Modeling of Dynamic Charging on SEM specimens using a circuit model
Elroy Tatem
Cherrice Traver
Bradley Thiel
Fall 05
Abstract:
I am creating a more precise model of artifacts in SEM images caused by the specimen charging. The charging effect is caused by a build up of negative charge on the surface of the specimen over time. Typically, samples are coated with a conductive coating to decrease the discharging time. However, when trying to examine poorly conducting specimens, charging becomes an issue. The current model consists of an RC circuit which decays over time. The model I design will have more parameters such as secondary, auger, and backscatter electrons. Once the Circuit is completed, the derived equation will be put into a Microsoft Excel program where users can input SEM and sample parameters and see how a sample should react.
Table of contents
Abstract
Table of Figures
Introduction
Design
Relative Schedule
Fall 05
Winter 05-06
Spring 06-
Budget
Conclusion
Table of Figures
Figure 1: Scan coils control direction of the beam as it rasters the sample (left). Electrons detected and sent to monitor (right).
Figure 2: smaller initial beam energy gives a larger emission area (left) than a higher beam energy.
Figure 3: Secondary emission v initial beam intensity
Figure 4: Charge density on the surface of a sample.
Figure 5: (above) shows charging of a sample
Figure 6: (above) shows charging of a good conductor
Figure 7: (above) shows charging in a poor conductor
Figure 8: RC circuit with time constant e-t/RC
Figure 9: (A) charge on a sample at the beginning of each frame; the first on the left and last on the right. (B) Microscope parameters. (C) Sample parameters. (D) Function e-t/ηε.
Figure 10: The sheet contains data to be plotted. The “A” columns are data on the y-axis that represent surface charge density σ. The “B” columns are essentially a time scale.
Figure 11: When time constant ηε is large, charging occurs.
Figure 12: When time constant ηε is small, the sample is able to discharge fully before the next frame.
Introduction
An image is taken by a scanning electron microscope by exciting electrons on the surface of the sample with a high energy electron beam. With electromagnetic fields called scan coils controlling the direction, the beam scans the sample from left to right in the x direction then turns off, returns to the left, then moves down in the y direction, the beam turns back on, and then the process repeats until the beam reaches the end of the sample. Once the beam reaches the end of the sample, it returns to the top left and starts over.The electrons that exit the sample are seen by a detector, which sends the image to a monitor (Figure 1).
Figure 1:Scan coils control direction of the beam as it rasters the sample (left). Electrons detected and sent to monitor (right).
Sometimes when viewing images taken from an SEM, there are visible faults in the final image. Many of these come in the form of light or dark spots, lines, or general inconsistencies in the contrast of the image. These are caused by a build up of negative charge on the surface of the sample which causes inaccuracies by skewing electron velocities. The affects of charging have commonly been decreased by coating the sample with a conductive substance, thereby causing any excess electrons to return to ground state.
A qualitative explanation is that the higher the energy of the beam, the more electrons are being sent to one spot on the sample. The more electrons that are there causes a higher buildup of negative charge, which then repels electrons and essentially slows down the electrons and in some cases reverses their direction.
When quantifying this phenomenon we consider the factors affecting secondary electron emission. There equation 1shows the relationship between secondary electrons and the initial beam intensity. Any given sample has a certain emission depth ζ, which is usually around 10nm. This is the volume immediately beneath the surface of the sample where the electrons are emitted. Although this depth is fixed, the depth at which the beam can penetrate through the rest of the sample increases with the beam intensity EB. When the beam penetrates a sample, the well where the particles are excited becomes deeper and narrower as the beam intensity increases. The beam can penetrate a few hundred nm while affecting a smaller volume area in the emission region. This narrowing decreases the secondary emission ES (figure2).
Figure 2: smaller initial beam energy gives a larger emission area (left) than a higher beam energy.
From this, we can attain a constant β which is the ratio of secondary electron emission ESE to the initial beam intensity EIB.
Equation 1
In figure 3, this equation is shown graphically.
Figure 3: Secondary emission v initial beam intensity
As the beam energy increases on a single spot on the surface of the sample, the charge density also increases. The charge density of the beam is calculated using the settings of the microscope. The charge density, σ, is characterized by equation 2;
Equation 2
where σB is the total charge on the sample from the initial beam, M is the magnification setting of the microscope, I is the current, F is the frequency of each frame, and A is the area of the sample.When taking the loss of charge due to secondary emission, we introduce the secondary emission coefficient β. Therefore, equation 2 can be modified as follows.
Equation 3
β will lie on the graph shown in figure 3. Changing the beam energy will cause a shift in the value of β. Considering that the beam is a pulse, graphing the sum of σi for i={1,2,3,…,n}results in the graph in figure 4 below.
Figure 4: Charge density on the surface of a sample.
Since the charge on the sample does not dissipate immediately, the discharging constant for materials must be taken into consideration. The discharging coefficient is inserted to form equation 4.
Equation 4
In equation 4, η is the resistivity of the sample ε is the permittivity and t is time. The graph of σ(t) as a sum of σi for i={1,2,3,…,n} results in 3 possible representations. Figure 5 is the case where ηε and F are close to each other. Figure 6 shows the case where F>ηε (good conductor), and figure 7 is where ηε > F (poor conductor).
Figure 5: (above) shows charging of a sample
Figure 6: (above) shows charging of a good conductor
Figure 7: (above) shows charging in a poor conductor
The phenomenon can also be modeled using an RC timed circuit. The current model utilized a simple RC model shown below in figure 8.
Figure 8: RC circuit with time constant e-t/RC
Design Requirements
My goals for this project are to improve upon this model and derive equations from the new circuit. Those equations will be programmed into a Microsoft Excel workbook and where users can input specimen and microscope parameters and see information about secondary emissions. I would also like to see what kind of information about the sample can be attained from the theoretical results as compared to actual experimental results.
Design
The First step in the design process was to understand the concepts of charging and to write an algorithm which would allow me to eventually write a program in Visual Basic (a program that I had no idea how to use at the time).
-Simple algorithm-
*electron beam parameters*
Get beam current density
Get frame rate
Get pixel
Get number of frames
*sample parameters*
Get permittivity
Get resistivity
Calculate runtime
Calculate
Initialize surface charge
For t= 0 to runtime
Calculate surface charge
Store in vector(t)
Increment t
Store vector in cells
Figure 9: (A) charge on a sample at the beginning of each frame; the first on the left and last on the right. (B) Microscope parameters. (C) Sample parameters. (D) Function e-t/ηε.
Figure 9 above shows a sample from the program. All of the frames in the seventh row show the surface charge density σ for the beginning of each frame. Frame A8 shows the decay over time and resets if the time constant ηε reaches zero by the time if the next frame. Otherwise, charging takes place.The data to be used in plotting the graph is on the second sheet (see figure 10 below). For the moment, the plot is done manually to save time when the program must be edited. The final product will make calculations and plot in one program. The plots are made by highlighting the rows for the x and y axis then clicking on the “chart” button.
Figure 10: The sheet contains data to be plotted. The “A” columns are data on the y-axis that represent surface charge density σ. The “B” columns are essentially a time scale.
The graphs are shown below in figures 11 and 12. The value of σ should stay the same when the constant ηε of the material is small. When it is large, the material will begin to charge.
Figure 11: When time constant ηε is large, charging occurs.
Figure 12: When time constant ηε is small, the sample is able to discharge fully before the next frame.
Relative Schedule
Fall 05
-Read papers and understand the concepts and physics of charging.
-Understand charging equations
-Start writing algorithm for translating equations into code
-Understand and learn how to use Visual Basic with Microsoft Excel
-Start programming code in Visual basic for basic charging model
Fall term goal: Have a working bug-free Visual basic program that can easily simulate simple charging phenomena.
Winter 05-06
-Incorporate secondary emission coefficient β into the program
-Study other parameters affecting the charge on the surface
-Use circuits to incorporate different terms in the equation
-Put circuit equations into code to more closely replicate charging effects
-Test how closely the model is to real situations
Spring 06-
Keep adding parameters to equation to make it more precise
Budget
This project is advancing knowledge in the study of specimen charging. As this is mostly simulation, there are no costs for parts or services. When actually experimenting, we will use Albany’s facilities.
Conclusion
The first half of this project consisted mostly of learning how to program in visual basic. Some issues that I had to deal with when working with Excel was the limitations of charts and cells in Excel. I had reached the physical limit of data per sheet in Microsift Excel, and also the maximum number of data points per chart. Each of which were problems which had to be worked around. The different stages of code are attached in the appendix. Now that the program is working, I can start on the second part of the project.
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