Experimental study of the influence of laser radiation power on the reflection coefficient of germanium and silicon at a wavelength of 355 nm

The dependences of the reflection coefficients at a wavelength of λ = 355 nm for germanium and silicon single crystals on the energy density of impacting laser radiation in the range 0.01 - 0.1 J/cm2 have been measured. Analytical expressions were obtained. It is assumed, that they are also valid in the range 0.1 - 1.0 J/cm2. With a further increase in the energy density, the dependence should acquire a more complex character due to the resulting optical breakdown.


Introduction
Laser radiation is widely applied in the technology of semiconductor materials [1,2]. It is used for cutting, annealing, surface modification and for a number of other applications. However, in practical use, one has to deal with a change in the reflection coefficient of a semiconductor with an increase in the radiation power density. The phenomenon is caused by the fact that laser radiation, being absorbed in a crystal, transfers energy to electrons of the valence band, transferring them to the conduction band [3,4]. This leads to the formation of a significant number of nonequilibrium electron-hole pairs, leading to an increase in the reflection coefficient. The phenomenon of the so-called plasma resonance in semiconductors is known, when at carrier concentration of 10 20 -10 21 cm -3 the reflection coefficient can approach 95 -98% [5].
For a number of technological processes, it is preferable to use ultraviolet (UV) radiation [6][7][8], in particular, a nanosecond pulsed Nd: YAG laser emitting at the third harmonic (wavelength λ = 355 nm) [9]. This is due to the high proportion of absorbed radiation.
UV radiation is used for the treatment of semiconductors in cases, where it is necessary to minimize the size of the irradiated area, which is proportional to the wavelength.
The refractive index of germanium was studied in [10][11][12]. At λ = 355 nm, the value of the refractive index (n) is slightly higher, than in the IR region: n Ge = 4.0746 [10], 4.0238 [11], 4.1150 [12]. Reflection coefficient at λ = 355 nm is slightly higher in magnitude, than for the infrared region (R  0.36). For silicon, according to [13] ( = 355 nm), R 0.49. However, these values were obtained for low-power radiation.  [14][15][16][17][18][19] interesting results on the modification of the surface of single crystals of germanium and silicon under the action of frequency-pulse laser radiation (λ = 355 nm) of nanosecond duration were obtained. To analyse these results, it was necessary to know the values of the reflection coefficient of the impacting radiation. This article is devoted to obtaining these data.

Experimental technique
The optical scheme of measurements is shown in figure 1. The radiation source was, used in [6,7,10], a solid-state Nd: YAG laser, operating at the third harmonic (λ = 355 nm, pulse duration τ = 10 ns, pulse energy (W) up to 8 mJ , pulse repetition rate (f) up to 100 Hz, laser beam diameter -3 mm, divergence -1-2 mrad). The measurements were carried out as follows. The laser emitted a series of 12 pulses with a frequency of 2 Hz, which was recorded by measuring devices in accordance with the scheme shown in figure 1. In the calculations, the average value of the energy density was selected from 12 pulses.
Before the start of measurements, mutual calibration of the ILD-2M and NOVA II measuring devices was carried out. For this, measuring device NOVA was placed in position 6, in front of the lens to record the radiation, directed on the sample. The radiation of laser 1, passing through nonlinear crystal 2, which converts laser radiation into the third harmonic (λ = 355 nm), and UV filter 3, was reflected by a quartz beam splitter 4 onto an ILD calorimetric laser energy measuring device ILD (6). During the calibration, the coefficient 1 was calculated, which was used to determine how the energy measured using NOVA and ILD, и , respectively, is related: = The reflection coefficient was measured in this way. The radiation of laser 1 was reflected by a quartz beam splitter 4 onto an ILD calorimetric laser measuring device (6), which controls the laser output energy. Then, the radiation was collected on the surface of a polished semiconductor sample by a quartz lens 7 with a focal length f = 250 mm into a spot with diameter varied from 1 mm 2 to 2 mm 2 by displacing the sample from the focal plane of the lens. As shown in the calculations performed in [6], during the time between pulses, the sample surface completely cooled down to room temperature. For each series, the arithmetic mean values of the pulse energy of the incident and reflected radiation were calculated. The energy of the radiation reflected from the radiation was recorded with a NOVA calorimetric detector located in the 6´ position.The reflection coefficient R was measured according to the standard technique as the ratio of the radiation flux reflected from the sample to the incident one: where: τ -the transmittance of the lens, which is 0.9; -the radiation flux reflected from the sample; 0 -radiation flux incident on the sample; -energy of reflected pulsed radiation in mJ; 1 -the energy of the incident pulsed radiation in mJ. For a given energy density, the indications of the and measuring devices were measured, and the R value was determined from them. The laser pulse energy was changed in accordance with the laser control program.

Experimental results and discussion
The values of the specular reflection coefficients of polished samples of single crystals of germanium and silicon with a change in the energy density of the laser pulse (λ = 355 nm) in the range 0.01 -0.1 J/cm 2 were obtained. As expected, the reflection increases with pulse energy density rising. In figure 2 and 3, the solid line shows the measured values of the reflection coefficients of germanium and silicon, and the dotted line shows the approximation results. It turned out to be impossible in this case to obtain experimental values of the specular reflection coefficients at an energy density of W ≥ 0.1 J/cm 2 due to the incipient degradation of the sample surface, accompanied by a noticeable increase in radiation scattering. These processes are described in detail in [14,15].
In figure 2 and 3, the dotted lines show the estimated reflection losses at a laser pulse energy density of 0.1 -2 J/cm 2 , which we could not measure. We presume, that in the range of 0.1 -1.0 J/cm 2 , this dependence will be quite valid, since the degradation of the surface occurs in a condensed state.
However, the need for extrapolation to the energy density range of 0.1-1 J/cm 2 arose due to the fact that data on the reflection coefficient in the energy density range of 0.1-1 J/cm 2 are necessary to understand surface processes, leading to an increase in radiation scattering on the surface at high energy density. However, at 1.0 -2.0 J/cm 2 , a new factor arises, associated with optical breakdown and, associated with it, melting and evaporation of the material. In this case, the dependence apparently will become more complicated. When impacted to a high-power short laser pulse, in addition to the generation of nonequilibrium carriers by absorbing photons, thermal generation of carriers also occurs due to heating of the surface layer. At the same time, intense diffusion of nonequilibrium carriers into the interior of the crystal occurs, as well as mutual annihilation of nonequilibrium donors and acceptors. However, reflection increases.
Experiments related with the impact of laser pulses on the surface of semiconductors and dielectrics showed, that the concentration of generated nonequilibrium carriers becomes so high, that the surface layer acquires the properties of a metal during the pulse. In [3] it is reported, that, when impacted to intense laser radiation, a semiconductor in its optical properties approaches metals -its reflection coefficient increases significantly. In this case, the reflection coefficient for germanium doubles at a power density q ~ 10 7 W/cm 2 , and the absorption coefficient in this case reaches values of 10 4 -10 5 cm -1 [3].
Reflectivity is associated with a change in the number of non-equilibrium carriers -electrons, the generated concentration of which (n) can be determined from the ratio realized for quasi-stationary lighting conditions: 0 nF   (5) where α -is the absorption coefficient; β -coefficient showing the ratio of the generated carriers to the number of absorbed quanta; F 0 -the radiation flux incident on the sample.

Conclusion
The dependences of the reflection coefficients at a wavelength of λ = 355 nm for germanium and silicon single crystals on the energy density of the acting laser radiation in the range 0.01 -0.1 J/cm 2 have been measured. Analytical expressions were obtained. It is assumed, that they are also valid in