Using thermally induced nanosize surface deformations to attenuate pulsed light fluxes N. V. Prudnikov Applied Problems Section, Presidium of the Russian Academy of Sciences, Moscow
V. V. Chesnokov, D. V. Chesnokov,a兲 S. L. Shergin, and V. B. Shlishevski Siberian State Geodesic Academy, Novosibirsk
共Submitted May 14, 2008兲 Opticheski Zhurnal 76, 36–41 共February 2009兲 This paper gives an analysis of the possibility of attenuating the pulsed light fluxes of reflective surfaces by subjecting them to nanosize deformations excited by powerful pulsed laser radiation. The proposed physical model is used as a basis for discussing the thermophysical aspects of the appearance of thermally induced deformations, the characteristic times of their existence, and the functional characteristics when they interact with optical radiation. © 2009 Optical Society of America.
Deformations induced in a solid by laser radiation are being fairly actively studied in terms of the physics of the interaction of light fields with metals,1 in connection with developments in high-power optics2 or with the use of laser probes to study surface acoustic waves3 from deformations of the substrate surfaces. Kamanina’s article4 presented a review of the results achieved in the creation of passive filters as intensity limiters of laser radiation. Such devices change their absorption as a result of the incident radiation energy, with this dependence having a substantially nonlinear character—the effect is observed only at high light-flux intensities. Dye solutions or media that contain nanoparticles of metals, fullerenes, or carbon nanotubules are used as absorbers. The limited use of this type of elements is caused by the resonance, narrowband character of their operation. Below we shall discuss the possibilities of creating alternative light-attenuating devices, using surfaces that are smooth and mirrorlike when they are illuminated by weak light fluxes but that scatter intense 共harmful兲 pulsed laser radiation. As will be shown below, the indicated surfaces can provide the necessary light attenuation, in particular, when a solution is obtained for the crucial problem of protecting eyes and photoelectric radiation sensors from blinding laser flashes, in which the energy of even a single laser pulse often breaks down the photo-or heat-sensitive elements of image converters, and, as a consequence, puts the observation facilities out of order. Laser-irradiation-induced thermal deformation of the surfaces of bodies is caused by thermal expansion of the material. In semiconductors, there is a mechanism by which the volume changes as a consequence of charge-carrier generation, but the deformations are usually small in any case. One possibility of increasing the deformations and, consequently, of increasing the efficiency with which such a deformed surface interacts with a light flux is to use a special two-layer surface structure. This consists of an upper reflective layer and a lower layer made from a material which, under the action of heat, can undergo a phase transition with an increase of volume—for example, it can be melted or 82
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vaporized. The layers are locally heated during the reception of a pulse of focused laser radiation. The lower layer is vaporized at the heating site, while the upper layer is deformed by the excess vapor pressure, takes the shape of a dome, and scatters the incident radiation. After the action of the irradiation pulse ends, the mirror assumes its original flat shape in a time of the order of microseconds, and the entire blindingproof observation medium goes back into operation. As a result, the lower layer returns to the condensed state when it cools to a temperature below the phase-transition temperature. The fact that the initiation of the surface activity of the mirror has a thermal character allows it to be used in a fairly wide region of the spectrum. The requirements imposed on the optical properties of the reflective layer are contradictory: On one hand, it must thoroughly absorb the energy of the blinding radiation and must quickly transmit heat to the second layer. On the other hand, it must possess high reflectivity as an element of the optical system. The problem must be solved in each concrete case starting from the technical specification on the system as a whole, but, from general considerations, the reflectance in the working range of the spectrum obviously must be no less than 0.8. The scattering properties of the surface increase if the two-layer structure is made in the form of an array of cells filling the surface of the substrate; in such a case, when a laser pulse is absorbed, the illuminated part of the surface acquires relief in the form of a multitude of regularly spaced microdomes. By using an aperture stop mounted further along the optical axis, the radiation scattered at angles that exceed some specified limiting angle is cut off and does not reach the photodetector. In practice, the time it takes the microdomes to appear 共the response time兲 must be about 0.1-0.2 of the width of the blinding radiation pulse 共i.e., about 1 – 10 ns兲, and the fraction of scattered energy of the pulse must be at least 80–90%. Figure 1 schematically shows the layout of a cell of the array in the original position 共a兲 and its configuration after responding to the action of incident radiation 共b兲. When the light is normally incident, the maximum scattering angle of
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QS共1 − Rref兲 = c1m1⌬T + c2m2⌬T + m2Lm + m2Levap + c3m3⌬T,
FIG. 1. Layout of an optical shutter cell that uses thermally induced deformation of a mirror surface. 共a兲 Arrangement of the cell of the array in the original position, 共b兲 configuration of the cell of the array after it responds to the action of incident radiation. See text for explanation.
the radiation on the microdomes is max ⬇ 2r / rc = 4h / r, where r is the radius of the base, and rc is the radius of curvature of the dome. The process for fabricating silicon microcircuits can be regarded as one possible technological implementation for creating a shutter. An array of cavities 2 about 10 nm deep is formed photographically and by selective etching on a flat silicon substratem 1. An easily evaporable compound is placed in each cavity. A metallic membrane about 0.05 m thick, connected with the chamber walls and thus forming a “lid” for them, is deposited on top of the array. The reflectance of the membrane is about 80%. The finished shutter chip is placed in a housing with an optical window that protects the surface from mechanical damage and is connected as part of a blinding-proof optoelectronic system as a flat mirror 共oblique or autocollimation兲. When radiation is incident on it, the absorbed part of its energy heats the membrane and the cavity under it, evaporating the substance in the cavity and creating a pulsed jump of pressure that deforms the membrane and deflects it upward—it assumes the shape of a segment of a sphere, forming cavity 2⬘. This deformation is partially counteracted by desorption of the gas from the upper surface of membrane 1. Let QS be the radiation energy incident on the surface of a cell with area S. Then the fraction of this energy absorbed in the cell is Qabs = QS共1 − Rref兲, where Rref is the reflectance of the membrane surface. The absorbed energy is consumed in heating the membrane of thickness d1 and mass m1, a layer of thickness d2 of evaporated substance of mass m2, and a certain layer of the substrate 共thickness d3 and mass m3兲 to an approximately identical 共in first approximation兲 temperature. For rough calculations, as will be seen from what follows, it is justifiable to use the equality d3 = 3, where 3 is the length of the thermal wave in the substrate material. In general, it would be required to solve numerically the thermal conductivity equation for a multilayer structure—a second-degree differential equation in partial derivatives. In the process of heating, mass m2 undergoes successive phase transitions from the solid state to the liquid state, and then the vapor state. The energy spent on these processes is determined by the specific thermal melting Lm and the specific thermal evaporation Levap according to the balance equation 83
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共1兲
where c1, c2, and c3 are the specific heats of layers d1, d2, and d3, respectively, and ⌬T = T − 293 K is the increase of their temperature under the action of the laser pulse, in first approximation equal for all the layers. Since the terms m2Lm and c2m2⌬T2 can be neglected in comparison with the other terms because they are small, we get QS共1 − Rref兲 ⬇ c1m1⌬T + c3m3⌬T + m2Levap .
共2兲
Let us divide each term of Eq. 共2兲 by the area S of the cell. Recalling that QS = PSt pS and m1–3 = 1–3d1–3S, where PS is the power density of the radiation incident on the mirror, t p is the laser pulse width, and 1–3 is the density of the substances corresponding to the subscripts, we get PSt p共1 − Rref兲 ⬇ c11d1⌬T + c33d3⌬T + 2d2Levap .
共3兲
This equation makes it possible to introduce criteria for choosing the materials for all three layers. The last term in it determines the threshold power of the cell response, since its value significantly exceeds the sum of the other terms of the equation. Therefore, in order to reduce the threshold power of the laser radiation, a substance with the minimum possible value of the product 2d2Levap should be chosen as the evaporant. On the other hand, since ⌬T = Tboil + ⌬T⬘ − 293 K, where ⌬T⬘ is the excess of temperature to which the cell is heated above the boiling temperature, an increase of Tboil results in an increase of ⌬T and consequently increases the first two terms on the right-hand side of Eq. 共3兲, and this is undesirable. Consequently, the evaporating substance must also have a fairly low boiling temperature. From a thermophysical viewpoint, the membrane must possess the maximum thermal conductivity and the minimum heat capacity in order to unimpededly transmit the absorbed energy of the radiation into layer 2. The value of the component c11d1⌬T also depends on the membrane thickness d1, which is limited from below by requirements of mechanical strength. Conversely, it is desirable to fabricate the substrate from a material with low thermal conductivity a = kTc 共kT is the thermal conductivity兲, for example from quartz, in order to reduce in it the outflow of heat, determined by the term c33d3⌬T. Taking the indicated considerations into account in the initial analysis, molybdenum and titanium were determined to be the most suitable materials for the membrane, iodine for the evaporable layer, and quartz for the substrate. We shall carry out the further discussion of the processes that accompany the laser evaporation of thin films in accordance with the data of Ref. 5, according to which the conditions at each point of the evaporable medium are in equilibrium at each instant, and this makes it possible to use the laws of equilibrium thermodynamics. Moreover, the process of heating the film can be regarded as steady-state, since, according to the analysis carried out in the indicated paper, the time to establish the density-distribution profile of the Prudnikov et al.
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substance 共in our case, under the membrane兲 is less than the characteristic time to change the radiation intensity. When the temperature T is above the boiling temperature under normal conditions and below the critical temperature for determining the vapor pressure p, it is possible to use the adiabatic dependence5 p = p0
冋 冉 冊册
T MLevap 1 1 exp − T0 R T0 T
,
共4兲
where p0 is the saturated vapor pressure at temperature T0 , M is the molar mass of the substance of the vapor, and R is the universal gas constant. For rough calculations, it is convenient to replace T0 by the boiling temperature Tboil of the substance at normal atmospheric pressure 共p0 = 105 Pa兲. The specific energy Qevap consumed in the solid-vapor transition depends on the temperature, namely Qevap ⬇ ⌬H +
R⌬T ; 2M
where ⌬H is the enthalpy change corresponding to the transition from the liquid to the vapor state. The pressure determined by Eq. 共4兲 is established in the cell receiving the radiation, when all of its internal surfaces are heated to temperature T. Since the cell membrane is only slightly transparent, the thermal flux through the cell to the substrate results from thermal conductivity, and in time t p it propagates to a distance in general about equal to the length of a thermal wave in the membrane-medium system in the cell. When the width of the laser pulse is t p ⬇ 1 ns, the length of the thermal wave for possible materials of the membrane and the evaporant filler of the cell is no greater than 100– 200 nm. Since the action of the radiation and the corresponding deformation of the membrane under the action of vapor pressure have a short-term character, it is important to know the dynamic behavior of the membrane. Information on this can be obtained by determining its normal vibration frequency 0. Let us use the results given in Ref. 6 for a circular membrane rigidly attached at the edges,
0 ⬇
N2i ␣2 , 2r2
where Ni is the root of a Bessel function of the first kind, i = 1 , 2 , 3 , . . . is the order of the root, r is the radius of the membrane, and ␣2 = d1冑EY / 12共1 − 2兲1 is the cylindrical rigidity 共EY is Young’s modulus, and is Poisson’s ratio兲. Substituting here the proposed values of the membrane parameters 共EY = 2 ⫻ 1011 Pa, = 0.3, 1 = 10.2⫻ 103 kg/ m3, d1 = 10−7 m, r = 5 ⫻ 10−6 m, Ni=1 = 2.405兲, we get 0 ⬇ 4.9 ⫻ 106 Hz 共i.e., the period of the normal vibrations of the membrane is about 2 ⫻ 10−7 sec兲. This means that, after the action of a laser pulse of width t p ⬇ 10−9 − 10−8 sec, the membrane continues to move in the direction of the received impact action and 共if the interaction with the environment is neglected兲 will vibrate with a period of about 2 ⫻ 10−7 sec. The amplitude of the vibrations, as it is easy to see, significantly exceeds its displacement during the time of impact. 84
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TABLE I. Thermophysical parameters of some materials.7 Substance
Mo
Ti
I2
SiO2
Tboil, K 共for t p = 1 ns兲, m c, J/kg-deg , kg/ m3 M, kg/mol a, cm2 / sec Levap, J/kg
0.2 290 10.2⫻ 10−3 0.096 0.38
0.07 740 4.5⫻ 103 0.05 0.06
456 0.012 632.8 4.93⫻ 103 0.127 1.44⫻ 10−3 8.40⫻ 105
0.03 1250 2.6⫻ 103 0.06 0.009
The time of the first return of the membrane to the initial state 共the relaxation time of the shutter兲 can be estimated as half the vibrational period, i.e., about 10−7 sec, but the final damping of the vibrational motion of the membrane occurs after completing several 共about 3–5兲 vibrations. If the time of action of the laser pulse is much less than the period of the normal vibrations of the membrane, the membrane’s motion at the instant the laser acts will no longer be determined mainly by its elastic properties but by the inertial properties of the substance—i.e., by Newton’s second law and by the equation of accelerated motion,
h=
pt2p . 2 1d 1
共5兲
Table I shows a number of thermophysical parameters for the membrane materials 共Mo, Ti兲, the evaporant 共I2兲, and the substrate 共SiO2兲 needed for calculations using Eqs. 共2兲–共5兲. As an example, Table II presents the results of a calculation of the saturated vapor pressure p of the working substance under the membrane for two different temperatures T to which the cell is heated, the absorbed energy Qabs needed for such heating, and the corresponding power density PS of the radiation incident on the cell. It was assumed that the membrane material is a molybdenum film of thickness d1 = 100 nm 共c1r1d1 = 0.296 J / m2 deg兲, the working substance is an iodine film about 10 nm thick 共2d2Levap = 41.4 J / m2 deg兲, and the substrate is made from fused quartz 共c333 ⬇ 0.1 J / m2 deg兲. Let us consider the factors that determine a fast response in such an optical shutter. In first approximation, its action can be represented in the form of a sequence of steps: 共a兲
absorption of optical radiation by the membrane and energy transfer to the crystal lattice of the metal,
TABLE II. Energy absorbed by the cell, saturated vapor pressure, and power density of incident radiation at two different temperatures.
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共b兲
共c兲 共d兲
propagation of heat from the membrane and heating of the region occupied by layers, 1, 2, and 3 共see Fig. 1兲 to the boiling temperature under the given conditions of the working substance, conversion of the working substance into a vapor, deformation of the membrane.
In the system under consideration, the complex processes of heat transport and evaporation are triggered by the front of the laser pulse and occur continuously and in parallel. However, Ref. 8 substantiates the possibility of a simplified step-by-step treatment of the processes, provided it is assumed that the processes begin in a given layer only after the thermal front reaches it, and, when they are finished, the thermal processes make a transition to the next layer, etc. The duration of the first stage is determined by the interaction of the photons with the electron gas, which transfers thermal energy to the lattice. For metals, the time to convert radiation energy into the heat of the substance is t1 ⬇ 10−11 sec.1 It can be approximately assumed that a membrane layer several tens of nanometers thick is heated with a lag of about 10−11 sec from absorption of radiation. The heat then propagates because of the thermal conductivity of the substance. The time it takes the temperature front to move a distance l in a substance with thermal conductivity a is determined by the expression tl = l2 / a. The time needed to absorb enough radiation energy for the cell to respond is t2 = Qabs / 共PSS兲. Finally, the time th required for the membrane to be deformed to the deflection value h can be determined from Eq. 共5兲, if it is assumed that the saturated vapor pressure is unchanged. However, in fact, since the cell is continuously acted on by irradiation, the temperature of the working region constantly increases, and this results in a pressure increase. The volume under the membrane occupied by vapor increases at the same time, because of its deformation, and this, conversely, promotes a decrease of the pressure. In each specific case, it is necessary to separately estimate the significance of both of these processes. In subsequent rough calculations, we shall assume that the pressure that deforms the membrane during the response of the cell remains constant and equal to one third of the saturated vapor pressure under the membrane; i.e., th = 冑61d1h / p. Thus, the overall duration t⌺ of the processes that cause the valve to respond is
t⌺ ⬇ t1 + tl + t2 + th = 10−11 +
l2 Qabs + + a P SS
冑
6 1d 1h . p
The calculated comparison of the relative role of the components of the response time shows that the period in which the cell membrane bends to the amount needed for scattering radiation has the greatest duration; the sum of the times t1 + t2 + t3 ⬇ 1.0– 1.5 ns characterizes the delay time of the beginning of the response of the cell after radiation is incident on the mirror being deformed. 85
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FIG. 2. Dependences of the deflection of molybdenum and titanium membranes on deformation time for various power densities of the incident radiation. 1 and 3—molybdenum, 2 and 4—titanium; 1 and 2—PS = 3.26 ⫻ 1011 W / m2; 3 and 4—PS = 3.72⫻ 1011 W / m2.
Figure 2 shows how the deflection of a molybdenum and titanium membrane 100 nm thick depends on the deformation time for various power densities of the incident radiation 共as before, the working substance is an iodine film about 10 nm thick, and the substrate is made from fused quartz兲. The maximum light-scattering angle in this case varies from 0.8 to 8 mrad. The thermal energy absorbed by the deformed surface must then be emitted from the site where it is given off in order to reduce the surface of the mirror to the initial state after the end of the pulse of surface irradiation. The problem can be solved by using a four-layer structure, if the heat can be discharged through the SiO2 layer forming the bottom of the cell into a thermally conductive substrate. The time constant of heat dissipation in the approximation in which the substrate temperature remains unchanged equals
⬇ R TC =
d3 共c11d1 + c22d2 + c333兲, k
where RT = 3 / k is the thermal resistance of the oxide film, k is Boltzmann’s constant, and C = c11d1 + c22d2 + c333 is the heat capacity of the cell. Calculations give the value = 共5 – 10兲 ⫻ 10−8 sec. It is important to emphasize that the effect of thermally induced attenuation of the intensity of the light fluxes has a threshold character. When the power density of the incident radiation is less than some value at which the working substance can boil, the cells do not respond. Thus, if the cell membrane with iodine in the example considered above has a diameter of 10 m, the total pulse power needed to make it respond in 1 ns must be at least 30 W 共the irradiation energy is Q ⬇ 3 ⫻ 10−8 J, and the energy density in the incident radiation pulse is P ⬇ 370 J / m2兲. Our analysis shows that mirror film structures in which thermally induced phase transitions of the substance with a change of the volume occur under the action of intense radiation can be the basis for creating micromechanical devices Prudnikov et al.
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with nanosecond response time for protecting optoelectronic devices and systems from damaging laser radiation. a兲
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1
A. M. Prokhorov, V. I. Konov, I. Ursu, and I. N. Mikhéilesku, Interaction of Laser Radiation with Metals 共Nauka, Moscow, 1988兲. 2 V. A. Shmakov, High-Power Optics 共Nauka, Moscow, 2004兲. 3 A. A. Oliner, ed., Acoustic Surface Waves 共Springer-Verlag, New York, 1978; Mir, Moscow, 1981兲.
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4
N. V. Kamanina, “Photophysics of fullerene-containing media: laserradiation limiters, diffraction elements, dispersed liquid-crystal light modulators,” Nanotekhnika No. 1, 86 共2006兲. 5 S. I. Anisimov, Ya. A. Imas, G. S. Romanov, and Yu. V. Khodyko, Action of High-Power Radiation on Metals 共Nauka, Moscow, 1970兲. 6 G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev, Handbook on the Resistance of Materials 共Naukova Dumka, Kiev, 1988兲. 7 B. P. Nikol’ski, O. N. Grigorov, M. E. Pozin et al., Handbook of Chemistry, vol. 1, General Information, the Structure of Matter, the Properties of the Most Important Substances, and Laboratory Technique 共Khimiya, Leningrad, 1966兲. 8 N. V. Karlov, N. A. Kirichenko, and B. S. Luk’yanchuk, Laser Thermochemistry 共Nauka, Moscow, 1992兲.
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