Generation of Extreme Ultraviolet Radiation

BRIEF HISTORY
Over the past few decades breakthroughs in the production of intense laser fields have meant that multi-terawatt and even petawatt systems are now standard in laboratories**. This has been achieved through reduction of the pulse duration, originally from nanosecond pulses down to femtosecond and recently reaching attosecond levels (1as =10-18s)**. This coupled with important improvements to systems, such as the chirped pulse amplification technique (CPA)**, has allowed laser pulses to be amplified to higher peak powers than ever before and used in laser-matter interactions. The resulting scientific drive from developments such as these pushed achievable laser intensities from 109W/cm2 to the 1014W/cm2, at which the interaction between these high intensity lasers and dense electron-free gas was studied**.
Only recently thanks to advances in both laser performance and computer simulation tools has study on laser-plasma interactions in the generation of HHG made progress, providing the possibility to generate sources of incoherent electromagnetic radiation of short wavelength and pulse durations**. As further study was carried out on the interaction of light with relativistic free electrons in plasma, it has reached a point now in which generation of high-harmonics of the fundamental laser, soft and hard x-rays, and shorter pulse duration (1as) lasers of intensities reaching 1018W/cm2 are now possible**. Due to this the generation of high-order-harmonics from high-intensity laser interactions has been a major area of attoscience research within the last decade.
HHG PRODUCTION
High harmonic generation (HHG) refers to the process in which a high intensity laser pulse is focused onto a target, classically a noble gas, in which strong nonlinear interactions result in the generation of very high harmonics of the optical frequency of the pulse**. This will occur for intensities of 1014W/cm2 and above, where typically only a small amount of this energy is converted into the higher harmonics. From these high-harmonics, spatially and temporally coherent attosecond pulses of extreme ultraviolet light can be generated, which can then be used as a reliable source of highly tuneable short wavelength radiation in many different applications e.g. x-ray spectroscopy**.
In the case of high intensity laser-gas interactions this is achieved by tailoring the intensity of the laser pulse so that its electric field amplitude is similar to the electric field in the target atoms**. From this the laser’s electric field is able to remove electrons from the atoms through tunnel ionisation, at which point the electrons are accelerated in the field and, with certain conditions controlled, are made to collide with the newly created ion upon recombination. The resulting collision generates the emission of high energy photons**, as shown in fig 1.
Fig. 1: HHG three step model.
This is known as the three step model; electron is detached from atom through tunnel ionisation, then accelerated within the field away from atom, then accelerated back towards atom where it collides and recombines, from this collision all the energy lost appears as emitted HHG ultraviolet photons.
HHG from laser-gas interactions have been used extensively to generate attosecond pulses but is limited in flux and photon energy by low conversion efficiencies between the driving laser energy and the attosecond pulses, this can be attributed to two key factors; loss of phase matching between the driving laser to the generated extreme ultraviolet (XUV) radiation as its propagated through the gas over a relatively large distance, and a restriction on the intensity of the driving laser due to the ionisation threshold of the target gas, this saturation intensity is roughly 1016W/cm2**. Meaning laser intensities above this threshold limit will over-ionise the gas leaving no neutral atoms left to generate the XUV harmonics.
The use of laser-solid interaction offers the opportunity of reaching much higher attosecond pulse intensities and generation efficiencies beyond the capabilities of gas based HHG**. The method of generating high-harmonics in laser-solid interactions is fundamentally different than that of laser-gas interactions.
Interaction of intense ultrashort laser pulses (of pulse duration around a few femtoseconds) on an optically polished solid surface results in the target surface being completely ionised, generating a dense plasma which will act as a mirror, called a plasma mirror**. The reflection of these high intensity laser pulses will be affected by a wave motion set-up in the electrons within the plasma surface causing it to distort the reflected laser field, resulting in the production of upshifted light pulses and the generation of high-order harmonics**. Due to the coherent nature of this process, these generated harmonics are phase-locked and emerge as attosecond pulse.

Fig. 2 Laser pulse moving towards overdense plasma.
A key property of this plasma is its electron density, this determines whether the laser is reflected, absorbed or not allowed to pass through. This is known as the density gradient scale length, as the laser pulse interacts with the target and forms a plasma it creates a profile that extends out into the vacuum, forming a plasma density profile. This is a critical factor in HHG and consists of two regions:
Overdense scale length, Lod –
If the electron density is equal to the critical density of the target or above, extending up to the maximum target density, the laser pulse is unable to penetrate through the target and is so reflected or absorbed.
Underdense scale length, Lud –
If the electron density is below this critical density the laser will penetrate through, with some absorption.

Fig. 3 Plasma density profile, Lud is underdense region, Lod is overdense region.
The critical density is determined from:

Where is the angular frequency of the laser.
As stated before the target surface is highly ionised by the leading edge of the laser pulse, known as the pre-pulse, therefore becoming rapidly over-dense and creating a plasma mirror of sufficient electron density, ne>nc**. HHG within plasma requires laser intensities >1015W/cm2 for 800nm field**, which is usually stated in terms of a normalised vector potential of a­0, where:

In which; e and m are electron charge and electron mass respectively. c is speed of light in vacuum. E is the amplitude of the lasers electric field. I is the lasers intensity. ωl is the laser frequency and λl is the laser wavelength.
Therefore HHG in plasma requires at least an a0≥0.03.
Recently is was discovered** that there are two mechanisms that lead to HHG from solid density plasma surfaces;
– Relativistic oscillating mirror (ROM)
– Coherent wake emission (CWE)
These two process result in different distortions to the reflected laser field and therefore a completely different harmonic spectra produced.
CWE
Coherent wake emission is a process of three steps;

Electrons on the surface of the plasma are drawn into the vacuum by the laser field and accelerated back into the dense plasma once they have gained energy from the driving laser field.
When propagating within the dense plasma these fast electrons form ultrashort bunches, creating plasma oscillations in their wake.
Within the non-uniform region of the plasma (produced from the density gradient between the plasma-vacuum boundary) the electron oscillations will radiate energy in the form of light of various local plasma frequencies found within this gradient.

This process will occur once for every laser cycle therefore the spectrum of the emitted light will consist of harmonics of the laser frequency, in which CWE harmonic spectra have a cutoff at the maximum plasma frequency ω­­pmax **. This mechanism is predominant at moderately relativistic intensities of a0≤1, and short but finite plasma gradient lengths of **.
Coherent wake emission has only recently been identified as a factor in HHG in laser-solid interactions but it is known that it along with ROM contributes to the generation of high-harmonic orders below ω­­pmax and the strength of their respective influence below this threshold is determined by laser intensity**.
ROM
The other mechanism involved in the generation of high-harmonics from laser-plasma interactions is the relativistic oscillating mirror process, this dominates for relativistic normalised vector potentials of a0>>1, although recent studies have shown that ROM harmonics can be observed even at lower intensities when the plasma gradient length is about **.
ROM process occurs when surface electrons in the plasma are oscillated collectively by the high intensity incident laser field to relativistic speeds, the plasma will reflect what it observes as a laser pulse of frequency ω+. This ω+ frequency is a higher upshifted frequency of the fundamental pulse due to a Doppler effect produced from the relative motion of the laser field to the moving reflection point on the oscillating plasma surface. The actual reflected laser pulse will have a frequency of ω++ due to a second Doppler upshift effect as it moves towards an observer/target. This is known as Einstein’s relativistic Doppler effect, in which the reflected pulse frequency is upshifted by a factor of 4γ2**.
Fig 4. Schematic of a relativistic oscillating critical density plasma interaction.
From past research it has been found that from this mechanism a power-law decay scaling of I(n)ROMn-8/3 is dominant (where n is the harmonic order) in the harmonic spectrum for harmonic orders above the CWE cut-off point, nCWE,** this is the harmonic order related to the maximum plasma frequency of the target, ωpmax, mentioned previously. Where:
nCWE = nωmax = ωpmax/ωl =
In which; ωl is the frequency of the laser, is the maximum electron density of the target, Nc is the critical density shown previously.
From this process initial femtosecond pulses can be used to create attosecond pulses. When coupled to a relativistic oscillating mirror it adds an oscillatory extension to Einstein’s relativistic Doppler effect, so due to the periodic motion of the mirror to the laser field and the double Doppler upshifts this results in the production of extreme ultraviolet (XUV) harmonics**. These ultra-short pulses have been the focus of much scientific research recently as they offer a promising way to resolve in the time domain the ultrafast dynamics of electrons within materials**.
Although the relativistic oscillating mirror process is more suited as a macroscopic model for the effective reflection point of the laser field. It assumes that the surface electrons bunch together as the target is ionised and move out into the vacuum to form the plasma where they remain in the overdense region ensuring that the laser field is completely reflected. More recently studies have discovered there is another mechanism in the relativistic regime that can contribute to the harmonic spectrum via a different process entirely.
CSE
This other process is known as Coherent synchrotron emission (CSE)** and is needed to explain observations that do not fit the previous two models, in which dense electron nanobunches are created at the plasma-vacuum boundary where they produce coherent XUV radiation through coherent synchrotron emission. This is a microscopic model of HHG in laser-solid interactions. It models the electrons in the plasma moving, in dense bunches, under the influence of the incident laser field and subsequent fields produced from the movement of charges within the plasma. These nanobunches are periodically formed and coherently accelerated through an instantaneously synchrotron-like orbit during each laser cycle, for oblique laser incidences. As certain conditions, such as ultrashort plasma density scale length, are met these bunches emit bursts of sub-femtosecond intense high-frequency radiation. This radiation has properties dependent on the electron trajectories and it has been shown that it can be modelled as synchrotron radiation**, therefore the coherent XUV emissions are distinctly different from that produced in ROM from relativistic Doppler upshifts. In reality actual electron dynamics may be a mix of CSE and ROM, but due to the complex nature of the changing fields within a plasma it makes it impossible to analytically model with accuracy. Therefore requiring the use of computer simulations to deal with the electron trajectories and their respective radiation emissions.
PREVIOUS EXPERIMENTS
Based on the work of Edwards et al, 2014, in which the study of attosecond XUV pulse generation from relativistic driven overdense plasma targets with two-colour incident light was performed they used 1D, three velocity, particle-in-cell (PIC) code simulations, which treat oblique incidence with boosted frames, to show how pulse intensity can be improved. They converted a small amount (~5%) of the fundamental laser field energy to an additional laser operating at the second harmonic of the fundamental frequency, to significantly enhance the intensity of the generated attosecond pulses by multiple orders of magnitude.
This was based on previous work in which mixing of the fundamental driving laser frequency with the second harmonic was performed on laser-gas interactions to increase the attosecond pulse intensity and isolation (K. J. Schafer et al, 1992).
Edwards demonstrated that a significant improvement was also possible through this mixing method in laser-solid interactions following the Similarity theory (proposed by Gordienko and Pukhov,**), that suggests the behaviour of laser-plasma interactions follow a similarity parameter of:
1/S = a0/N ωl
Where S = ne/a0nc, is a similarity parameter and N = ne/nc which is the ratio of electron density of the plasma to its critical density.
Therefore from this it would appear that by doubling ωl while using the same laser field amplitude the reflected attosecond pulse intensity would also be increase by a factor of two.
One of the main limiting parameters in these experiments is the achievable value of a0, while the largest solid material value of N (lithium at λ=800nm) is 75, so this type of frequency doubling appears to be a promising pathway to optimising attosecond pulse intensity, although a drawback of this is the negative effect it has on the isolation of the reflected pulses.
Therefore they stated that a two-colour method, of partially converting a portion of the fundamental laser field energy to the second harmonic, would be a more attractive alternative. Through this process the advantages of using a higher incident frequency, by increasing the gradient of the electric field at certain points within the pulse generation cycle, without the related decrease in pulse isolation and loss of energy associated to simple frequency doubling can be exploited.
In their study they used a normal-incidence beam on a step-like plasma density profile using a mix of the first and second harmonic with a phase difference of to produce harmonics with a higher intensity than either incident field individually. They demonstrate substantial gains after the addition of a small amount of the second harmonic to achieve attosecond pulse enhancement of factors >10. As well as a 10-fold enhancement when using density gradients of 0.05λ and 0.15λ with conversions of the fundamental to the second harmonic of 5%-10% at an angle of incidence of ϴ=30o.
Therefore Edwards was able to go on and state that the relative phase of the two incident harmonics were a critical factor in the improvement in attosecond pulse intensity. This is due to the difference in the driving electric field waveform and corresponding resultant electron motion as is varied. Where they linked the strongest attosecond pulse intensities with sharp transitions in the driving electric field that are aided by the addition of the second harmonic at optimum phases, while phases that break the driving field transition reduce the attosecond intensities to levels sometimes substantially below what could be achieved pre-mixing of the harmonics.
Therefore when harmonics are combined without thought to their phases they do not always improve the attosecond strength.
Further detail into the trajectories of dense electron bunches, which emit synchrotron like radiation (CSE) was given to help explain this effect, where supressed pulse electrons were shown to follow a longer and slower motion before being accelerated and subsequently emitting, resulting in longer elongated trajectories. Whereas electrons that contribute to the improvement of the attosecond pulse strength are shown to experience a larger field before and during emission. This meant their velocity and acceleration components were larger than the suppressed electrons, giving them more energy as it is driven back into the plasma.
Overall they state that the larger the electric field experienced by the electrons increases the intensity of the reflected attosecond pulse, due to the number of electrons travelling in a dense bunch increasing as this larger field that the electrons near the surface experience compresses them into higher density bunches.
Another study performed by Yeung et al, 2016, focused on controlling the attosecond motion of strongly driven electrons at the boundary between the pre-formed plasma and the vacuum. They demonstrated experimentally that by precisely adding an additional laser field, at the second harmonic of the fundamental driving frequency, attosecond control over the trajectories of the dense electron bunches involved in intense laser-plasma interactions can be achieved. From this considerable improvements in the high-harmonic generation intensity was observed, which confirms the theoretical work by Edwards in two-colour fields reviewed previously while developing upon this to further factors.
Experimentally they showed that attosecond control over the phase relationship of the two driving fields is necessary to optimise the reflected attosecond pulse intensity. While also using PIC simulations to determine the optimal and worst phase relationships, in which a phase of was found to optimise the emission.
Microscopic focus determined that during each cycle the emission of the attosecond pulse begins as a primary electron bunch which is compressed and then quickly accelerated away from the surface up to relativistic velocities, from here it emits before it disperses and returns back to the plasma. Secondary bunches are also present but these were found not to have a significant effect harmonic spectrum for orders >20. These bunches were found to emit when their velocities where at their max, which confirmed that the two-colour field phase matched the emitted XUV to the acceleration produced from the fundamental laser field. While at the poorest phase relationship, which Yeung found to be , a plateau in the driving laser field is created which impedes the acceleration of the electrons from the surface, therefore reducing the density of the electron bunch produced that can emit.
They concluded from the data provided by the simulations that control of the relative phase of the two colour driving fields has a significant effect the electron bunch dynamics.
While from the experimental data their collected it was demonstrated that the HHG produced from the two-colour field was increased substantially when no laser pre-pulse was involved, or equivalently when the plasma has shorter density scale length. Confirming the work of Edwards et al, 2014, that two-colour fields generate significantly more higher-harmonic orders than that of a fundamental field alone, even when only a small percentage (5%-10%) of the fundamental laser energy is converted to the second harmonic.
INTRODUCTION TO TWO-COLOUR HARMONICS
———————-
ABSTRACT

BRIEF SUMMARY OF EXPERIMENT, RESULTS AND CONCLUSION 1x

INTRODUCTION

BRIEF HISTORY .5x
HHG PRODUCTION .5x
CWE 1x
ROM 2x (inc. plasma theory e.g. scale length)
CSE 1x
COMPARISON WITH GAS EXPERIMENTS 1x
PAST EXPERIMENTS LEADING UP TO THIS ONE 2x
INTRODUCTION INTO SPECIFICS OF THIS EXPERIMENT 1x

METHOD

PIC CODES EXPLAINED 2x
EPOCH DETAILS 1x
LASER DETAILS 1x
PROCESS OF ANALYSIS .5x
CREATION OF GRAPHS .5x

RESULTS

GRAPHS
COMPARE & CONTRAST
IMPLICATIONS

CONCLUSION

FURUTRE RESEARCH 1x
IMPROVEMENTS 1x      

Effect of Nuclear Radiation on the Environment

 
Introduction
By the early 17th century, certain electrical devices and power generators were being invented by certain scientists, who did not yet know that they were scratching the surface to a much more dangerous form of energy, to be discovered by scientist Einstein a few centuries later. This form of energy to be produced through a substance named Uranium was to be introduced as a more efficient power source. However, the process with which this energy was created was to be exploited, which would result in what is known today as “The Weapons of Mass Destruction.”

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The use of such form of powerful energy for certain military uses can result in horrific results. A quick study shows that even a minor war would quickly decline the world climate and environment, inflicting harm that could last for decades. Richard Turco, a scientist at the UCLA said that exploding only between 30 and 70 missiles – just 0.03% of the entire storage – would cause enough pollution to create climatic disasters unseen before in human history. He also said the effects would be “much greater than what we’re talking about withglobal warming and anything that’s happened in history with regards volcanic eruptions.” Summarily, it can alter and damage not only the atmosphere, but also all forms of life such as humans, animals, and plants. (Jha)
The Invention of Nuclear Power and Missiles
Problems Encountered During Creation:
The invention mainly started to take place during midst 1939, just before the beginning of the second Great War. It all commenced when Albert Einstein and several other scientists wrote to President Franklin D. Roosevelt, informing him of the Nazi’s efforts to cleanse and exploit Uranium-235, which could be used to build a weapon of mass destruction. It was at that moment that FDR decided to begin “The Manhattan Project”, which was simply to produce a viable nuclear bomb. However, there were many complicated issues to be faced. The most significant of these issues was the inability to extract “enriched” uranium to maintain a series of reactions. Back then, uranium-235 was extremely difficult to extract, and the ratio of extracted ore to uranium metal was as low as 500:1. Furthermore, over 99% of the refined metal from the ore was uranium-238, which was rendered useless for the invention of an atomic bomb. The two different types of isotopes were nearly identical in their chemical makeup, and only possibly separated by mechanical means.
Solution of the Problem and Testing of the new Invention:
Soon thereafter, a massive enrichment lab was erected at Oak Ridge, Tennessee. Harold Urey and his colleagues came up with an extraction system, which worked on the principles of gas diffusion, while Ernest Lawrence put into action a process which involved magnetic force to separate the two isotopes. A gas centrifuge was then used to separate the lighter uranium-235 from the heavier uranium-238. After this separation, all that was needed was for the scientists to put the concept of atomic fission (which involves splitting the atom) to the test. Overall, approximately two billion dollars were invested into “The Manhattan Project.” Throughout the entire path, it was a scientist by the name of Robert Oppenheimer who oversaw the progress of the campaign from beginning to end. Finally, the day of testing arrived. It was on July 16, 1945 where it would be found out if the entire project was just a complete dud, or if it would put an end to the massacre. Upon placing the missile in the sea, a massive white blast took place. The light turned red as the power of the explosion shot upwards at 360 feet per second. The explosion resembled the shape of a mushroom. “The Manhattan Project had been a success.” (Bellis)
Effect of Nuclear Radiation on Humans
Immediate (Short Term) Effects:
Survivors of such a devastating blast will be killed within a few days due to radioactive fall-out. The severity of the fall-out will be determined by whether the nuclear bomb explodes in mid-air, or upon impact with the ground. The first of these will leave a larger blast impact. The latter, however, will throw much higher quantities of radioactive debris into the surrounding atmosphere. The area included in this fall-out is strictly dependent upon the wind speed and its direction. The heavier the particle of radioactive debris, the higher the chance it drops in close vicinity. Smoother and rather smaller particles, however, are thrown over longer distances before their fall. Some of these particles are so fine that they can combine with vaporized water and fall as radioactive rain 1700 miles from the original blast. Anyone who is in the range of this radioactivity will suffer from hair loss, internal bleeding, fever, bleeding from the gums, and terminal coma. Much of these have no effective medicine and are fatal. (Carnegie)
Long Term Effects:
Genetic studies on the children of nuclear bomb survivors who were exposed to the atmosphere afterwards was conducted by the Atomic Bomb Casualty Commission and the Radiation Effects Research Foundation ever since 1948. The analysis of past studies shows signs of abnormal pregnancy outcomes: deformation, stillbirth and early child death. Other effects include chromosome aberrations. Chromosome aberrations can be defined as an extra, irregular, or missing portion of a certain chromosomal DNA. This alteration of chromosomes can cause several inborn diseases due to aneuploidy. An example of such a human disease is Down syndrome, where the affected have three copies of chromosome 21 instead of a natural two. (Nakamura)
Effect of Nuclear Bombs on the Climate and Atmosphere
General Effects on the Climate:
Although there has been a two-thirds decrease in the world’s nuclear arsenal since 1987, scientific research clarifies that the results of even a minor nuclear war can end human history and leave mother earth inhabitable. Studies conducted at several U.S universities predict that the explosion of a tiny amount of the global nuclear storage within large metropolitan areas would cause catastrophic disruptions in the Earth’s climate and massive destruction of out protective ozone layer. Studies conclude that a small or rather regional conflict between two nations such as India and Pakistan would disrupt the climate for decades to come.
Details:
In a small-scale war, denotation of about 100 Hiroshima-sized bombs – under half a percent of the world’s arsenal- would send over five million tons of soot and smoke over cloud-level. This could prevent almost 10% of the sunlight from reaching the northern hemisphere; this smoke and soot can remain in the atmosphere for a couple of decades. This would cause average surface temperatures beneath this layer to become lower than it has ever been in the last 1000 years. However, if a large-scale war event was to take place, and the United States and U.S.S.R ere to launch their full arsenal, over 150 million tons of smoke would rise above cloud-level. This would block over 75% of sunlight from reaching the northern hemisphere, and 30% of sunlight from reaching the southern hemisphere. Under such extreme and severe conditions, it only requires a few days for the temperatures to drop below freezing levels in agricultural areas. Average surface temperatures would become colder than it has ever been in the past 18,000 years which coincides with the peak of the previous ice age. Rainfall would decrease by 90%, growing seasons would be completely eliminated, and the majority of the human and animal populations would die of starvation.
 

Interaction of Electromagnetic Radiation: Quantum Structures

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.

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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 Ψa and Ψb 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.
Ψ(0) = Ca Ψa + Cb Ψb
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, Ψ(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
ÄŠa =
And
ÄŠb =
Where ÄŠa and ÄŠb 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,
ÄŠa =
ÄŠb =
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.
Ψ 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 Ψa and Ψb should be of opposite parity since z is odd. In addition, direction of P depends on Ψa and Ψb. 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.

Polarization

Ex

Ey

Ez

Propagation along z

Forbidden

forbidden

Impossible

Propagation along x

Impossible

forbidden

Allowed

Propagation along y

Forbidden

impossible

Allowed

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.
 

Low Temperature Radiation Response of SiGe HBTs

Abstract. Radiation degradation rate of base current in SiGe HBTs was experimentally investigated using X-ray irradiation source with Cu anode at room and low temperatures. The dependences of base and collector current on the emitter-base voltage of the transistors were measured during radiation impact and presented for different total dose levels and irradiation conditions.

Introduction

SiGe HBTs are widely used in modern high-frequency electronic devices due to low cost and compatibility with convention silicon technology. There a lot of different applications of high-frequency devices based on SiGe transistors. Excellent balance of electrical performance and compatibility properties of SiGe technology provides a wide range of possibilities for applications of SiGe devices in special operation conditions such as front-end-electronics of particle accelerators or data communication equipment of space-crafts. The common property of both cases is radiation impact during operation. For accelerator applications, it is high energy slowing-down radiation [1]. In the space environment, the main reason of radiation damage of electronics is the impact of protons and electrons from radiation belts of the Earth [2], which can be simulated in laboratory conditions by Co-60 or X-ray sources [3].

As in conventional silicon devices, the radiation impact leads to accumulation of interface traps at the interface of chip substrate and a passivation layer in SiGe transistors. The interface traps act as recombination centers and increases surface component of base current [4]. The increase of base current reduces current gain of the transistors and leads to parametric and functional failures of semiconductor microelectronic devices.

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Unlike accelerator applications, the operation temperature of electronic devices during space mission varies in a wide range. The most typical for temperature values for space applications are near the low limit of the operation temperature range. It was experimentally obtained, that low-temperature irradiation reduces the degradation rate of conventional silicon devices [5]. Since it increases failure total dose level, we can consider this feature as very useful. The main purpose of this work is to investigate the degradation rate in SiGe transistors for room and low temperature irradiation.

Experimental equipment

As in conventional silicone devices, main electrical performance characteristics of SiGe transistors are the dependences of base and collector current on emitter-base voltage at a fixed bias of the collector junction. Using this data, we can determine the current gain for any emitter junction bias. To perform set different values of emitter junction bias and to measure base and collector currents during irradiation an experimental installation was used. The structure diagram of the installation is presented in Fig.1.

Figure 1. Structure diagram of the experimental installation

To perform measurements during irradiation, a SiGe-transistor is soldered into printed circuit board (7) with a resistive temperature sensor. The board (7) is in good thermal contact with the active surface of temperature control device (6), the base of thermoelectric modules (Peltier elements). The temperature control device and the board with SiGe-transistor are located in X-ray chamber (8), which involves X-ray source with Cu-anode. The energy of the X-ray beam is 8 keV. The temperature control device and the board with SiGe-transistor are connected with measure (3) and control (4) devices respectively by cable (5). General control and the user interface are provided by the computer (1) through cable (2).

The experimental installation has followed performance parameters:

–       available voltage range: -10.0 V … 10.0 V

–       absolute voltage accuracy: ±1.0 mV

–       available current range: ±0.1 nA … ±100 mA

–       relative current accuracy: ±1%

–       available temperature control and stabilization range: -400C … +1250C

–       absolute temperature stabilization accuracy: ± 0.10C

–       available range of irradiation dose rates: 1.0∙10-3 rad(Si)/s … 50 rad(Si)/s

Experimental results and discussion

For experimental investigations, a sample of commercial available BFU768F SiGe transistor was selected. The BFU768F are NPN wideband silicon germanium radiofrequency bipolar transistors manufactured by NXP Semiconductor in the plastic SOT343F package.

The dependences of base and collector currents of the transistor were measured at various emitter-base voltage values and zero collector junction bias. The dependence of current gain on emitter junction bias was calculated using measured data. The measurements were performed at (25.0±0.1)0C.

The irradiation of the sample was performed at 10 rad(Si)/s by X-ray source with Cu-anode in three steps. During the first step, the temperature of the sample was 250C. The second and the third irradiation steps were performed at -400C. After each step, the measurements were performed at (25.0±0.1)0C. The dependences of base current and collector current on total dose are presented in Fig.2 during the first step, after the second step and after the third step of the irradiation. The dependence of base and collector current measured at (25.0±0.1)0C on emitter-base voltage before irradiation and after each irradiation step and corresponding current gain data are presented in Fig.3.

           a)                                                                              b)

Figure 2. Dependence of base current on total dose during irradiation steps (a); Dependence of collector current on total dose during irradiation steps for BFU768F SiGe-transistor

              a)                                                                          b)

Figure 3. Dependence of base and collector current measured at (25.0±0.1)0C on emitter-base voltage before irradiation and after each irradiation step (a) and corresponding current gain data (b) for BFU768F SiGe-transistor

From Fig.2 and Fig.3 it is clear, that, as in conventional silicon transistors, current gain radiation degradation is connected with radiation-induced an increase of base current because collector current doesn’t depend on the total dose significantly for all the emitter-base voltage range. From Fig.4 we can see, that, unlike conventional silicone transistors, the decreasing of the irradiation temperature down to -400C doesn’t lead to decreasing of the radiation degradation rate. It can be explained by decreased oxide thickness over emitter-base junction in comparison with conventional silicon structure. Typical cross section of the SiGe bipolar structure is presented in Fig.4.

Figure 4. Typical cross section of SiGe bipolar structure [1]

Conclusion

As in conventional silicone transistors, the main reason of current gain degradation during radiation impact is increasing of surface component of the base current. Unlike silicon devices, the decreasing of irradiation temperature doesn’t decrease the rate of the radiation degradation of SiGe bipolar transistors. It can be explained by decreased oxide thickness over emitter-base junction in comparison with conventional silicon structure. To affect the radiation degradation rate of SiGe device, it is necessary to decrease irradiation temperature down to the low limit of operation temperature range.

References

[1] J. D. Cressler, 2013 IEEE Transactions on Nuclear Science. 60, 3

[2]   R. L. Pease, R. D. Schrimpf, D. M. Fleetwood, 2013 IEEE Transactions on Nuclear Science. 56, 4

[3]   L. N. Kessarinskiy, D.V. Boychenko, A. G. Petrov, P. V. Nekrasov,  A.V. Sogoyan, V. S. Anashin,  P. A. Chubunov, 2014 IEEE Transactions on Nuclear Science. 52, 2

[4] V. S. Pershenkov, D. V. Savchenkov, A. S. Bakerenkov, A. S. Egorov, 2009 Russian Microelectronics. 38, 1

[5]  P. C. Adell ;  I. S. Esqueda ;  H. J. Barnaby ;  B. Rax ;  A. H. Johnston, 2012 IEEE Transactions on Nuclear Science. 59, 6
 

Effects of Nuclear Radiation on the Environment

Nuclear power is generated through the use of nuclear fission. This process produces a large amount of heat and electricity. The nuclear waste and radiation that nuclear fission produces are harmful to living organisms; however, the benefits of nuclear power are too tempting to refuse.
As a testament to that fact, there are currently 437 nuclear power plants worldwide, generating a total of 372,210 megawatts worth of electricity. A further 68 nuclear power plants are under construction with an expected net output of 65,406 megawatts.
This report will outline the effects of nuclear radiation on the environment, including all biological organisms and the abiotic environment as well as both benefits and drawbacks.
Effects on Organisms
Using humans as an example, nuclear radiation have very detrimental and adverse effects on human beings. Being exposed to high amounts of radiation for an extended period of time will cause humans to experience radiation sickness. Symptoms of radiation sickness can include headaches, nausea, fevers as well as the possibility of obtaining cancer or causing severe damage to ones DNA.
Nuclear radiation consists of ionizing particles, which are particles that individually have enough energy to displace electrons in an atom or molecule. By forcibly removing an electron and taking its place, the particle forms an ion-pair that are immensely reactive. This reactivity can cause major damage to cells and DNA.
The Diagram shows how an Ionizing particle displaces an electron.
As seen in the previous diagram, the ionizing particle, represented in yellow, will have enough energy to “knock off” the electron of an atom, represented in green. The resulting ion-pair is very reactive and the reactions that follow can damage human DNA and tissue.
Radiation Chart: Relation between Dosage and Symptoms
Sieverts, or Sv, is the international standard for measuring radiation dosage. It is meant to measure the biological effects of ionizing particles. Below is a chart provided by environmental journalist Ben Jervey that shows the dosage as well as consequences of exposure to nuclear radiation.
The Effects of Nuclear Radiation on Plants and Soil
Similarly to humans and animals, plants and soil are also affected negatively from high amounts of nuclear radiation. Just like in humans, radioactive material can damage plant tissue as well as inhibit plant growth. Mutations are also possible due to the damage caused to the DNA. Radioactive material in soil can prevent nutrient from being taken in by plants, causing it to be infertile.

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The effects of nuclear radiation can sometimes change the biodiversity of an area completely. Taking the “Red Forest” in Chernobyl, Russia as an example, the area is filled with radioactive material such as Iodine-131 and Cesium-137 due to the nuclear power plant disaster. Many plants and organisms died within days of the disaster and the soil of the forest could not support life. However, after many years, as the radioactive material began to reach their half-life, sturdier plants and animals began to inhabit the contaminated zone. Although the Red Forest is still too radioactive for humans to settle in, it has been proven that the biodiversity of life within the forest is currently higher than it was before the nuclear disaster. The forest is now currently a wildlife refuge where all kinds of animal and plant species thrive.
Another example of nuclear radiation’s effects on soil is the Fukushima Daiichi nuclear disaster in Japan. The explosion at the nuclear reactor released clouds of radiation over much of Japan’s agricultural land. This caused crops to become irradiated and unsafe for consumption. The irradiated soil also bore irradiated plants or became infertile. Over 81,000 hectares of land were affected by the radiation. Unlike Chernobyl, where European soil is good at absorbing radiation, and thus limits the amount of radiation absorbed by plants, Japanese soil is sandy, offering less resistance to radiation. Due to the lack of crops and food, many of Japan’s consumers have to rely on aid from other countries or imports. This has put considerable stress on Japan’s economy, not including the $13 billion that will cost Japan to completely decontaminate the affected area. 
http://gdb.rferl.org/65D2A05D-CADB-40BA-92D2-533441CAE636_w640_r1_s.jpg
A Journalist checking radiation levels at Fukushima Daiichi power plant.
Radiation Therapy
Ironically, while radiation in high, uncontrolled doses can be detrimental and even fatal to a person’s wellbeing, it also has been proven that radiation can be used to treat certain health problems. The most significant of which are tumours and cancer cells. Radiation therapy is the use of x-ray, gamma rays or charged particles to kill cancer cells and reduce tumour growth. The treatment works by using the radiation to selectively damage the cancer cell’s DNA impeding or stopping its ability to replicate and grow. As the cancer cells slowly degrade, the human body’s natural defenses are able to naturally destroy the cancer cells.
Radiation therapy is not without risks. The radiation used is also very harmful to every other type of cell within the human body. This is why the radiation used is mostly in the form of a pin-point laser directed at an angle so as to not affect other tissue other than the cancer cells and tumours.
Food Irradiation
Another benefit of nuclear radiation can be found in our everyday lives in the form of food irradiation. As explained in the Fukushima case study previously, irradiation of food will make it unsafe for consumption, however, small amounts of nuclear radiation are able to kill bacteria and sterilize food, preventing spoilage. The amount of radiation needed for the process is so minute that it is safe for human consumption.
To emphasize the safety of the food irradiation process, only gamma rays are used, which means that no neutrons are present to cause radioactivity in the food. Furthermore, the source of the gamma radiation never makes contact with the actual foodstuff.
The extension of shelf life due to killing bacteria and other organisms can result in the lesser use of pesticide and preservatives in food. This also means that there is a lower risk of invasive species being exported to another country through the food. The increased spoilage time also allows for easier exporting over long distances.
Conclusion
Based on the information and case studies presented in this report, we can conclude that nuclear power and radiation can be both beneficial and harmful to humans and the environment. Nuclear energy is dangerous and unstable and may result in great damage to the environment if something goes wrong. However, if used properly, it can provide large amounts of energy for in place of fossil fuels and other non-renewable resources. Nuclear radiation has also proven to be effective in certain medical treatment and food processing that benefit humanity. On the other hand, many are skeptical about the use of radiation in everyday life due to the volatile and dangerous nature of radiation.