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On interaction of vibrationally excited molecules with a semiconductor wall
Solid State Communications, Vol. 56, No. 12, pp. 1063-1064, 1985. Printed in Great Britain.
0 0 3 8 - 1 0 9 8 / 8 5 $3.00 + .00 Pergamon Press Ltd.
ON INTERACTION OF VIBRATIONALLY EXCITED MOLECULES WITH A SEMICONDUCTOR WALL V.A. Namiot Institute of Nuclear Physics, Moscow State University, Moscow, 119899, USSR
(Received 22 August 1985 by V.M. Agranovich ) This paper is devoted to problems related to the interaction ofvibrationally excited molecules with a wall made of a semiconductor. When the width of the forbidden zone is close to the energy of a vibrational quantum, the main process induced by the collision of a molecule with such a wall is the production or annihilation of an electron-hole pair. THE RECENT INTENSIVE DEVELOPMENT of lowionized plasma physics [ 1 - 3 ] has stimulated the study of the interaction of different plasma components with the wall [4]. One of such components is the vibrationally excited molecules. It is in these molecules the main part of the energy released in plasma is very often concentrated, while the energy spent on their translational motion is still sufficiently small. This is due to the fact that the characteristic times of the vibrational ( V - V ) exchange are practically always considerably smaller than the times of the vibrational-translational (V-T) relaxation [3]. As a wall bordering the plasma we propose to use the surface of a semiconductor with the width of the forbidden zone close or equal to the energy of a vibrational quantum of plasma molecules. There is quite a large number of such narrow-zone semiconductors [5], for example, among the lead chalcogenides [6]. The collision of a vibrationally excited molecule with such a wall may induce a new, yet unstudied elementary process in which the energy of the vibrational quantum is transferred directly to excitation of an electron-hole pair. In most cases the probability of this process essentially exceeds the probability of the energy being transferred to excitation of atoms of the crystal lattice of the wall as well as the probability of emitting a quantum (especially, when in the dipole approximation, the excited molecule is not emitting). If we create a p-n junction immediately beneath the surface of the wall, there must occur a spatial separation of electrons and holes resulting in the appearance of a potential difference at the surface of the semiconductor*. By this potential difference one may in principle determine the time dependence of the concentration of vibrationally
* In order to drain the current from the surface of the semiconductor one may in principle use a grid electrode on which the holes (or electrons) will gather owing to their lateral mobility.
excited molecules of a given kind. The semiconductor walls may be used for recovering the part of the energy wasted as heat losses, and thus, to reduce the effective energy expenditure on useful reactions generated in plasma. There has been discussed a number of other possibilities of recuperation or of autorecuperation of the energy lost by a beam of charged particles in gas or in plasma [ 7 - 9 ] . Finally, there is a possibility of obtaining the vibrationally excited molecules via a reverse process the recombination of the electron-hole pair with transmission of the energy to the molecules hitting the wall, which is achieved by applying a potential difference produced by an external source to the p-n junction. In principle, this way one may even obtain an inverse population of vibrationally excited states. One may also achieve a varying in time heating of the gas in contact with the wall without heating the wall itself, and thus, control the pressure in the gas, create flow, etc. Here is the estimate of the probability of an electron-hole pair being produced in the collision of a vibrationally excited molecule with the wall c X/~'/3(coo)t~(w o) Q2o
Pa ~ 161rZeoMco~R4A2VT
(1)
where c is the speed of light; e is the relative permittivity (eo is the vacuum permittivity); coo is the frequency of molecular vibrations; M and A are respectively the characteristic mass of the atoms forming the molecule and the characteristic distance between them; R is the minimum distance between a molecule and the walL; vT is the thermal velocity of molecules; Qo is the quadrupole moment; ~(~o0)=/-1(CO0) , where l(~oo) is the average path-length of a quantum in the semiconductor; the dimensionless factor ~(Wo) is introduced to make allowance for the fact that the absorption of a quantum by the region near the surface may be different from volume absorption. When hob0 essentially exceeds e~
1063
INTERACTION OF VIBRATIONALLY EXCITED MOLECULES
1064
(the width of the forbidden zone), /3(6Oo)- 1. In the vicinity of the threshold a signficant contribution to absorption may be given by the surface levels lying near the bottom of the conductivity zone (if such levels do exist)t. In this case for direct allowed transitions we have
ra
mI'
/3(~Oo)-~ (m--;~) (h~oo- %)-v2,
Vol. 56, No. 12
levels in the gas. The total energy carried away by excited molecules from the wall is
E ~ nVT P2hwo, 4
(4)
where n is the concentration of molecules. At n ~ 102s m -3 and/'2 ~ P1 ~ 0.1, E is about 107 W m -2.
(2) REFERENCES
where X is the thickness of the layer in which the surface level is located, and m* and m* are the effective masses of particles respectively in the surface level and in the conductivity zone. For Wo~ 3" 1014s -~, e ~ 30, A ~ 0.1 nm,R ~ 0.2 nm,M ~ 3" 10-27 kg, vT, ~ 10 a m/s, Q 0 ~ 3 " 1 0 - 4 ° C ' m 2, /3(Wo)-K(Wo)~3"106m -1, we have P~ ~ 0.1. Under same conditions, the probability of the energy being transferred to vibrations of the wall lattice amounts to about 10-3--10 -4 [3]. The probability of the reverse process (the recombination of an electron-hole pair with excitation of a molecule) P2 is
eu - h~Oo ] P2 ~ P1 exp kT ]'
1. 2. 3. 4. 5. 6.
(3)
where u is the voltage applied to the p-n junction, e is the charge, and T is the temperature. At eu > hco there exists a possibility of obtaining an inversion in vibrational
7.
t They can be created artificially by introducing the necessary admixtures into the region near the surface.
9.
8.
B.M. Smirnov, Physics of Low-Ionized Gases (in Russian), Nauka, Moskva, 415 (1978). Yu.G. Rayzer, Principles o f Modern Physics o f Gas-Discharge Processes (in Russian), Nauka, Moskva, 414 (1980). V.D. Rusanov & A.A. Fridman, Physics of Chemically Active Plasma (in Russian), Nauka, Moskva, 415 (1984). Yu.V. Gott, Interaction of Particles with Matter in Plasma Studies (in Russian), Atomizdat, Moskva, 270 (1978). V.I. Fistul, Introduction to Physics of Semiconductors (in Russian), Vysshaya Shkola, Moskva, 352 (1984). Yu.I. Ravich, B.A. Efimova & I.A. Smirnov, Methods of Studying Semiconductors in Application to the Lead Chalcogenides PITe, PISe, and P1S (in Russian), Nauka, Moskva, 383 (1968). V.A. Namiot, Decrease of Energy Losses in a Beam Passing Through a Medium, Zh. Eksp. Teor., Fiz., 82, 1780 (1982). V.A. Namiot, An Example of a Class o f Systems with a High Autorecuperation Coefficient (in Russian), ZhTF, 52, 2319 (1982). V.A. Namiot, On a Multi-State Autorecuperation (in Russian), ZhTF, 53, 811 (1983).
0 0 3 8 - 1 0 9 8 / 8 5 $3.00 + .00 Pergamon Press Ltd.
ON INTERACTION OF VIBRATIONALLY EXCITED MOLECULES WITH A SEMICONDUCTOR WALL V.A. Namiot Institute of Nuclear Physics, Moscow State University, Moscow, 119899, USSR
(Received 22 August 1985 by V.M. Agranovich ) This paper is devoted to problems related to the interaction ofvibrationally excited molecules with a wall made of a semiconductor. When the width of the forbidden zone is close to the energy of a vibrational quantum, the main process induced by the collision of a molecule with such a wall is the production or annihilation of an electron-hole pair. THE RECENT INTENSIVE DEVELOPMENT of lowionized plasma physics [ 1 - 3 ] has stimulated the study of the interaction of different plasma components with the wall [4]. One of such components is the vibrationally excited molecules. It is in these molecules the main part of the energy released in plasma is very often concentrated, while the energy spent on their translational motion is still sufficiently small. This is due to the fact that the characteristic times of the vibrational ( V - V ) exchange are practically always considerably smaller than the times of the vibrational-translational (V-T) relaxation [3]. As a wall bordering the plasma we propose to use the surface of a semiconductor with the width of the forbidden zone close or equal to the energy of a vibrational quantum of plasma molecules. There is quite a large number of such narrow-zone semiconductors [5], for example, among the lead chalcogenides [6]. The collision of a vibrationally excited molecule with such a wall may induce a new, yet unstudied elementary process in which the energy of the vibrational quantum is transferred directly to excitation of an electron-hole pair. In most cases the probability of this process essentially exceeds the probability of the energy being transferred to excitation of atoms of the crystal lattice of the wall as well as the probability of emitting a quantum (especially, when in the dipole approximation, the excited molecule is not emitting). If we create a p-n junction immediately beneath the surface of the wall, there must occur a spatial separation of electrons and holes resulting in the appearance of a potential difference at the surface of the semiconductor*. By this potential difference one may in principle determine the time dependence of the concentration of vibrationally
* In order to drain the current from the surface of the semiconductor one may in principle use a grid electrode on which the holes (or electrons) will gather owing to their lateral mobility.
excited molecules of a given kind. The semiconductor walls may be used for recovering the part of the energy wasted as heat losses, and thus, to reduce the effective energy expenditure on useful reactions generated in plasma. There has been discussed a number of other possibilities of recuperation or of autorecuperation of the energy lost by a beam of charged particles in gas or in plasma [ 7 - 9 ] . Finally, there is a possibility of obtaining the vibrationally excited molecules via a reverse process the recombination of the electron-hole pair with transmission of the energy to the molecules hitting the wall, which is achieved by applying a potential difference produced by an external source to the p-n junction. In principle, this way one may even obtain an inverse population of vibrationally excited states. One may also achieve a varying in time heating of the gas in contact with the wall without heating the wall itself, and thus, control the pressure in the gas, create flow, etc. Here is the estimate of the probability of an electron-hole pair being produced in the collision of a vibrationally excited molecule with the wall c X/~'/3(coo)t~(w o) Q2o
Pa ~ 161rZeoMco~R4A2VT
(1)
where c is the speed of light; e is the relative permittivity (eo is the vacuum permittivity); coo is the frequency of molecular vibrations; M and A are respectively the characteristic mass of the atoms forming the molecule and the characteristic distance between them; R is the minimum distance between a molecule and the walL; vT is the thermal velocity of molecules; Qo is the quadrupole moment; ~(~o0)=/-1(CO0) , where l(~oo) is the average path-length of a quantum in the semiconductor; the dimensionless factor ~(Wo) is introduced to make allowance for the fact that the absorption of a quantum by the region near the surface may be different from volume absorption. When hob0 essentially exceeds e~
1063
INTERACTION OF VIBRATIONALLY EXCITED MOLECULES
1064
(the width of the forbidden zone), /3(6Oo)- 1. In the vicinity of the threshold a signficant contribution to absorption may be given by the surface levels lying near the bottom of the conductivity zone (if such levels do exist)t. In this case for direct allowed transitions we have
ra
mI'
/3(~Oo)-~ (m--;~) (h~oo- %)-v2,
Vol. 56, No. 12
levels in the gas. The total energy carried away by excited molecules from the wall is
E ~ nVT P2hwo, 4
(4)
where n is the concentration of molecules. At n ~ 102s m -3 and/'2 ~ P1 ~ 0.1, E is about 107 W m -2.
(2) REFERENCES
where X is the thickness of the layer in which the surface level is located, and m* and m* are the effective masses of particles respectively in the surface level and in the conductivity zone. For Wo~ 3" 1014s -~, e ~ 30, A ~ 0.1 nm,R ~ 0.2 nm,M ~ 3" 10-27 kg, vT, ~ 10 a m/s, Q 0 ~ 3 " 1 0 - 4 ° C ' m 2, /3(Wo)-K(Wo)~3"106m -1, we have P~ ~ 0.1. Under same conditions, the probability of the energy being transferred to vibrations of the wall lattice amounts to about 10-3--10 -4 [3]. The probability of the reverse process (the recombination of an electron-hole pair with excitation of a molecule) P2 is
eu - h~Oo ] P2 ~ P1 exp kT ]'
1. 2. 3. 4. 5. 6.
(3)
where u is the voltage applied to the p-n junction, e is the charge, and T is the temperature. At eu > hco there exists a possibility of obtaining an inversion in vibrational
7.
t They can be created artificially by introducing the necessary admixtures into the region near the surface.
9.
8.
B.M. Smirnov, Physics of Low-Ionized Gases (in Russian), Nauka, Moskva, 415 (1978). Yu.G. Rayzer, Principles o f Modern Physics o f Gas-Discharge Processes (in Russian), Nauka, Moskva, 414 (1980). V.D. Rusanov & A.A. Fridman, Physics of Chemically Active Plasma (in Russian), Nauka, Moskva, 415 (1984). Yu.V. Gott, Interaction of Particles with Matter in Plasma Studies (in Russian), Atomizdat, Moskva, 270 (1978). V.I. Fistul, Introduction to Physics of Semiconductors (in Russian), Vysshaya Shkola, Moskva, 352 (1984). Yu.I. Ravich, B.A. Efimova & I.A. Smirnov, Methods of Studying Semiconductors in Application to the Lead Chalcogenides PITe, PISe, and P1S (in Russian), Nauka, Moskva, 383 (1968). V.A. Namiot, Decrease of Energy Losses in a Beam Passing Through a Medium, Zh. Eksp. Teor., Fiz., 82, 1780 (1982). V.A. Namiot, An Example of a Class o f Systems with a High Autorecuperation Coefficient (in Russian), ZhTF, 52, 2319 (1982). V.A. Namiot, On a Multi-State Autorecuperation (in Russian), ZhTF, 53, 811 (1983).