Exposure of a Transparent Material with a Laser Radiation Band Gap with a Wavelength from the Spectral Region of the Absorption Edge
This work is a fundamental study of the process of motion of the heating region towards laser radiation during laser pulsed modification of the transparent materials structure. Numerical estimates of the magnitude of thermomechanical stresses in the material (2–3 GPa) are given. This significantly exceeds the elastic limit of semiconductor materials (40–100 MPa). A mechanism for the formation of linear tracks of microcracks directed from the focusing region of the laser pulse to the surface of the material is proposed. As a result, the effect of blocking the temperature rise in the focal region arises during the remaining pulse duration.
The choice of the energy and time parameters of the laser pulse, the geometrical position of the focus makes it possible to implement two types of changes in the material structure: spot or extensional. An experimental confirmation of this possibility has been obtained for monocrystalline semiconducting zinc selenide. Both types of structural changes can be used to solve a wide range of practical problems.
A. M. Grigoriev
Laser technologies center, St. Petersburg, Russia
This work is a fundamental study of the process of motion of the heating region towards laser radiation during laser pulsed modification of the transparent materials structure. Numerical estimates of the magnitude of thermomechanical stresses in the material (2–3 GPa) are given. This significantly exceeds the elastic limit of semiconductor materials (40–100 MPa). A mechanism for the formation of linear tracks of microcracks directed from the focusing region of the laser pulse to the surface of the material is proposed. As a result, the effect of blocking the temperature rise in the focal region arises during the remaining pulse duration.
The choice of the energy and time parameters of the laser pulse, the geometrical position of the focus makes it possible to implement two types of changes in the material structure: spot or extensional. An experimental confirmation of this possibility has been obtained for monocrystalline semiconducting zinc selenide. Both types of structural changes can be used to solve a wide range of practical problems.
Keywords: material heating by laser radiation, monocrystalline semiconductor zinc selenide, multiphoton absorption, optical breakdown, ultrashort pulse lasers, thermomechanical stresses
Article received: 12.05.2021
Article is accepted: 09.06.2021
Introduction
Currently, laser modification of the structure of transparent materials is based on the processes of nonlinear absorption of laser radiation. Usually these are processes of multiphoton absorption or optical breakdown (electron avalanche). In multiphoton absorption, an electron passes from the valence band of the material to the conduction band as a result of the absorption of several photons (interband absorption). In the case of optical breakdown, an electron is already in the conduction band and accelerates due to the absorption of a photon or several photons (intraband absorption), followed by impact ionization of nearby atoms.
Under conditions of both multiphoton absorption and optical breakdown, the absorption of laser radiation by the material increases sharply when the laser radiation intensity is equal to or greater than the threshold value, which is usually in the range of 1012–1014 W / cm2. This intensity is provided by focusing pico or femtosecond laser pulses inside a transparent material [1, 2].
However, in the case of laser modification of the structure of transparent materials with a band gap, including semiconductors, it is advisable to use the process of thermal increase in the absorption of laser radiation by the material with a wavelength from the spectral region of the absorption edge of the material [3].
Process theory
As is known, semiconductor materials are transparent to light with a photon energy below the band gap and completely absorb light with a higher energy. The transition zone from material transparency to complete absorption is the intrinsic absorption edge of a semiconductor material. Here, the light absorption coefficient increases exponentially and is described by the Urbach formula, which establishes a relationship between the absorption coefficient and the photon energy [4]:
, (1)
where αG is the absorption coefficient at EG = E, EG is the energy of the band gap, E is the photon energy, EU is the Urbach energy.
If the semiconductor heats up, then its band gap decreases in proportion to the temperature rise EG ≈ EG0 – ξΔT, here ξ is the coefficient of thermal change in the band gap, ΔT is the temperature variation of the material. In this case, the absorption edge moves to the long-wavelength side of the spectrum by an amount ξΔT, which leads to a significant increase in the absorption coefficient of light with the photon energy Ep from the spectral region of the absorption edge tail [3]. This situation is shown in Fig. 1.
Here, the solid curve α(E) is the absorption edge before heating, and the dash-dotted curve αΔT(E) is the edge after increasing the temperature by ΔT. The increase in the absorption coefficient of photons with energy Ep occurs exponentially from the initial coefficient α0 to αΔT and is described by the expression following from the Urbach formula:
. (2)
The effect of thermal increase in the absorption coefficient can be used for laser action on a transparent semiconductor material in order to locally change the structure of the material by heating. At the beginning of exposure, the material can be practically transparent and very weakly absorb laser radiation, but the presence of even slight absorption leads to the fact that the material is slightly heated by the laser radiation. A slight rise in temperature increases the absorption coefficient, the heating rate increases, and the temperature rises. This leads to a further increase in the absorption coefficient, intensification of heating and, ultimately, a rapid rise in temperature. In this case, a process is realized with a positive feedback between heating and an increase in the absorption coefficient.
To find out the conditions for the implementation of this process, it is necessary to solve the problem of heating the material by laser radiation with an absorption coefficient that depends on temperature. When the material is exposed to laser pulses of short duration τp << a2 / μ, the thermal conductivity of the material can be neglected, here a is the transverse size of the laser-affected zone, µ is the thermal diffusivity of the material. This is true when the material is exposed to laser pulses with a duration of τp less than a few hundred nanoseconds and an impact zone size of about 10 µm. It is assumed that the laser pulse is rectangular, and the intensity distribution in the area of influence on the material is uniform. In this case, the change in the temperature of the material with time is described by the equation:
, (3)
where cv and ρ are the specific heat and density of the material, respectively, ΔT is the temperature change, α is the absorption coefficient of the material, R is the reflection coefficient of the material, and I is the laser radiation intensity.
The dependence of the absorption coefficient α on temperature is determined by relation (2). In this case, the heating equation takes the form:
.
This equation is solved by the method of separation of variables. With initial conditions ΔT = 0; t = 0 the equation has the following solution:
, (4)
where t is the time of laser action on the material, which varies within the laser pulse duration τp: 0 ≤ t ≤ τp.
The graph of the dependence of temperature on the intensity of laser radiation is shown in Fig. 2.
From formula (4) and the graph of the dependence it follows that the temperature increases very rapidly when the value of the difference under the sign of the logarithm tends to 0.
Obviously, in this case the relation α0 · I · t · = cv ρ EU / ξ (1 –R). Therefore, a sharp increase in temperature occurs at a well-defined value of the intensity Ith, the value of which can be estimated by the formula:
. (5)
This means that the process of heating the material by a laser pulse with a wavelength from the absorption edge has a threshold character and is realized only when the laser radiation intensity is equal to or exceeds the threshold value Ith.
It can be assumed that the threshold nature of the heating process will allow local heating and a change in the structure inside a transparent semiconductor material by focusing laser radiation in the bulk of the material to a threshold intensity level or more. However, inside the material, the conditions for the passage of the laser pulse differ significantly from the conditions of free space. In the material, the pulse energy is absorbed and heats the material along the entire path of radiation from the surface of the material to the focusing region, which causes an increase in the absorption coefficient and affects the conditions for the passage of the laser pulse. Under these conditions, the heating of the material is described by an equation in which the increase in temperature is determined by the absorbed radiation as the laser beam propagates inside the material:
. (6)
It is assumed that the laser beam propagates in the material along the X axis. Equation (6) contains two unknown functions T(x, t) and I(x, t). Therefore, to solve the problem of heating a semiconductor material by a laser pulse focused inside the material with a photon energy from the spectral region of the absorption edge, it is necessary to compose and solve a system of two equations connecting the unknown functions: T(x, t); I(x, t). Under conditions of focusing laser radiation inside a material with an absorption coefficient depending on x and t, a lens with a focus f located at a distance L from the material surface at time t is determined by the following expression [4]:
. (7)
Here d − spot size in the lens focal plane, P is the pulsed power, D is the diameter of the laser beam on the focusing lens. In expression (7), the first factor reflects the increase in intensity due to focusing, and the second factor characterizes the decrease in intensity due to absorption of radiation by the material.
As a result, we have a system of two equations (6, 7), which describes the process of changing the temperature and intensity under the conditions of focusing the laser pulse inside the material, taking into account the dependence of the absorption coefficient on temperature. The heating process is nonlinear and non-stationary; therefore, the solution was realized numerically, by the method of finite differences in [4]. Numerical simulation of the heating process of a transparent material with a forbidden gap has shown that, under the conditions of focusing inside the material of laser pulses with a wavelength from the absorption edge region, heating of two types is realized: spot or extensional, linear. The implementation of the type of heating depends on the duration and energy of the laser pulse. Fig. 3 shows the graphs of the temperature distribution inside the material during a laser pulse with a duration of 100 ns.
It can be seen from the presented dependences that at the beginning of the pulse, heating is localized in the plane of focusing of the laser radiation, and with time, the heating region begins to propagate towards the laser radiation. A similar situation with the movement of the heating region towards the laser radiation is also observed with an increase in the pulse energy at a constant duration.
The results of numerical simulations show that the temperature difference between the heated area and the cold material surrounding this area varies in the range from several hundred to several thousand degrees. Under these conditions, strong thermomechanical stresses arise, the magnitude of which can be estimated by the formula:
,
where E is Young’s modulus, γ is the coefficient of linear expansion, ΔT is the temperature difference between the heated area and the surrounding material, ν is Poisson’s ratio.
The estimated value of thermomechanical stresses in the heating zone reaches 2–3 GPa, which significantly exceeds the elastic limit of semiconductor materials of 40–100 MPa. Therefore, a linear microcrack track should form inside the material, directed from the focusing region of the laser pulse to the material surface.
It should be noted that an increase in both the pulse energy and the pulse duration with constant power does not lead to an increase in the temperature in the focal region. This is due to the fact that heating the areas of the material in front of the focus leads to a significant increase in the absorption coefficient in these areas and blocking the passage of laser radiation to the focus area. Therefore, from the moment of time when the area of the material in front of the focus begins to warm, the temperature at the focus no longer increases and remains constant for the remaining time of the pulse duration.
Experiment
Experimental verification of the possibility of changing the internal structure of semiconductor materials by laser radiation with a wavelength from the spectral region of the intrinsic absorption edge was realized by exposing the samples of semiconductor zinc selenide to laser pulses with a duration of 25 ns and a wavelength in the range of 475–490 nm, which corresponds to the intrinsic absorption edge of ZnSe. A tunable LOTIS laser generating pulses with a maximum energy of ~1 mJ and a duration of 25 ns was used as a light source with a wavelength from the spectral range of the intrinsic absorption edge of zinc selenide. Laser pulses were focused into the sample by a lens with a focal length of 50 mm and a depth of approximately 1.5–2 mm. The nature of structural changes is determined by the magnitude of the pulse energy. When the sample is exposed to laser pulses with an energy of the order of 2 · 10–6 J, a local region with a modified structure and a transverse size corresponding to the diameter of the focused laser radiation is formed inside the material. With an increase in the pulse energy above 10–5 J, a change in the structure of the material is formed, which is linear and is oriented along the direction of propagation of the laser beam in the material. The nature of the structural changes is microcracks, the total length of the linear change in the structure is about 200 microns. The linear change in the structure, consisting of microcracks, confirms the results of numerical simulations on the propagation of heating from the focus towards the laser beam. Changes in the structure of the material induced by spot and extensional heating are shown in Fig. 4.
Thus, the experiment confirms the results of numerical simulation on the possibility of realizing two types of material heating: spot and linear.
Conclusion
The results of numerical simulation and experiment clearly demonstrate the possibility of local heating and changes in the structure of transparent semiconductor materials by a laser pulse focused inside the material with a wavelength from the spectral region of the material’s intrinsic absorption edge. The change in structure occurs as a result of local heating due to the effect of a thermal increase in the absorption coefficient. An experimental confirmation of the possibility of realizing a spot and linear change in the structure of the material for single-crystal semiconducting zinc selenide has been obtained. However, the mechanism of the thermal increase in absorption due to the shift of the intrinsic absorption edge should work for any material with a band gap. These are crystalline dielectrics, polycrystalline and amorphous semiconductors, various glasses, for example, chalcogenide ones.
The choice of the energy and time parameters of the laser pulse, as well as the focusing conditions, makes it possible to implement two types of changes in the material structure: spot or extensional, linear. Both types of structural changes can be used to solve a wide range of practical tasks. A spot change in the structure can be used for optical recording of information, as well as for the formation of various photonic or other microstructures of complex topology inside transparent materials with a forbidden gap, for example, Bragg gratings or optical fibers. Linear modification can be applied to separate semiconductor wafers into chips by stealth dicing.
AUTHOR
Grigoriev Alexander Mikhailovich, grigoriev@ltc.ru, Head of the Laser Technology Laboratory, Laser technologies center, St. Petersburg, Russia. Research interests: laser and optical technologies, semiconductor optics.
ORCID: 0000-0002-8545-7848