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Electron Beam Lithography Process Optimization

An Experimental Design Study

by Rohan Handa (Author) Linfei Gu (Author)

Technical Report 2011 14 Pages

Design (Industry, Graphics, Fashion)

Excerpt

OBJECTIVE

This project is aimed to design apt experimental plans and analysis procedures to:

Explore the relationships between the responses (pitch and opening diameter), and four factors (step size, working distance, electron dosage and acceleration voltage);

Identify optimal setting for each factor to obtain 500nm pitch and 200nm opening diameter, with minimum response variances.

PROBLEM STATEMENT

Background

Currently, nanowires have aroused intensive attention due to their interesting electric and optical properties as well as potentially wide application (For example, nanowires can be used as a promising structure for transistor channels). For compound semiconductor nanowires, Nanoscale Selective Area MOCVD (Metalorganic Chemical Vapor Deposition), or NS-SAG, is a very attractive growth technique for the fabrication of sophisticated nanowire structure, because by using this technique, diameter and location of wires are controllable, with no incorporation of unwanted metals. It is achieved by deposition of a nano-opening-array -patterned dielectric mask above the substrate. Since crystals cannot be formed on dielectric mask, nanowire growth only occurs at openings, with desired diameters and locations, as shown in Fig 1. Pattern of nano opening arrays is of vital importance since it governs the size, location and density of nanowires as wells as growth rate and behavior.

Among many nano lithography techniques for generating nano opening arrays, Electron Beam Lithography (EBL) is the most mature and most frequently adopted one. However fabricating uniform and well controlled arrays is still a big challenge, and in order to achieve expected opening diameters and locations, many of its parameters should be appropriately selected. Four important and adjustable parameters are step size, working distance, electron dosage and acceleration voltage. This project designed several experiment plans to investigate their optimal settings, and also compared advantages and disadvantages of these plans.

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Figure 1: Process Flow of Nanowire NS-SAG

Experimental Responses

Two responses are studied in this project, pitch and opening diameter, shown above in Fig.2. Pitch is controlled by step size and working distance, while opening diameter is controlled by electron dosage,, step size and working distance. Target values are 500nm pitch and 200nm opening diameter, with minimum response variances.

Design Assumptions

Among parameters which can affect array patterns, tip parameters are not adjustable for general users, and hence are fixed. Focus, stigmation control, aperture alignment and coordinate calibration are inter-independent and set at their own optimal levels. Consequently, only, working distance, step size, and electron dosage are adjustable and therefore investigated in the experiment.

There are six arrays in one writing process, and only the factor step size can be changed between arrays during one process.

There exists run-to-run variance of opening diameters even under the same parameter settings.

Size of the writing field in this experiment is fixed at 100µm100 µm.

EXPERIMENTAL DESIGN

Factors and Levels

Factors are identified and listed in Table1, along with their experimental ranges.

All four factors are controllable factors.

Working distance, electron dosage and are quantitative factors, whose values can be taken over a continuous range. While step size is treated here as a qualitative factor, whose value can only be taken on discrete levels.

The step size, which refers to the distance between two neighboring pixels, depends on the type of digital-to-analog converter (D/A converter). For example, 16 bit D/A converter can discretize the writing field into pixel array. Since the size of writing field is 100µm100 µm, the step size is. In this experiment, D/A converter is selected to be 8 bit, 16 bit, or 24 bit. Therefore the corresponding step sizes would be, and, respectively.

Table 1 Factor and Experimental Range

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Replication

Since there is run-to-run variation even under same parameters settings, replication is necessary to analyze response variances. It also eliminates the magnitude of experimental error against the differences among treatments. Two-level factorial design has three replicates for each treatment. Because only step size can be changed between arrays during one writing process, and one process has six arrays in total, under same levels of other three factors, each level of step size can be randomly tested on three arrays. For three-level factorial experiment, design can have either two or four replicates for each treatment. Under same levels of other three factors, each level of step size can be randomly tested on two arrays in one process, and four arrays in two processes. Increasing the number of replicates can provide more accurate analysis results, but increases the amount of runs and consequently costs more time and money. Therefore, trade-off is necessary.

Two-Level Full Factorial Experimental Designs

Factors and levels are given in Table2. In full factorial experimental design, all combinations of factor levels are tested, and consequently treatments are required. In order to give three replicates per treatment, writing processes are needed, with measures. Planning matrix is given in Appendix.

Table 2 Factors and Levels

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Three-Level Full Factorial Experimental Designs

Factors and levels are given in Table 3. In full factorial experimental design, all combinations of factor levels are tested, and consequently treatments are required. In order to give four replicates, writing processes are needed, with measures. Alternatively, in order to give two replicates, writing processes are needed, with measures. Planning matrix (4 replicates) is given in Appendix.

Table 3 Factors and Levels

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(*)Note: The level “1” is chosen to be at 10kV, instead of the average between 2.5 and 25, is primarily because 10kV is highly possible to be an optimal setting, based on past experience.

Fractional V.S Factional Factorial Design

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Details

Pages
14
Year
2011
ISBN (eBook)
9783656083306
ISBN (Book)
9783656083160
File size
696 KB
Language
English
Catalog Number
v183131
Institution / College
University of Southern California
Grade
Tags
electron beam lithography process optimization experimental design study

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Title: Electron Beam Lithography Process Optimization