7 J/cm2 at 248 nm and about 0.9 J/cm2 at 308 nm. Additionally, at fluences around 10 J/cm2, the maximum measured etching rates at 248 and 308 nm are about 3 and 6 pm/pulsc, respectively. While the etching rate for the 248 nm ablation of the 0.2% polyimide-doped sample has begun to saturate, the corresponding curve for the 308-nm ablation is still increasing. In comparison, the threshold fluence for the ablation of neat PTFE using 300 fs... 

Furzikov79 proposed a thermal model to describe the etching rate that led to an inverse square root dependence of the threshold fluence on a modified absorption coefficient, aeff, which includes possible changes in the singlephoton absorption coefficient owing to thermal diffusion. This inverse square root relation is given by... 

Figure 5.25. Dependence of the threshold fluence Fth on the dopant concentration cp at 248 ( ) and 308 (A) nm (from D Coputo et al.7S).

Fig. 10.3. Threshold fluence for positive ions of (O) cytochrome c and ( ) sinapinic acid as function of the molar matrix-to-protein ratio. Reproduced from Ref [42] by permission. John Wiley Sons, 1994.

Medina, N. Hudi-Fdire, T. Westman, A. Sundqvist, B.U.R. Matrix-Assisted Laser Desorption Depend ce of the Threshold Fluence on Analyte Concentration. Org. Mass Spectrom. 1994, 29, 207-209. 

From a knowledge of the absorption coefficient tteff and the threshold fluence... 

As shown earlier, at low fluence levels, several sludies have found the relationship derived from Beer s law (Eq. (2)] suitable for predicting how the etch rate L varies with the fluence F and the threshold fluence Fth. In this limited-fluence region, the relationship between fluence and Umax can be derived using Eq. (2). Several investigations have shown that Fth decreases as a increases. 

Lasers have been used to initiate deton in RDX. Three types of initiation mechanisms have been described (Ref 102) (1) instantaneous deton caused by a shock wave in a thin metallic film (deposited on the expl) with the shock wave generated by a Q-switched laser pulse (2) instantaneous deton by direct interaction of a Q switched laser pulse and the test expl and (3) DDT produced by free-running laser pulses. Coarse RDX cannot be initiated, but milled RDX (particle size less than 40 microns) is readily initiated at various packing densities. The threshold fluences for the initiation of 1.18g/cc l,52g/cc milled RDX via mechanism (1) are 45,3J/cm2 and 127.9J/cm2, respectively. Detons are either essentially instantaneous or the sample bums without deton. For direct initiation [mechanism (2)], the threshold laser energy for 1.18g/cc RDX was 0.8J, or the same as in thin film initiation. However, deton was no longer instantaneous but required about 2 microsec for build-up. The 1.52g/cc RDX was initiated directly without delay (laser energy not given)... 

In the investigation of non-thermal damage to dielectrics, the Fokker-Planck equation is applied to describe the transient behaviors of electron densities, and to predict the damage threshold fluences for various laser pulse widths ranging from 10 femtoseconds to 10 picoseconds [13]. This model includes the effects of electron avalanche and multiphoton ionization on the generation of electrons. 

Figure 9 Comparisons ofthe predictions of damage threshold fluences with experimental data of Stuart et al. [24J at /l= 1053 and 526 nm for vanous pulse durations [13]...

Figure 11 Influence of applied electric flelds on damage threshold fluence for different laser pulse durations atA= 1053 nm [13]...

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