FIB - Science method

I am attempting a numerical modeling of a pullout test for reinforced concrete. I have calculated the stiffness parameters following the FIB 2010 standard. I used cohesive contact interaction property for modeling ineraction between embedded length of rebar and concrete. However, for some reason, my bond stress vs. slip curve is not declining as expected. I also tried randomly increasing the stiffness parameters (Knn, Kss, Ktt), but the curve still does not behave as it should. Can you suggest what I should do?"

I am using grids made of Cu for my in-situ heating experiments (from 400°C to 600°C). However, there is a huge Cu- contamination after the heating, which is due to Cu thermal evaporation at high temperatures. Is the any TEM FIB Lift-Out Grids that doesn't produce metal evaporation at high temperatures?

Dear community,

Many papers have been published on FIB/SEM imaging of porous electrodes of Li-ion batteries. A quick Google search only gives the 3D SEM images of separator kindly shared by Prof. Wood from ETH. Seems there is no open source depository of 3D FIB/SEM images of NMC, LFP, LCO, etc.

So, my question is where to find these open source 3D FIB/SEM data (NMC, LFP, LCO)?

My search may be incomplete and any help will be greatly appreciated.

Thanks in advance.

Xiaoguang

Hello,

Recently, I am learning how to develop a full microstructure-resolved 3D model. And I want to use X-ray nano-tomography or focused ion beam/scanning electron microscope (FIB/SEM) to reconstruct the microstructure of commercial electrodes with sufficient nanoscale details. The microstructure-resolved models can be imported into computational programs to mimic the electrode behavior under the battery operation condition. But I encountered some questions. Firstly, how to add the current collector and separator into the segmented volume to construct a battery half-cell? Secondly, how to export the battery half-cell and import it into computational programs like COMSOL? Does any examples or source code about these questions?

I would appreciate it if you can help me.

The excellent book on the Introduction to FIB by Gianuzzi et. al. states the following:

"FIBs are most often used to create features of high aspect ratio (i.e., deep narrow trenches). Sputtered material and backsputtered ions may therefore deposit on surfaces that are in close proximity to the active milling site (e.g., the sidewalls of a deep narrow trench)."

However, backsputtered ions are ions that exit out of the material. I presume these ions exit from the back of the sample. Thus, how could these ions possibly contribute to redeposition of the milled structure?

I tried to visually represent my question with an image, which is attached.

Hello,

I have a large set of data from a serial imaging FIB/SEM tomography of a superalloy microstructure in binarised form. I was wondering whether there is some sort of programme that allows for automated measurement using the linear intersect method on those binary images. Ideally, I'd be able to compute not only the mean size thickness of the matrix channels, but also get the statistical distribution.

Many thanks in advance!

Hello, everyone

This is biaobiao.

In recent days, I have tried to do EBSD at the FIB milled surface. Well, using a 30 kV Ga+ ion beam, and ion beam currents ranging from 40 pA to 790 pA, I still cannot see the Kikuchi lines.

I also tried to adjust the EBSD capture parameters like exposure time and binning modes low as 1×1, unfortunately, I still cannot see the Kikuchi lines. Of course, no indexing.

The Ga+ influenced depth, in my view, should be around 10-20 nm. Well, the EBSD detects the information of depth as 10 nm, I guess. Is that meaning, I will not get the EBSD after FIB milling?

If anyone has successfully performed FIB-EBSD on Mg, pls. give me your suggestion or experience.

That's it.

Thanks a lot.

Best wishes,

To prepare TEM samples from a wire of 1 mm in diameter, I am looking for a suitable preparation method other than the FIB.

Hi!

I'm looking forward to making a 3D reconstruction of tubular structures in zebrafish using FIB/SEM Microscopy.

I have the possibility of using a Lyra3 TESCAN FIB/SEM for this purpose, but our technicians don't know how to adjust the equipment and prepare our samples for this.

Does anyone have a detailed protocol or a paper that could guide us?

Recently I have started preparing cross-sectional TEM lamella from the bulk sample using FIB. But I am not aware of how to prepare plane view TEM lamella. Actually, I want to cut a piece of the surface from the bulk sample and wield it to the TEM grid for TEM imaging. Can anyone suggest how can I prepare plane view TEM lamella?

Hi all,

Are there non-destructive ways to measure the thicknesses of the bilayers made of SiO2 and Si3N4 in a multilayer stack? I have 23 bi-layers, for a total thickness of about 11 um. I was told ellipsometry can't deal with that many layers.

I've tried FIB + TEM (destructive), but it is not a reliable technique nor very practical. Also, measuring the thicknesses of a few micro samples over a surface that is of the order of the cm^2 is not very representative of the entire stack.

Looking forward to hearing your ideas!

Thanks,

Laura

I would like to deposit a single Pt nano-column with GIS and FIB of a diameter <100 nm and height >500 nm. Is it possible? What values of parameters of ion beam (accelerating voltage, current) and scanning (mode, dose, dose factor, pixel spacing, numer of cycles) should be used?

I achieved 200 nm column with parameters as shown in the attachment. I have been trying to fine-tune the parameters but I could not decrease the diameter.

I tried both single point and small square (nominal dimensions 100 nm x 100 nm) as a layout.

Hello all

I have to get an SEM image for my perovskite LED device cross section but I am not able to get a clear image. It is very blurry and I am not able to get any information from there. The machine I am using is Tescan FIB FERA. Can anyone help me with this?

Hi Fellows, I would like to know if there is a good way to characterize surface defects or strain. Our recent finding shows that scratched surfaces show different electrochemical properties from non-scratched surfaces. However, the scratch did not generate any SEM-level cracks/fractures (invisible in SEM). I am thinking either nano-cracks were generated on the surface or a strain field was built up. My initial thought was using TEM to look at it. However, the sample preparation may cause new strain field if a FIB method was used. Is there any way to detect such small defects (if any) or the strain field?

I am doing some FIB cuts and analyzing my layer stack. I always see dots in the InP and InGaAsP layers, but I don't know their origin. These dots do not appear when I do a SEM of a cleaved sample, so I assume the origin is related with the Ion beam process. I attached a picture of a SEM image after an FIB to make clear which dots I am referring to. Any help or reference to solve this question is highly appreciated!

I want to see the cross section of PDMS substrate.

As far as I search, direct focused ion beam irrdiation makes the PDMS surface wrinkled.

Before FIB milling, if the metallic coating (Pt, Os, etc) with O(1nm) is performed, is it possible to do FIB milling of PDMS layer as minimizing the wrinkling?

Thanks in advance.

I have attached a metallic thin sample in Si substrate using FIB. After that, I have made the connection by depositing platinum in FIB with the sample and the pre-pattern platinum electrode. The prepattern platinum electrode is made by photolithography which has contact resistance around 10 ohms. But after making the connection with the pre-pattern platinum electrode by depositing the platinum in FIB the resistance become very high.

Can anyone suggest how can I improve my connection?

My point is - I want to get a 3D model of a sample with nano-scale resolution but with a relatively large field of view (tens of microns). I'm planning to use FIB for 3D reconstruction. Have you seen any study about the large field of view FIB imaging? I'm particularly interested in the application of FIB for geology. Thank you in advance for your help

I need to find a method to cut (i.e. remove) the unwanted parts of my polymeric sample under a microscope. The sample is small and I need to have cutting-accuracy about 1 micron.

Now, I am planning to use FIB for this purpose. However, FIB's resolution is much more than my needs.

Do you know an alternative method for me?

Dear colleagues,

A good FIB-SEM data stack can contain a few thousands pictures. It is very tricky and annoying process to segment them all manually. Which software do you use (real practical experience with big data) for such tasks?

Cheers,

Denis

Dear 'Named Data Networking' researchers,

As you know the current Vanilla NDN works over IP. If we assume that NDN architecture become the used Internet Architecture instead of TCP/IP, what will be the address of the final users (source of interest packet)? The physical address?!

In other words, does the interface in the FIB equal to physical address?

If not, for the case of wireless interfaces, we may have multiple users connecting through the same interface entry (university router for instance) How the address problem is solved when the data arrives back?

Our FIB source was opened to air prematurely resulting in gallium oxide (water insoluble) coating some parts of the ion source. Does anyone know a simple means of removing it ? I guess HCL is best but just thought it'd be worth asking anyway.

I am analysing wear track of CoCrMo alloy using FIB-SEM. Unfortunately, every time Beam is shifting out of sight after some time. I am mounting my sample using carbon tape and later painting the side of the sample using Ag paint (from sample to sample holder). If anyone has faced a similar problem and found a solution please share if you can.

Thanks in advance!

I'm modelling a RC beam structure using LSDYNA. I want to include the rebar bond-slip relation in the model. The *CONTACT_1D has different parameters, such as Bond Shear Modulus GB, Maximum shear strain displacement SMAX, and Exponent in Damage Curve EXP.

- Are there any recommended values backed up from your experience ? Any guidance through the calculation of those parameters ? I read few literature and they refer to FIB Model Code for Concrete 2010, clause 6.1.1 and Table 6.1-1. But no any clue regarding relating those to GB, SMAX, or EXP. And also, what are the units for each? Is it MPa or MPa/mm for GB ? mm or unitless for SMAX ? Because I came across both units in some literature.

- Is it a must to have mesh conformity between rebar and concrete to implement a correct *Contact_1D ?

Im trying to find out if it would be possible to create a stencil from a metal plate by removing a thin strip of material all the way through. The groove would need dimensions of : 100nm wide and about 500 micrometres deep. The length doesn't really matter. Im trying to think of ways to grow nanowires using a metal stencil instead of growing onto a layer of resist and removing via liftoff. Iv heard that FIB can reach the resolution I need but not sure if it could reach the depths im looking for.

Any suggestions? Thankyou

I covered (MBE) the half of my nanowires (1um long and 50nm diameter) with a 20nm layer of Fe. Now the question is, how can I destroy the Fe film to release the nanowires and disperse them in solution without destroying them? Cutting the nanowires one by one with the FIB is not really working well.

SEM images are attached (the maximum that I was able to break the Fe film).

Thank you very much for the answers in advance. I hope someone has some ideas :)

I am using molecular dynamics to study Ga interaction with Silicon. The simulations at low kV (1-5kV) with 0.1fs time-step works well and are in accordance with SRIM generated values. The simulations at 30kV, however, with time-step 0.1-0.002fs do not predict actual results (the Ga ions just passes through Si lattice and travel more than 100nm Si depth), potentially arising from interaction issues. I am using a combination of ZBL and tersoff potentials. Has anyone encountered such issue in their MD simulations? Any feedback or suggestion in this regard would be highly appreciated.

Regards,

Vivek

I am looking for performing some EBSD analysis on electroplated Indium, The tough task is preparing it, its very soft and ductile metal. Gallium beam from FIB is melting Indium and even electron beam assisted platinum deposition is deforming it. Similar result with Argon ion beam too. Is there any mechanical precise way such as vibromet or power head assisted polishing can help in this situation ? Aslo how much effect does surface roughness have on indexing the patterns? Because the specific chemistry I am using to plate Indium has pyramid type of micro structure with sharp apex on top, is there any way I can polish few nano meters away and look for pattern from surface rather than cross sectioning?

I need to solve the ion mirror phenomenon that occurs in FIB

Like FIB-TEM.

I am looking for a technique by which polymer composite properties remain constant.

Plz insight us

Thanks in advance.

Actually, i am looking forward to prepare lamella with thickness about 50 nm from silicon nano wires on silicon wafer substrate, using it to study its interface with cells, but i don't know the exact procedure of doing that. I have a FIB-SEM and TEM.

Focused ion beam (FIB) devices can generate beams with a diameter (FWHM) of less than 10 nm. What are the methods for measuring diameter of Focused ion beam (FIB)?

Thanks

Mohsen

Recently I am using Focus ion beam to prepare TEM lamella, but came to a dilemma that the crystalline sample is either too thin for SAD (losing Kikuchi lines for two beam conditions) or too thick for HRTEM. The interested area is very localized. Could some scientists or experts give me some clues on the critical thickness for both that? (80-120 nm)? Thanks a lot in advance.

Best regards,

Sincerely,

I am working on soft lithography and trying to modify the patterned silicon wafer (pattern made by FIB) surface with trichloro(1h 1h 2h 2h-perfluorooctyl)silane, according to this instruction: https://hms.harvard.edu/sites/default/files/assets/Sites/Microfluidics/files/Silanization%20of%20Photoresist%20Master%20Protocol.pdf

But I found that the silane chemical is unevenly distributed on my wafer and dirty, even damaged my pattern on Si wafer, does anyone know how exactly I should do the modification?

I have some cold-rolled NiTi sheets (0.8 mm in thick). I want to observe the microstructure of the side face using TEM. So how to prepare a TEM film in this case. FIB is costly. I just want to use mannual grinding and then twin-jet electropolishing.

I am currently working on new TBC materials which can replace the famous 8 wt% Yttria stabilized Zirconia. I would like to know If FIB SEM can be used in analysis of such materials?

I am planning to deposit a thin gold film on YIG and after some patterning using FIB, i need to remove it using an etchant. I need to make sure if the chemicals in the gold etchant wont etch through YIG or not. 

I am planning to make patterns on YIG thin film using Focussed Ion beam. But YIG thin film is insulating and deviates the ion beam. I am planning to deposit a thin film of metal, such as gold and then perform patterning using FIB. I would etch the gold layer using an etchant but would it also etch through YIG? 

I want to use FIB milling technology for drug localization. Could any one suggest me to some articles regarding this topic.

I have a 50nm Yittrium iron garnet which is highly insulating and gets charged up while trying to create patterns using Focused Ion beam. I need to create patterned structures on the thin filmusing FIB.  Is it possible to coat the thin film with some kind of metal which will get rid of the charging problem? And then etch out the metal coating. If so, what metal should i use and which etchant that wont affect the underlying YIG film. 

I am investigating some off-stoichiometric delafossite structure by TEM. I am observing some missing atomic lines (10- 20 atoms missing). This happens for many grains (hence not an isolated case) but not for all samples. Therefore I would like to know if this defect is characteristic for the sample or is possible to appears during sample preparation. During this preparation process I am using a FIB based on Galium. My question is then: does somebody already observed this kind of defect appearing during an ion bombarding? 

Please write which kind of project you started. I am interested in FIB analyze after fs laser irradiation of thin films.

We have had in 2011 a common in SCT a paper titled: Femtosecond laser modification of multilayered TiAlN/TiN coating.

I wish you success, Biljana  

Focused ion beam (FIB) instruments can provide beams with a diameter (FWHM) of less than 10nm, however, the interaction between ions and target occurs over a large volume, given by the influence of the probe tails and multiple scattering laterally and the depth penetration of the ions in the vertical direction. What are the smallest nano-structures that have been made by FIB?

The straightforward way of converting probe current into ions per second (A-->C/s-->ion/s) and dividing by the beam area is giving me values much higher than usually quoted in literature.

Am I forgetting to consider some aspect of the rastering? I couldn't find any source describing this, among lots of papers and books about FIB.

Thanks in advance,

I am trying to test a custom implementation of a packet forwarding algorithm for an IPV4 router. To test the performance of my algorithm, I need the forwarding table (FIB) from a real router and a trace of the packets received by the router. I was looking at www.ripe.net and www.caida.org, but could not quite understand how to get the exact information I need. Any help from the community would be highly appreciated.

I am working on characterizations of mullite needles, which exhibits nano-scale size, in order to investigate their Al/Si ratio. The needles possess 100-200 nm long and about 20-50 nm diameter in average. And the needles are embedded in a silicate-glass matrix. 

I have done SEM-EDS but I could not get the Al/Si ratio since the EDS signal were not indicated mullite characteristic. It supposed to have large interaction volume and the obtained signal included both mullite and glass matrix. I also performed FIB/SIMS which is about 10 nm of interaction volume, again I could not get the signal.

I am thinking what can I characterize the needles chemically to find out the Al/Si ratio.

Any suggestions will be really appreciated

Normally we believe Xe ions must be more detrimental to the specimen's surface compare to Ga ions, since they are heavier and larger.

So personally I would not consider PFIB method suitable for TEM lamella preparation.

But I heard somewhere that using PFIB (using Xe) the amorphous layer of the TEM lamella is even thinner compare to the normal FIB (using Ga)! Physically I can not digest this as a fact!

Any experience?

I am planning to use the diamond themselves as sample container (to avoid flaws related to noble metal use) for a Hydrothermal Diamond Anvil Cell.

To do so, I need to have a square 300x300 microns and 50 microns deep recess milled on the culet of one of the anvils. FIB is the only technique which can produce a virtually perfect shape, which is paramount for my experiments (I tried laser milling but it does not work). I also need to FIB-cut glass wafers 200x200x40 microns dimensions out of glass chips (roughly 1x1x1 mm size, but could be made bigger, if necessary).

Dear All,

I am working on using the FIB to create 200nm-in-diameter cavities. But I would love to have more control on the geometry of the FIB. So I am wondering what would be the controllable variables in the FIB processing. Any opinion is welcomed!

i.e current, loops, dwell time, etc. 

Letian

Sample Preparation, HR-TEM, Ion Milling, FIB, Glaze

Our group is working  with coatings and we have done few erosion tests. We need somebody, who can help us to do FIB sample preparation for our coatings. We are planning also to do some corrosion tests and wirite few publikations. Sharing authorship will be a possible.

Those interested, please send message to my RGate mailbox or here.

Thank you

Assume you have two FIB system with almost the same specifications, and the only difference is that one of them can provide a probe current of up to 60 nA and the other one up to 100 nA.

But the first one has other advantages over the second system.

So, I want to know how important the FIB probe current is (for 3D EBSD and EDS analysis). Is there a significant difference between 60nA and 100nA, when it comes to milling speed and resolution?

How is the energy of the FIB dependent on the process parameters.? In other words what is the relation (mathematical) between beam voltage, beam current, dwell time, etc on the energy of the ion beam?

I would be most interested in an application capable of running machine learning algorithms

I have seen some systems, such as FEI requires a particular sample preparation (rectangular thin samples with 90 degree edges). Their configurations can only do 3D EBSD on the edge of the rectangular specimens.

It means that we can not do 3D EBSD on the normal 2D EBSD samples (normal mounted samples).

Is this the normal procedure for all the 3D EBSD configurations our in the market? Is there any possibility to run 3D EBSD tests on the normal samples, i.e. not those special rectangular shapes?

Any specific guideline for sample preparation for 3D EBSD analysis, using normal grinding/polishing equipment?

For my experience, every time I prepare a TEM lamella from a bulk Al sample it starts bending when its thickness is below 100 nm.

It cannot be charging because there is electrical continuity through the Pt and the Omniprobe needle.

One reasonable explanation would be partial melting, but is that possible when using as little as 0.28 pA and 16 kV? Al has a melting point around 930 ºK..

Ideally I would like to know the thickness of both the barrier and the porous layer formed when aluminium is anodised.

One way I can think of is by taking a cross section of the anodised aluminium using a FIB and then examining under a TEM. This can be very time consuming however.

Does anyone have any other suggestions?

I want to make an Ag pattern of nano-disc on top of ITO. I know I can use DWL(EBL,FIB and TPP). I need to know the pros and cons of each of these relative to write time, economics and quality of nanostructures.

In slice and view applications of FIB/SEM dual beam systems, which software has a high quality 3D reconstructed volume image? 

I want to see the damage created by laser using tight focusing inside sio2, for this I need to etch it or polish it up 5~10 micron. Can someone give suggestions on how to do this. FIB is one method but it is quite expensive. Is there any other inexpensive method?

I'm interested in the 3D microstructure of a deformed Mg alloy. I would have access to a FIB and to a SEM with EBSD detector, which are two separate instruments.

Can anybody suggest a reliable procedure to realign the sample within both instruments avoiding misalignments (rotation and translation)? 

Can anyone suggest parameters for FIB preparation of Mg alloys?

Thanks.

Should I use composer stack or a visualizer Kai? is there any guide book for these softwares? I have some slice and view images and I want to do some reconstruction to obtain a 3-D image.

I have Ni nano wire of ~200 nm diameter and 20 micron length. I am not able to get contact using EBL and lift off. FIB exposure damages nano wires, hence trying EBL. Deposition is not continuous, break near the nanowire, due to step. I hope I am able to explain.

The attached file shows an EBSD image for a Ti strip with a thickness around 30 micrometers. The sample was prepared by fine mechanical polishing. The image quality is poor. How can I improve the image quality?

I have tried electropolishing, and I could not keep the sample edge well. In the next step, I will try FIB, but I don't know the parameters. Any suggestions? Thanks in advance.

When I prepare the 3DAP sample of Mg alloy by FIB, the needle surface is not smooth. Is the rough surface due to the re-deposition. How could I improve the sample quality? BTW, I cleaned the sample by low voltage and low current, but it seems useless. Thanks.

I am looking for some extended information regarding the called "Theater Curtain" or "Waterfall" effect in FIB.

I checked in the book "Introduction to Focused Ion Beams: Instrumentation, Theory, Techniques and Practice" (by Lucille A. Gianuzzi and Fred A. Stevie), and in many articles ("Improvements in performance of focused ion beam cross-sectioning: aspects of ion–sample interaction", by Tohru Ishitani, Kaoru Umemura, Tsuyoshi Ohnishi, Toshie Yaguchi and Takeo Kamino was especially useful), but all the authors seem to describe it phenomenologically. I'm trying to get a deeper, more physical (basic) understanding of it, so I interpreted the descriptions and tried to figure out their meaning, but I'm not sure that my interpretation was fully correct.

If there is any expert in FIB milling or anyone who understands theater curtain effect well enough, just tell me what you think about it. Any help will be very appreciated.

For what I understood, the curtain effect is defined by the presence of striations in the milled cross-section, independently of their origin. Thus, if we classified it by the physical causes, there would be more than one kind of curtain effect, with different explanations for each one:

- A very typical case is when the topography of the samples is uneven due to an inefficient polishing or no polishing at all. We can take a rough surface as one with local "valleys" and regions with slope. In the valleys, the incidence angle will be ~90º and the sputtering yield will be maximum (the sputtering yield has a big dependence on the incidence angle), and in the regions with higher slope the sputtering yield will be very small.

If the beam is hitting a valley, the volume under the valley is milled. In this case, the beam tails won't have much importance since they will hit regions with a high slope and low sputtering rate (anything next to a valley has slope).

If the beam is hitting a region with a certain slope, the sputtered atoms will most likely go down that slope and cause a second order sputtering in the valley at the bottom of the slope, and the beam tails will do approximately the same. This way, the milled region will cover a larger area of the sample surface. I also think that it is quite possible that the ions themselves go down the slopes without the need of second order sputtering (something like ions not causing sputtering, but just rebounding with the slope surface) if the angle of incidence is small enough, but I am not really sure of that.

In any case, the combination of regions with valleys and varying slope will cause differences in the size of the milled regions of the sample, thus exhibiting the curtain effect.

- Another common case is when the composition of the milled material is not homogeneous, and consists in various components with different sputtering rates (due to different hardnesses, atomic numbers, etc.). As the sample moves (relatively to the beam) at a constant speed, the regions of its top surface (the one perpendicular to the beam) with lower sputtering rates get milled a smaller area than the regions with higher sputtering rates, which are more affected by the beam tails because milling is faster there.

If there wasn't anything else going on there, any changes in the composition under the top surface would also generate curtain effect (and kind of steps when the harder material is below), but to the extent I know, that doesn't happen. The explanation for that could be that because the tails affect mainly the parts closer to the top surface, instead of the cross-section being parallel to the beam, a slope is created in it (that actually is known to happen), so it covers a higher part of the top surface and more tails impact on it. The ions colliding against that inclined cross-section will generate sputtered atoms that will go down the slope, and cause second order sputtering if they hit an obstacle in their way, so that would sharpen the cross section in the direction (almost) parallel to the beam. That would explain why the changes in composition only have an effect in curtaining if they are in the top surface. Again, the possibility of ions going down the slope without causing sputtering in it would help that explanation a lot, since the sputtering yield against the cross-section is minimal due to the low angle of incidence. If ions from the tails rebounded against the cross section in a quite elastic way, they would go down it with almost the same kinetic energy than the others, and that would cause a higher concentration of ions than when the beam first impacts a region of the top surface. Due to this concentration of the beam, harder regions of the sample would be milled anyway.

- The third condition that can cause the theater curtain effect is the orientation of the sample, if it is crystalline, because ion channeling (ions penetrating greater distances across crystalline planes with lower Miller indices) results in preferential milling along low index directions. In this case I think that what simply happens is that, as planes with low Miller indices have greater distances among them, there is less linear density of atoms along their direction and more freedom for ions to travel across them (and the atoms of the sample are easier to move in those directions, too), so their impact on the material is greater.

I have seen other causes for curtain effect (the beam dose, bad aligning, the speed at which the sample is moved...), but I consider that they are circunstances that affect the three mentioned physical causes, but not causes by themselves.

That is what I was able to find out. Am I missing something? Is there something that I said that you don't agree with? Thank you very much in advance.

I'm sorry if it was messy to read. It was hard to explain it without any drawing.