V Lisovskiy, J Booth, K Landry - Electron drift velocity in n2o in strong electric fields determined from rf breakdown curves - страница 1
Institute of Physics Publishing
Journal of Physics D: Applied Physics
J. Phys. D: Appl. Phys. 39 (2006) 1866-1871 doi:10.1088/0022-3727/39/9/022
Electron drift velocity in N2O in strong electric fields determined from rf breakdown curves
V Lisovskiy13, J-P Booth1, K Landry2, D Douai2, V Cassagne2 and V Yegorenkov3
1 Laboratoire de Physique et Technologie des Plasmas, Ecole Polytechnique, Palaiseau 91128, France
2 Displays Division, Unaxis France SA, 5 Rue Leon Blum, Palaiseau 91120, France
3 Department of Physics and Technology, Kharkov National University, Kharkov 61077, ukraine
Received 11 January 2006, in final form 6 March 2006
Published 20 April 2006
Online at stacks.iop.org/JPhysD/39/1866
We report measurements of the breakdown curves of an rf capacitive discharge in low pressure nitrous oxide. The electron drift velocity was determined from the locations of the turning point and of the minimum in the breakdown curves in the range E/p = 87-840 V cm-1 Torr-1.We compare our results with values calculated from the published cross-sections in the range E/p = 1-5000 V cm-1 Torr-1 and find good agreement.
RF discharges in N2O are used in many applications including removing hydrocarbon impurities from silicon wafers, oxidizing silicon surfaces  and creating silicon oxynitride films on silicon . RF discharges in N2O + SiH4 mixtures are used for depositing amorphous oxynitrides films (a-SiNxOy and a-SiNxOy :H) [3-7]. In a number of cases rf discharges in N2o + siH4 mixtures are used to deposit SiO2 films [8-12]. Typically the N2O concentration in the N2O + SiH4 mixture is 2-Ю times higher than that of silane. consequently it is of considerable interest to study the properties of rf capacitive discharges and electron transport parameters in pure N2O.
In order to use fluid simulations it is necessary to know the electron transport parameters of the gas under study. Electron swarm motion through gases is described by the following parameters: the electron drift velocity, Vdr, the first Townsend coefficient, a, the rate of electron attachment to gas molecules, n, the average electron energy, (ee>, and the ratio of radial electron diffusion coefficient to mobility, De /лe. To our knowledge, these transport parameters have only been measured in N2O for small values of the reduced electric field (E/p < 174 V cm-1 Torr-1 [13-20]). However the reduced field, E/p, may reach hundreds of V cm-1 Torr-1 in the near-electrode sheaths of rf discharges, in the cathode sheath of dc discharges, during a gas breakdown and in a number of other cases. under these conditions the electrons can acquire considerable energy, and therefore it is necessary to know the electron transport parameters in these strong electric fields.
The electron drift velocity in an electric field, Vdr, characterizes the conductivity of a weakly ionized gas and is one of the most important electron transport parameters. There are a number of well-known techniques (the time-of-flight technique, observation of the optical radiation of a moving electron swarm, the shutter technique and so on) that have been used to measure the electron drift velocity. However, these only work for comparatively small reduced fields, E/p, because at higher values a self-sustaining discharge is ignited which impedes the measurement. Lisovskiy and co-workers [21-24] have used a novel method to determine the electron drift velocity from the location of the turning point in the breakdown curves of rf capacitive discharges. In addition Lisovskiy et al  proposed a new technique for determining Vdr from the location of the minimum in the rf breakdown curve and applied it to argon, ammonia, nitrogen, hydrogen and oxygen. Whereas conventional techniques become inapplicable after the ignition of the self-sustaining discharge, these two methods are actually based on discharge ignition, allowing measurements of Vdr in strong electric fields.
In this paper we have used these techniques to determine the electron drift velocity in N2O. Measurements were made
0022-3727/06/091866+06$30.00 © 2006IOP Publishing Ltd Printed in the UK
in the range E/p = 87-840 V cm-1 Torr-1. With the help of the 'Bolsig' numerical code and published cross-sections  we have calculated the electron transport parameters in N2O in the range E/p = 1-5000 V cm-1 Torr-1, and the drift velocity values obtained from our experiment agree well with the calculated values.
2. Experimental set-up
The rf discharge was ignited in N2O over the pressure range p ~ 0.05-17 Torr with rf field frequencies f = 2MHz, f = 13.56 MHz and f = 27.12MHz. The distance between the flat circular aluminium electrodes (143 mm in diameter) was varied over the range L = 2-27 mm. RF voltage (amplitude Urf < 1500 V) was fed to one of the electrodes, while the other was grounded. The electrodes were located inside a fused silica tube with an inner diameter of 145 mm (see figure 1). The gas was supplied through small orifices in the powered electrode and then pumped out via the gap between the second electrode and the wall of the fused silica tube.
The gas pressure was monitored with 10 and 1000 Torr capacitive manometers (MKS Instruments). The gas flow was fixed with a mass flow controller to 5 sccm and the pressure regulated by throttling the outlet to the pump. The rf voltage was measured with an rf current-voltage probe (Advanced Energy Z'SCAN).
We used the technique proposed by Levitskii to measure the rf breakdown curves. Near and to the high pressure side of the minimum in the breakdown curve, the N2O pressure was fixed before slowly increasing the rf voltage until gas breakdown occurs. To the low pressure side of the minimum the curve may be multi-valued, i.e. the curve turns around and breakdown occurs at two different values of the rf voltage. Therefore in this range we first decreased the N2O pressure, then fixed the rf voltage value and only then increased the N2O pressure slowly until discharge ignition occurred. When discharge ignition occurs the rf voltage decreases sharply, and a glow appears between the electrodes indicating the onset of gas breakdown. The uncertainty in the measured breakdown voltages did not exceed 1-2 V over the whole Urf range under study.
3. Experimental results
3.1. Breakdown curves in N2O
The breakdown curves of rf capacitive discharges can be divided into different branches according to the processes by which the charged particles are generated: emission-free, diffusion-drift, Paschen and multipactor branches, as described in detail elsewhere .
Figure 2(a) shows the rf breakdown curves determined with a frequency f = 13.56MHz and a range of inter-electrode gap values, L. With L = 25 mm the breakdown curve possesses a diffusion-drift branch with a clearly-expressed region of multi-valued dependence of the rf breakdown voltage on gas pressure (at low gas pressure), as well as the emission-free branch (at high pressure, p> 1Torr). The Paschen and multipactor branches were not observed with this large inter-electrode gap.
Decreasing the inter-electrode gap, L, shifts the diffusion-drift branch towards higher rf voltages and gas pressures. At the same time a section of the Paschen branch appears in the low pressure region (to the left of the breakdown curve minimum). For example, with L = 13.5mm the Paschen branch appears in the low pressure region forvoltages, Urf > 350 V: in this region the breakdown voltage increases as the pressure is decreased. Decreasing the gap, L, reduces the range of the multi-valued region, and it disappears when L< 12 mm. Further decrease in the inter-electrode gap leads to the disappearance of the diffusion-drift branch (in the breakdown curve for L = 6 mm the diffusion-drift branch appears only at gas pressures, p> 7 Torr), and at low
Figure 1. Schematic of the experimental setup.
Figure 2. RF discharge breakdown curves in N2O for different inter-electrode gap values and frequencies.
gas pressures and high rf voltages a multipactor branch is observed (a section with practically constant rf breakdown voltage, seen for example with L = 5 mm and gas pressures p< 0. 4 Torr).
It should be remarked that these features (a multi-valued section, Paschen and multipactor branches at low gas pressure) are only observed in symmetric rf discharges , i.e. the planar electrodes must be situated inside a dielectric tube with an inner diameter close to the outer diameter of the electrodes. If the electrodes are located inside a grounded chamber of larger dimensions and their radial boundary is not limited with a dielectric tube then the rf breakdown curve will not possess these features [28,29].
Let us now discuss how the rf field frequency affects the shape of breakdown curves. Figure 2(b) presents breakdown curves for inter-electrode gaps of L = 5 mm and L = 11.9 mm and frequencies f = 13.56MHz and f = 27.12MHz. The breakdown curves for L = 11.9 mmpossesses no multi-valued region in the low pressure range for f = 13.56 MHz, whereas a wide multi-valued region is seen for f = 27.12 MHz. In the high pressure region the breakdown curves for both frequencies coincide, in agreement with previous studies [30, 31] which have shown that the rf breakdown voltage is independent of the frequency at high pressure. The breakdown curve for L = 5 mm and f = 13.56MHz possesses no diffusion-drift branch, consisting of the Paschen branch with multipactor branch at low pressure. However, with f = 27.12 MHz (keeping L = 5 mm) we see a diffusion-drift branch with a small multi-valued region and in the low pressure region a Paschen branch and a multipactor branch. We could not record the curve over the entire multipactor region for L = 5mm and f = 27. 12 MHz due to a technical problem, but the behaviour of the curves for L = 5 mm and f = 13.56 MHz and f = 27.12 MHz shows that increasing the frequency of the rf electric field leads to an increase in the ignition voltage in the multipactor regime, in agreement with previous papers
Figure 2(c) shows the effect of changing the frequency from f = 13.56 to 2MHz with L = 20.4mm. The curve for f = 13.56 MHz possesses a diffusion-drift branch with a multi-valued region as well as part of the Paschen branch. The curve for f = 2 MHz consists almost entirely of the Paschen branch. Only at low N2O pressure is the beginning of the transition to the multipactor branch observed, and the last recorded point at high gas pressure may show the beginning of the transition to the diffusion-drift branch.
up to now no similarity law has been proposed for rf breakdown curves, even for a single rf frequency. For dc discharges Paschen's law [36,37] states that the breakdown voltage depends only on the value of the product pL. However, figure 3 shows that for rf breakdown, in the high pressure range (to the right of the breakdown curve minima), this does not hold, and the breakdown voltage is found to decrease approximately linearly as L is increased. Figure 4 shows breakdown curves for different gaps, L, plotted as a function of the product pL instead of simply pressure. However, this does not lead to convergence of the diffusion-drift branches recorded for different gap values, except for the sections of Paschen branches near and to the right of their minima for small gaps (L < 6 mm). However, in the low pressure range (to the
Figure 3. Breakdown rf voltage against inter-electrode gap value for f = 13.56 MHz pL = 3 Torr cm.
Figure 4. Breakdown curves for f = 13.56 MHz and different gap values, plotted as a function of the product pL.
left of minima) the Paschen branches for different gap values diverge. The breakdown curves for microwave discharges have been found to obey the similarity law EA = x//(pA) , where Erf = Urf /L is the rf electric field strength and A is the diffusion length of the discharge chamber (of length L and radius R) given by the relation
/2.405Ч2 / n\2
However, when our data is plotted in this way the curves do not superpose, and this law appears to be inapplicable for rf gas breakdown (at least for N2O).
Thus, as is clear from figure 2(c), the breakdown curve for L = 20. 4 mm (as well as some of the other breakdown curves presented in figure 2) possesses a region of multivalued dependence of the rf breakdown voltage on gas pressure [21-25,27,28,39], i.e. at certain given gas pressures the rf discharge can be ignited at two and even three different values of the rf voltage (e.g. in the N2O pressure range p ~ 0.120.14 Torr in figure 2(c)). The diffusion-drift branch shows a well-expressed turning point with the coordinates p = pt and Urf = Ut. For the conditions corresponding to the turning point the amplitude of the electron displacement in the rf field is equal to one-half of the inter-electrode gap value, as discussed below.
3.2. Electron drift velocity determination from rf breakdown curves in N2O
Let us consider the equation of motion for the electron velocity, V, in a uniform rf electric field:
m- = — eErf sin at
where e and m are the electron charge and mass, respectively, Erf is the rf field amplitude, ven is the effective frequency of collisions between electrons and gas molecules and a = 2nf is the angular frequency of the rf field. By integrating (2) and the equation for oscillatory motion, dr /dt = V,wefind
m^/a2 + vt
= • cos(at + ф),
sin (at + ф),
where ф = arctan(ven/a). The amplitude, A, of the electron displacement in an rf electric field is given by
ma^/a2 + v2
where the maximum instantaneous drift velocity of electrons, Vdr,isgivenby
m a2 + ve2n
Let Urf = Urf(p) be the amplitude of the rf voltage at breakdown. A minimum in the rf breakdown curve, Urf (p), occurs when dUrf (p)/dp = 0, and a turning point occurs when dUrf (p)/dp -—oc. At the turning point of the breakdown curve (corresponding to p = pt and Urf = Ut) the amplitude of the electron displacement is equal to half of the gap :
Hence the electron drift velocity, Vdr, at the turning point of the rf breakdown curve is equal to
The same equation was derived previously for the collisional regime (ven ^> a)[21-25]. Here we show that the same equation is valid for all values of ven and a. It follows from equation (8) that the value of the electron drift velocity at the turning point of the breakdown curve depends only on the values of the inter-electrode gap and the frequency of the rf field. At the same time it is independent of the gas species. However, the corresponding value of E/p at this point will be different for each gas. The coordinates of the turning point permit us to determine the reduced field, E/p, corresponding to this electron drift velocity.
At the breakdown curve minimum (with the coordinates Umin and pmin) the following expression for the electron drift velocity was derived by Lisovskiy et al :
aL B - (1/V2)(E/p)B
B + (1/J2)(E/p)a
Figure 5. Electron drift velocity in N2O against E/p. The solid curve presents the data calculated with the Bolsig code, solid circles are for our measured data (from the turning points), empty circles are for our measured data (from the minima), solid triangles are for the experimental data from , empty triangles are for the experimental data from , solid squares are for the experimental data from , empty squares are for the experimental data from  and solid diamonds are for the experimental data from . The dashed curve presents the calculation data from .
Thus we can also determine the electron drift velocity fromthe measured coordinates of the rf breakdown curve minimum. A disadvantage of this technique is that it depends on knowledge of the constant B, which is related to the first Townsend coefficient a by
a = A1 • p • exp I
where Eeff is the effective electric field strength, Eeff = Erf /\/2, A1 and B are constants depending on the gas species. Therefore this technique can only be applied to gases for which this first Townsend coefficient is known. However, this technique enables the electron drift velocity to be determined from rf breakdown curves which show no turning point.