Isaac Trachtenberg

Constructing a reliable neural network model for a plasma etching process using limited experimental data

Plasma etching has been widely used in the microelectronics industry to pattern submicro device geometries on silicon wafers. However, the fundamental plasma chemistry and physics in plasma etching reactors are not easy to model. Reliable empirical models for such a process are desirable for investigating the process behavior and realizing real-time control. One of the main difficulties encountered in this endeavour is that frequently very limited experimental data are available for model development for any particular apparatus. In the present work, a special artificial neural network (ANN) method is presented which shows how to develop satisfactory models even though fewer experimental data exist than there are coefficients in the ANN models. The method aims at constructing a model which can satisfy the criteria of minimum training error, maximum smoothness, and simplest network structure. Two ANN models were developed for a plasma etching reactor using CF/sub 4//O/sub 2/ or CF/sub 4//H/sub 2/ as a reactant that relate the manipulated and controlled variables or the manipulated and performance variables, respectively. Comparison of the predictions made by the ANNs with those made by the second order regression models that were used as the basis of the experimental design to get the data indicated that the ANNs predicted the process behavior more reasonably than the classical regression models when the process is operated at various operating conditions. >

Ion Selective Electrochemical Sensors—Fe+3, Cu+2

Ion selective electrochemical sensors which respond to Fe+3 and Cu+2 have been developed. The sensor material consists of a chalcogenide glass (60% Se, 28% Ge, and 12% Sb) doped with Fe0, Co0, or Ni0. Response has been observed at concentrations as low as 10−6 moles/liter (0.056 ppm Fe) in both membrane and electrode configurations. Nernstian behavior is observed in the 10−5 to 10−1 moles/liter concentration range. Interference tests demonstrate good selectivity for Fe+3 in the presence of most cations, particularly Fe+2. Potential response behavior supports a redox potential mechanism rather than the ion exchange mechanism.

Modeling and control of microelectronics materials processing

Abstract Major advances in modeling and control will be required to meet future technical challenges in microelectronics manufacturing. This paper reviews the recent applications of fundamental mathematical modeling to unit operations such as crystal growth, lithography, chemical vapor deposition and plasma etching, where there have been some notable successes. Important characteristics of these processes are identified, and the evolution of the standard multiwafer reactor to single wafer reactors processing larger wafers is discussed. The implementation of closed-loop control on key unit operations in microelectronics manufacturing has been extremely limited due to a lack of suitable on-line measurements. There remains considerable promise for application of modern control and optimization techniques in manufacture of integrated circuits.

Modeling of silicon etching in CF sub 4 /O sub 2 and CF sub 4 /H sub 2 plasmas

A one-dimensional radial flow reactor model that includes fairly detailed free radical gas-phase chemistry has been developed for the etching of silicon in CF{sub 4}/O{sub 2} and CF{sub 4}/H{sub 2} plasmas. Attention has been restricted to transport and reaction of neutral species. The model equations were solved by orthogonal collocation. The sensitivities of the model predictions to flow rate, inlet gas composition, electron density, silicon loading, and other factors have been examined. The major loss path for fluorine atoms is different in CF{sub 4}/O{sub 2} and CF{sub 4}/H{sub 2} systems, and this results in significant qualitative differences in the parametric sensitivities of the two systems.

Modeling of Plasma Etch Systems Using Ordinary Least Squares, Recurrent Neural Network, and Projection to Latent Structure Models

In microelectronics manufacturing, control strategies for plasma etch systems have been limited to traditional statistical process control and recipe control techniques. The lack of in situ real-time measurements of process performance and appropriate models has hindered the introduction of feedback control systems. This paper focuses on empirical model building for advanced process control using two real-time diagnostic sensors for measurement of the reactor state. Laser interferometry for measurement of etch rate and voltage and current probes for measurement of effective radio-frequency power and sheath voltage, coupled with data acquisition hardware and software, provided the foundation for steady-state and dynamic model development of the plasma etch process. Several linear and nonlinear steady-state techniques including ordinary least squares, neural networks, and projection to latent structures were used in empirical model building. Both linear regression and recurrent neural network model structures provided a satisfactory fit of the data for the operating space investigated. Projection to latent structures techniques indicated that the most relevant variables were power, pressure, and chamber impedance. The addition of the impedance measurement significantly improved the predictive capability of the model.

Model-based control of rapid thermal processes

Model-based control for two rapid thermal processing systems has been performed. The condition number of the process influences the control strategies selected and the quality of control that can be achieved. For the Texas Instruments RTP system, a successively linearized quadratic dynamic matrix control (QDMC) strategy using a reduced set of outputs has been developed. Experimental results of the control strategy are presented and compared with internal model control with gain scheduling. The nonlinear controller discussed shows superior performance for the test case studied. The second RTP system designed by SEMATECH exhibits improved controllability. This system has the potential for tighter control of wafer temperature using gain scheduling.<<ETX>>

Modeling the Wafer Temperature Profile in a Multiwafer LPCVD Furnace

A mathematical model has been developed to predict wafer temperatures within a hot-wall multiwafer low pressure chemical vapor deposition (LPCVD) reactor. The model predicts both axial (wafer-to-wafer) and radial (across-wafer) temperature profiles. Model predictions compare favorably with in situ wafer temperature measurements described in an earlier paper. Measured axial and radial temperature nonuniformities are explained in terms of radiative heat-transfer effects. A simulation study demonstrates how changes in the outer tube temperature profile and reactor geometry affect wafer temperatures. Reactor design changes which could improve the wafer temperature profile are discussed.

Radio Frequency Diagnostics for Plasma Etch Systems

Selective etching of silicon dioxide over silicon is a frequently used process in the manufacture of semiconductor devices. Limited diagnostic capabilities have forced plasma etch systems to rely on traditional statistical process control and recipes. With the addition of in situ measurements, however, automatic feedback control could be employed for control of the process variables. This paper focuses on the implementation and installation of a radio frequency power sensor suitable for advanced process control of plasma etching. The sensor measured information about the direct current bias voltage, radio fequency voltage, current, and phase angle at three locations in the power delivery system: before the matching network, after the matching network, and at the lower electrode. Matching network efficiency and transmission line analysis were used to transform between each measurement. This information showed the importance of accurate characterization of stray capacitance and inductance in the power delivery system. Plasma parameters of impedance, delivered power, sheath thickness, and sheath capacitance were computed using simple equivalent circuit models for the plasma discharge. Measurement of the fundamental and harmonic components of the voltage, current, and phase showed that the power generated in the plasma at the harmonic frequencies was approximately 3% of the generator power. Amplitudes of harmonic voltage matched analytical predictions.

Mathematical Modeling of a Single‐Wafer Rapid Thermal Reactor

Transient two-dimensional models have been used to simulate rapid thermal processing (RTP) in a cylindrical single-wafer reactor. The modeling has been analyzed at various levels of simplification to identify the dominant factors governing heat transfer and fluid flow inside the reactor. In each case, the thermal patterns on the wafer surface, both in the dynamic and steady states, are of special interest since temperature profiles are predominantly responsible for the thickness variation in the as-deposited or thermally grown RTP films. The thermal distribution is a function of process variables such as the ambient gas and operating pressure. Additionally, the thermal profiles predicted by the model are in good qualitative agreement with those found experimentally

Real-time monitoring and control in plasma etching

Process control strategies have been developed for plasma etching of silicon (Si) and silicon dioxide (SiO/sub 2/) in a CF/sub 4//O/sub 2/ plasma. The analysis considered four measured variables, four manipulated variables, and up to seven performance variables. Empirical input-output models were developed by regression analysis. Relative gain array analysis and singular value decomposition were used to select manipulated/process variable control loop pairings and to evaluate potential difficulties in control system performance. Singular value decomposition was also used to determine process/performance variable pairings. Block relative gain analysis of multivariable interactions in the process indicated that partial decoupling was necessary for adequate control, and this was verified by simulation. >