Wednesday, October 14, 2009

The Nature of Light - Part 7 (Bibliography)

Bibliographic Refrences


Baierlein, Ralph. Newton to Einstei: The Trail of Light. Great Britain. Cambridge University Press. 1992.

Buil, Christian. CCD Astronomy: Construction and Use of an Astronomical CCD Camera. Richmond, Virginia. Willmann-Bell Inc. 1991.

Goldin, Edwin. Waves and Photons: An introduction to Quantum Optics. United Sates. John Wiley & Sons, Inc. 1982.

Hayat, William H. Engineering Electromagnetics. United States. McGraw-Hill. 2001.

Peleg,Yoav. Schaum’s outline of Quantum Mechanics. United States. McGraw-Hill. 1998.

Pierret, Robert F. Semiconductor Device Fundamentals. United States. Addison-Wesley. 1996.

Ziemer, R.E. Principle of Communications: System, Modulation, and Noise. United States. John Wiley & Sons, Inc. 1995.

The Nature of Light - Part 6 (MOSFET and Charge-Coupled Devices)

MOSFET Devices

The two main advantages of Metal Oxide Semiconductor Field Effect Transistors have made them the most widely used transistors in the new digital world. They have a much smaller size and faster switching time.

Cross-section view of n-channel MOSFET. (Pierret, 612)

In these devices the voltage that is applied to the gate (G) controls the width or ON/OFF states of the channel, consequently this voltage controls the flow of charges from source (S) to drain (D) (in conventional form, from drain to source). There are three types of current flowing inside of a MOSFET. First one is the drift current, which is generated by an applied electric field. The diffusion current exists because of the holes and electrons potential difference. Charges like to travel from a higher potential to a lower potential level. The third one is the current as a result of thermal or light effect on semiconductor. This last type of current is used to measure light wavelength and intensity. The most advanced use of MOSFET devices is in CCD camera. A CCD is an area array of MOSFETS that acts similar to a human eye’s retina. It converts the photon energy to electric energy.

In MOSFETs if the transistor is of type npn it means that the substrate is a p-type semiconductor and the channel will be a n-channel. In order to create an n-channel we have to apply a positive voltage to the gate in order to attract electrons to the surface. We could use the same analogy for a pnp p-channel MOSFET to see that the voltage on the ate should be negative. There many different MOSFET technologies available but they are out of scope of this paper.

Charge Coupled Devices (CCD)

A side view of an array of transistors in a CCD. (Pierret, 240)

The charge-coupled devices are the image detectors that were developed in 1970. There are two types of CCD’s, linear array and area array. The linear array is typically used in scanners but area array CCD’s are good as an advanced photodetectors in digital cameras.

After a period of time is being exposed to light, photocharges will be transferred one after the other to the output stage. The exposure time is named the integration time. The readout electric signal at the output stage is directly proportional to the charge was generated by the incident illumination falling on the CCD.



A is the area, L is length, GL is photo generation rate/, and q is the charge.

There is always a constant voltage applied to input and output stages. The light illumination causes variation in this constant voltage. Therefore by measuring the output signal after integration time we should get the photogeneration rate . Of course, because is function of light wavelength therefore we can approximate the wavelength of each light incident.

Let’s see how really a MOSFET forms a light trap. A MOSFET is an actually a capacitor. The oxide layer works as an insulator. The substrate material can be n or p-type semiconductor. The gate is made of metal. The voltage applied to the gate absorbs the minority carriers of the substrate forming a conducting channel to let the charges pass through. This channel in CCD is called the charge well.

Side view of a MOS capacitor. (Buil, 2)

Side of a MOS Capacitor after applying a positive voltage to the gate G. (Buil, 3)

As one can see in the last picture the gate voltage has pushed the positive charges (holes) of the substrate down and has opened a channel of electrons. This channel will eventually direct the current of charges to the output stage. The channel is named charge well and is the space that charges are not in equilibarium state. It means that because of the forced voltage, applied gate voltage, the electron-hole pairs are separated, electrons became absorbed to the surface and holes are pushed back to the bottom of the device. Because Semiconductor in general and MOSFETs specificly are very temperature dependent there is a phenamenon known as dark current. This current is the result of thermal energy absorbed by the semiconductor during a period known as thermal relaxation time without the presence of light. In CCD technology we should always avoid dark current because the only thing we need to impact our CCD is light not the heat. To get around this problem we need to cool down the CCD in order to minimize the process of electron-hole pairs generation by the temperature. Sdlkjfnbs

On the other hand the depth of the charge well is directly related to the voltage applied to the gate. This means the stronger gate voltage the deeper charge well. As you see in the following picture the two identical MOSs have different volume of well. This is because has a higher voltage that . Notice that there is a barrier between two wells this is because of the gap between two gate leads put them apart.

Two identical MOS with different gate voltage. (Buil, 4)

The charge transfer machanisim is based on the arrangement of MOS and their gate voltages. If two considered MOSs were so close to each other then there would not be any barrier in between them.

The same MOSs but now closer together. (Buil, 5)

There are numerous techniques for transfering charges mainly based on the phase difference between voltages for each gate. For example in three-phase charge transfer as in the following figure is shown a deep voltage well is produced under electrod 1 by appling an strong gate voltage. The charge accordingly will be stored under this lead.

Three-phase transfer technique. (Buil, 6)

Then when electrod 2 is prograssively asserted the charge will be transferred from under the previous electrod to under this present electrod which meand from lead 1 to the lead 2. If we constantly continue asserting and disasserting consecetive electrodes we can transfer the charge from under the first electrod to the last electrod and then output stage to read the signal. This is because the charge acts as a flowing water. As water like to travel from a higher potential level to a lower potential level, charges also want to get to the lower energy level. These techniques are for preventing charges to be mixed together. We need to transfer each packet of charge separately to measure it in a voltage scale. Each amount of charge transfers valuable information about the picture.

There are also different number of phase that can be used to transfer charges. The advantage of using phases more than three-phase is speed. For example in four-phase clock timing sequence the structure four consecutive MOS are in charge of one packet of charge. This reduces greatly the chance of charge backflow.

After all transfer quality is the most important part of transfering charges. During switching the phases there would be certain amount of charge that are left behind. These charges either can be recombined or mixed with the next packet of charge. This problem is known as transfer inefficiency. The main reson behind this problem is the impurity in semiconductor that holds some charges still. To reduce this phenomenon we should use a burried channel to facilitate charge transformation through the device. If we are using a npn transistor we need to add a n-channel between two ends of the transistor.

The last and most complicated part of a CCD is the output stage. Usually engineers should design this part because the CCD manufacturers would not add this part to their CCD array. It is simply because the output stage will form the final shape of the video signal and there are different type of video signals for different standards such as PAL, NTSC, SECAM, and so on.

The next figure shows the output register of a CCD’s output pin. This satge use a floating diode technique. This technique is based on precharging a diod which acts as a capacitor at a refrence level. The capacitor is then partly discharged by a packet of incoming charge. The difference between the refrence level voltage and the varied level voltage is the encountoured photon energy at that particular x and y coordination system in a CCD area array.

A typical output stage of a CCD array. (Buil, 9)

At time t=t1 a signal 0R is send to the transistor Tr1 to turn it on. Consequently the capacitor Cs is being precharged to the value of Vdr voltage. At time t2 the switch Tr1 is off which isolates the Cs. At time t3 electrode 02 releases the carrying charge into the output stage. Remember that the upper side of the capacitor is already positively charged. The charge is beginning transferred is negative therefore as soon as the carried charge arrives at the output stage it reduces the potential level of the capacitor making a deviation in the reference level. Then the transistor Tr2 reads this new voltage.





The Nature of Light - Part 5 (Wave Packet and Semiconductors)

The last concept that I want to talk about is the wave-packet. The wave-packet is a superposition of waves. This concept brings the particle and wave properties of light together. A wave-packet consisting of a plane wave in one dimension is:


The Gaussian wave-packet and its Fourier transform. (Goldin, 82)

The G(k) function is Gaussian distribution function. The smaller gets the more F(x) spreads out along x axis. When becomes a delta function, F(x) becomes a sinusoidal function, in which it will comply with the classic light wave laws. F(x) and G(k) are Fourier transform pairs.

So far we have just reviewed a very brief history of optics from Newton to Einstein. In the next part I like to review some materials on MOSFET devices technology and design.

Photoelectric Effect in Semiconductors

There are two major types of semiconductors that use and work with the photoelectric effect, diodes and photocells. The transistor with the GaAs substances will do very well with the photoelectric effect. These types of transistors are called direct transistors because in their recombination process photon emits as result of electrons moved to a less energy level.

The photon emitted in recombination process in a direct semiconductor. (Pierret, 109)

As soon as monochromatic light strike the surface of the semiconductor some of it reflects and the rest of it has intensity of I0. This intensity decays as far the photon penetrates the semiconductor.



The intensity of light at the distance x from the surface is I. After a photon transfer its energy to the semiconductor, pairs of electron-hole will be created. The rate of photogeneration / is , which is the essence of created current in the material and is function of depth of light penetration and the frequency of the light.

If n and p are number of generated minority carrier, holes in the sea of electrons then:


;


is the rate of photogeneration/ at the surface of semiconductor where the light strikes first.

Therefore if there is not any other effect than light on the semiconductor the generated current is directly proportional to the photogeneration rate. For example in a N-type semiconductor if the minority carrier is p and Dp is the exceeded minority carriers as a result of light then:



is the minority lifetime in from generation to recombination process. As a result of quantitative solution and boundary conditions to the photogeneration problem we can formulate the following equation for the excess minority carriers, in here holes.



The current that is produced as a result of photogeneration process can be calculated as follows:



A is the area, L is the length and q is the charge as a result of generated electron-hole pairs. Also:


Tuesday, October 13, 2009

The Nature of Light - Part 4 (Einstein and the Photoelectric Effect)

Heinrich Hertz discovered the photoelectric effect in 1887. Einstein in 1905 developed Planck’s quanta and introduced the photon.

Photoelectric-effect circuit. (Peleg, 1)

In photoelectric effect a piece of metal sheet is biased above a threshold voltage V0 and exposed to the light. A galvanometer measures the current upon light incident. When monochromatic light with high enough frequency falls on a metal electrons eject form the sheet to the anode pole, this happens instantaneously even for a very weak light intensity. This means that a change in the frequency of the radiation changes the maximum kinetic energy of electrons, , while a change in the light intensity does not affect this energy. However the current read by the Galvanometer is intensity dependent.

The following figures illustrates the properties of photoelectric effect:

Properties of photoelectric effect. (Peleg, 2)

a) If the light intensity stays constant the current proceed to its steady-state position. The transition time is about .

b) The relationship between light intensity and the photoelectric current is linear.

c) The photocurrent stops at potential that reaches the maximum energy of electrons.

d) For different frequency of light there is a different maximum energy.

But in classical explanation of light the intensity of light determines the maximum energy absorbed by the electrons. However we just saw that based on Planck’s quantum theory the maximum absorbed by the electron is frequency dependent not intensity.

If E = hf is absorbed energy by the electron through light incident, then:

in the frequency form we have:

” is the minimum energy to overcome atomic binding energy to generate a free electron.

“v” is the speed of the electron proportional to the frequency of the incident light.

Therefore the minimum threshold frequency is:



In Einstein’s relativity theory where is the rest mass of a particle.

If then where p is the momentum p = mv. In case of photon then:

E = pc.

Therefore:

E = pc = hf

p =hl

These are the Planck-Einstein relations.

Based on observation it was discovered that an electron in an atomic structure could absorb and cancel discrete frequencies. This formed the Niels Bohr model of atomic structure in terms of wrapping orbits around the core of the atom. His mathematical model of orbits is:

The difference in the energy level:

The Nature of Light - Part 3 (Black Body Radiation)

Several years after Maxwell introduced his model, which concluded light as an electromagnetic wave, the black body radiation dilemma arose. In the black body radiation we learn that a radiant energy emitted from a material body is temperature dependent and is independent of the property of the material. In the other words a material emit the same amount of energy that it absorbs. An ideal black body material absorbs all energy it gets and radiates all energy it has absorbed. The total radiation of an ideal black body is expressed as its intensity and is:

and by Stefan-Boltzmann law is:



Intensity spectral for the different temperature T4>T1. (Goldin, 127)

All models within the electromagnetic theory failed to be fitted into the real data in black body experiments. The best model that could get too close to the real data was Wien’s law, which is:

The results could not fit into the real data as the wavelengths were increasing.

Wien’s law vs. experiment. (Goldin, 127)

Max Planck introduced quanta in order to explain the black body radiation. He believed that each oscillator has a discrete energy states and can absorb or emit a quantum of energy .

Planck’s radiation law was formed as the following equation: