Interaction of Electromagnetic Radiation: Quantum Structures

Interaction of Electromagnetic Radiation: Quantum Structures Preparation and Characterisation of Quantum Dot Infrared Photo Detector and Its Application in Night Vision Devices Submitted by Mangala Gowri M Focus of the study during this period was to understand interaction of electromagnetic radiation with quantum structures. Interband transition and intraband transition are two types of transition possible in semiconductors. Intraband transitions are unique for the quantum semiconductor structures. Intraband transitions between the quantized energy levels are possible depending on several parameters. The resonance wavelength depends on effective masses of the carriers, parameters like size, shape and composition of the quantum structures. Practical observations made on quantum structures like quantum wells and quantum dots were very interesting. â€Å"The first direct observation of infrared absorption between conduction subbands of n-doped GaAs/AlGaAs quantum wells was reported in 1985. It was confirmed that intersubband transitions between electronic states of quantum wells are strongly polarized along the confinement potential direction.† [1] Therefore light whose polarization has component along the confinement potential direction gets absorbed. Therefore â€Å"light must have a polarization component perpendicular to the quantum well layers.† [1] This is the strong limitation for the quantum well infrared photo detectors. On the other hand, quantum wires and quantum dots theoretically do not have this limitation on the polarization direction of incident radiation. For quantum well polarization, direction radiation should not be normal (perpendicular) to the confinement potential direction, whereas t his type of normal incidence is allowed for quantum dots. Oscillator Strength: â€Å"Oscillator strength is a dimensionless quantity that expresses the probability of absorption or emission of radiation in transitions between energy levels of an atom or molecule.† [2] When an electronic transition occurs an oscillating dipole moment will be induced by interaction of electric field of the system with electromagnetic radiation. The following illustration explains the mechanism of transition in a system in general. Suppose an electron changes its energy from En to Em by changing its state from ψn to ψm. During the transition it will be in a state which is superposition of the two states. ÃŽ ¨ = aψn + bψm Probability that the electron in the state ψn is |a|2 and probability that it is in state ψm is |b|2 so that at any time |a|2 + |b|2 =1. We can see that expectation value mn oscillates at frequency ÃŽ ³nm = , ÃŽ ³nm is the transition frequency. mn is the oscillator strength as the strength of the oscillation is proportional to the expectation value of intermediate state. It is also called the transition matrix element. For allowed transitions mn is a nonzero value and for forbidden transitions it is zero. Transition Dipole Moment: Transition dipole moment is the dipole moment associated with the transition between two states. It is a complex vector quantity. It encodes phase factors associated with the two states. The direction of this dipole moment is the polarization of the transition. The polarization of the transition determines the interaction of the system with electromagnetic radiation with a given polarization. Square of the dipole moment of transition gives the strength of the transition. Transition dipole moment is off-diagonal matrix element of position operator multiplied by the particle’s charge. Classically, dipole moment is product of charge and separation between the two charges. In the presence of an electric field, the two charges will experience a force in opposite direction so that a torque acts on the dipole. Similarly, during transition, coupling between an electromagnetic wave and transition dipole moment of the system depends on the charge distribution within the system, strength of the field and the relative polarization of the field and the transition. Also transition dipole moment depends on the geometries and relative phases of the two states involved in transition. The concept of transition dipole moment is very useful to determine whether a transition is allowed or not. If the integral defining transition dipole moment is nonzero, that transition is allowed. Perturbation Theory: To understand the mechanism of interaction between the system and electromagnetic radiation, we adopt quantum mechanical perturbation theory. Incident radiation is treated as a perturbation. Electromagnetic radiation provides a time dependent potential, which assists quantum jumps between energy levels. So total Hamiltonian of the system has two parts, one is time independent and another is time dependent. If time dependent part is small compared to time independent part, then that can be treated as a perturbation. Considering two level system, where ÃŽ ¨a and ÃŽ ¨b are two eigen states of unperturbed Hamiltonian H0. The two states are orthonormal. Any other state of the system can be written as a linear combination of those two states. ÃŽ ¨(0) = Ca ÃŽ ¨a + Cb ÃŽ ¨b Ca and Cb are constants, which include information about probability of finding the system in respective states. Suppose we are curious to know the state of the system after a time t. If there is time dependent perturbation, ÃŽ ¨(t) is again superposition of the two states. Not only the two states evolve with time, but also coefficients Ca and Cb are also functions of time. If we can determine Ca(t) and Cb(t) we can understand the system at time t. Several mathematical steps lead us to ÄÅ  a = And ÄÅ  b = Where ÄÅ  a and ÄÅ  b are time derivatives of Ca(t) and Cb(t) respectively. Both of the above equations taken together are equivalent to time dependent Schrodinger equation for a two level system. The diagonal matrix elements of H’ vanish. Therefore, ÄÅ  a = ÄÅ  b = With Considering that H’ is small, above equations can be solved by a process called successive approximations. Here we also consider that perturbation is having sinusoidal time dependence. Then And In the first order we have ω is the driving frequency and ω0 is the transition frequency. If ω and ω0 are very close to each other second term in the square brackets dominates. So we can say ω + ω0 >> | ω0 ω| We drop first term and after simplification The transition probability gives the probability that a particle started from the initial state will reach at final state in time t. We can see here that transition probability as a function of time oscillates sinusoidally. Fig: Transition probability as a function of time, for sinusoidal perturbation. Maximum value of probability is . The probability of rising to the maximum value is much less than 1 for small perturbation. Another thing to observe here that the probability of transition is highest when ω ω0. Fig: Transition probability as a function of driving frequency. Thus as time goes on width of the peak becomes narrower and height of the peak becomes higher. That means that the system will undergo transition with higher probability. Emission and Absorption of Radiation: An electromagnetic wave consists of transverse oscillating electric and magnetic fields. An atom reacts primarily to the oscillating electric component of radiation. Assume that an atom is exposed to a sinusoidally oscillating electric field. Consider that the field is polarized along z direction. Then the perturbing Hamiltonian is written as Note: Considering that the period of oscillation of the field is long compared to the time taken by the charge to move around within the atom we adopt electrostatic formula for Vab that is equal to Then Where P = is transition dipole moment. ÃŽ ¨ is an odd or even function of z. We consider that the diagonal matrix elements of H’ vanish. Then the interaction of radiation with the system is governed by precisely the kind of oscillatory perturbation with Vab Note: P is off-diagonal matrix element of z component of dipole moment operator qr. Transition probability is proportional to the energy density of the perturbing fields. And we see that the probability is proportional to time. If incident radiation is monochromatic, transition probability oscillates. However, if the system is exposed to incoherent spread of frequencies that flopping nature disappears. The transition rate will be a constant. In the calculations, we have assumed that the direction of propagation of perturbing radiation is y direction and it is polarized along z axis. However, in practice the system (like quantum well, quantum dot) is exposed to a radiation coming from all directions and with all possible polarizations. Then the energy of the field is shared equally among these different modes. So in the place of we have to substitute the average of |P.n|2 with n is the direction of polarization of radiation. Average is over all polarizations and all incident directions. Quantum Well: A quantum well can be considered as idealized square, finite and symmetrical potential well. It is now evident that absorption of radiation by quantum well depends on the direction of the transition dipole moment and direction of polarization of incident radiation. It can be shown that the wave function of quantum well is a even function in ground state and it is alternatively even or odd in higher states. In order to P be nonzero ÃŽ ¨a and ÃŽ ¨b should be of opposite parity since z is odd. In addition, direction of P depends on ÃŽ ¨a and ÃŽ ¨b. Since the wavefunction of the quantum well has only z component, transition dipole moment will also be directed along the z direction i.e. along the direction of potential Vwell(z). In the case of normal incidence, the polarization of radiation is perpendicular to the walls of the well barrier or to the potential. The n that refers to polarization direction of radiation is in xy plane. So choosing cylindrical polar coordinates, we have And . Thus, . Then, Which implies that normal incidence in quantum wells is forbidden. The polarization selection rules for transitions in quantum wells are summarized below. Quantum Dot: Quantum dot is a quantum structure, which is confined three dimensionally. Thus, the confinement potential has all the three x, y, z components. Similarly the wave functions representing the states of quantum dot have x, y, z components. So the scalar product between transition dipole moment and the polarization direction of incident radiation will not be equal to zero. Average of is not zero in quantum dots. Thus, the quantity in quantum dots is nonzero. There is no restriction for direction of polarization of radiation theoretically. Even though normal incidence intraband absorption is forbidden in quantum wells, they are allowed in quantum dots. This is major fact of great interest in the development of infrared photodetectors. I attended a two-day collaborator’s workshop organized by Centre of ART, SIT, Tumkur from 20-02-2014 to 21-02-2014. Study Plan: In the next half year, focus of the study will be MOCVD growth process of quantum dots. Signature of the CandidateSignature of the Guide (Manala Gowri M) (Prof. (Dr.) Ganesh N. Raikar) References: A. Weber. Intraband Spectroscopy of Semiconductor quantum dots, 1998. 2. http://en.wikipedia.org/wiki/Oscillator_strength 3. Proefschrift. Optical Properties of Semiconductor Quantum Dots, 2011 4. Griffith. D.J, Introduction to quantum Mechanics, 2nd Ed, Pearson Education Inc, 2006.

New Faces for Mars

Mars often referred to as the Red Planet, has long been a subject of fascination; speculation about the existence of â€Å"Martians† was widespread early in the twentieth century; for example, issues of Scientific American in 1920 described possible communication with Mars using search lights and giant mirrors to reflect sunlight (Greeley 115). According to Greeley (2001), other proposals for communicating including digging huge trenches in the form of mathematical symbols in the Sahara Desert; these trenches were to be filled with kerosene and signal aflame to signal Mars. Based on Greeley (2001), although these ideas were never carried out, they reflected intense public interest in Mars. Telescopic observations of Mars began in the late nineteenth century and provided fuel for speculation about the nature of Mars. Space exploration of mars was initiated with the Mariner flyby in 1965; although it took only 22 close-up pictures covering a tiny fraction of the surface and showed the presence of a lunar like craters (Greeley 115). According to Greeley (2001), the geologic diversity of Mars was finally revealed by the Mariner 9 spacecraft. The Viking mission was the most complicated unmanned mission flown in the solar system according to Greeley; consisting of two orbiters and two landers. And in 1997, Mars Pathfinder landed and returned information for a third site on Mars; these missions have set the stage for more complex future missions including the return of samples to earth. It has been discovered before that more craters are older with some around 19 km across. Volcanism is also fascinating on Mars, which is said to have lava flowing but I’m not sure if this was really true. It is also said that the Red Planet has no plate tectonics and its outer layer doesn’t move horizontally, only its outer layer moves vertically. As for Mars’ other features, it is said that weathering and erosion are observed with dominated dust storms – global dust storms and sand dunes. It has also been said that there has been past flowing water before but this argument hasn’t been verified yet. As for the aliens wearing helmet, I doubt it because as of now there hasn’t been any findings of its existence. Maybe this might be true if water will be discovered in Mars. Due to advance research and technologies, I think that as time passes by, more and more findings could be discovered. If before, images are vague and cannot be distinguished easily, today, more and more sophisticated tools are being used to capture Mars’ images. Now, Mars’ tectonic features are more detailed compared before. It has also been found out that Mar’s volcanism is widespread and more diverse and young. Despite a virtual generation of studies based on newly devised technologies of space, Mars remains something of an enigma to man; fly-by, orbiting and landing missions by increasingly sophisticated space probes have revealed more about the Red planet in the last thirty years that had been gleaned in all previous centuries, but there are still many mysteries to be solved (Kargel ix). According to Kargel (2004), they range from the question of where Phobos and Deimos, the diminutive Martian Satellites, came from whereabouts of water which once sculptured much of the planet’s surface; these many more questions will only be answered after years, perhaps decades, of effort; and because the planet and its satellites preserve much of the ancient history of the solar system, they are important questions of science. Works Cited Kargel, J. S. Mars: A Warmer, Wetter Planet. New York: Springer Publishing 2004. Greeley, R. & Batson, R. The Compact NASA Atlas of the Solar System. New York: Cambridge University Press, 2001.

Funeral Oration of Pericles Essay

In the reading of the Funeral Oration of Pericles, I do not believe what Pericles says about Athens. I believe he made his speech to boost morale for his people and for the soldiers, and to keep the war going. In the Funeral Oration of Pericles, they were there to honor the fallen soldiers and to have a burial for them, but Pericles made it about the war. He used it to boost morale for the soldiers, to get them excited and to give them a reason to keep fighting, he also used it to give a reason behind the war to the citizens. It was a political move on its own. These tactics are still used in the world today, such as the war in Iraq and Afghanistan and as far back as the Gettysburg Address. Pericles believed that personal glory was one of the rare things you could have, and fighting in the war and giving your life for your city was one of the highest glories you could bestow, so therefore he glorified the war not the people that lost their lives fighting in it. Pericles was trying to persuade the people that the war was worth people losing their lives over and that there was a meaning and cause for it. The funeral oration can be seen in the world today with the war in Iraq, where the President gives the speeches about why we are fighting in a war, the reasons and the cause, which is really not known today, such as weapons of mass destruction, it was said that Iraq possessed these and come to find out they had none, so many people lost their lives for what reason? There was hype, and glorification given to the men and women that fought, to boost their morale and for them to know they were doing something that helped the country. The President tried to persuade the citizens with his speeches that it was just and there was a reason for the war. In conclusion, the question asked was do I believe everything Pericles says about Athens in the Funeral Oration. The answer to that would be no. I do not believe that Pericles was there to honor the fallen soldiers. I belie ve he was there to persuade the citizens and the soldiers that what they were doing was right and was just and if they continued then they would be glorified.

sales development and Merchandising Essay - 1212 Words

Task A Research report describing the elements of the product in a business and services context After selecting a hotel of your choice, carry out an individual research into the element of the product of this hotel, and produce a written report of your findings which should include: a) A discussion about the key components of the product and how the product mix contributes to sales and profit (ref. 1.1, 1.2) b) An assessment on how market segmentation contribute to maximise sales (ref. 1.3) Task B Research report describing the external sales development techniques Carry out an individual research into external sales techniques using the same hotel you selected for task A and produce a written report of your findings which should†¦show more content†¦Ã¢â‚¬ËœCollusion occurs when, unless with official approval (e.g. in the case of group projects), two or more students consciously collaborate in the preparation and production of work which is ultimately submitted by each in an identical, or substantially similar, form and/or is represented by each to be the product of his or her individual efforts. Collusion also occurs where there is unauthorised co-operation between a student and another person in the preparation and production of work which is presented as the student’s own. (ibid)’ Programme: BTEC Higher National Diploma in Hospitality Management Unit Title and Number: Sales Development and Merchandising (Unit 16) Module Tutor: Pratika Teyssedou Learner’s Name :__________________________________Learner ID:____________ Assessment Criteria Met Evidence Feedback 1.1 evaluate the key components of the product 1.2 discuss the range of contributions to sales and profit of elements in the product mix 1.3 assess how market segmentation contributes to sales maximisation 2.1 discuss the factors affecting buyer behaviour 2.2 assess appropriate advertising media for sales development situations 2.3 evaluate the role ofShow MoreRelatedJob Analysis : Visual Merchandising And Store Manager1469 Words   |  6 PagesJob Analysis: Visual Merchandising and Store Manager This paper analyzes the position of a visual merchandising and store manager. It documents critical factors for entry and promotion, fundamental duties, and critical skills, knowledge, and abilities. 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