Verification of the Algorithm for Emission Tomography of Plasma Inhomogeneities in a Plasma-Chemical Reactor Using the Langmuir Multiprobe

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1 ISS , Russian Microelectronics, 214, Vol. 43, o. 4, pp Pleiades Publishing, Ltd., 214. Original Russian Text A.V. Fadeev, K.V. Rudenko, 214, published in Mikroelektronika, 214, Vol. 43, o. 4, pp Verification of the Algorithm for Emission Tomography of Plasma Inhomogeneities in a Plasma-Chemical Reactor Using the Langmuir Multiprobe A. V. Fadeev and K. V. Rudenko Physico-Technological Institute, Russian Academy of Sciences, Russia rudenko@ftian.ru, AlexVFadeev@gmail.com Received January 14, 214 Abstract The few-view emission tomography (ET) of plasma, which introduces physical properties of objects into a reconstruction algorithm, requires a reliable experimental verification using independent methods for validating an adopted model of plasma inhomogeneities. The chosen test object low-temperature argon plasma in a reactor with a remote plasma source allows one to study the two-dimensional spatial distribution of a concentration of Ar + ions, which is calculated using the two-view ET, and to verify results using direct measurements by a Langmuir multiprobe located in the plane of tomographic scanning. Studies are carried out for the chamber pressure 2 12 mtorr; the sensitivity of the ion-field homogeneity to the external magnetic field is estimated. A close agreement between concentration fields of Ar +, which are measured and reconstructed by tomography, is obtained. The divergence between the probe method and the ET data reconstruction with respect to two views is not above 1%. DOI: /S ITRODUCTIO The lateral density homogeneity of active plasma particles in close proximity to plates being processed is a key parameter of plasma processes in microelectronic technology, which is responsible for the qualitative characteristics of IC structures. The lateral homogeneity of ion fluxes and active radicals provides the homogeneity of the rate of the anisotropic etching or layer deposition along the area of the plate. The present level of manufacturing technologies allows it to be used on plates up to and 4 mm, where the requirements for plasma homogeneity are rather rigid. The lateral homogeneity of electrically charged components (ions, plasma potential, etc.) can be measured quite accurately using special instrumental plates [1], which are a set of spaced integrated probe sensors with an information-processing system that are placed into the reactor s chamber. In contrast, spatially-resolved measurements of the density of active uncharged plasma radicals in conditions of commercial reactors have no equally obvious solutions. In order to solve such problems, the diagnostics method based on two-view spectrally resolved optical emission tomography of plasma, wherein the scanning scheme is compatible with commercial reactors, has been developing by the authors over a period of years [2 4]. The proposed algorithm using emission actinometry [] determines the lateral distribution of charged plasma particles and uncharged active radicals with respect to their characteristic optical radiation. Using tomographic phantoms, results indicating a sufficiently high quality of tomographic reconstruction have previously been obtained [4]; however, in order to test the emission tomography (ET) algorithm in actual practice, an experiment is required whereby the lateral density distribution of the particles in the section of the reactor would be measured using both ET and independent method. For such an experiment, argon plasma (more precisely, its ion component) is chosen to be a test object. In low-temperature low-pressure plasma, there is a singly-ionized Ar + ion which is the only possibility (multiple ionization can be neglected). Therefore, the density distribution of an Ar + ion can uniquely be measured using an instrumental plate with Langmuir probe sensors (Langmuir multiprobe). On the other hand, the spectrally-resolved optical emission of the excited state of the ion (for example, with wavelength λ = 488. nm) is available for gathering tomographic data. Providing the homogeneity of the electronic temperature of the plasma in the diagnosed region of the reactor, the tomographic reconstruction algorithm must provide, using the data on optical emission of Ar +, the same spatial distribution of ion density as that provided by the probe method. The condition for spatial homogeneity of electronic temperature can also be checked using the Langmuir probe. 2

2 VERIFICATIO OF THE ALGORITHM FOR EMISSIO TOMOGRAPHY 3 2. MULTIPROBE MEASUREMET TECHIQUE Experiments are carried out in the chamber of an experimental technological reactor with a remote source of inductively coupled plasma (ICP), which is meant for plasma-immersion ion implantation [6]. The true lateral distribution of the ion density in plasma in proximity to the plate s surface is determined using an instrumental plate, i.e., an automated multiprobe with corresponding software [7]. The sensor system is a plate of dielectric material with 13 spaced flat Langmuir probes with insulated measuring circuits (Fig. 1). The multiprobe is placed into the reactor instead of the silicon plate being processed. Using E-I characteristics measured by individual probes, the parameters of the plasma in close proximity to each flat probe (in particular, electronic temperature and ion concentration) are calculated according to the Langmuir theory. In addition, the electronic temperature of plasma in the section of the reactor is measured more reliably by a traveling cylindrical Langmuir probe. Ion concentration in plasma ( n i ) is determined with respect to the ion saturation current of the measured E-I characteristic of flat probes according to Bohm s formula [8]: saturation kt Ii =.2 nes i e, M (1) where S is the area of a probe, M is the ionic mass, T e is the electronic temperature, and k is the Boltzmann constant. The experiment is conducted in Ar plasma for the following pressures in the reactor s chamber: 2, 6.7, and 12 mtorr. In order to analyze the operation of the ET algorithm, the inhomogenuities are artificially introduced into the parietal magnetic field of the reactor. Electronic temperature in Ar plasma is as follows: Т е = 3.23 ev for P = 2 mtorr; Т е = 2.4 ev for P = 6.7 mtorr; and Т е = 1.47 ev for P = 12.1 mtorr. Departure from the values of T e in the zone of the plate is less than %, which is comparable to the error in measuring electronic temperature by the probe method. Therefore, the values of the ion saturation currents obtained from each sensor can be interpreted using relation (1) as a normalized concentration of Ar + ions in proximity to a corresponding sensor. The densities for Ar + in intermediate points within the plate are determined using interpolation function (2). If required, the extrapolation of the ion density function into the region outside the sensors at a distance less than a step between individual probes is performed according to the following formula: c 2 i i i i i = 1 i = 1 f() r = f() r + w( r r ) ln( r r ), (2) where r i is the radius vector of the ith sensor with respect to the center of the plate; f( r i ) is the concentration in the location of one of the = 13 sensors; w i are weights of the function, which are determined from the condition that f( r ) is known in points r i ; and c is the normalization constant chosen to be.8, which provides the required smoothness of the ion density distribution in the region outside the extreme sensors. 3. COMPUTATIOAL EXPERIMET OF EMISSIO TOMOGRAPHY AD COMPARISO OF RESULTS The intensity I of radiating by excited particles in the region of plasma is proportional to the concentration of particles n in this region. Therefore, the twodimensional concentration field of Ar + ions, which is obtained by experiments with the plate-multiprobe, is used to generate tomographic data in the two-view fan-shaped circuit (Fig. 1), wherein aspect views are rotated by 9 relative to each other. The formation of radial sums, which imitate the line integrals of radiation intensity of Ar + ions for each scanning view, is performed along the 31 stequidistant beam according to the following expression: L p = f( x, y) dz, (3) where f( x, y) is the radiation intensity of Ar ions at a point with coordinates ( x, y), while the integration is performed along the straight line L between boundaries of the reconstruction region. The radiation intensity function f( x, y) for Ar + is calculated using the experimentally measured distribution of ion density, taking into account interpolation (2). As is known [], for the homogeneous spatial distribution of T e, the spectral line intensity of radiation of an atom or an ion is a linear particle-density function. Such a statement of the computational experiment excludes the inevitable errors due to the hardware RUSSIA MICROELECTROICS Vol. 43 o

3 4 FADEEV, RUDEKO 1 2 Fig. 1. Measuring plate of the multiprobe with 13 flat Langmuir probes and the fan-shaped scheme of tomographic scanning with aspect views 1 and 2. accumulation of the initial tomographic data by the optical scanning system from the verification of the mathematical tomographic reconstruction algorithm and allows the inherent error of the reconstruction algorithm to be estimated. The tomographic reconstruction of the twodimensional density field of Ar + ions from the formed data uses the optimized algorithm previously proposed by authors [4]. The main feature of the developed algorithm, which allows reconstruction artifacts to be eliminated or considerably reduced for an extremely low number of aspect views, is that plasma in the diffusion zone of the reactor with a remote plasma source can be represented in the form of the sum of a certain homogeneous particle distribution (background) and overbuilt superposition of unitary (elementary) spatial inhomogenuities of particle density [3]. In order to describe the concentration distribution of Ar ions with respect to the section of the reactor, a parabolic function is chosen to be the function of elementary inhomogenuity. This is the well-known solution for spatial density inhomogenuities of charged particles in solving the pinching plasma problem [9]. Thus, instead of calculating the arbitrary function of spatial distribution of the ion concentration in the section of the reactor, it is required to determine the value of the background and parameters of all elementary inhomogenuities: amplitudes of peaks A p _ i, their width σ p_ i and locations ( xp_ i, yp_ i). The introduction of such information a priori into the tomographic algorithm sharply reduces the number of unknowns in the inverse ill-conditioned recon- struction problem. With the correct determination of parameters of the reconstructed peak, after the elimination of its contribution from radial sums, artifacts due to the subtracted peak are also eliminated during the repeated reconstruction. This key procedure is used to select tomogram artifacts. Figure 2 shows the interpolated distributions of Ar ions and their reconstruction by the ET method for pressure in the reactor s chamber 12.1 mtorr. The contour indicates the location of the silicon plate being processed. The error of the tomographic reconstruction is calculated as the mean square deviation in concentration at 13 points that correspond to the locations of multiprobe sensors: (4) where I i and I i are the currents obtained from the ith sensor and after the reconstruction, respectively. The value of the relative inhomogenuity of the reconstructed field in the region bounded by multiprobe sensors is considered as a characteristic of plasma inhomogenuity with respect to a section of the reactor: where reconstruction 2 ( Ii Ii ) error = 1%, 2 ( I ) reconstruction n ε= sd 1%, n i () RUSSIA MICROELECTROICS Vol. 43 o

4 VERIFICATIO OF THE ALGORITHM FOR EMISSIO TOMOGRAPHY 2 1 (a) (b) Fig. 2. (a) ormalized distribution of ion concentration (P = 12.1 mtorr) obtained by interpolation of multiprobe data and (b) its tomographic reconstruction (error = 2.8%, ε = 6.7%). n 1 ni i = 1 = is the mean concentration of particles with respect to mesh cells and 1 i = 1 n = ( n n ) 2 sd is the mean square deviation in the concentration of particles with respect to mesh cells. i The figure shows that the tomographic reconstruction correctly reproduces departures from the cylindrical symmetry of spatial density distribution with respect to the area of the reactor. Moreover, the twoview tomographic reconstruction reproduces the asymmetry of lateral ion distribution with respect to the center of the reactor; this is infeasible using the one-view tomography based on the Abelian transformation. Quantitative inconsistency between the tomographic reconstruction of ion density in the plasma and data obtained by the multiprobe is less than 6%. RUSSIA MICROELECTROICS Vol. 43 o

5 6 FADEEV, RUDEKO 2 1 (a) (b) Fig. 3. (a) ormalized distribution of ion concentration (P = 12.1 mtorr + magnet) obtained by interpolation of multiprobe data and (b) its tomographic reconstruction (error =.%, ε = 8.%). The probe measurements (see Table 1) show that the increase of pressure results in an increasing inhomogenuity in the spatial distribution of the Ar + ions. This result is supported qualitatively and quantitatively by the ET method. The additional peak (nonmonotonic drop of concentration from the center), which can be seen in Fig. 2b, is believed to be an artifact; i.e., there is no local spike of the ion concentration here. This is due to, on the one hand, the interpolation and extrapolation of the probe data obtained at 13 points of the reconstruction region and, on the other hand, the adopted inhomogenuity model that describes any plasma inhomogenuity in the form of a finite number of local peaks. However, the computational experiment shows that ET possesses the required features of the noncontact diagnostics method for selecting the optimal pressure range in the reactor in terms of plasma homogeneity. RUSSIA MICROELECTROICS Vol. 43 o

6 VERIFICATIO OF THE ALGORITHM FOR EMISSIO TOMOGRAPHY 7 Table 1. Error of the tomographic reconstruction and the lateral inhomogenuity of Ar + plasma for different pressures in the camber of the plasma-chemical reactor Chamber pressure P, mtorr Tomographic reconstruction error, % Plasma inhomogenuity with respect to section ε, % Table 2. Error of the tomographic reconstruction and the lateral inhomogenuity of Ar + plasma for different pressures in the camber of the plasma-chemical reactor with a disturbed parietal magnetic field Chamber pressure P, mtorr Tomographic reconstruction error, % Plasma inhomogenuity with respect to section ε, % It is common knowledge that the applied magnetic field affects the homogeneity of the spatial distribution of the plasma particles. In our experiment, the parietal magnetic field of the plasma-chemical reactor can be measured. It is of interest to study how this factor affects the results of the probe and tomographic diagnostics. Figure 3 shows the effect of the magnetic field asymmetry on the lateral distribution of the Ar ions in the technological reactor. As is seen from Fig. 3a (probe measurements), the variation of the magnetic field symmetry by placing additional constant magnets on the wall results in the shift of the maximum of the inhomogenuity in the lateral ion distribution. This is in complete agreement with the results obtained by the ET method (Fig. 3b). With the increase of pressure (see Table 2), the effect of the asymmetry of the parietal magnetic field on the central symmetry of the ion distribution is increased, which is characterized by the value of the lateral plasma s inhomogenuity with respect to the section of the reactor. 4. COCLUSIOS The few-view emission tomography algorithm is verified in the scheme compatible with commercial reactors using low-temperature Ar plasma and an experimental plasma-chemical reactor. In all the experimental cases, the algorithm is shown to provide the qualitatively correct two-dimensional spatial distribution of the Ar ions with respect to the section of the reactor. The quantitative inconsistency between the ET method and the direct experimental results obtained by the multiprobe method is less than 6% (mean square error). With the increase of the pressure in the reactor s chamber, the lateral inhomogenuity of particle distribution in its center increases relative to the perimeter zones, which is physically correct for such a reactor and is correctly represented during the tomographic reconstruction of the emission data. For the asymmetry of the magnetic field, the spatial shift of the inhomogenuity in ion distribution is also correctly reconstructed by the ET algorithm. The lateral plasma inhomogenuity in proximity to the plate s surface is shown by the measurements to be below 8.% at worst. The mistuning of the parietal magnetic field is important for the inhomogenuity of the spatial distribution of the Ar + ions with respect to the section of the reactor on the whole, rather than just in its perimeter zones. REFERECES 1. KLA-Tencor Corporation Rudenko, K.V., Fadeev, F.V., Orlikovsky, A.A., and Valiev, K.A., Tomographic reconstruction of space plasma inhomogeneities in wide aperture plasma sources under strong restriction on the points of view, Proc. of SPIE, 24, vol. 41, pp Fadeev, A.V., Rudenko, K.V., Lukichev, V.F., and Orlikovskii, A.A., Emission tomography of plasma in technological reactors of microelectronics, Russ. Microelectron., 29, vol. 38, no. 2, pp Fadeev, A.V., Rudenko, K.V., Lukichev, V.F., and Orlikovskii, A.A., Optimization of the tomographic algorithm of the reconstruction of plasma irregularities in process reactors of microelectronics, Russ. Microelectron., 211, vol. 4, no. 2, pp Ochkin, V.., Spectroscopy of Low Temperature Plasma, Wiley, Orlikovsky, A.A., Rudenko, K.V., and Averkin, S.., Fine-line plasma-enhanced processes on the basis of a set of pilot units with a scalable inductively coupled plasma source for use in microelectronics, High Energy Chem., 26, vol. 4, no. 3, pp Miakonkikh, A., Lisovsky, S., Rudenko, M., and Rudenko, K., Instrumented wafer as a Langmuir multiprobe tool for lateral plasma homogeneity measurements in processing plasma reactors, Proc. of SPIE, vol. 87, pp Raizer, Yu. P., Gas Discharge Physics, London: Springer, Golant, V.E., Zhilinsky, A.P., and Sakharov, I.E., Fundamentals of Plasma Physics, Wiley, 198. Translated by Yu. Kornienko 1 RUSSIA MICROELECTROICS Vol. 43 o SPELL: 1. mistuning