Light can change its shape when it bounces off a surface. Ellipsometry uses this to measure films only nanometres thick.
Where this happens: in chip making, thin films of glass-like oxide, nitride and polymers are grown on wafers all the time. Ellipsometry checks their thickness after each step, without touching the wafer.
Step 1. Light passes through a polariser. Now its wave wiggles along one straight line.
Step 2. It hits a thin glass-like film (SiO₂, silicon dioxide) on silicon. The angle is steep, e.g. 70° from straight down.
Step 3. The incoming beam, the reflected beam and the line straight up from the surface all lie in one flat plane. It is called the plane of incidence. The light has two parts. One wiggles inside this plane. We call it 'p'. One wiggles across it, sideways. We call it 's'. The film treats them differently.
Step 4. One part comes back a little weaker. It also slips a little behind the other part in time.
Step 5. So the straight line turns into an ellipse. Seen from the side, this is hard to spot, because the s-part points towards you. Turn the view in 3D, and the tip of the wave runs around a flattened spiral. The detector, looking into the beam, sees that spiral as an ellipse.
Step 6. A second polariser, the analyser, reads the ellipse. Two numbers come out. Ψ (Psi) tells how much weaker one part is. Δ (Delta) tells how far it slipped.
Step 7. This is repeated for every colour of light. A film of e.g. 100 nm and a film of e.g. 300 nm give very different patterns.
Step 8. A computer model tries different thicknesses and refractive indices until its curves match. That gives the answer, e.g. 100 nm thick with n ≈ 1.46.
What is 'n'? It is the refractive index. It tells how much a material slows light down. Light in the film travels n-times slower than in air. For silicon dioxide, n is e.g. about 1.46. So light moves about 1.46 times slower inside it.
Why it matters: it does not touch or damage the film. It can sense changes far below one nanometre. This is why it is used frequently to check thin layers on chips and coatings.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. Not to scale. All numbers are examples. The curves are calculated from a textbook thin-film model with typical values for SiO₂ on silicon. They are not measured data. Real results also depend on the model chosen.)
Why does a silicon wafer with a thin glass layer look blue, gold or pink? The colour tells something interesting about characterization. It comes from the thickness.
Step 1. White light shines straight down on the wafer. A clear SiO₂ film sits on the silicon.
Step 2. Some light reflects from the top of the film. Some goes through and reflects from the silicon below.
Step 3. The two reflected waves meet. For some colours, the crests line up. Those colours come back bright. For other colours, the waves cancel. Those come back dim.
Step 4. The mix of colours that comes back is the colour we see. A 100 nm film looks violet-blue. A 500 nm film looks blue-green.
Step 5. A spectrometer reads how much light comes back at each wavelength. The curve has ripples.
Step 6. A thicker film gives more ripples, closer together.
Step 7. The spacing between two ripples gives the thickness. Here it gives about 1000 nm.
It is fast, it does not touch the film, and it works on films from a few tens of nanometres to many micrometres.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. The light paths are drawn side by side; in actual practice, they go straight down and straight up. The curves are calculated from textbook optical values for SiO₂ on silicon. The colours are approximate. It is not measured data.)
What if we could take a material apart one atom at a time, and write down where each atom was?
That is what atom probe tomography does.
Step 1. The sample is shaped into a very sharp needle. The rounded end of the tip has a radius of only about 50 to 100 nm. It is kept very cold and held at a high voltage.
Step 2. The electric field at the tip is huge. A short extra pulse is enough to pull one surface atom off. It leaves as an ion.
Step 3. The ion flies to a detector. The spot where it lands tells us its x and y position.
Step 4. The time of flight tells us its mass-to-charge ratio. For the same charge, light ions arrive first and heavy ions arrive later. So each ion is named: aluminium, magnesium, silicon or copper.
Step 5. Atoms leave the tip layer by layer. So the order of arrival tells us the depth.
Step 6. Put all the ions back together, and we get a 3D map of the needle, atom by atom.
In this simple aluminium alloy, the map shows tiny clusters of magnesium and silicon inside the aluminium. Clusters this small are hard to see any other way.
The mass spectrum below tells us which atoms we caught. One element can give more than one peak. Some ions carry one charge and some carry two. Most elements also have more than one isotope.
Where is it used?
It works best on materials that conduct electricity. Think metals, alloys and semiconductors. Insulators are harder, but they can be done too.
It is the tool to pick when we need to know where a few atoms ended up after a process step. Some examples: - After ion implantation and annealing: where did the dopant atoms, like boron or arsenic, move inside a transistor? - After thin film deposition: did two layers mix at the interface? - After a silicide step (the metal-silicon contact layer): how far did the metal go into the silicon? - After heat treatment of an alloy: did tiny clusters form, like the magnesium-silicon clusters here? - In steels and high-temperature alloys: which atoms collect at the grain boundaries? - In LEDs and lasers: are the indium atoms in a quantum well spread evenly?
To make the needle, a tiny piece is cut from the exact spot of interest. This is usually done with a focused ion beam (FIB). Then it is sharpened into a needle.
As the atoms leave, the needle gets shorter. In the animation, the tip moves back while the 3D map fills up.
Why it matters: many alloy and chip properties are set by a few atoms in the wrong (or right) place. Atom probe lets us see them in 3D.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. Not to scale. Peak positions use textbook isotope masses and natural abundances. Peak heights, widths, composition and the 3D map are typical, made-up values, not measured data. A real detector catches only part of the atoms, not every one. A real tip also gets a little blunter as it gets shorter.)
Why can't a chip factory print lines as small as it likes? The answer is a little maths and one lens.
First, where this happens. Most chips are patterned by a process called photolithography. The silicon wafer is coated with a light-sensitive layer called photoresist. Light then shines through a photomask, which carries the circuit pattern, a bit like a stencil. Between the mask and the wafer sits a large projection lens. It shrinks the pattern, often four times, and focuses it onto the resist. Wherever enough light lands, the resist changes. After developing, the pattern is left on the wafer. So this one lens decides how small a line we can print.
Step 1. Take the simplest pattern on a mask: equal lines and spaces. Light passes through the spaces and the lines block it. So just after the mask, the light goes bright, dark, bright, dark. In maths, this shape is called a square wave.
Step 2. Here is an interesting result from maths. A square wave can be built by adding sine waves together: square wave = (4/π) [ sin x + sin 3x/3 + sin 5x/5 + … ] The first wave sets the basic rhythm. Each next wave is faster and smaller. The more waves we add, the sharper the corners become.
Step 3. Even with many waves, the sum overshoots a little at each edge, by about 9%. This is called the Gibbs effect. It never fully goes away.
Step 4. Now back to the lens. When light passes through a fine pattern, it spreads out. Each of those sine waves leaves the mask at its own angle. The faster the wave, the steeper the angle.
Step 5. A lens can only collect light inside a certain cone. The width of that cone is described by a number called the numerical aperture, usually written as NA. A larger numerical aperture means a wider cone, so more of the steep waves are caught.
Step 6. The waves that miss the lens are simply lost. Only the slower ones reach the resist. So the printed line has soft, rounded edges instead of sharp corners.
Step 7. Now put the lines and spaces closer together. All the waves move to steeper angles. Soon only the first wave gets through, along with the plain average brightness. The image becomes one smooth wave. It still prints, because the resist only reacts where the light goes above a set level.
Step 8. Bring the lines even closer. Now even the first wave misses the lens. Only a flat, even glow is left. No pattern reaches the resist, so nothing prints.
That is the resolution limit of lithography. With light coming straight down, the smallest repeat distance of the pattern is about the wavelength of the light divided by the numerical aperture. If the light is tilted on purpose, it can go down to about half of that. Engineers write this rule with a factor called k1. In this simple picture, k1 cannot go below 0.25.
Why it matters: this is why the chip industry keeps moving to shorter wavelengths of light, to lenses with a larger numerical aperture, and to clever ways of shaping the light. Each step lets a few more of those waves through the lens. That is how the lines on a chip keep getting smaller.
(Simplified illustration. The lens is treated as perfect. The light comes straight down. The resist is treated as a simple on and off switch at one brightness level. All values are textbook values, written in terms of the wavelength and the numerical aperture; not from any real tool. The bottom plot shows brightness, which is the square of the waves that get through. Real lithography uses tilted light and introduces more intertwined functioning.)
A beam of X-rays meets a crystal, and almost everywhere, nothing much happens. Then, at one precise angle, a bright reflection appears.
That moment is described by one short line: nλ = 2d sin θ.
This is the interrelated concept illustration of XRD via Bragg's Law.
Inside a crystal, atoms are arranged in flat, evenly spaced layers. When X-rays arrive at an angle θ, part of the beam is reflected by the top layer, and part travels on to the next layer before being reflected. The second beam covers an extra distance of 2d sin θ, where d is the spacing between the layers.
If that extra distance equals a whole number of wavelengths, the reflected waves leave in step, and they reinforce one another. At every other angle they fall out of step and largely cancel.
In the animation, the angle is swept slowly. The red segment marks the extra path. When it reaches exactly one wavelength, the waves line up, the detector lights, and a peak rises on the intensity plot.
This is how layer spacings far too small to see are measured: the angle of a peak is recorded, the wavelength is known, and d follows from a single line of trigonometry.
(Simplified illustration: two reflecting layers are traced and three are drawn; real crystals involve many layers, which make the peak sharper. Wave size, layer spacing and angles are chosen for visibility and are not to scale.)
A magnet can tell us what carries the current in a semiconductor. It can even count those carriers.
Step 1. Take a thin, flat bar of the material. Put metal contacts on its two ends. A small current, here 1 mA, flows from one end to the other.
Step 2. Put two more contacts in the middle, one on the top edge and one on the bottom edge. A voltmeter sits between them.
Step 3. Switch on a magnetic field. It points straight through the bar, out of the screen.
Step 4. The field pushes the moving charges sideways. They pile up on one edge.
Step 5. That edge charge makes a sideways voltage. It grows until it pushes back just as hard as the magnet. This is the Hall voltage.
Step 6. Sweep the field from negative to positive. The voltage follows in a straight line.
Step 7. Now a p-type bar. Here holes carry the current. They move the other way, but the magnet pushes them to the same edge.
Step 8. Holes are positive, so now the voltage is positive. The line slopes the other way.
The sign tells us electrons or holes. The size tells us how many. Fewer carriers give a bigger voltage.
Why it matters: doping sets how every transistor, sensor and solar cell behaves. A Hall measurement checks it directly.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. Not to scale. The values are typical, calculated from the textbook Hall equation for a 0.5 mm thick bar and 1 mA of current. Real samples shift a little. The voltage builds slowly here so you can see it. In reality it appears almost at once.)
In the earlier Raman post, silicon showed a peak at 520 cm⁻¹. That peak has a mirror image on the other side of the laser line, at −520 cm⁻¹.
When light scatters from a crystal, almost all of it leaves with exactly the colour it arrived with. A tiny fraction, however, exchanges energy with the vibrations of the lattice.
If the light leaves some energy behind and sets the lattice vibrating, it comes out slightly redder. This is the Stokes line, the one usually reported.
If the light meets a lattice that is already vibrating, it can pick that energy up and come out slightly bluer. This is the anti-Stokes line.
The anti-Stokes line depends on vibrations that are already there, and how many there are depends on temperature. At room temperature, the anti-Stokes peak of silicon is roughly ten times weaker than the Stokes peak. As the crystal warms up, more vibrations are present and the anti-Stokes side grows.
That gives Raman a useful second job. Comparing the two sides gives an estimate of the local temperature, without touching the sample.
(Simplified illustration. Peak heights follow the thermal population of the vibration only; real intensity ratios also depend slightly on the measurement conditions. The laser line is clipped and peak widths are illustrative.)
In the earlier Raman post, silicon showed a peak at 520 cm⁻¹. That peak has a mirror image on the other side of the laser line, at −520 cm⁻¹.
When light scatters from a crystal, almost all of it leaves with exactly the colour it arrived with. A tiny fraction, however, exchanges energy with the vibrations of the lattice.
If the light leaves some energy behind and sets the lattice vibrating, it comes out slightly redder. This is the Stokes line, the one usually reported.
If the light meets a lattice that is already vibrating, it can pick that energy up and come out slightly bluer. This is the anti-Stokes line.
The anti-Stokes line depends on vibrations that are already there, and how many there are depends on temperature. At room temperature, the anti-Stokes peak of silicon is roughly ten times weaker than the Stokes peak. As the crystal warms up, more vibrations are present and the anti-Stokes side grows.
That gives Raman a useful second job. Comparing the two sides gives an estimate of the local temperature, without touching the sample.
(Simplified illustration. Peak heights follow the thermal population of the vibration only; real intensity ratios also depend slightly on the measurement conditions. The laser line is clipped and peak widths are illustrative.)
In XRD, each peak had its own place. But why are the peaks not the same height? And why is one expected peak missing?
Step 1. A quick recap. Peak position comes from the spacing between atomic planes.
Step 2. Peak height comes mainly from how the waves add up. Every atom in the unit cell scatters a small wave. Those waves meet and add.
Step 3. Silicon has two atoms in its basic building block. For the (111) planes, the second atom is a quarter step off. The waves partly add.
Step 4. For the (200) planes, the second atom sits exactly half way between planes. Its wave is upside down compared with the first. They cancel to zero. So the (200) peak, near 33°, is missing.
Step 5. For the (220) planes, both atoms sit on planes. The waves are fully in step. They add the most.
Step 6. Some plane sets come in many copies that point in different directions. (111) has 8, (220) has 12, (311) has 24. More copies give more signal.
Step 7. Scattering gets weaker at higher angles. Each atom scatters less. The angle itself also lowers the signal. So peaks fade as the angle grows.
Step 8. Put together, a silicon powder gives heights of about 100 : 55 : 30 for (111), (220) and (311) respectively.
(Note for extra reference: In a thin film, the grains often line up in one direction. Then the heights can change a lot.)
Position tells you the spacing. Height tells you how the atoms are arranged inside.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. The atoms and planes are a sketch, not to scale. Peak positions are the same silicon pattern as before. Heights are typical textbook values for a random silicon powder.)
The SEM image shows the surface. But the EDX signal comes from much deeper.
Step 1. The electron beam enters the sample. The electrons bounce off atoms again and again. Their paths spread out into a pear shape.
Step 2. The image uses secondary electrons. These are very slow. Only the ones made in the top few nanometres can escape. So the image shows the surface.
Step 3. X-rays are different. They are made all through the pear. In silicon at 15 keV, the pear is nearly 3 µm deep.
Step 4. Now put a tiny gold particle, 100 nm across, on a silicon wafer. The beam goes right through it. So the spectrum shows gold, and also a big silicon peak from the wafer below.
Step 5. Lower the beam energy to 5 keV. Now most electrons stop inside the gold particle. In bare silicon, the pear would now be only about 0.5 µm deep. So the silicon peak almost disappears.
Step 6. There is a limit. The beam must still have enough energy to make the X-rays you want. At 5 keV, both the gold and the silicon lines are still made.
So, for small features, a lower beam energy often gives a cleaner answer.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. The electron paths are drawn for the idea only. The pear depth uses a textbook range equation for silicon. The particle is drawn to scale, so it looks tiny. Peak heights are illustrative. Real samples vary.)
Bharat S.
Light can change its shape when it bounces off a surface. Ellipsometry uses this to measure films only nanometres thick.
Where this happens: in chip making, thin films of glass-like oxide, nitride and polymers are grown on wafers all the time. Ellipsometry checks their thickness after each step, without touching the wafer.
Step 1. Light passes through a polariser. Now its wave wiggles along one straight line.
Step 2. It hits a thin glass-like film (SiO₂, silicon dioxide) on silicon. The angle is steep, e.g. 70° from straight down.
Step 3. The incoming beam, the reflected beam and the line straight up from the surface all lie in one flat plane. It is called the plane of incidence. The light has two parts. One wiggles inside this plane. We call it 'p'. One wiggles across it, sideways. We call it 's'. The film treats them differently.
Step 4. One part comes back a little weaker. It also slips a little behind the other part in time.
Step 5. So the straight line turns into an ellipse. Seen from the side, this is hard to spot, because the s-part points towards you. Turn the view in 3D, and the tip of the wave runs around a flattened spiral. The detector, looking into the beam, sees that spiral as an ellipse.
Step 6. A second polariser, the analyser, reads the ellipse. Two numbers come out. Ψ (Psi) tells how much weaker one part is. Δ (Delta) tells how far it slipped.
Step 7. This is repeated for every colour of light. A film of e.g. 100 nm and a film of e.g. 300 nm give very different patterns.
Step 8. A computer model tries different thicknesses and refractive indices until its curves match. That gives the answer, e.g. 100 nm thick with n ≈ 1.46.
What is 'n'? It is the refractive index. It tells how much a material slows light down. Light in the film travels n-times slower than in air. For silicon dioxide, n is e.g. about 1.46. So light moves about 1.46 times slower inside it.
Why it matters: it does not touch or damage the film. It can sense changes far below one nanometre. This is why it is used frequently to check thin layers on chips and coatings.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. Not to scale. All numbers are examples. The curves are calculated from a textbook thin-film model with typical values for SiO₂ on silicon. They are not measured data. Real results also depend on the model chosen.)
#Ellipsometry #ThinFilms #Optics #Polarization #MaterialsScience #Semiconductors #Characterization #STEM
2 hours ago |[YT] | 0
View 0 replies
Bharat S.
Why does a silicon wafer with a thin glass layer look blue, gold or pink? The colour tells something interesting about characterization. It comes from the thickness.
Step 1. White light shines straight down on the wafer. A clear SiO₂ film sits on the silicon.
Step 2. Some light reflects from the top of the film. Some goes through and reflects from the silicon below.
Step 3. The two reflected waves meet. For some colours, the crests line up. Those colours come back bright. For other colours, the waves cancel. Those come back dim.
Step 4. The mix of colours that comes back is the colour we see. A 100 nm film looks violet-blue. A 500 nm film looks blue-green.
Step 5. A spectrometer reads how much light comes back at each wavelength. The curve has ripples.
Step 6. A thicker film gives more ripples, closer together.
Step 7. The spacing between two ripples gives the thickness. Here it gives about 1000 nm.
It is fast, it does not touch the film, and it works on films from a few tens of nanometres to many micrometres.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. The light paths are drawn side by side; in actual practice, they go straight down and straight up. The curves are calculated from textbook optical values for SiO₂ on silicon. The colours are approximate. It is not measured data.)
#ThinFilms #Reflectometry #Optics #Semiconductors #MaterialsScience #Characterization #Nanotechnology #STEM
23 hours ago |[YT] | 1
View 0 replies
Bharat S.
What if we could take a material apart one atom at a time, and write down where each atom was?
That is what atom probe tomography does.
Step 1. The sample is shaped into a very sharp needle. The rounded end of the tip has a radius of only about 50 to 100 nm. It is kept very cold and held at a high voltage.
Step 2. The electric field at the tip is huge. A short extra pulse is enough to pull one surface atom off. It leaves as an ion.
Step 3. The ion flies to a detector. The spot where it lands tells us its x and y position.
Step 4. The time of flight tells us its mass-to-charge ratio. For the same charge, light ions arrive first and heavy ions arrive later. So each ion is named: aluminium, magnesium, silicon or copper.
Step 5. Atoms leave the tip layer by layer. So the order of arrival tells us the depth.
Step 6. Put all the ions back together, and we get a 3D map of the needle, atom by atom.
In this simple aluminium alloy, the map shows tiny clusters of magnesium and silicon inside the aluminium. Clusters this small are hard to see any other way.
The mass spectrum below tells us which atoms we caught. One element can give more than one peak. Some ions carry one charge and some carry two. Most elements also have more than one isotope.
Where is it used?
It works best on materials that conduct electricity. Think metals, alloys and semiconductors. Insulators are harder, but they can be done too.
It is the tool to pick when we need to know where a few atoms ended up after a process step. Some examples:
- After ion implantation and annealing: where did the dopant atoms, like boron or arsenic, move inside a transistor?
- After thin film deposition: did two layers mix at the interface?
- After a silicide step (the metal-silicon contact layer): how far did the metal go into the silicon?
- After heat treatment of an alloy: did tiny clusters form, like the magnesium-silicon clusters here?
- In steels and high-temperature alloys: which atoms collect at the grain boundaries?
- In LEDs and lasers: are the indium atoms in a quantum well spread evenly?
To make the needle, a tiny piece is cut from the exact spot of interest. This is usually done with a focused ion beam (FIB). Then it is sharpened into a needle.
As the atoms leave, the needle gets shorter. In the animation, the tip moves back while the 3D map fills up.
Why it matters: many alloy and chip properties are set by a few atoms in the wrong (or right) place. Atom probe lets us see them in 3D.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. Not to scale. Peak positions use textbook isotope masses and natural abundances. Peak heights, widths, composition and the 3D map are typical, made-up values, not measured data. A real detector catches only part of the atoms, not every one. A real tip also gets a little blunter as it gets shorter.)
#AtomProbe #APT #Tomography #AtomProbeTomography #MaterialsScience #Characterization #Semiconductors #Nanotechnology #Metallurgy #MassSpectrometry #STEM
23 hours ago |[YT] | 0
View 0 replies
Bharat S.
Why can't a chip factory print lines as small as it likes? The answer is a little maths and one lens.
First, where this happens. Most chips are patterned by a process called photolithography. The silicon wafer is coated with a light-sensitive layer called photoresist. Light then shines through a photomask, which carries the circuit pattern, a bit like a stencil. Between the mask and the wafer sits a large projection lens. It shrinks the pattern, often four times, and focuses it onto the resist. Wherever enough light lands, the resist changes. After developing, the pattern is left on the wafer. So this one lens decides how small a line we can print.
Step 1. Take the simplest pattern on a mask: equal lines and spaces. Light passes through the spaces and the lines block it. So just after the mask, the light goes bright, dark, bright, dark. In maths, this shape is called a square wave.
Step 2. Here is an interesting result from maths. A square wave can be built by adding sine waves together:
square wave = (4/π) [ sin x + sin 3x/3 + sin 5x/5 + … ]
The first wave sets the basic rhythm. Each next wave is faster and smaller. The more waves we add, the sharper the corners become.
Step 3. Even with many waves, the sum overshoots a little at each edge, by about 9%. This is called the Gibbs effect. It never fully goes away.
Step 4. Now back to the lens. When light passes through a fine pattern, it spreads out. Each of those sine waves leaves the mask at its own angle. The faster the wave, the steeper the angle.
Step 5. A lens can only collect light inside a certain cone. The width of that cone is described by a number called the numerical aperture, usually written as NA. A larger numerical aperture means a wider cone, so more of the steep waves are caught.
Step 6. The waves that miss the lens are simply lost. Only the slower ones reach the resist. So the printed line has soft, rounded edges instead of sharp corners.
Step 7. Now put the lines and spaces closer together. All the waves move to steeper angles. Soon only the first wave gets through, along with the plain average brightness. The image becomes one smooth wave. It still prints, because the resist only reacts where the light goes above a set level.
Step 8. Bring the lines even closer. Now even the first wave misses the lens. Only a flat, even glow is left. No pattern reaches the resist, so nothing prints.
That is the resolution limit of lithography. With light coming straight down, the smallest repeat distance of the pattern is about the wavelength of the light divided by the numerical aperture. If the light is tilted on purpose, it can go down to about half of that. Engineers write this rule with a factor called k1. In this simple picture, k1 cannot go below 0.25.
Why it matters: this is why the chip industry keeps moving to shorter wavelengths of light, to lenses with a larger numerical aperture, and to clever ways of shaping the light. Each step lets a few more of those waves through the lens. That is how the lines on a chip keep getting smaller.
(Simplified illustration. The lens is treated as perfect. The light comes straight down. The resist is treated as a simple on and off switch at one brightness level. All values are textbook values, written in terms of the wavelength and the numerical aperture; not from any real tool. The bottom plot shows brightness, which is the square of the waves that get through. Real lithography uses tilted light and introduces more intertwined functioning.)
#Mathematics #FourierSeries #Lithography #Nanofabrication #Semiconductors #Electronics #Optics #Nanotechnology #STEM
1 day ago |[YT] | 0
View 0 replies
Bharat S.
A beam of X-rays meets a crystal, and almost everywhere, nothing much happens. Then, at one precise angle, a bright reflection appears.
That moment is described by one short line: nλ = 2d sin θ.
This is the interrelated concept illustration of XRD via Bragg's Law.
Inside a crystal, atoms are arranged in flat, evenly spaced layers. When X-rays arrive at an angle θ, part of the beam is reflected by the top layer, and part travels on to the next layer before being reflected. The second beam covers an extra distance of 2d sin θ, where d is the spacing between the layers.
If that extra distance equals a whole number of wavelengths, the reflected waves leave in step, and they reinforce one another. At every other angle they fall out of step and largely cancel.
In the animation, the angle is swept slowly. The red segment marks the extra path. When it reaches exactly one wavelength, the waves line up, the detector lights, and a peak rises on the intensity plot.
This is how layer spacings far too small to see are measured: the angle of a peak is recorded, the wavelength is known, and d follows from a single line of trigonometry.
(Simplified illustration: two reflecting layers are traced and three are drawn; real crystals involve many layers, which make the peak sharper. Wave size, layer spacing and angles are chosen for visibility and are not to scale.)
#BraggsLaw #XRayDiffraction #Crystallography #MaterialsCharacterization #MaterialsScience #Physics #Mathematics #Trigonometry #Nanotechnology #STEM #EngineeringEducation
1 day ago |[YT] | 0
View 0 replies
Bharat S.
A magnet can tell us what carries the current in a semiconductor. It can even count those carriers.
Step 1. Take a thin, flat bar of the material. Put metal contacts on its two ends. A small current, here 1 mA, flows from one end to the other.
Step 2. Put two more contacts in the middle, one on the top edge and one on the bottom edge. A voltmeter sits between them.
Step 3. Switch on a magnetic field. It points straight through the bar, out of the screen.
Step 4. The field pushes the moving charges sideways. They pile up on one edge.
Step 5. That edge charge makes a sideways voltage. It grows until it pushes back just as hard as the magnet. This is the Hall voltage.
Step 6. Sweep the field from negative to positive. The voltage follows in a straight line.
Step 7. Now a p-type bar. Here holes carry the current. They move the other way, but the magnet pushes them to the same edge.
Step 8. Holes are positive, so now the voltage is positive. The line slopes the other way.
The sign tells us electrons or holes. The size tells us how many. Fewer carriers give a bigger voltage.
Why it matters: doping sets how every transistor, sensor and solar cell behaves. A Hall measurement checks it directly.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. Not to scale. The values are typical, calculated from the textbook Hall equation for a 0.5 mm thick bar and 1 mA of current. Real samples shift a little. The voltage builds slowly here so you can see it. In reality it appears almost at once.)
#HallEffect #Semiconductors #Doping #MaterialsScience #Electronics #Characterization #Nanotechnology #STEM
2 days ago |[YT] | 0
View 0 replies
Bharat S.
In the earlier Raman post, silicon showed a peak at 520 cm⁻¹. That peak has a mirror image on the other side of the laser line, at −520 cm⁻¹.
When light scatters from a crystal, almost all of it leaves with exactly the colour it arrived with. A tiny fraction, however, exchanges energy with the vibrations of the lattice.
If the light leaves some energy behind and sets the lattice vibrating, it comes out slightly redder. This is the Stokes line, the one usually reported.
If the light meets a lattice that is already vibrating, it can pick that energy up and come out slightly bluer. This is the anti-Stokes line.
The anti-Stokes line depends on vibrations that are already there, and how many there are depends on temperature. At room temperature, the anti-Stokes peak of silicon is roughly ten times weaker than the Stokes peak. As the crystal warms up, more vibrations are present and the anti-Stokes side grows.
That gives Raman a useful second job. Comparing the two sides gives an estimate of the local temperature, without touching the sample.
(Simplified illustration. Peak heights follow the thermal population of the vibration only; real intensity ratios also depend slightly on the measurement conditions. The laser line is clipped and peak widths are illustrative.)
#Raman #RamanSpectroscopy #Silicon #MaterialsScience #Characterization #Spectroscopy #Nanotechnology #STEM
2 days ago |[YT] | 0
View 0 replies
Bharat S.
In the earlier Raman post, silicon showed a peak at 520 cm⁻¹. That peak has a mirror image on the other side of the laser line, at −520 cm⁻¹.
When light scatters from a crystal, almost all of it leaves with exactly the colour it arrived with. A tiny fraction, however, exchanges energy with the vibrations of the lattice.
If the light leaves some energy behind and sets the lattice vibrating, it comes out slightly redder. This is the Stokes line, the one usually reported.
If the light meets a lattice that is already vibrating, it can pick that energy up and come out slightly bluer. This is the anti-Stokes line.
The anti-Stokes line depends on vibrations that are already there, and how many there are depends on temperature. At room temperature, the anti-Stokes peak of silicon is roughly ten times weaker than the Stokes peak. As the crystal warms up, more vibrations are present and the anti-Stokes side grows.
That gives Raman a useful second job. Comparing the two sides gives an estimate of the local temperature, without touching the sample.
(Simplified illustration. Peak heights follow the thermal population of the vibration only; real intensity ratios also depend slightly on the measurement conditions. The laser line is clipped and peak widths are illustrative.)
#Raman #RamanSpectroscopy #Silicon #MaterialsScience #Characterization #Spectroscopy #Nanotechnology #STEM
2 days ago |[YT] | 0
View 0 replies
Bharat S.
In XRD, each peak had its own place. But why are the peaks not the same height? And why is one expected peak missing?
Step 1. A quick recap. Peak position comes from the spacing between atomic planes.
Step 2. Peak height comes mainly from how the waves add up. Every atom in the unit cell scatters a small wave. Those waves meet and add.
Step 3. Silicon has two atoms in its basic building block. For the (111) planes, the second atom is a quarter step off. The waves partly add.
Step 4. For the (200) planes, the second atom sits exactly half way between planes. Its wave is upside down compared with the first. They cancel to zero. So the (200) peak, near 33°, is missing.
Step 5. For the (220) planes, both atoms sit on planes. The waves are fully in step. They add the most.
Step 6. Some plane sets come in many copies that point in different directions. (111) has 8, (220) has 12, (311) has 24. More copies give more signal.
Step 7. Scattering gets weaker at higher angles. Each atom scatters less. The angle itself also lowers the signal. So peaks fade as the angle grows.
Step 8. Put together, a silicon powder gives heights of about 100 : 55 : 30 for (111), (220) and (311) respectively.
(Note for extra reference: In a thin film, the grains often line up in one direction. Then the heights can change a lot.)
Position tells you the spacing. Height tells you how the atoms are arranged inside.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. The atoms and planes are a sketch, not to scale. Peak positions are the same silicon pattern as before. Heights are typical textbook values for a random silicon powder.)
#XRD #Crystallography #MaterialsScience #Nanotechnology #StructureFactor #Characterization #Silicon #STEM #Maths #Mathematics
2 days ago |[YT] | 0
View 0 replies
Bharat S.
The SEM image shows the surface. But the EDX signal comes from much deeper.
Step 1. The electron beam enters the sample. The electrons bounce off atoms again and again. Their paths spread out into a pear shape.
Step 2. The image uses secondary electrons. These are very slow. Only the ones made in the top few nanometres can escape. So the image shows the surface.
Step 3. X-rays are different. They are made all through the pear. In silicon at 15 keV, the pear is nearly 3 µm deep.
Step 4. Now put a tiny gold particle, 100 nm across, on a silicon wafer. The beam goes right through it. So the spectrum shows gold, and also a big silicon peak from the wafer below.
Step 5. Lower the beam energy to 5 keV. Now most electrons stop inside the gold particle. In bare silicon, the pear would now be only about 0.5 µm deep. So the silicon peak almost disappears.
Step 6. There is a limit. The beam must still have enough energy to make the X-rays you want. At 5 keV, both the gold and the silicon lines are still made.
So, for small features, a lower beam energy often gives a cleaner answer.
Characterization is how we find the problem — and map it to the solution.
(Simplified illustration. The electron paths are drawn for the idea only. The pear depth uses a textbook range equation for silicon. The particle is drawn to scale, so it looks tiny. Peak heights are illustrative. Real samples vary.)
#EDX #EDS #ElectronMicroscopy #SEM #MaterialsScience #Characterization #Nanotechnology #STEM
2 days ago |[YT] | 0
View 0 replies
Load more