A synchrotron is a device in which electrical and magnetic fields are utilized to accelerate a charged particle (electron or proton) around a circular loop. Because the particle is accelerating, it emits em waves (perpendicular to it's acceleration, thus, tangent to the circlular loop). If a tube in connected to the synchrotron tangent to the loop, the tube will see extremely short bursts of light.
A Bragg reflector is a series of material layers of different thickness and refractive index which casues constructive intereference of the reflected light. Each layer partialy reflects light, causing a high amount of light to be reflected. The end result is a highly reflective device.
MBE = Molecular Beam Epitaxy
MCVD = Metal Chemical Vapor Deposition
A raster scan is scan that sequentially looks at every element in a grid. A vector scan only looks at the areas that need attention (i.e. that have data).
Friday, July 31, 2009
Thursday, July 30, 2009
Light in a Medium
Got a new batch of books from the library, mainly on lasers, photonics, fiber optics, and semiconductor fabrication.
Some topics I have been learning about are crystal growth, Snell's law, and Fresnel's law. I also did some reading on electromagnetic waves to solidify my understanding of them.
One thing I found very interesting, is how light travels through mediums. Essentially, the photon is absorbed by the medium, and the electron is bumped up to a higher energy state, and then drops back down again. This energy drop in the electron emits a photon, and the emitted direction is perpendicular to the acceleration of the electron. I am still not certain why photons are emitted in the forward direction, as opposed to the opposite direction.
Some topics I have been learning about are crystal growth, Snell's law, and Fresnel's law. I also did some reading on electromagnetic waves to solidify my understanding of them.
One thing I found very interesting, is how light travels through mediums. Essentially, the photon is absorbed by the medium, and the electron is bumped up to a higher energy state, and then drops back down again. This energy drop in the electron emits a photon, and the emitted direction is perpendicular to the acceleration of the electron. I am still not certain why photons are emitted in the forward direction, as opposed to the opposite direction.
Sunday, July 26, 2009
Energy of Light, DeBroglie Wavelength
For light:
E = hf
Where h is Planck's constant and f is the frequency of the radiation. Can also be expressed as:
E = hc/lambda
Where lambda is the wavelength and c is the speed of light.
DeBroglie combined the above equation with the mass-energy equation, e = mc^2. The result had a funny term in it, the "wavelength" of the electron. This became known as the DeBroglie wavelength:
lambda = h/mv
Where m is mass and v is speed. The wavenumber is the inverse of the wavelength.
E = hf
Where h is Planck's constant and f is the frequency of the radiation. Can also be expressed as:
E = hc/lambda
Where lambda is the wavelength and c is the speed of light.
DeBroglie combined the above equation with the mass-energy equation, e = mc^2. The result had a funny term in it, the "wavelength" of the electron. This became known as the DeBroglie wavelength:
lambda = h/mv
Where m is mass and v is speed. The wavenumber is the inverse of the wavelength.
Thursday, July 16, 2009
Laser Modes and Active Layer Carriers
Laser Modes
Because the light in a laser bounces back and forth, and since light is a wave, the light waves constructively and destructively interface, resulting in standing waves of light output. The peaks of the waves correspond to the length of the active layer. There's a lot more than that, but that's the general idea.
Carriers in the Active Layer
After the lasing threshold, the number of carriers in the active layer becomes constant (or nearly constant). This is because of how fast stimulated emission occurs; as soon as new carriers move into the active layer, they are stimulated.
As discussed before, stimulated emission only occurs as wavelengths that correspond to the wavelength of the incident light (caused by spontaneous emission). The corresponding energy levels of this wavelength will be somewhere above the conduction band to somewhere below the valence band. Only carriers in these states can recombine via stimulated emission. After carriers recombine in this manner, vacancies are left behind. Other carries will naturally fill these vacancies; this is called intraband relaxation. The speed in which these vacancies are filled by other carries is called the relaxation time, and is on the order of 1 to .1 ps.
Because the light in a laser bounces back and forth, and since light is a wave, the light waves constructively and destructively interface, resulting in standing waves of light output. The peaks of the waves correspond to the length of the active layer. There's a lot more than that, but that's the general idea.
Carriers in the Active Layer
After the lasing threshold, the number of carriers in the active layer becomes constant (or nearly constant). This is because of how fast stimulated emission occurs; as soon as new carriers move into the active layer, they are stimulated.
As discussed before, stimulated emission only occurs as wavelengths that correspond to the wavelength of the incident light (caused by spontaneous emission). The corresponding energy levels of this wavelength will be somewhere above the conduction band to somewhere below the valence band. Only carriers in these states can recombine via stimulated emission. After carriers recombine in this manner, vacancies are left behind. Other carries will naturally fill these vacancies; this is called intraband relaxation. The speed in which these vacancies are filled by other carries is called the relaxation time, and is on the order of 1 to .1 ps.
Boltzmann Statistics and Negative Temperature
Maxwell-Boltzmann Statistics
Maxwell-Boltzmann statistics is a thermodynamics model that describes the distribution of non-quantized particles over possible energy states given the bulk temperature of the particles. It's pretty complicated stuff.
A Boltzmann distribution is always of the form exp(-E/kT), where E is an energy level, k is Boltzmann's constant, and T is absolute temperature. Boltzmann's constant, k, has units of J/K, hence, it relates energy (at the particle level) to temperature (in the bulk level).
The form in which I have seen it most is n2/n1 = exp(-(E2-E1)/kT), where n2 is the number of particles in energy state 2, n1 is the number of particles in energy state 1, and E2/E1 are the corresponding energy levels.
Population Inversion
Consider the following Boltzmann distribution:
n2/n1 = exp(-(E2-E1)/kT)
where E2 is greater than E1. In this situation, E2-E1 will always be positive, and so the ratio n2/n1 will always be less than unity. This means that the number of particles occupying a higher energy state will always be less than the number of particles occupying a lower energy state. That makes sense.
However, what if we could create a situation in which n2/n1 > 1? That would mean that the higher energy states were more populated than the lower energy states. Such a situation is called population inversion.
Negative Temperature
Looking at the equation above, the only way for population inversion to occur is if the temperature goes negative. This concept seem bogus at first, but it actually makes a lot of sense.
Negative temperature is "hotter" than infinite positive temperature. On the "hotness" scale, it goes like this:
+0K < +100K < +∞K = -∞K < -100K < -0K To understand the difference between positive and negative temperature, I will give a few ascii diagrams showing different temperature levels. The numbers on the left indicate energy states (higher number = higher energy state) and the boxes on the right indicate filled states.
+0K:
4
3
2
1
0 ███████
+100K:
4
3 █
2 ███
1 █████
0 ███████
10^10K:
4 █████
3 ███████
2 ███████
1 ███████
0 ███████
+∞K=-∞K:
4 ███████
3 ███████
2 ███████
1 ███████
0 ███████
-10^10K:
4 ███████
3 ███████
2 ███████
1 ███████
0 █████
-100K:
4 ███████
3 █████
2 ███
1 █
0
-0K:
4 ███████
3
2
1
0
Notice that adding a negative temperature to a nearly infinite positive temperature results in a negative temperature that could not be achieved by the addition of more positive temperature. Combining a negative temperature with any positive temperature results in heat flowing from the negative temperature to the positive temperature. That is why negative temperature is "hotter" than any positive temperature.
I may be wrong in parts of my explanation, but this is the basic idea.
Population Inversion and Lasers
Population inversion is a requirement for lasing. When light strikes the active layer, the probability of stimulated emission occurring is directly proportional to the probability of absorption occurring, with the proportionality constant being the ratio of the electrons in the conduction band to the electrons in the valence band. Basically, the ratio of emission to absorption is:
n2/n1 = exp(-(E2-E1)/kT)
And therefore, for lasing to occur (amplification of light; more emission than absorption), population inversion is a requirement.
Maxwell-Boltzmann statistics is a thermodynamics model that describes the distribution of non-quantized particles over possible energy states given the bulk temperature of the particles. It's pretty complicated stuff.
A Boltzmann distribution is always of the form exp(-E/kT), where E is an energy level, k is Boltzmann's constant, and T is absolute temperature. Boltzmann's constant, k, has units of J/K, hence, it relates energy (at the particle level) to temperature (in the bulk level).
The form in which I have seen it most is n2/n1 = exp(-(E2-E1)/kT), where n2 is the number of particles in energy state 2, n1 is the number of particles in energy state 1, and E2/E1 are the corresponding energy levels.
Population Inversion
Consider the following Boltzmann distribution:
n2/n1 = exp(-(E2-E1)/kT)
where E2 is greater than E1. In this situation, E2-E1 will always be positive, and so the ratio n2/n1 will always be less than unity. This means that the number of particles occupying a higher energy state will always be less than the number of particles occupying a lower energy state. That makes sense.
However, what if we could create a situation in which n2/n1 > 1? That would mean that the higher energy states were more populated than the lower energy states. Such a situation is called population inversion.
Negative Temperature
Looking at the equation above, the only way for population inversion to occur is if the temperature goes negative. This concept seem bogus at first, but it actually makes a lot of sense.
Negative temperature is "hotter" than infinite positive temperature. On the "hotness" scale, it goes like this:
+0K < +100K < +∞K = -∞K < -100K < -0K To understand the difference between positive and negative temperature, I will give a few ascii diagrams showing different temperature levels. The numbers on the left indicate energy states (higher number = higher energy state) and the boxes on the right indicate filled states.
+0K:
4
3
2
1
0 ███████
+100K:
4
3 █
2 ███
1 █████
0 ███████
10^10K:
4 █████
3 ███████
2 ███████
1 ███████
0 ███████
+∞K=-∞K:
4 ███████
3 ███████
2 ███████
1 ███████
0 ███████
-10^10K:
4 ███████
3 ███████
2 ███████
1 ███████
0 █████
-100K:
4 ███████
3 █████
2 ███
1 █
0
-0K:
4 ███████
3
2
1
0
Notice that adding a negative temperature to a nearly infinite positive temperature results in a negative temperature that could not be achieved by the addition of more positive temperature. Combining a negative temperature with any positive temperature results in heat flowing from the negative temperature to the positive temperature. That is why negative temperature is "hotter" than any positive temperature.
I may be wrong in parts of my explanation, but this is the basic idea.
Population Inversion and Lasers
Population inversion is a requirement for lasing. When light strikes the active layer, the probability of stimulated emission occurring is directly proportional to the probability of absorption occurring, with the proportionality constant being the ratio of the electrons in the conduction band to the electrons in the valence band. Basically, the ratio of emission to absorption is:
n2/n1 = exp(-(E2-E1)/kT)
And therefore, for lasing to occur (amplification of light; more emission than absorption), population inversion is a requirement.
Misc LED Stuff and Lasers
Misc LED Stuff
The frequency response of an LED (or any diode) is limited at lower frequencies by the junction capacitance, and at higher frequencies by the carrier lifetime. I believe the idea is that the carriers don't have time to recombine after traveling through the pn junction.
The wavelength of light emitted from an LED corresponds to the energy difference between the quasi fermi levels in the active layer. Higher energy = higher frequency = shorter wavelength.
The higher energy (shorter wavelength) light emitted from an edge emitting LED is absorbed back into the active layer, giving the edge emitting LED a smaller FWHM (Full Width At Half Maximum), which represents the range of light emitted.
General Laser Operating Principles
Laser stands for Light Amplification by Stimulated Emission of Radiation.
The basic idea behind the laser is similar to that of the LED: double injection occurs within a thin active layer which causes spontaneous emission. In fact, at lower biases, a laser operates in LED mode. At higher biases, different things happen however.
Stimulated emission is when incident light "stimulates" an electron and causes it to descend to the valence band, emitting a photon in the process. Due to some complex processes that occur when the light stimulates the electron, the emitted light is of the same wavelength and phase as the incident light. Thus, coherent light is produced.
These are the two sources of photon generation in a laser: spontaneous emission and stimulated emission.
There are many sources of absorption in a laser; the same as in an LED or any other device.
The lasing threshold is the level of excitation at which light generated by stimulated emission equals light absorption. Below the lasing threshold dP/dI is low; above the threshold it is high.
The active layer of a laser is capped at each end with mirror facets (in some laser diodes), which cause the light to bounce back and forth and grow in intensity. The layers directly beside the active layer (cladding layers) are set such that their refractive indices bounce light back into the active layer.
The frequency response of an LED (or any diode) is limited at lower frequencies by the junction capacitance, and at higher frequencies by the carrier lifetime. I believe the idea is that the carriers don't have time to recombine after traveling through the pn junction.
The wavelength of light emitted from an LED corresponds to the energy difference between the quasi fermi levels in the active layer. Higher energy = higher frequency = shorter wavelength.
The higher energy (shorter wavelength) light emitted from an edge emitting LED is absorbed back into the active layer, giving the edge emitting LED a smaller FWHM (Full Width At Half Maximum), which represents the range of light emitted.
General Laser Operating Principles
Laser stands for Light Amplification by Stimulated Emission of Radiation.
The basic idea behind the laser is similar to that of the LED: double injection occurs within a thin active layer which causes spontaneous emission. In fact, at lower biases, a laser operates in LED mode. At higher biases, different things happen however.
Stimulated emission is when incident light "stimulates" an electron and causes it to descend to the valence band, emitting a photon in the process. Due to some complex processes that occur when the light stimulates the electron, the emitted light is of the same wavelength and phase as the incident light. Thus, coherent light is produced.
These are the two sources of photon generation in a laser: spontaneous emission and stimulated emission.
There are many sources of absorption in a laser; the same as in an LED or any other device.
The lasing threshold is the level of excitation at which light generated by stimulated emission equals light absorption. Below the lasing threshold dP/dI is low; above the threshold it is high.
The active layer of a laser is capped at each end with mirror facets (in some laser diodes), which cause the light to bounce back and forth and grow in intensity. The layers directly beside the active layer (cladding layers) are set such that their refractive indices bounce light back into the active layer.
Tuesday, July 14, 2009
Current Drift in pn Junctions
In some pn junctions, the current through a pn junction degrades exponentially with time. This effect is only noticeable at a low bias with tens of mA. The current drift happens because at this low bias, much of the current (in these certain diodes) is carried by surface recombination current. Over time, heat caused by the current flow causes oxidation of the surface of the active layer, thus reducing the empty sites at the surface and decreasing surface recombination current.
Sunday, July 12, 2009
Double Heterostructures, Qunatum Wells
More from Optical Semiconductor Devices.
Double Heterostructures
A double heterostructure is two pn junctions in a row, where each of the three materials has different band-gap energies. The most widely used structure (at least in optics) is a p-type wide band-gap / p-type narrow band-gap / n-type wide band-gap. This combination creates an impressive barrier that must be overcome for diffusion current to flow. However, diffusion current only occurs in very high excitation conditions. In normal forward bias operation, carriers crowd into the middle narrow band-gap material (the active layer), and spontaniously recombine through the material. The high density of carriers, caused by both the narrow band-gap and the injected carriers, causes a high rate of spontanious recombination. This recombination is the central operation principle behind LEDs.
Quantum Wells
A quantum well is created by a p(wide)/p(narrow)/p(wide) or n(wide)/n(narrow)/n(wide) heterostructure. The first thing to realize is that many carriers will be trapped in the "well" formed by the heterostructure, unable to move to either wide band-gapped material. The key, is that the narrow band-gap material's thickness is comprable to the de Broglie wavelength of the carriers. Since the length is comprable to the de Broglie wavelength of the carriers, the possible energy states of the carriers in this direction become quantized into discrete levels, greatly reducing the number of possible states. This means that the carriers in the well have limited motion in that direction (the direction of the thickness), confining them to a two-dimensional plane.
When multiple quantum wells are put together, and if the wide band-gap materials are also very thin, then a super lattice structure is formed.
Double Heterostructures
A double heterostructure is two pn junctions in a row, where each of the three materials has different band-gap energies. The most widely used structure (at least in optics) is a p-type wide band-gap / p-type narrow band-gap / n-type wide band-gap. This combination creates an impressive barrier that must be overcome for diffusion current to flow. However, diffusion current only occurs in very high excitation conditions. In normal forward bias operation, carriers crowd into the middle narrow band-gap material (the active layer), and spontaniously recombine through the material. The high density of carriers, caused by both the narrow band-gap and the injected carriers, causes a high rate of spontanious recombination. This recombination is the central operation principle behind LEDs.
Quantum Wells
A quantum well is created by a p(wide)/p(narrow)/p(wide) or n(wide)/n(narrow)/n(wide) heterostructure. The first thing to realize is that many carriers will be trapped in the "well" formed by the heterostructure, unable to move to either wide band-gapped material. The key, is that the narrow band-gap material's thickness is comprable to the de Broglie wavelength of the carriers. Since the length is comprable to the de Broglie wavelength of the carriers, the possible energy states of the carriers in this direction become quantized into discrete levels, greatly reducing the number of possible states. This means that the carriers in the well have limited motion in that direction (the direction of the thickness), confining them to a two-dimensional plane.
When multiple quantum wells are put together, and if the wide band-gap materials are also very thin, then a super lattice structure is formed.
Deep Level Recombination and Surface Recombination
I am currently reading Optical Semiconductor Devices (1999) by Mitsuo Fukuda. I am being introduced to many new concepts and am coming to a greater understanding of older concepts.
Deep Level Recombination
Due to crystal defects and impurities, available states are formed in the middle of the band-gap (deep level). Electrons from the conduction band jump down to this recombination center, and from there jump down to the valence band. When the electron jumps down to the valence band, this is the same thing as a hole jumping up into the recombination center. The hole then jumps up to the conduction band as another electron jumps into the center and so on. Electrons in the valence band and holes in the conduction band are not carriers, thus, the carriers have recombined.
Deep Level Recombination Current
If a pn junction has a recombination center in the depletion layer, it will conduct current even if the junction is reversed biased. In reverse bias, some electrons that are pushed by diffusion into the depletion layer will jump down into the recombination center, and likewise some holes pushed into the depletion layer will jump up into the recombination center. Thus, current from one direction will be carried by electrons and by holes in the other direction.
Surface Recombination and Surface Recombination Current
At the surface of a crystal, the lattice structure ends, and atoms are inherently filled with holes. From a band-gap perspective, the conduction band and valence band join. Thus, carriers easily recombine at the surface. As deep level recombination, surface recombination can also carry current, even through a reverse bias pn junction.
Total Current
Considering the above, the total current through a pn junction can be expressed as:
I = Across(Jdiff + Jdeep) + AsurJsur
Deep Level Recombination
Due to crystal defects and impurities, available states are formed in the middle of the band-gap (deep level). Electrons from the conduction band jump down to this recombination center, and from there jump down to the valence band. When the electron jumps down to the valence band, this is the same thing as a hole jumping up into the recombination center. The hole then jumps up to the conduction band as another electron jumps into the center and so on. Electrons in the valence band and holes in the conduction band are not carriers, thus, the carriers have recombined.
Deep Level Recombination Current
If a pn junction has a recombination center in the depletion layer, it will conduct current even if the junction is reversed biased. In reverse bias, some electrons that are pushed by diffusion into the depletion layer will jump down into the recombination center, and likewise some holes pushed into the depletion layer will jump up into the recombination center. Thus, current from one direction will be carried by electrons and by holes in the other direction.
Surface Recombination and Surface Recombination Current
At the surface of a crystal, the lattice structure ends, and atoms are inherently filled with holes. From a band-gap perspective, the conduction band and valence band join. Thus, carriers easily recombine at the surface. As deep level recombination, surface recombination can also carry current, even through a reverse bias pn junction.
Total Current
Considering the above, the total current through a pn junction can be expressed as:
I = Across(Jdiff + Jdeep) + AsurJsur
Beginnings
Hello!
I am Matthew Nile Miskiewicz, currently a senior at North Carolina State University in Electrical and Computer Engineering. I intend for this blog to be a journal of my academic knowledge and learning. Expressing what I have learned in writing will help solidify the ideas and concepts that I have learned. I may use this blog to post other miscellaneous tech things as well, or I may start another blog for that.
I am Matthew Nile Miskiewicz, currently a senior at North Carolina State University in Electrical and Computer Engineering. I intend for this blog to be a journal of my academic knowledge and learning. Expressing what I have learned in writing will help solidify the ideas and concepts that I have learned. I may use this blog to post other miscellaneous tech things as well, or I may start another blog for that.
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