Modelling, simulation and multivariable control of plasma etching of silicon and silicon dioxide
Tan, Liang (1994) Modelling, simulation and multivariable control of plasma etching of silicon and silicon dioxide. PhD thesis, Dublin City University.
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Plasma etching has been used extensively in the microelectronics industry for integrated circuit fabrication. However, the optimisation of this process is quite challenging because the plasma etching process is complex and not fully understood. An experimental and theoretical study of the etching characteristics of silicon (Si) and silicon dioxide (SiC^) in a sulphur hexafluoride (SFg) with Argon is reported. The selected manipulated variables or inputs are radio-frequency (RF) discharge power density, chamber pressure and gas component ratios. The semi-outputs or process variables are the relative percent concentration of plasma species: fluorine [F], [SFX] (x=3-»6) and the electric field to pressure ratio E/p. The outputs or performance variables are Si and Si02 etch rates and (centre-to-edge ) etching uniformity.
The etch rates of silicon and silicon dioxide in SFg/Ar plasma are statistically investigated based on the effects of different settings of the manipulated variables. Optical emission spectrometry and laser interferometry have been employed to monitor spectral emission and etch rate in real time for plasma diagnostics, endpoint detection, and process control. The results obtained from this study have shown that etching Si and Si02 in SFg/Ar leads to higher etch rates in comparison to other reported systems. Variations in optical parameters associated with manipulated conditions, such as RF power density etc., have been studied over a limited parameter space to obtain their effects on the etch rates of Si and Si02.
A dynamic mass balance has been employed to construct a comprehensive reactor model for a basic study of plasma etching o f Si and Si02 with SF6/Ar. The model includes diffusion and convection of molecular fragments in a duct geometry, which is estimated by using an effective diffusion length which takes surface reflection into account. Electron impact dissociation and ionisation reactions which depend on the electric field and gas density are the dominant sources of active species generation. Fluorine atom generation is also described by dissociative chemisorption. Fundamental plasma parameters such as electron density and electric field are estimated from impedance measurements in designed experiments under the various operating conditions. Results presented show relatively good agreement between the model predictions and the experimental data.
Using regression analysis a steady-state model which relates the manipulated conditions to both the process and performance quantities has been developed. Optical emission spectroscopy and laser interferometry (both non-intrusive technologies) are again employed in order to maintain the integrity of the etching environment. This information can be used to find correlations and also feed into the model to track proper operating conditions. It is found that a fast, uniform Si and Si02 etch rate could be achieved in the SFg/Argon process by using high RF power density, low pressure, high SFg/Ar ratio. Correlations are developed to directly relate inputs, semi-outputs and outputs in the SFg/Ar system. Response surface methodology (RSM) is used as a basis for further modelling of the non-linear plasma etching process. Results presented in this study compare favourably with the known discharge characteristics, some interpretations of the etching and discharge mechanism and also the comprehensive reactor model. The singular value decomposition (SVD) technique has been applied to determine the pairings between performance quantities, process and manipulated variables. The non-intrusive techniques are also used for dynamic measures of interaction and are found to very rarely change the variable pairings. Step tests are run to determine process variable time constants for use in dynamic process simulation. The SVD pairings with input and output structural compensators designed by using the SVD technique form a multi input-multi output (MIMO) decoupled control system. The robust multivariable control system analysis based on structured uncertainties of inputs and outputs has been formulated as a "block diagonal bounded perturbation" problem (BDBP). The solution to this problem involves the structured singular value (SSV), a generalisation of the singular value decomposition, which is useful for robust multivariable control analysis since the model uncertainty due to the non-linear behaviour of the plasma etching is highly structured. The robust stability and performance properties of the system subject to disturbances and structured perturbations are developed.
Results presented show that the closed loop transient responses for SVD pairings with the structurally compensated MIMO control strategies are typically much faster than the conventional scheme. Both of the control strategies satisfy the robustness requirements but the robust stability of conventional control is worse for multiplicative input uncertainties and the structurally compensated scheme is less sensitive to input perturbations.
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