Tag Archives: Optoelectronics

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).


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 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.


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.


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.


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.

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.


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.


E-K Diagrams

As previously concluded, solids can be characterized based on energy band diagrams. A conductor has a valence and conduction bands that are very close or overlap. In addition a conductor will have a completely filled valence band and an almost full conduction band. The “forbidden region of the conductor is very small and little energy is required for an electron to move from conduction to valence band. In the presence of an external field, it is very easy for electrons to move from the valence band to the conduction band.

For semiconductors, at absolute zero the valence band is also completely full and the bandgap is typically about 1eV to 3eV, however even a bandgap of .1eV could be considered a semiconductor. Therefore, a semiconductor at 0K is an insulator. Semiconductors are very temperature sensitive. The subsequent figure illustrates the temperature dependence. The resistivity is very high at absolute zero, making the semiconductor behave like an insulator. However at higher temperatures the semiconductor can become quite conductive. At room temperature (300k), the semiconductor behaves more like a conductor.


With band diagrams, not much information is given therefore it is necessary to also analyze an E-K (Energy momentum) diagram. E is the energy require for an electron to traverse the bandgap. For example in Silicon with a bandgap of 1.1eV, it would take an energy level of 1.1eV for an electron to move from conduction to valence band. Energy is given as E = kT where T is a given temperature.

For intrinsic semiconductors like Silicon, the structure is crystalline and periodic. The wavefunction (which describes probability of finding an electron) should therefore be of periodic nature (sinusoidal). From the Schrodinger equation, it can be found that the Energy is periodic with k as well. For the diagrams, E is plotted against k.


The borders of the first Brillouin zone are from -π/a to π/a. These are cells of the crystalline lattice. Since the wavefunction is periodic, we only care about one of the zones. The above figure can be considered the “reduced zone” figure. Sometimes the x axis is given as the moment or wavenumber, since these only differ by a factor of Planck’s constant. From this diagram: the bandgap energy is shown, the effective mass of electrons and holes are shown as well as the density of states. The effective mass is shown by the curvature of the bands. For example, a heavy hole band could be found by observing the diagram that is less curved. From the above diagram, it is also noticeable that the material is direction bandgap (such as GaAs). The basic energy gap diagram compares to the E-k diagram in that the maximums and minimums correspond. However, the original band gap diagram does not give any other characteristics. It is for this reason the E-k diagram is so useful.

High Speed Waveguide UTC Photodetector I-V Curve (ATLAS Simulation)

The following project uses Silvaco TCAD semiconductor software to build and plot the I-V curve of a waveguide UTC photodetector. The design specifications including material layers are outlined below.


Simulation results

The structure is shown below:



Forward Bias Curve:



Negative Bias Curve:



Current Density Plot:



Acceptor and Donor Concentration Plot:



Bandgap, Conduction Band and Valence Band Plots:




Construct an Atlas model for a waveguide UTC photodetector. The P contact is on top of layer R5, and N contact is on layer 16. The PIN diode’s ridge width is 3 microns. Please find: The IV curve of the photodetector (both reverse biased and forward bias).

The material layers and ATLAS code is shown in the following PDF: ece530proj1_mbenker



Photovoltaic Effect and Theory of Solar Cells

Just as plants receive energy from the sun and use it to produce glucose, a photovoltaic cell receive energy from the sun and generates an electrical current. The working principle is based on the PN junction, which will be revisited here.

Silicon can be subdivided into several discrete energy levels called “bands”. The major bands of concern are the valence and conduction bands. The bottom bands are fully occupied and don’t change.


For silicon, the bandgap energy is 1.1eV. For an intrinsic semiconductor, the Fermi level is directly between the conduction and valence band. This is because there is an equal number of holes in the valence band as electrons in the conduction band. This means the probability of occupation of energy levels in both bands are equal. The Fermi level rises in the case of an n-type semiconuctor (doped with Phosphorous) and declines towards the valence band in a p-type (doped with Boron).

The following illustrates an energy band diagram for a semiconductor with no bias across it. Photodiodes (light sensors) operate in this manner.


The Fermi energy is shown to be constant. On the far right hand side away from the depletion region, the PN junction appears to be only P-type (hence the low Fermi level with respect to the conduction band). Likewise, on the left the Fermi level is high with respect to the conduction band. The slope of the junction is proportional to the electric field. A strong electric field in the depletion region makes it harder for holes and electrons to move away from the region. When a forward bias is applied, the barrier decreases and current begins to flow (assuming the applied voltage is higher than the turn on voltage of 0.7V). Current flows whenever recombination occurs. This is because every time an electron recombines on the P side, an electron is pushed out of the N side and beings to flow in an external circuit. The device wants to stay in equilibrium and balance out. This is why solar cells (as opposed to photodiodes) are designed to operate in a forward bias mode.

The sunlight produces solar energy in the frequency bands of Ultraviolet, infrared and visible light. In order to harness this energy, silicon is employed (made from sand and carbon). Silicon wafers are employed in solar cells. The top layer of the silicon is a very thin layer doped with phosphorous (n-type). The bottom is doped with P-type (doped with Boron). This forms the familiar PN junction. The top layer has thin metal strips and the bottom is conductive as well (usually aluminum). Only frequencies around the visible light spectrum are absorbed into the middle region of the solar cell. The photon energy from the sun knocks electrons loose in the depletion region which causes a current to flow. The output power of a single solar cell is only a few watts. To increase power, solar cells are wired in series and parallel to increase the voltage and current. Because the output of the solar cells is DC, the output is run through an inverter, a high power oscillator that converts the DC current to an 240V AC current compatible with household appliances.