2-DIMENSIONAL MODELING OF PULSED INDUCTIVELY COUPLED PLASMAS*
Pramod Subramonium** and Mark J. Kushner***
**Department of Chemical & Biomolecular Engineering
***Department of Electrical & Computer Engineering
University of Illinois at Urbana-Champaign
1406 W. Green St., Urbana, IL 61801
1. Pulsed Plasmas
Pulsed electronegative plasmas are promising candidates for improving etch processes for microelectronics fabrication. Extraction of negative ions from electronegative pulsed plasmas has been proposed as a method to reduce charge buildup in features, thereby reducing undesirable notching and bowing. Negative ions are extracted from the plasma during the power-off phase and accelerated into the features neutralizing positive charge which typically accumulates at the bottom of features. The extraction of negative ions is generally possible during the power-off phase because the electron density and electron temperature drop to sufficiently small values that charge balance in the plasma is sustained between negative and positive ions (an ion-ion plasma). Negative ions are able to escape the plasma when the plasma potential drops to values commensurate with the ion temperature as opposed to the electron temperature. The pulsed systems of interest are typically inductively coupled plasmas (ICPs) powered at radio frequency (rf) where the carrier frequency (the power) is square wave modulated. An additional rf bias is capacitively applied to the substrate for ion acceleration. [The pulse repetition frequency (PRF) in these systems refers to the number of power-on, power-off modulation periods of the ICP power per second. The duty cycle refers to the fraction of a given modulation period that the power is on. The peak-power refers to the maximum instantaneous power applied during the power-on portion of the pulse.]
|Fig. 1: ICP power modulation during pulsed operation (PRF: 10kHz, Duty cycle: 33.33%).|
|Fig. 2: Typical plasma properties during pulsed operation in a Argon ICP. The base conditions are peak power of 300 W, pressure of 20 mTorr, PRF of 10kHz and duty cycle of 50%.|
2. Parallel Hybrid Model Description
The model employed in this investigation is a moderately parallel implementation of the Hybrid Plasma Equipment Model (HPEM). The parallel hybrid model (HPEM-P). Task parallelism is employed in HPEM-P to execute the Electromagnetics Module (EMM), Electron Energy Transport Module (EETM), and Fluid Kinetics Module (FKM) of the HPEM in parallel as different tasks on three processors of a symmetric multi-processor computer having shared memory. The model is implemented using the compiler directives provided in OPENMP15 for shared memory parallel programming. In doing so, parameters from the different modules can be exchanged through shared memory on a frequent and, in some cases, arbitrarily specified basis without interrupting the time evolving calculation being performed in any other module. For example, the plasma conductivity and collision frequency are continuously updated during execution of the FKM. These updated parameters are made available in shared memory as they are computed so that they can be accessed by the EMM to produce nearly continuous updates of the electromagnetic fields. These more frequent updates of the electromagnetic fields are then made available to the Electron Monte Carlo Simulation (EMCS) of the EETM, through shared memory, along with parameters from the FKM to continuously update electron impact source functions and transport coefficients. The electron impact source functions and transport coefficients computed in the EETM are then transferred to the FKM through shared memory, as they are updated, to compute densities, fluxes and electrostatic fields. Using this technique, the parameters required by different modules are made available "on the fly" from other modules. The methodology adequately captures long-term transients as it directly interfaces the short scale plasma time scales with the long-term neutral time scales.
|Fig. 3: Schematic of HPEM|
|Fig. 4: Schematic of parallel HPEM|
3. Modeling of pulsed Cl2 ICPs with and without radio frequency substrate bias
Pulsed inductively coupled plasmas (ICPs) sustained in electronegative gas mixtures such as Cl2 with and without continuous wave (cw) substrate biases are being investigated to achieve improved etching characteristics in microelectronics fabrication. We have computationally investigated Cl2 pulsed ICPs with and without a continuous rf substrate bias. The model predictions are validated with experiments by Malyshev et al. The model was employed to investigate pulsed Cl2 plasmas with and without a continuous substrate bias. The base case conditions are 10 mTorr, time averaged ICP power of 300W (peak power 600 W) at 10 MHz, continuous substrate bias of 250 V at 10 MHz (approximately 70 W), PRF of 10 kHz and duty cycle of 50%. The electron temperature (Te) and density (ne) as a function of time at the reference point without and with a substrate bias are shown in Fig. 5 and Fig. 6 respectively. The ramp-up in ne during the ICP power-on pulse is similar in both cases, reaching a maximum of 8 x 1010 cm-3 at the end of the power-on period (50 ms). Upon termination of the power, ne begins a rapid decay, due largely to the decrease in ionization rates and increase in the rate of attachment to Cl2 which accompanies the decrease in Te. The decay in ne is more rapid without the bias, a difference attributed to the more positive time averaged plasma potential with the bias. With the bias, the rate of decay in ne significantly slows with an increase in Te late in the afterglow as discussed below. If the afterglow period is extended to a few 100s ms, ne eventually attains a quasi-steady state corresponding to a capacitively coupled discharge.
|Fig. 5: Electron densities and temperature in Cl2 plasmas at 10 mTorr with a time averaged power of 300 W, PRF of 10 kHz, duty cycle of 50% and gas flow rate of 100 sccm with and without substrate bias. Comparison of model predictions with measurements by Malyshev et. al.|
|Fig. 6: Electron densities and temperature in Cl2 plasmas at 10 mTorr with a time averaged power of 300 W, PRF of 10 kHz, duty cycle of 50% and gas flow rate of 100 sccm with substrate bias. Comparison of model predictions with measurements by Malyshev et. al. The time averaged substrate power of 70 W was produced with a bias voltage of 250 V.|
The spatiotemporal dynamics of electron density in a pulsed ICP reactor with and without substrate bias are shown below:
|Fig. 7: Electron density in Cl2 plasmas without substrate bias.|
|Fig. 8: Electron density in Cl2 plasmas with substrate bias.|
1. P. Subramonium and M. J. Kushner, "Pulsed Inductively Coupled Chlorine Plasmas in the Presence of a Substrate Bias ", Appl. Phys. Lett. 79, 2145 (2001).
2. P. Subramonium and M. J. Kushner, "Two-dimensional Modeling of Long-term Transients in Inductively Coupled Plasmas using Moderate Computational Parallelism. II. ArCl2 Pulsed Plasmas ", J. Vac. Sci. Technol. A 20, 325 (2002).
*This work was supported by Semiconductor Research Corporation and the National Science Foundation (CTS 99-74962, CTS03-15353).
Last updated: August 26, 2003.