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8PHYSICAL SCIENCES
MODEL OF A STREAMER DISCHARGE CHANNEL IN MONOCRYSTALLINE CDS
Kulikov V.
Doctor of Physical and Mathematical Sciences. Professor Tomsk Agricultural Institute - a Branch of the Novosibirsk State Agrarian University, Tomsk, Russia
Yakovlev V.
Doctor of Physical and Mathematical Sciences. Professor National Research Tomsk Polytechnic University, Tomsk, Russia
Bobkova L.
Candidate of Chemical Sciences. Associate Professor National Research Tomsk State University, Tomsk, Russia
Abstract
Partial breakdown of a crystalline cadmium sulfide sample in a pulsed inhomogeneous electric field was
considered. Streamer discharge channels are oriented in the equivalent planes of sulfur ions (11 2 0), (1 2 10),
(2 110) and along the c axis of the crystal. It has been shown that the crystallographic orientation, radial stability and high velocity of streamer discharge channels are satisfactorily described in terms of the mechanism of cascade Auger transitions, taking into account the crystallochemical symmetry of the cadmium sulfide lattice.
Keywords: streamer discharge in semiconductors, electrical breakdown of crystals
Introduction
Partial streamer breakdown is observed in single crystals of semiconductor compounds of the type A2B6, when they are excited by high-voltage (~50-150 kV) nanosecond pulses [1-8]. Brightly glowing tracks propagate in certain crystallographic directions without destroying the substance. The velocity increases super linearly with the growth of voltage applied and ranges from ~108 to 109 cm/s. The length of channels is -5-10 mm at a diameter of ~2-3 m. The radiative transition mechanism is related to the recombination of electron-hole pairs in the discharge channel. High concentration of nonequilibrium charge carriers inside the channel creates the conditions for population inversion and stimulated emission. A reversible electrical breakdown can be applied in the development of streamer pulsed lasers [1, 5-8]. Advances in the physics and technology of semiconductor lasers connected with the understanding of streamer discharge formation, including streamer propagation anisotropy, high concentrations of carriers and high channel velocity. In Refs. [5, 6], streamer discharge is considered as a conducting channel with a region of strong electric field in the front section. The field front movement is determined by the tunnel-impact mechanism, where tunneling generates primary charge carriers with their subsequent impact multiplication [5, 9]. In the adopted model of substance atom ionization by accelerated electrons, the avalanche multiplication of charge carriers makes it possible to provide a significant concentration (~ 1018 cm-3) of nonequilibrium carriers [5], though it does not reflect the crystallo-graphic orientation of breakdown channels. A high velocity of streamers (up to 3T09 cm/s [5, 6]) does not go well with the drift velocity of avalanches. The latter does not exceed ~107 cm/s in CdS, using the data from Ref. [5].
In general, the properties of streamer discharges in wide-bandgap semiconductors and breakdown channels in ion compound crystals [10] are similar. The electrical breakdown of alkali-halide crystals, quartz has the following consistent patterns: crystallo-graphic orientation and anodic nature, high channel front velocity (~107-108 cm/s) and breakdown current density (~104 A/cm2). They are satisfactorily described in terms of the mechanism based on cascade Auger transitions in valence band of the dielectric [1116].
This paper presents a description of crystallo-graphic orientations of partial electrical breakdown channel propagation in a single crystal of cadmium sulfide. It also discusses the formation of a streamer discharge in terms of the mechanism of free electron generation by means of interatomic Auger transitions.
Experimental results and discussion
In the study, we used single crystals of hexagonal CdS, grown by vapor deposition, using the Davydov-Markov method (Platan, Fryazino town) with electrical resistivity of ~109 Om-cm. To investigate the crystallographic orientation of discharges, a wafer 6 mm in thickness, positioned in the (0001) plane, was cut out from the single-crystal ingot and ground. After cleaving the crystal sides, the dimensions of the sample were -6*13*23 mm3. The method of generating a strong electric field (~106 V/cm) using an electron beam of the accelerator is described in Ref. [11]. The accelerator had the following parameters: average electron energy ~250 keV, duration of beam current pulse (at half-height) ~18 ns, current density ~100 A/cm2. The sample was positioned between two electrodes, the upper being a point electrode, the lower - a round aluminum plate ~1 mm in thickness and ~9 mm in diameter (Fig. 1). An electron beam was applied to the lower electrode. In this case, under irradiation, a
capacitor is formed with a negative charge in the Al target and induced positive charge in the upper point
electrode. For the maximum accumulation of charge.
the lower electrode was fixed on a dielectric support. The experiment was conducted at room temperature in
vacuum (-0.13 Pa).
Fig. 1. Photograph of streamer discharges in crystalline CdS sample
Streamer discharges are shown in Fig. 1. The
channels look like direct rays. In the (10 1 0) plane, five channels are observed, directed from the surface to the volume. In the (0001) plane, these discharges emerge as projections making angles of 60°. In the electric field configuration with the point-plane structure of electrodes, discharge channels are formed in
equivalent planes: (11 2 0), (1 2 10) and ( 2 110).
Streamer tracks in the (11 2 0) and (1 2 10) planes make angles of ~ 90°. The sixth channel goes from the
discharge in the (1 2 10) plane and is directed along the c axis. The luminous intensity of channel regions far from the observation surface is lower than that of regions close to it due to the absorption of streamer radiation in the sample volume. Interestingly, the channel diameter remains stable along the length of the discharge.
The streamer channels observed in the (11 2 0)
and (1 2 10) planes, as well as the projections of channels in the (0001) plane are in good agreement with the data from Refs. [2-4]. The channels along the c
axis were observed by the authors [3] only in highresistance (~1010 Om-cm) samples. As compared with the data in Refs. [2-4], there are no discharges in the
(10 1 0) plane at an angle of -45° and -85° to the c axis.
The emergence and growth of breakdown shapes can be linked to the mechanism of free electron generation by means of cascade Auger transitions in valence band of the dielectric [11-16]. The orientation of Auger transitions is determined with due consideration of data on the crystallochemical and energy structure of a crystal.
A binary compound CdS has a hexagonal wurtz-ite lattice. Particles in the wurtzite structure are arranged in the following way: every atom of one element is surrounded by four atoms of another element like in a tetrahedron. The hexagonal atomic packing of sulfur (in two projections) in the crystalline structure of CdS is presented in Fig. 2 [17]. The unit cell has the following dimensions: a = 4.13 A, c = 6.70 A [18].
Fig. 2. Hexagonal packing of sulfur atoms in the crystalline structure of CdS. Arrows indicate the direction of
interatomic Auger transitions
The experimental results for the photoemission spectra of electrons of hexagonal cadmium sulfide are presented in Refs. [19, 20]. The calculations of the band structure and density of electron states of CdS [21] show a satisfactory correlation with the experimental results. According to Refs. [20, 21], two upper valence bands have a 3 s-character, the electron density is located on sulfur atoms. The more intensity peak of the density of states is at -1 eV and less intensity at -4 eV. The total width of 3s-bands is -4.5 eV. The next region of bands comes from 4d- orbitals of Cd. The maximum of a narrow sharp peak of the 4d- band corresponds to -6.9 eV, the width is less than -1 eV. A deep valence band with the maximum of 12 eV consists of 3^-orbitals of sulfur. In the first two conduction bands, 5s-states of Cd prevail. The width of the band gap of CdS is - 2.58 eV [21].
According to [11-16], the start of the breakdown channel formation is determined by the processes at
the metal-dielectric interface. When the field strength in the dielectric is - 106 V/cm, the real field strength near the electrode micropoints can exceed - 108 V/cm. In the near-surface area of the dielectric, S0 ions with two holes are formed at the 3s -level due to the tunnel transition of electrons to metal. It is most likely that the recombination of the hole involves a neighboring sulfur ion and takes place through an interatomic Auger transition of the electron from the 3 s -level of the S2- ion to S0, with subsequent generation of the Auger electron to the conduction band (Fig. 3). According to the estimates in Ref. [21], the electrons on the 4d -level of energy of Cd ions lie deep in the valence band and are not involved in the hole recombination.
The transition of Auger electron to the conduction band occurs if the minimal energy gap between the 3s - levels of the neighboring sulfur ions (Fig. 3) is not narrower than the band gap of the crystal.
Fig. 3. Scheme of cascade Auger transitions in CdS crystal in a strong electric field. Wc, Wv, WF - energy levels of the conduction band bottom, crystal valence band ceiling and the Fermi metal, respectively.
In alkali-halide crystals, the necessary band bending for Auger transitions is provided by the electric field of the space charge, including a layer of doubly charged and layers of singly charged haloid ions [12, 13, 16]. The breakdown channel front coincides with the space charge boundary. A single cycle of space charge movement can be divided into two successive stages. At the first stage, when the critical strength (~108 V/cm) of the local electric field is achieved, the hole decays due to the interatomic Auger transition of the electron from the neighboring anion. An Auger electron is generated to the conduction band of the crystal. The channel moves one interatomic spacing. At the second stage, electrons are drawn from the space charge area by the external electric field. This provides the critical field strength for the next cycle to occur. The cycle time At can be presented as
At = ta+T1 , (1)
where ta ~10-16 s is the time of Auger transition, T1 is the time of achieving the critical field strength. According to Ref. [13], T:~1/(E0C0), where E0 is the strength of the external electric field in the sample, and G0 is the breakdown channel conductivity. Indeed, the rate of breakdown channel propagation in the experiment increases with the growth of external field strength and conductivity [10, 15]. In the NaCl crystal, At is -5.6-10-16 s at a discharge velocity of -6-107 cm/s [13]. That is how the breakdown channel in cadmium sulfide is probably formed. This is suggested by the anodic nature of breakdown, high rates of breakdown channel propagation (-5-108 cm/s) and dependence of streamer front movement on the breakdown voltage.
The movement of the discharge channel in CdS is generally connected with a straight-line transfer of the positive charge successively to the nearest sulfur ions and generation of Auger electrons to the conduction band (Fig. 3). As seen from the atomic packing of sulfur (Fig. 2), such directions (shown by arrows) are formed in each of three equivalent planes of sulfur ion
arrangement (11 2 0), (1 2 10), (2 110) and parallel to the c axis of the crystal. The angle between the planes is 60°. In each plane, two directions of breakdown channel are formed from the electrode along the sulfur atoms: to the left and to the right into the sample depth. The angle between the channels is ~90°. In this case, if the breakdown originates on the (0001) plane from the electrode, six channels propagate in the
(11 2 0), (1 2 10), (2 110) planes and along the c axis, which is experimentally confirmed. A streamer may
propagate in the (0001) plane in equivalent directions
[01T 0] (Fig. 2).
The streamer channel structure is formed by a set of single Auger transition channels (Fig. 3), going in the same direction. It includes a positive space charge and a conductive channel with electron-hole plasma. The channel diameter is probably determined by the size of the layer of S0 ions, formed by tunnel transitions of electrons to metal in the near-surface area of the dielectric, and is proportional to the external voltage. According to Ref. [10], the breakdown channel diameter in KCl and KBr samples increases linearly with the voltage in the range of 100-300 kV. The streamer discharge may be delayed due to the time of S0 ion layer formation.
The observed radial stability of the channel (Fig. 1) is possible if the front boundary is flat and the velocity of space charge surface regions is identical. This requires the time of achieving the critical field strength T1 in the space charge region to remain constant all over the front. According to (1), the current density E0C0 in the cross-section of the channel must be constant. On the periphery of the space charge area, the conductivity becomes lower than in the center due to the emission of Auger electrons beyond the channel. However, in alternating and pulse electric fields, the skin-effect is observed, manifesting itself in an increase in the electric field strength on the conducting channel surface. The antibate nature of E0 and 00 changes in the cross-section of the channel probably contributes to the condition when E000 ~ const in the plane of the space charge front and, thus, to the radial stability of the channel. The radial stability of discharge can be considered a characteristic aspect of the breakdown channel in CdS, as well as in alkali-halide crystals, quartz [16].
Using the model of cascade Auger transitions, we can explain the specific aspects of streamer discharge properties in semiconductors, as compared with the electric breakdown in ion crystals.
A higher velocity of discharges in CdS as compared with alkali-halide crystals is determined by a higher electron mobility. It is ~220 cm2/V-s for CdS vs. ~13 cm2/V-s for NaCl [22, 13]. This contributes to a shorter time of drawing electrons from the space charge area.
The destruction of ion crystals in the breakdown channel is associated with energy release due to the impact recombination of electrons and an increase in the thermal pressure in the breakdown channel [13]. In
CdS, the quadratic and impact recombination of carriers is characterized by low value of the capture cross section of an electron by a hole, (-10-20 cm2) and low impact recombination coefficient (10-31 cm6-s"'), as compared with ion crystals (10-12 cm2 and 10-20 cm6-s-\ respectively [13, 23].) Low recombination coefficients in semiconductors can be explained, in particular, by the condition of equality of crystal momentums of recombining electrons and holes. In alkali-halide crystals, the effect of hole autolocalization eliminates the need for equality of particle momentums during recombination, and impact recombination occurs at a carrier concentration of -1016 cm-3 [13, 23]. In the CdS crystal, the quadratic recombination with light emission and weak impact recombination do not provide the necessary thermal pressure for destruction in the streamer channel.
The difficulties of streamer generation in low-resistance materials with electrical resistivity of less than -103 Om-cm and streamer quenching, when the crystal region near the point electrode is radiated with nitrogen laser light [2], are caused by an increased concentration of free carriers and, thus, screening of the space charge field.
Conclusion
In nanosecond, inhomogeneous electric fields, streamer discharge channels in crystalline CdS are oriented along the equivalent planes of sulfur ions
(11 2 0), (1 2 10), (2 110) and parallel to the c axis of the crystal. The paper presents a qualitative model of streamer channel formation in cadmium sulfide samples, based on the mechanism of free electron generation by means of cascade Auger transitions with due consideration of the crystallochemical structure of CdS. The model satisfactorily explains the crystallo-graphic orientation of streamer discharges, high velocity of the discharge front, radial stability and absence of destruction in the discharge channel.
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