dependence of the nonlinear absorption of AgBr nanoc- ... AbstractâThe photolysis of AgBr nanocrystals irradiated by picosecond light pulses with quantum ...
ISSN 0030-400X, Optics and Spectroscopy, 2007, Vol. 103, No. 5, pp. 777–782. © Pleiades Publishing, Ltd., 2007. Original Russian Text © A.V. Ivanov, R.S. Levitskiœ, E.Yu. Perlin, D.I. Stasel’ko, 2007, published in Optika i Spektroskopiya, 2007, Vol. 103, No. 5, pp. 802–807.
CONDENCED-MATTER SPECTROSCOPY
Interband Phototransitions in AgBr Nanocrystals Assisted by Free Carriers A. V. Ivanov, R. S. Levitskiœ, E. Yu. Perlin, and D. I. Stasel’ko Center of Information and Optical Technologies, St. Petersburg State University of Information Technologies, Mechanics, and Optics, St. Petersburg, 199034 Russia Received January 10, 2007
Abstract—The photolysis of AgBr nanocrystals irradiated by picosecond light pulses with quantum energies of 3.51 and 1.17 eV is theoretically analyzed. The observed dependences of the photometric density on the long-wavelength radiation intensity are shown to be determined by the photogeneration of nonequilibrium electron–hole pairs as a result of indirect interband phototransitions involving free electrons. For such electrons to be involved in this process, they should possess a high kinetic energy, which is acquired due to intraband nonlinear absorption of the intense long-wavelength radiation. PACS numbers: 73.63.Bd, 78.67.Bf DOI: 10.1134/S0030400X07110161
INTRODUCTION The study of nonlinear photogeneration of electron– hole pairs (EHPs) involving free carriers was begun in [1, 2], where three-photon transitions between the upper valence band and the lower conduction band in semiconductor InAs crystals irradiated by a CO2 laser were considered. In [3], multiphoton interband transitions involving free carriers were theoretically investigated for the case of a three-band model of a crystal. In [4, 5], it was demonstrated that, under certain conditions, transitions of this type may give rise to the initiation of a multiphoton avalanche and, eventually, to a breakdown of the crystal. Silver halides are very convenient materials for studying various mechanisms of nonlinear optical absorption. The study of highly nontrivial nonlinear optical processes that occur at high excitation levels in light-sensitive media of this type is of great applied interest for the practical use of these materials. Multiphoton interband transitions governed by the resonance optical Stark effect can be considered as such processes. It was shown in [6–8] that an anomalous dependence of the nonlinear absorption of AgBr nanocrystals in high-resolution holographic photoplates on the excitation radiation intensity j is determined by transitions of this type. In the range j > 100 MW/cm2 , this dependence was accompanied by a considerable increase in the photolysis efficiency and photosensitivity of photolayers with increasing j. At the same time, a study of photographic processes in wide-gap I–VII semiconductor compounds employed in ultradisperse holographic silver halide emulsions with crystal diameters from 20 to 40 nm revealed nonlinear effects of another type [9, 10]. The
results obtained in [10] indicated that two-photon interband transitions involving free carriers play a predominant role. However, because crystals of the AgBr and AgCl type are indirect-gap materials, it was impossible to directly apply the theory developed in [1–5] to the description of direct-gap (in the k space) compounds. For indirect-gap semiconductors, the theory of multiphoton interband transitions involving free carriers was developed in [11], where nonlinear absorption of high-intensity laser radiation was considered for the photon energy less than one-half of the indirect-gap width of a crystal. The deficiency in the energy necessary for two-photon excitation of the electron-hole pair is made up by the kinetic energy of free electrons, which was acquired in intraband two-photon absorption of light. The probabilities of Auger-type indirect two-photon interband transitions involving free electrons were calculated in [11] by the perturbation theory. It was shown that, for the initial free-carrier concentration in the conduction band nc 1015 cm–3 and the radiation intensity range of interest for the experiment, j ~ 1010–1011 W/cm2, the calculated probabilities of such transitions exceed by several orders of magnitude the probabilities of “ordinary” direct and indirect (involving phonons) multiphoton transitions which can occur in the system considered. EXPERIMENTAL DATA It was observed in [12, 13] that a photolysis efficiency of a photographic material appreciably increases if this material is subjected to the combined action of two 3–7-ps pulses one of which is the pulse of the socalled actinic radiation (AR), whose photon energy (ωa = 3.51 eV) exceeds the indirect-gap width of
777
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IVANOV et al. D, arb. units 2.0
1
1.6 2 1.2 3 0.8 0.4 4 0
50
150 jna, GW/cm2
Fig. 1. Dependence of the photographic density D of a developed photolayer on the power density jna of NAR pulses that act simultaneously with excitation AR pulses (the duration of NAR and AR pulses is 5 ps) measured for the time delay: (1) 0, (2) 100, and (3) 500 ps. Curve 4 shows this dependence measured in the absence of excitation AR pulses.
AgBr, while the second pulse belongs to the so-called nonactinic radiation (NAR), and its photon energy is considerably smaller (ωna = 1.17 eV). It is important that the photolysis efficiency was increased not only when the two pulses acted simultaneously, but also if the NAR pulse was delayed by 400–500 ps relative to the AR pulse, which indicates that the NAR pulse is related to the formation and capture of free carriers. In [12], this process was qualitatively interpreted as a result of the release of electrons captured by recombination centers. However, this interpretation contradicts the results of a recent study [14] in which it was shown that, under similar conditions, the free-carrier capture time should be about 100 ps, which considerably exceeds the pulse durations used in [12, 13]. The fact that the effect observed was maximal upon the simultaneous action of pulses indicates that a decisive role in it was played precisely by free carriers. However, it remained unclear how the interaction of the long-wavelength radiation with free carriers could lead to such a considerable increase (up to 10 times) in the experimentally observed photolysis efficiency. Indeed, the estimates of the maximal heating of the photolayer taking into account the values of the induced long-wavelength absorption (about 1% at a wavelength of 1000 nm) and the heat capacity of the photolayer (about 2 J/cm3 deg) measured in [14] under similar conditions show that, in the studied range of the energy density of the long-wavelength, radiation (0.2–1 J/cm2), the heating does not exceed 3–15 K, which is completely insufficient to explain the effect observed. In addition, if the quantum energy of the IR radiation was reduced to 0.8 eV [15], the effect was markedly reduced (down to three times the initial value), which also contradicts the assumption about the thermal
mechanism of the effect, because, according to the classical theory, the absorption by free carriers should quadratically increase with increasing radiation wavelength. Figure 1 presents the dependences of the photographic density of developed high resolution holographic photoplates on the power density of the longwavelength nonactinic pulsed radiation which were experimentally determined in [16] for different time shifts of this radiation relative to the excitation pulses. The duration of AR and NAR pulses was 5–7 ps, the photon energy of AR pulses was 3.51 eV and that of NAR pulses was 1.17 eV (the wavelengths were, respectively, equal to 355 and 1060 nm). The AR energy density does not exceed 10–3 J/cm2, which corresponded to the density of absorbed photons by about 1018 cm–3. In the absence of the short-wavelength excitation (curve 4), the photographic density of the developed photolayer was characterized by a steep rise beginning from the power density near 150 GW/cm2. In the presence of the short-wavelength excitation with the power density indicated above and with the exact coincidence of the pulses, the beginning of the steep rise of this dependence was shifted to 40 GW/cm2, which corresponded to a fourfold increase in the photographic density of the developed photolayer compared to that achieved in the absence of the NAR action. The steepness of this dependence was also considerably reduced. If the delay time of the NAR pulse with respect to the AR pulse was increased to 100–500 ps, the effect observed was monotonically decreased, while the required power density was increased by a factor of 1.5–3 compared to that required upon the simultaneous action of the pulses. THEORETICAL MODEL To theoretically describe the nonlinear absorption observed in AgBr crystals, we will consider a two-band model of the energetic structure of such crystals. The model includes a valence band v and a conduction band c, in which we will separate two regions: the region c1 near the minimum at the point Γ1 at the center of the Brillouin zone and the region c2 near the maximum at the point L 1' near the boundary of the Brillouin zone. The width of each of these regions is assumed to be small compared to ω (Fig. 2). Consider the main transitions significant for processes observed. Under the action of high-intensity long-wavelength NAR pulses, ordinary multiphoton interband transitions occur. They include (Fig. 2) (i) indirect (involving phonons) interband three-photon transitions near the center of the Brillouin zone, (ii) direct four-photon transitions near the center of the Brillouin zone, (iii) direct four-photon transitions between the upper branch Λ3 of the valence band and the lower branch Λ1 of the conduction band, OPTICS AND SPECTROSCOPY
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INTERBAND PHOTOTRANSITIONS IN AgBr NANOCRYSTALS E, eV
779
E, eV Γ25 '
6
Δ'2
' Γ25
6
Λ3
Λ3 Λ1
2
X3
L'2 Λ1 L'1 ωna –2 c2 ωa
c 1 Γ1
k0
–2 c2
X1
Λ1
L'3 L'2
Λ1
Δ5 Γ15 Γ12
L'3 X5' X1' X4 X5
Δ1
' Γ25
–10
k2
c1
Δ Eg
2π/a (110)
0
Fig. 2. Two-band model of the energy structure of AgBr with an indirect band gap: ν is the valence band, and c1 and c2 are the two conduction bands. The arrowed vertical lines denote NAR photons with the energy ωna and AR photons with the energy ωa.
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Λ1
L'3 –14 –π/a
Λ3
L'3 L'2
k3
ωa
Λ3
L'3
Λ1
Γ15 Γ12
L'2
Λ3 L'3
' Γ25
L'3
L'2 0
π/a
Fig. 3. Multiphoton transitions involving free carriers according to the two-band model of the energy structure of AgBr with an indirect band gap. The dotted curves show the c2 c1c1v Auger transitions. Δ is the energy deficiency for indirect two-photon transitions.
and (iv) direct five-photon transitions between the branch Δ5 of the valence band v and the branch Δ1 of the conduction band c. Note that the four-photon transitions indicated in (ii) are forbidden, which significantly decreases their probability. During the joint action of AR and NAR pulses, interband transitions with simultaneous absorption of one AR photon and one or two NAR photons (Fig. 2) become possible. These transitions occur in the same regions of the Brillouin zone as four- and five-photon transitions from (ii), (iii), and (iv) (ωa = 3ωna). The action of AR pulses initiates indirect one-photon transitions between the top of the valence band near the point L 3' at the boundary of the Brillouin zone and the region c1 of the conduction band, which are analogous to three-photon transitions (ii) for NAR pulses. Apart from processes listed above, interband transitions involving highly excited free carriers (for definiteness, we will consider electrons) also lead to the generation of nonequilibrium EHPs. Precisely these processes (we will term them the Auger-type processes) play a key role at intensities jna 1011 W/cm2. Under conditions of experiments performed, there are three processes of the Auger-type that are worth considering OPTICS AND SPECTROSCOPY
Λ3
L'2
L'1
Λ1
–6
Λ3
L'3
L'2 –14 π/a (111)
ωna
Γ1
Λ3 L'3
L'2
k1
Eg
–6
–10
L'2 L'1
Δ1
Λ1
Λ1
2
2007
(Fig. 3): (v) “ordinary” impact ionization, which generates an EHP at the expense of the kinetic energy of a free electron (the photonless process of the Augertype); (vi) an EHP is generated at the expense of the kinetic energy of a free electron and the energy of an absorbed photon (single-photon process of the Augertype); and (vii) an EHP is generated at the expense of the kinetic energy of a free electron and the energy of two absorbed photons (two-photon process of the Auger-type). If one takes into account the energy and momentum conservation conditions, which are necessary to satisfy for the Auger-type processes (v)–(vii) to occur, it emerges that free electrons involved in these processes should be in the region c2. At first glance, it may appear that the probability of the photonless process is definitely greater than those of processes involving photons. It is clear, however, that the number of highly excited electrons (their kinetic energy should exceed Eg, and Eg > 2ωna) that can stimulate such a process is small. Analysis of the contributions made by Auger-type transitions involving n photons (n = 0, 1, 2) shows that, in the range of light intensities jna ~ 1011 W/cm2, these contributions are comparable in value. The probabilities of such pro-
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IVANOV et al.
cesses are calculated in the (n + 1)th order of the perturbation theory (in the first order with respect to the interelectron Coulomb interaction and in the nth order with respect to the interaction of the electronic system with the radiation field). In the situation under consideration, very narrow regions of the initial and final electronic states in the Brillouin zone contribute to the process of photonless impact ionization, which follows from the energy and momentum conservation laws for this process. This factor significantly reduces the efficiency of the photonless process. If Auger-type transitions involve one or, which is better, two photons (processes (vi) and (vii)), then the region of the Brillouin zone that is active in this transitions is significantly broadened due to an efficient narrowing of the band gap by the energy corresponding to these photons. At such high light intensities, this excessively compensates for the increase in the order of the process. Electrons can arrive at the high-excitation region c2 as a result of the following processes: (viii) indirect two-photon intraband transitions between the c1 and c2 regions under the action of NAR pulses; (ix) a cascade of two single-photon intraband transitions (including transitions involving phonons), as a result of which electrons pass from the region c1 to the region c2; and (x) indirect one-photon intraband transitions from that region of the Brillouin zone at which electrons arrive as a result of four-photon transitions (iii) to the c2 region. Clearly, only a portion of the electrons that arrived at the conduction band as a result of transitions (iii) will pass to the c2 region, whereas the remaining electrons will pass to the c1 region near the band bottom as a result of intraband relaxation. We will describe the kinetics of phototransitions with the help of the system of balance equations for the populations p of holes in the valence band and the populations of electrons n1 and n2 in the c1 and c2 regions, respectively. To set up the balance equations, apart from the transitions indicated above, it is necessary to take into account intraband relaxation processes, due to which electrons return from the region c2 to the region c1. As a result, the system of the balance equations takes the form (2) 2
2
n˙ 1 = W 21 n 2 – σ 12 j na n 1 + 2 ( γ 0 + γ 1 j na + γ 2 j na )n 2 (3) 3
(4) 4
(5) 5
(a)
(a + 1)
+ σ v 1 j na + σ v 1 j na + σ v 1 j na + σ v 1 j a + σ v 1 + (2) 2
j a j na
(a + 2) 2 σ v 1 j a j na , (4 + 1) 5 j na
n˙ 2 = σ 12 j na n 1 + σ v 2
(a + 2)
+ σv 2
2
j a j na – W 21 n 2
2
– ( γ 0 + γ 1 j na + γ 2 j na )n 2 , (3) 3
(4) 4
(5)
(4 + 1)
p˙ = σ v 1 j na + σ v 1 j na + ( σ v 1 + σ v 2 (a)
(a + 1)
+ σv 1 ja + σv 1
(a + 2)
j a j na + ( σ v 1
2
(a + 2)
+ σv 2
+ ( γ 0 + γ 1 j na + γ 2 j na )n 2
5
) j na 2
) j a j na
(1)
with the initial conditions n1(0) = n10 and n2(0) = 0. In (n)
formulas (1), σ ij are the cross sections of the n-photon (3)
optical transitions between the bands i and j;1 σ v 1 is the cross section of the indirect three-photon transition (a + n) involving phonons; σ v 1 is the cross section of the (n + 1)th transition, involving n NAR photons and one (a) AR photon; σ v 1 is the cross section of the one-photon (4 + 1) transition induced by the actinic radiation; σ v 2 is the cross section of the cascade process that includes the interband four-photon transition between the upper branch Λ3 of the valence band and the lower branch Λ1 of the conduction band and the intraband single-photon (a + 2) transition; σ v 2 is the cross section of the analogous cascade process involving actinic photons; W21 is the intraband relaxation rate for the conduction band; and γn j nn2 are the rates of indirect interband transitions of the Auger-type, as a result of which n photons are absorbed and a EHP with the hole near the band top v and the electron in the c1 region is generated, whereas a highly excited electron that initiates the process passes from the region c2 to the region c1. Because the durations of light pulses used are small compared to the characteristic recombination times, in system (1), the terms that take into account the electron–hole recombination and the carrier capture by traps are omitted. Taking into account these processes, the kinetics of electrons was studied in [7], where it was shown that the photographic density D, which is proportional to the number of captured electrons (after the establishing of the quasi-equilibrium distribution), is, in turn, proportional to the number of free carriers created by AR and NAR pulses. System (1) was set up additionally assuming that the final states for all transitions are not occupied. This assumption is justified by the fact that electrons that pass to the c1 region of the conduction band as a result of the absorption of AR and NAR photons are reside in states located fairly far from the bottom of the conduction band. In addition, because of the energy and momentum conservation laws, states in the c1 region in which two electrons reside as a result of Auger-type transitions are also located far from its bottom. In these approximations, the system of balance equations is linear and can easily be solved analytically. However, such an approximation for the description of the kinetics of phototransitions in the conduction band is very rough. A more strict consideration requires taking into account the nonequilibrium distribution of electronic states in the conduction band, and the depletion of the top of the valence band, which is significant for high radiation intensities used in experiment. Nevertheless, as will be seen from the results obtained such (2)
cross section σ 12 is contributed both by the two-photon intraband transitions and by the cascade of two one-photon transitions, which transfer electrons from the c1 to the c2 region.
1 The
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INTERBAND PHOTOTRANSITIONS IN AgBr NANOCRYSTALS
a simplified model agrees qualitatively with the experimental data presented above.
nc, 1018 cm–3 10
CALCULATION FORMULAS AND DISCUSSION OF RESULTS
8
The analytical solution of the system of balance equations for the concentrations of particles in bands takes the form
6
n1 ( t ) = p { e
– st/2
781
4
[ ( 1 + n 10 / p ) cosh ( rt/2 )
+ [ s ( p + n 10 ) + 2 ( c – bn 10 ) ] sinh ( rt/2 )/ pr ] – 1 }, n2 ( t ) = v { e
– st/2
[ cosh ( rt/2 )
2
(2) 100
+ ( vs + 2bn 10 + 2d ) sinh ( rt/2 )/vr ] – 1 },
200 jna, GW/cm2
where the following designations are introduced:
a = W 21 + g, (2) 2
b = σ 12 j na ,
2
g = γ 0 + γ 1 j na + γ 2 j na , (4 + 1) 5 j na
d = σv 2
(a)
(a + 1)
c = σv 1 ja + σv 1 (3) 3
Fig. 4. Dependence of the electron concentration in the conduction band of AgBr on the radiation intensity calculated according to the two-band model for the (solid curve) nonactinic irradiation alone and (dotted curve) simultaneous action of AR and NAR pulses.
2
( a + b ) + 4bg , v = ( c + d )/g,
s = a + b, r = p = ( av + d )/b,
(a + 2)
+ σv 2
(a + 2)
j a j na + σ v 1
(4) 4
2
(3)
j a j na , 2
j a j na
(5) 5
+ σ v 1 j na + σ v 1 j na + σ v 1 j na . Among the parameters of system (1), it is most difficult to estimate the cross section γ2 of two-photon interband transitions of the Auger-type. For the case under consideration, the calculations of [11] yield γ2 ≈ 6.6 × 10–2 cm4 GW–2 ps–1. Similar but considerably simpler estimations of γ0 and γ1 yield γ0 ≈ 3.8 ps–1 and γ1 ≈ 6.7 × 10–1 cm2 GW–1 ps–1. The estimations of the cross sections of the direct four-photon and five-photon interband transitions performed based on the results of (4) (5) [17] yield σ v 1 ≈ 8.8 × 105 cm6 GW–4 ps–1 and σ v 1 ≈ 3 7 –5 −1 8.9 × 10 cm GW ps . The values of the remaining parameters used in the calculations are as follows: (4 + 1) (3) W21 = 50 ps–1, σ v 2 ≈ 9.7 × 104 cm7 GW–5 ps–1, σ v 1 = (a) 7.3 × 107 cm3 GW–3 ps–1, σ v 1 = 1015 cm–1 GW–1 ps–1, (a + 1) (a + 2) =1.3 × 1015 cm GW–2 ps–1, σ v 1 σv 1 = 3.9 × (a + 2) 13 3 –3 –1 12 3 10 cm GW ps , σ v 2 = 2.0 × 10 cm GW–3 ps–1, ja = 1.0 GW/cm2 , and n10 = 1015 cm–3 . The estimation (2)
of the cross section of intraband transitions yields σ 12 ≈ 3.0 × 10–5 cm4 GW–2 ps–1. In addition, it was shown in [11] that, at the initial concentration of carriers in the conduction band ~1015 cm–3, the probability of this process is several orders of magnitude greater than the probabilities of other processes of EHP generation, i.e., interband fourphoton and indirect three-photon processes involving photons. OPTICS AND SPECTROSCOPY
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The results obtained indicate that, in the considered case of the wide indirect band gap in the picosecond time scale, indirect two-photon interband transitions of the Auger-type involving highly excited free carriers play a significant role in the EHP generation. Figure 4 presents the dependences of the electron concentration in the conduction band expressed as a sum n = n1 + n2 on the NAR intensity jna calculated for the pulse duration τI = 5 ps. It is seen that the results of (2)
the calculations strongly depend on the parameter σ 12 . Thus, if this parameter were decreased by two orders of magnitude and the material were irradiated only by NAR pulses, the threshold intensity would be shifted to the range ~103 GW/cm2. The dependence of the electron concentration on the NAR intensity and in the absence of actinic irradiation is shown by solid curve in Fig. 4. It is seen that this dependence has a threshold character. At a relatively small change in jna in the range ~100–200 GW/cm2, the electron concentration in the conduction band sharply increases from the initial value used in the calculation (~1015 cm–3), which is determined by a low impurity absorption of nanocrystals, to the value n ~ 1019 cm–3. If AR and NAR pulses act simultaneously, the role played by the AR pulses is mainly consists of rapid creating an additional concentration of nonequilibrium carriers, which makes it possible to initiate EHP generation processes that are nonlinear with respect to the concentration of free carriers at lower NAR intensities. This is ensured by an increase in the cross sections of optical transitions responsible for the EHP generation, because the cross sections of mixed two- and threephoton transitions are greater than the cross sections of
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four- and five-photon transitions, occurring only under the action of NAR pulses. The dependence of the electron concentration in the conduction band on the NAR intensity calculated for the simultaneous action of AR and NAR pulses is shown by the dotted curve in Fig. 4. It is seen that, in this case, the concentration depends less sharply on the NAR intensity, and the concentration value n ~ 1018 cm–3 is reached at a radiation intensities of tens of gigawatts per square centimeter. This result is qualitatively consistent with the experimental curves presented in Fig. 1 (curves 4 and 1, respectively). The exception is the range of electron concentrations n 1019 cm–3, where the effects of population can be substantial for optical transitions of all significant types and transitions of the Auger-type. Clearly, in this case, the concentration should increase more slowly with increasing NAR intensity, as is well seen in Fig. 1 (curve 1). To theoretically interpret curves 2 and 3 in Fig. 1, which correspond to the 100- and 500-ps delay times between the AR and NAR pulses, respectively, it is necessary to explicitly take into account the processes of recombination and electron capture by traps in system (1). This problem was solved in [7], where, in particular, a formula was obtained that described a decrease in the concentration of free carriers in the time interval between AR and NAR pulses. It is clear that such a decrease qualitatively explains the shift to the right of the curves D(jna) observed with increasing delay time. CONCLUSIONS The excitation processes of AgBr nanocrystals by actinic radiation with the quantum energy ωa = 3.51 eV, exceeding the indirect band gap width (Eg = 2.6 eV), and nonactinic radiation with ωna = 1.17 eV were analyzed. It was shown that the observed nontrivial dependences of the photographic density D of a material on the NAR intensity jna, in particular, an exclusively sharp rise of D at jna ≈ 1.5 × 1011 W/cm2 in the absence of actinic irradiation, occur as a result of interband transitions involving one or two photons and free electrons, intraband excitation of which is caused by one- or two-photon NAR absorption. ACKNOWLEDGMENTS
05-02-16212a) and a Ministry of Education program “Basic Research in Natural, Engineering, and Humanitarian Sciences” (project no. RNP.2.1.1.1089). REFERENCES 1. E. Yu. Perlin, A. V. Fedorov, and M. B. Kashevnik, Zh. Éksp. Teor. Fiz. 85 (4) 1357 (1983) [Sov. Phys. JETP 58, 787 (1983)]. 2. A. M. Danishevskiœ, E. Yu. Perlin, and A. V. Fedorov, Zh. Éksp. Teor. Fiz. 93 (4), 1319 (1987) [Sov. Phys. JETP 66 (4), 747 (1987)]. 3. A. V. Ivanov and E. Yu. Perlin, Opt. Spektrosk. 100 (1), 69 (2006) [Opt. Spectrosc. 100 (1), 49 (2006)]. 4. E. Yu. Perlin, A. V. Ivanov, and R. S. Levitskiœ, Zh. Éksp. Teor. Fiz. 128 (2), 411 (2005) [JETP 101 (2), 357 (2005)]. 5. E. Yu. Perlin, A. V. Ivanov, and R. S. Levitskiœ, Izv. Akad. Nauk 69 (8), 1129 (2005). 6. V. N. Mikhaœlov, V. N. Krylov, A. Rebane, et al., Opt. Spektrosk. 79 (4), 665 (1995) [Opt. Spectrosc. 79 (4), 613 (1995)]. 7. E. Yu. Perlin and D. I. Stasel’ko, Opt. Spektrosk. 88 (1), 57 (2000) [Opt. Spectrosc. 88 (1), 50 (2000)]. 8. E. Yu. Perlin and D. I. Stasel’ko, Opt. Spektrosk. 98 (6), 944 (2005) [Opt. Spectrosc. 98 (6), 844 (2005)]. 9. V. M. Mikhaœlov and D. I. Stasel’ko, Opt. Spektrosk. 75, 973 (1993) [Opt. Spectrosc. 75, 574 (1993)]. 10. E. Yu. Perlin, A. V. Ivanov, and D. I. Staselko, in Proceedings of the International Quantum Electronics Conference IQEC/LAT 2002 (Moscow, Russia, 2002), Tech. Digest QWE2, p. 385. 11. A. V. Ivanov and E. Yu. Perlin, Opt. Spektrosk. 102 (2), 262 (2007) [Opt. Spektrosk. 102 (2), 227 (2007)]. 12. I. O. Starobogatov, A. G. Belyaev, S. V. Vinogradov, et al., Pis’ma Zh. Éksp. Teor. Fiz. 46 (4), 153 (1987) [JETP Lett. 46 (4), 193 (1987)]. 13. I. O. Starobogatov, S. D. Nikolaev, D. I. Stasel’ko, et al., Usp. Nauchn. Fotogr. 26 (4), 8 (1990). 14. A. A. Bugaev, V. N. Mikhaœlov, D. I. Stasel’ko, and S. A. Tikhomirov, Opt. Spektrosk. 98 (2), 280 (2005) [Opt. Spektrosk. 98 (2), 240 (2005)]. 15. I. O. Starobogatov, S. D. Nikolaev, D. I. Stasel’ko, et al., Opt. Spektrosk. 72 (3), 639 (1992) [Opt. Spektrosk. 72 (3), 344 (1992)]. 16. I. O. Starobogatov, S. D. Nikolaev, D. I. Stasel’ko, et al., Usp. Nauchn. Fotogr. 26 (4), 8 (1990). 17. V. A. Kovarskii and E. Yu. Perlin, Phys. Stat. Sol. (b) 45 (1), 47 (1971).
This study was supported by the Russian Foundation for Basic Research (projects nos. 04-02-16175a,
Translated by V. Rogovoœ
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