LED Simulation in Atlas

This post features an LED structure simulated in ATLAS. The goal will be to demonstrate why this structure may be considered an LED. Light Emitting Diodes and Laser Diodes both serve as electronic-to-photonic transducers. Of importance to the operation of LEDs is the radiative recombination rate.

The following LED structure is built using the following layers (top-down):

  • GaAs: 0.5 microns, p-type: 1e15
  • AlGaAs: 0.5 microns, p-type: 1e15, x=0.35
  • GaAs: 0.1 microns, p-type: 1e15, LED
  • AlGaAs: 0.5 microns, n-type: 1e18, x=0.35
  • GaAs: 2.4 microns, n-type: 1e18

This structure uses alternating GaAs and AlGaAs layers.

 

06_0106_02

Pulsed Lasers and Continuous-Wave Lasers

Continuous-Wave (CW) Lasers emit a constant stream of light energy. Power emitted is typically not very high, not exceeding killoWatts. Pulse Lasers were designed to produce much higher peak power output through the use of cyclical short bursts of optical power with intervals of zero optical power output. There are several important parameters to explore in relation the pulsed laser in particular.

The period of the laser pulse Δt is the duration from the start of one pulse to the start of the next pulse. The inverse of the period Δt is the repetition rate or repetition frequency. The pulse width τ is calculated as the 3dB (half power) drop-off width.

The Duty cycle is an important concept in signals and systems for periodic pulsed systems and is described as the ratio of the pulse duration to the duration of the period. Interestingly, the continuous wave lase can be considered as a pulse laser with 100% duty cycle.

CaptureA

Power calculations and Pulse Energy remain as several important relations.

  • Average Power: the product of Peak pulsed power, repetition frequency and the pulse width
  • Pulsed Energy: Average power divided by the repetition frequency

Other formulations of these parameters are found above.rereate

 

Monochromaticity, Narrow Spectral Width and High Temporal & Spatial Coherence

A laser is a device that emits light through a process of optical amplification based on stimulated emission of electromagnetic radiation. A laser has high monochromaticity, narrow spectral width and high temporal coherence. These three qualities are interrelated, as will be shown.

Monochromaticity is a term for a system, particularly in relation to light that references a constant frequency and wavelength. With the understanding that color is a result of frequency and wavelength, a monochromatic system also means that a single color is selected. A good laser will have only one output wavelength and frequency, typically referred to in relation to the wavelength (i.e. 1500 nanometer wavelength, 870 nanometer wavelength).

A monochromatic system, made of only one frequency ideally is a single sinusoid function. A constant frequency sinusoid plotted in the frequency domain will have a line width approaching zero.

Cap00e!

The time τ that the wave behaves as a perfect sinusoid is related to the spectral line width. If the sinusoid takes an infinite time domain presence, the spectral line width is zero. The frequency domain plot in this scenario is a perfect pulse.

If two frequencies are present in the time domain, the system is not monochromatic, which violates one of the principles of a perfect laser.

CaptureXU

Temporal Coherence is essentially a different perspective of the same relation present between monochromaticity and narrow spectral width. Coherence is the ability to predict the value of a system. Temporal coherence means that, given information related to the time of the system, the position or value of the system should be predictable. Given a sinousoid with a long time domain presence, the value of the sinusoid will be predictable given a time value. This is one condition of a proper laser.

Spatial coherence takes a value of distance as a given. If the system is highly spatially coherent, the value of the system at a certain distance should predictable. This point is also a condition of a proper laser. This is also one differentiating point between a laser and an LED, since an LED’s light propagation direction is unpredictable at a certain time and certainly not in a certain distance. Light emitted from the LED may travel at any angle at any time. An LED does not produce coherent light; the Laser does.

AlGaAs/GaAs Strip Laser

This project features a heterostructure semiconductor strip laser, comprised of a GaAs layer sandwiched between p-doped and n-doped AlGaAs. The model parameters are outlined below. The structure is presented, followed by output optical power as a function of injection current. Thereafter, contour plots are made of the laser to depict the electron and hole densities, recombination rate, light intensity and the conduction and valence band energies.

 

1

2345678

Quality Factor

Quality factor is an extremely important fundamental concept in electrical and mechanical engineering. An oscillator (active) or resonator (passive) can be described by its Q-factor, which is inversely proportional to bandwidth. For these devices, the Q factor describes the damping of the system. In some instances, it is better to have either a lower or higher quality factor. For instance, with a guitar you would want to have a lower quality factor. The reason is because a high Q guitar would not amplify frequencies very evenly. To lower the quality factor, complex or strange shapes are introduced for the instrument body. However, the soundhole of a guitar (a Helmholtz resonator) has a very high quality factors to increase its frequency selectivity.

A very important area of discussion is the Quality Factor of a filter. Higher Q filters have higher peaks in the frequency domain and are more selective. The Quality factor is really only valid for a second order filter, which is based off of a second order equation and contains both an inductor and a capacitor. At a certain frequency, the reactances of both the capacitor and inductor cancel, leading to a strong output of current (lower total impedance). For a tuned circuit, the Q must be very high and is considered a “Figure of Merit”.

In terms of equations, the quality factor can be thought of in many different ways. It can be thought of as the ratio of “reactive” or wasted power to average power. It can also be thought of as the ratio of center frequency to bandwidth (NOTE: This is the FWHM bandwidth in which only frequencies that are equal to or greater than half power are part of the band). Another common equation is 2π multiplied by the ratio of energy stored in a system to energy lost in one cycle. The energy dissipated is due to damping, which again shows that Q factor is inversely related to damping, in addition to bandwidth.

Q can also be expressed as a function of frequency:

1

The full relationship between Q factor and damping can be expressed as the following:

When Q = 1/2, the system is critically damped (such as with a door damper). The system does not oscillate. This is also when the damping ratio is equal to one. The main difference between critical damping and overdamping is that in critical damping, the system returns to equilibrium in the minimum amount of time.

When Q > 1/2 the system is underdamped and oscillatory. With a small Quality factor underdamped system, the system many only oscillate for a few cycles before dying out. Higher Q factors will oscillate longer.

When Q < 1/2 the system is overdamped. The system does not oscillate but takes longer to reach equilibrium than critical damping.

 

 

Bragg Gratings

Bragg gratings are commonly used in optical fibers. Generally, an optical fiber has a relatively constant refractive index throughout. With a FBG (Fiber Bragg Grading) the refractive index is varied periodically within the core of the fiber. This can allow certain wavelengths to be reflected while all others are transmitted.

spec

The typical spectral response is shown above. It is clear that only a specific wavelength is reflected, while all others are transmitted. Bragg Gratings are typically only used in short lengths of the optical fiber to create a sort of optical filter. The only wavelength to be reflected is the one that is in phase with the Bragg grating distribution.

A typical usage of a Bragg Grating is for optical communications as a “notch filter”, which is essentially a band stop filter with a very high Quality factor, giving it a very narrow range of attenuated frequencies. These fibers are generally single mode, which features a very narrow core that can only support one mode as opposed to a wider multimode fiber, which can suffer from greater modal distortion.

The “Bragg Wavelength” can be calculated by the equation:

λ = 2n∧

where n is the refractive index and ∧ is the period of the bragg grating. This wavelength can also be shifted by stretching the fiber or exposing it to varying temperature.

These fibers are typically made by exposing the core to a periodic pattern of intense laser light which permanently increases the refractive index periodically. This phenomenon is known as “self focusing” which is when refractive index can be permanently changed by extreme electromagnetic radiation.

 

Photodetectors and Dark Current

A photodetector simply is a device that converts light energy to an electrical current. These devices are very much similar to lasers, although they are designed to operate in reverse bias. “Dark current” is a term that originates from this reverse bias condition. When you reverse bias any diode, there is some leakage current which is appropriately named reverse bias leakage current. For photsensitive devices, it is called dark current because there is no light absorption involved. The main cause of this current is random generation of electrons and holes in the depletion region. Ideally, this dark current is minimal (<< 1).

1

The basic structure of the photodiode is the “PIN” structure, similar to a semiconductor laser diode. An intrinsic (undoped) region occurs between the P-doped and N-doped region.  Although PIN diodes are poor rectifiers, they are much better suited for high speed, high frequency applications due to the high level injection process. The wide intrinsic region provides a lowered capacitance at high frequencies. For photodetectors, the process is photon energy being absorbed into the depletion region, causing an electron hole pair to be created when the electron moves to a higher energy level (from valence to conduction band). This is what causes an electrical current to be created from light.

Photodetectors are “photoconductive”. That is, conductivity changes with applied light. Like amplifiers and other devices, photodetectors have “Figures of Merit” which signify characteristics of the device. These will be briefly examined

Quantum Efficiency

Quantum efficiency refers to the number of carriers generated per photon. It is normally denoted by η. It can also be stated as carrier flux/incident photon flux. Sometimes anti-reflection coatings are applied to photodetectors to increase QE.

Responsivity

Responsivity is closely related to the QE (quantum efficiency). The units are amperes/watt. It can also be known as “input-out gain” of any photosensitive or detective device. For amplifiers this is known as “gain”. Responsivity can be increased by maximizing the quantum efficiency.

Response Time

This is the time required for the photodiode to increase its output from 10% to 90% of final output level.

Noise Equivalent power

This value corresponds to units of Watts/sqrt(Hz). It is another measure of sensitivity of the device in terms of power that gives a signal to noise ratio of one hertz per output bandwidth, Small NEP is due to increased sensitivity of the device.

Carrier Recombination

Carrier recombination is an effect in which electrons and holes (carriers) interract with each other in a way in which both particles are eliminated. The energy given off in this process is related to the difference between the energy of the initial and final state of the electron that is moved during this process. Recombination can be stimulated by temperature changes, exposure to light or electric fields. Radiative recombination occurs when a photon is emitted in the process. Non-radiative recombination occurs when a phonon (quanta of lattice vibrations) is given off rather than a photon. A special case known as “Auger recombination” causes kinetic energy to be transferred to another electron.

1

Band to band recombination occurs when an electron moves from one band to another. In thermal equilibrium, the carrier generation rate is equal to the recombination rate. This type of recombination is dependent on carrier density. In a direct bandgap material, this will radiate a photon.

An atom of a different type of defect in the material can form “traps” which can contain one electron when the particle falls into it. Essentially, trap assisted recombination is a two step transitional process as opposed to the one step band to band transition. This is sometimes known as R-G center recombination. A two step recombination is known as “Shockley Read Hall” recombination. This is typically indirect recombinaton, which emits lattice vibrations rather than light.

The final type is Auger Recombination caused by collisions. These collisions between carriers transfer motional energy to another particle. One of the main reasons why this is distinct from the other two types is that this transfer of energy also causes a change in the recombination rate. Like the previous type, this tends to be non radiative.

A distinction should be made for band-to-band recombination between stimulated and spontaneous emission. Spontaneous emission is not started by a photon, but rather due to temperature or some other means (sometimes called luminescence). As stated in a previous post, stimulated emission is what emits coherent light in lasers, however spontaneous emission is responsible for most light emission in general.

Rayleigh Scattering

Rayleigh scattering is an effect of the scattering of light or electromagnetic radiation by particles much smaller in size than the wavelength. For example, when sunlight emits photons which enter the earth’s atmosphere, scattering occurs. The average wavelength for sunlight is around 500nm, which is in the visible light spectrum. However, it is known that the sunlight also emits Infrared waves and of course, ultraviolet radition. Interestingly enough, Rayleigh scattering influences the color of the sky due to diffuse sky radiation.

The reason why a huge wavelength (compare 400 nm with nitrogen and oxygen molecules which are only hundreds of picometers) can scatter on a small particle is because of electromagnetic interractions. When the nitrogen/oxygen molecules vibrate at a certain frequency, the photons interract and vibrate at the same frequency. The molecule essential absorbs and reradiates the energy, scattering it. Because the horizontal direction is the primary direction of vibration, the air scatters the sunlight. The polarization is dependent on the direction of the incoming sunlight. The intensity is proportional to the inverse of the wavelength to the fourth power. The shorter the wavelength, the more scattering. This can explain why the sky is blue because blue is more likely scattered by Raleigh scattering due to higher frequency (smaller wavelength). It is not dark blue because other wavelengths are also scattered, but much less so.

emagspec

Rayleigh Scattering is quite important in optical fibers. Because the silica glass have microscopic differences in the refractive index within the material, Rayleigh scattering occurs which leads to losses. The following coefficient determines the scattering.

scattering

The equation shows that the scattering coefficient is proportional to isothermal compressibility (β), photoelastic coeffecient, the refractive index  as well as fictive Temperatue and is inversely proportional to the wavelength.

Rayleigh scattering accounts for 96% of attenuation in optical fibers. In a perfectly pure fiber, this would not occur. The scattering centers are typically atoms or molecules, so in comparison to the wavelength they are quite small. The Rayleigh scattering sets the lower limit for propagation loss. In low loss fibers, the attenuation is close to the Rayleigh scattering level, such as in Silica Fibers optimized for long distance propagation.

The Electronic Oscillator

The semiconductor laser is a device that can be compared to an electronic oscillator. An oscillator can be thought of as a resonator (a circuit that resonates or produces a strong output at a specific frequency) with gain. Resonators naturally decay over time by some factor, so adding in gain (so long as the gain is greater than or equal to the loss) can allow the resonator to become an oscillator that does not decay or dampen.

The stimulation of the oscillations of an oscillator is caused by electronic noise. A block diagram can demonstrate an oscillator in an abstract, easier to understand way.

block

The oscillator is built using an amplifier (transistor that is biased into active/saturation region) or op amp with positive and negative feedback. Noise in the circuit begins the oscillation, and this output is fed back into the input and is filtered along the way. This becomes an oscillation at a single frequency.

Oscillators can be built from RC circuits, LC circuits or can be crystal oscillators. RC circuit oscillators tend to be lower frequency oscillators in the audio range. The LC oscillator is often compared to the laser in terms of functionality. The negative reactance of the capacitor and positive inductive reactance cancel at a specific frequency, leaving the circuit with only resistance and a strong current is achieved. LC oscillators are much more important for RF/microwave purposes. A crystal oscillator produces its frequency through mechanical vibrations and has a much higher Q factor than the other resonator types, which provides greater temperature and frequency stability.

Two very important oscillator types for RF/microwave/mmWave circuits are dielectric resonators and SAW (surface acoustic wave) resonators. Dielectric resonators are mainly used as mmWave oscillators to drive antennas. They are generally made of a “puck” of ceramic which oscillates at a certain frequency dependent on its dimensions. Waves are confined inside the material due to an abrupt change in the permittivity. When the waves inside interfere and produce a standing wave, this increase of amplitude creates the resonance effect. SAW resonators are often used in cell phones and have distinct advantages over the LC oscillator or other types due to cost and size.

In a semiconductor laser (laser diode), the source of oscillations is the noise generated by spontaneous emission. Spontaneous emission is the result of recombination of electron and hole pairs within the material which produces photons. This spontaneous emission is how lasers begin their operation, and this is continued by stimulated emission. Stimulated emission is electron hole recombination due to photon energy which also produces a photon. The light emitted by this type of emission is coherent, a characteristic of a laser.

Pseudomorphic HEMT

The Pseudomorphic HEMT makes up the majority of High Electron Mobility Transistors, so it is important to discuss this typology. The pHEMT differentiates itself in many ways including its increased mobility and distinct Quantum well shape. The basic idea is to create a lattice mismatch in the heterostructure.

A standard HEMT is a field effect transistor formed through a heterostructure rather than PN junctions. This means that the HEMT is made up of compound semiconductors instead of traditional silicon FETs (MOSFET). The heterojunction is formed when two different materials with different band gaps between valence and conduction bands are combined to form a heterojunction. GaAs (with a band gap of 1.42eV) and AlGaAs (with a band gap of 1.42 to 2.16eV) is a common combination. One advantage that this typology has is that the lattice constant is almost independent of the material composition (fractions of each element represented in the material). An important distinction between the MESFET and the HEMT is that for the HEMT, a triangular potential well is formed which reduces Coloumb Scattering effects. Also, the MESFET modulates the thickness of the inversion layer while keeping the density of charge carriers constant. With the HEMT, the opposite is true. Ideally, the two compound semiconductors grown together have the same or almost similar lattice constants to mitigate the effects of discontinuities. The lattice constant refers to the spacing between the atoms of the material.

However, the pseudomorphic HEMT purposely violates this rule by using an extremely thin layer of one material which stretches over the other. For example, InGaAs can be combined with AlGaAs to form a pseudomorphic HEMT. A huge advantage of the pseudomorphic typology is that there is much greater flexibility when choosing materials. This provides double the maximum density of the 2D electron gas (2DEG). As previously mentioned, the field mobility also increases. The image below illustrates the band diagram of this pHEMT. As shown, the discontinuity between the bandgaps of InGaAs and AlGaAs is greater than between AlGaAs and GaAs. This is what leads to the higher carrier density as well as increased output conductance. This provides the device with higher gain and high current for more power when compared to traditional HEMT.

1

The 2DEG is confined in the InGaAs channel, shown below. Pulse doping is generally utilized in place of uniform doping to reduce the effects of parasitic current. To increase the discontinuity Ec, higher Indium concentrations can be used which requires that the layer be thinner. The Indium content tends to be around 15-25% to increase the density of the 2DEG.

1

Parameter Analysis of the MESFET, Channel Width Calculation

Engineering design regularly involves an analysis of the formulae behind the various parameters of a system one is trying to build or improve. Some parameters are static, such a particular qualities of the materials being used. Perhaps there is a constraint made on the system or a goal, such as achieving function at a certain frequency or to reduce the size as much as possible. Today, many programs exist that can perform complicated calculations for the engineer. To construct a problem or calculation that produces the desired result may need more attention.

The MESFET uses a contact between n-doped semiconductor material with highly n-doped semiconductor material to form a junction field effect transistor. The great advantage of not using a p-doped semiconductor material is that the transistor can be built without using hole transfer. Since hole transfer is much slower than electron transfer, the MESFET can function much faster than other types of transistors.

For the MESFET, it may not be possible to examine all parameters. Consider first the following:

eqmesfet

Potential variation along the channel (notice the similarity of the following to Ohm’s law, V=IR):

potentialvariation

Where the resistance along the channel is:

res2

Depletion Width (also referenced in the above formula) under the gate:

depletionwidth

Pinch-off Voltage:

vpinch

Threshold Voltage:

re4

Built-in Potential:

builtin

The above formulas alone would be enough to put to use. While constructing a MESFET, it was found that the doping concentration of donor electrons in the channel played an important role. N_D, the donor doping concentration is found in most of the above formulas. The doping concentration is of particular importance, since it can be directly manipulated. The pinch-off voltage and the donor concentration are directly proportional. By achieving an estimate (or of the values are known) for other parameters, it would be possible to perform a parameter sweep for the MESFET system for doping concentration. This method may become critical for optimizing semiconductor device designs.

 

MESFET Design Problem

Let’s say we want to calculate the channel width of an n-channel GaAs MESFET with a gold Schottky barrier contact. The barrier height (φ_bn) is 0.89 V. The temperature is 300 K. The n-channel doping N_d is 2*10^15 cm^(-3). Design the channel thickness such that V_T = +0.25V.

mesfetcalc1

GaAs MESFET Designs

A GaAs MESFET structure was built using Silvaco TCAD:

• Channel Donor Electrons: 2e17
• Channel thicknes s : 0.1 microns
• Bottom layer: p doped GaAs (5 micron thick, 1e15p doping)
• Gate length: 0.3 micron
• Gate metal work function: 4.77eV
•Separation between the source and drain electrode: 1 micron

p4struct

The IV curve is as follows. Of primary importance are the two bottom curves, which are for a gate voltage of -0.2V and -0.5V. The top curve is 0V, over which would be undesirable for the MESFET operation.

p4iv

Now, in terms of designing a MESFET, there is a large amount of theory that one may need to grasp to build one from scratch – you would probably first start by building one similar to a more common iteration. That said, there are a number of parameters that one may wish to tweak and to achieve, to name a few: saturation current, threshold voltage, transit frequency, maximum frequency, pinch-off voltage.

The iteration above does not show a highly doped region under the source and drain contacts. The separation between source and drain may also be increased and the size of the gate decreased.

08

Channel doping level was found to make a significant difference in overall function. The channel must be doped to a certain level, otherwise the structure may not behave properly as a transistor.

go atlas

Title GaAs MESFET

# Define the mesh

mesh auto
x.m loc = 0 Spac=0.1
x.m loc = 1 Spac=0.05
x.m loc = 3 Spac=0.05
x.m loc = 4 Spac =0.1

# n region

region num=1 bottom thick = 0.1 material = GaAs NY = 10 donor = 2e17

# p region

region num=2 bottom thick = 5 material = GaAs NY = 4 acceptor = 1e15

# Electrode specification
elec num=1 name=source x.min=0.0 x.max=1.0 top
elec num=2 name=gate x.min=1.95 x.max=2.05 top
elec num=3 name=drain x.min=3.0 x.max=4 top

doping uniform conc=5.e18 n.type x.left=0. x.right=1 y.min=0 y.max=0.05
doping uniform conc=5.e18 n.type x.left=3 x.right=4 y.min=0 y.max=0.05

#Gate Metal Work Function
models fldmob srh optr fermidirac conmob print EVSATMOD=1
contact num=2 work=4.77

# specify lifetimes in GaAs and models
material material=GaAS taun0=1.e-8 taup0=1.e-8
method newton

solve vdrain=0.5
LOG outf=proj2mesfet500mVm.log
solve vgate=-2 vstep=0.25 vfinal=0 name=gate
save outf=proj2mesft.str
#Plotting
output band.param photogen opt.intens con.band val.band

tonyplot proj2mesft.str
tonyplot proj2mesfet500mVm.log
quit

Basic Energy Band Theory

Band theory is essential in the study of solid state physics. The basic idea tends to center around two bands: the conduction and valence band (for reasons discussed later on). Between the two bands is a forbidden energy level (Energy gap) which depends on the resistivity or conductance of the material. In order to fully understand solid state devices such as transistors or solar cells, this must be discussed.

For a single atom, electrons occupy discrete energy levels called bands. When two atoms join together to form a diatomic element (such as Hydrogen), their orbitals overlap. The Pauli Exclusion Principle states that no two electrons can have the same quantum numbers. Now keep in mind that there are four types of quantum numbers. This means that when these two atoms combine the atomic orbitals must split to compensate so that no two electrons have the same energy. However for a macroscopic piece of a solid, the number of atoms is quite high (on the power of 10^22) and therefore the number of energy levels is also high. For this reason, adjacent energy levels are almost continuous, forming an energy band. The main bands under consideration are the valence (outermost band involved in chemical bonding) and conduction because the inner electron bands are so narrow. Band gaps or “forbidden zones” are leftover energy levels that are not covered by a band.

In order to apply band theory to a solid, the medium must be homogeneous or evenly distributed. The size of material must be considerable as well, which is not unreasonable considering the number of atoms in an appreciable piece of a solid. The assumption also must include that electrons do not interract with phonons or photons.

The “density of states” is a function that describes the number of states per unit volume, per unit energy. It is represented by a Probability Density function.

A Fermi-Dirac distribution function demonstrates the probability of a state of energy being filled with an electron. The probability is given below.

fuck

The μ is generally expressed as EF which is the Fermi energy level or total chemical potential. kT is the familiar thermal energy which is the product of the Boltzmann constant and the temperature. From this equation it is clear that absolute zero temperature, the exponential term increases to infinity, causing the entire term to trend to zero. This leads to the conclusion that semiconductors behave as insulators at 0K.

The density of electrons can be calculated by multiplying this value with the density of states function and integrating over all energy.

Band-gap engineering is the process of changing a material’s band gap. This is usually done to semiconductors by changing the composition of alloys in the material.