Pair Production - Conversion of Radiation into Matter

The cloud chamber experiments revealed that a Photon can give up its energy to materialize as two electrons of opposite charge. Certainly the Photon must have an energy of atleast 2mβ‚‘c² in order to produce a pair.

No photon, regardless of its energy, can produce a pair in a perfect vacuum.

Pair Production is strictly an Electromagnetic Process. It seems to occur mostly in the intense electric field near the nucleus rather than inside the nucleus.

At higher energies or with heavy targets it is typically reasonable to ignore the energy transferred to target, so that nearly all energy from Photon goes to electron-positron pair.

Energy equation

h𝜈 → 2mβ‚‘c²+E1+E2

holds approximately.

 mβ‚‘c²rest energy of each electron

 E1, E2 → Kinetic Energies of particles

 The heavier the target, the more nearly the equation is satisfied. 

Pair Production can occur in the vicinity of an electron.

Pair Annihilation

Positron and Electron coalesce to produce atleast two photons

e⁺ + e⁻→2𝛾

Annihilation into three or more Photons is possible but less likely. Each extra photon tends to supress the rate of annihilation by a factor of order of magnitude of fine structure constant 1/137.

A Positron moves thru matter and forms ion pairs giving up energy in the process. There is about 2% chance that a Positron will hit an electron and annihilate.

But more likely output is that Positron will stop and become attracted to an electron. The atom formed by these two particles is called Positronium.

The Positron-Electron system drops into successively lower energy states, emitting (low energy) photons, until it arrives in ground state.


Properties of Positronium

The lowest Bohr orbit of Positronium is one for which n=1 and l=0, so that the lowest is an S-state.

The S state has fine structure due to the spins of particles; when the two spins are oppositely directed, the atom is in a ¹S state. When the two spins are parallel, it is in a ³S state, and has higher energy.

The triplet state is a meta stable state and has longer life time than singlet state.

The life time of singlet state was revealed by J.Pirenne, J A wheeler and is of order 10⁻¹ΒΊ Sec.

The life time of Triplet state was revealed by Ore & Powell and is about 1.4x10⁻⁷ Sec.

Annihilation radiation emitted by combination of electron-Positron pair in ¹S state should consist of two gamma ray photons emitted simultaneously.

Radiation from ³S state of this system should consist of 3 𝛾 ray Photons emitted simultaneously.

The first experimental evidence for formation of Positronium was obtained by M. Deutsch, who observed time delay between emission of Positron from ²²Na and appearance of annihilation photon from substance in which Positrons are observed. Several gases N₂, O₂ etc are used as absorbers of Positrons. The time delay is due to formation of Positronium.

Properties of Pions

  • Pions are Mesons
  • There are 3 kinds of Pions: Ο€⁺, Ο€⁻, Ο€⁰
  • Either charged Pion possess a mass of 139.6 MeV and neutral Pion is 135.0 MeV.
  • Pions have spin zero.
  • P+P → Ο€⁺ + n + P
  • P+P → Ο€⁰ + P + P
  • P+n → Ο€⁻ + P + P

  • Charged Pions decay into Muons (Weak Process in Decay):

Ο€⁺ → πœ‡⁺ + 𝜈
Ο€⁻ → πœ‡⁻ + 𝜈

  • The mean life is 2.6 x 10⁻⁸ Sec. 

  • The neutral Pion decays in different way; process is 

Ο€⁰ → 𝛾 + 𝛾 ; This decay is Electromagnetic in nature.

The presence of photons in final state leads us to expect the process is electromagnetic in nature.

The Photons from the decay always seem to come from the spot at which Ο€⁰was produced in some bombardment process. The measurement of life time of such a short lived object is not easy but emulsion techniques provide enough spatial resolution so that in case of rare decay modes

 Ο€⁰ → 𝛾 + 𝛾
Ο€⁰ → 𝛾 + 𝛾 

it is barely possible to measure separation of electrons from place at which  Ο€⁰ was produced.

  •  The mean life of  Ο€⁰ is about 0.89 x 10⁻¹⁶ Sec.
 

CLASSIFICATION OF ELEMENTARY PARTICLES


How to calculate Electric Field from a Uniform Plane Sheet of Charge?

Assume that the sheet is infinite in extent and that the charge per unit area is 𝛔.

Considerations of symmetry lead us to believe that a field direction is every where Normal to Plane and if we have no field from any other charges in the world, the fields must be same in magnitude on each side.

Let us choose a Gaussian surface - a rectangular box that cuts thru the sheet as shown in figure below.





The field is Normal to these two faces. The two faces parallel to sheet will have equal areas say A.

As the electric field 'E' is parallel to area element dS;

∫E.dS = E∫dS = EA

The total flux from two faces is given by

∫E.dS1 + ∫E.dS2 = EA+EA

The total charge enclosed in the box is  𝛔A.

So according to Gauss Law, EA+EA = 𝛔A.

E=𝛔/2𝛆₀


What is Internal Conversion?

It is a process which enables an excited Nuclear state to come down to some lower state with out emission of a Gamma Photon. The energy ∆E involved in this Nuclear transition gets transferred directly to bound electron of atom. Such a electron gets knocked out of atom. Electrons like this are called conversion electrons and the process is called internal conversion.

It is interesting to note that wave mechanically, an atom electron spends part of its time inside a nucleus. This probability is highest for K-shell electrons which are closest to Nucleus. For such a case, Nucleus may de excite not by Ζ”- emission but by giving excitation energy ∆E directly to a K-shell electron.

Internal conversion is also possible for higher atomic levels L,M etc.

The kinetic energy of converted electron 'Ke' is Ke=∆E-Bβ‚‘

  Bβ‚‘ - atomic binding energy of electron

∆E = Ei-Ef ; Nuclear Excitation energy

Usually continuous 𝜷-spectra are super imposed by discrete lines due to conversion.

It was wrongly believed that internal conversion process is like Photoelectric effect; a Ζ”-photon emitted by a nucleus is absorbed by orbital electron which is emitted as in photoelectric effect.

The simplest situation which disproves this is a transition between two states having spin equal to zero.

A 0→0 transition (∆I=0) is forbidden for all multipole orders and so Ζ”-emission by nucleus is completely forbidden.

However 0→0 transition is readily found to proceed by internal conversion. The experiment was performed on 0.7MeV level of ⁷²Ge. This is a 0→0 transition and it was found that conversion electrons can be detected, but there is a complete absence of Ζ”- ray emission.

In 1932, Taylor and Mott suggested that transition probability 'Ξ»' from a Nuclear state 'a' to a Nuclear state 'b' is sum of two terms

Ξ»=Ξ»β‚‘+Ξ»α΅§

Ξ»β‚‘ & Ξ»α΅§ are partial decay constants for conversion electron emission  and for gamma emission respectively.

Ratio between two decay constants is called conversion coefficeint and is measured as ratio between total number of conversion electrons emitted  (N) and total no. of gamma rays (N) emitted in same transition over the same time.

Conversion Coeff(Ξ±) = Nβ‚‘/Nα΅§=  Ξ»β‚‘/Ξ»α΅§

 value of 'Ξ±' is found to depend on transition energy, multipole character of transition and atomic number Z.  

Born-Haber Cycle


PROPERTIES OF CRYSTAL STRUCTURES


The Seven Crystal Systems and Fourteen Bravais Lattices


ALL ABOUT HELIUM-I & HELIUM-II

Helium was the last gas to be liquefied on account of having lowest critical temperature -268 C of all known gases.

It is a colorless transparent very voltaile liquid and has the lowest boiling point at 4.2K at a pressure of 
1 atmosphere.

A peculiar property arising in the Helium system  is that solid cannot be obtained merely by lowering the temperature of the liquid.

Kamerlingh Onnes failed to solidify Helium despite the fact that he has reached a temperature of 0.84K.

Solid Helium was first obtained by "Keesom" who subjected liquid Helium to very high pressures. The solid is obtained at a pressure of 250 atm at 4.2K while it soldifies at only 23 atm at 1.1K.

Thus it is necessary to increase the pressure simultaneously while lowering the temperature of liquid.

Later investigations revealed that at high enough pressure, solid Helium could be obtained in equilibrium with the vapor at temperatures well above the critical point of gas. Thus at 5800 atm, solid Helium is obtained at a temperature as high as 42K. This is the curious property of Helium system that although liquid cannot exist above the critical temperature(5.2K), solid can exist if sufficiently great pressure is applied. Hence at high enough pressure, the melting pressure, the melting point exceeds the critical temperature and solid Helium melts to form gas.

The phase equilibria of Helium are represented diagrametically in Fig.


Phase diagram shows that it is entirely different from that of all other substances.

The fusion curve(or solid liquid phase line) and the saturated vapor pressure curve (or liquid vapor phase line) do not meet in a point, as in case of other substances and if we pursue the vapor pressure curve down to lower temperature it is found that the vapour and the liquid continue to be in equilibrium down to the absolute zero. Thus the 3 phases solid, liquid and vapor are never found to coexist or in otherwords, Helium has no triple point in conventional sense.

The helium will not solidify even at 0K if it is not subjected to pressures exceeding 25 atmospheres.

The SVP curve on the other hand, appears to proceed normally to the left towardsthe Origin(P=0, T=0) but to the right it terminates at critical point corresponding to a temperature of 5.2K and a pressure of 2.26 atmospheres.

The point A(2.19K) is known as the Lambda point of liquid Helium under its own pressure.

Phase Transition (Lambda Transition)

This transition divides the liquid state into two phases, Helium I and Helium II.

The fusion curve and SVP curve are joined by the Lambda line running between the points 'E'(T=1.75K, P=30atm) and A(T=2.19K and P=0.05atm) with Helium-I to its right and Helium-II to the left.

Thus, Helium is present in the liquid form on either side of Lambda line.

Kamerlingh Onnes, in course of his investigations found that liquid Helium shows an extremely interesting behavior if it is cooled below its boiling point (4.2K) to about 2.18K, he found that the density passes through an abrupt maximum at 2.19K decreasing slightly there after as shown in Fig.

The density first rise with fall of temperature from 4.2K up to 2.19K reaches a maximum value 0.1262 at 2.19K and then decreases with the decrease of temperature.

Thus below 2.19K, the liquid Helium which was contracting when cooled now begins to expand.

Specific Heat of liquid Helium at constant volume:

Cv increases upto 2.19K and at this temperature there is a sudden an abnormal increases in its value.
Beyond 2.19K the specific heat first decreases and then increases.

The Specific Heat temperature graph at 2.19K looks like the Greek letter Lambda and hence this temperature at which specific heat changes abruptly is called Lambda point.

Liquid Helium above 2.19K which behaves in a normal way is called liquid Helium-I.

Liquid Helium below 2.19K is called liquid Helium-II because of its abnormal properties.

No heat is evolved or absorbed during the transition from one form of Helium to another i.e. No latent heat is involved in He-I to  He-II and vice versa transition which suggests that 

a) The entropy is continuous across the curve i.e. The entropy of He-II is same as that of He-I.
b) There is no change of density during transitions i.e. density of both types of liquid is about same. 

while the viscosity of liquid increases with decrease in temperature, that of liquid He-I decreases showing He-I resembles a gas.

The viscosity of He-II is almost zero.

Peculiar Properties of Helium-II

A) Super Fluidity




At Lambda Point, the rate of flow increases abruptly and below it, the flow is found to be extraordinary large thus proving experimental evidence of a very low viscosity of liquid He-II.

The values of viscosity coefficient plotted as obtained by oscillating disc method.


There is a sharp discontinuity at Lambda point. The viscosity falls by a factor of about ten on passing through the lambda point.

Kapitza found that Ratio of Viscosity of HeliumII to HeliumI is approximately 10^-3.

Thus liquid He-II has practically zero viscosity and can flow rapidly with out resistance. This property is known as Super fluidity.

B) High Heat Conductivity


Helium-II is found to have an extraordinary high coefficient of thermal conductivity.
The heat transported per unit temperature gradient is several 10 times as great as that in copper at room temperature.
He-II is said to be about 800 times more conducting than copper.

It is found that heat flow in He-II is not proportional to temperature gradient.

Daunt and mendelsohn pointed out phenomenon of superconductivity in He-II.

C) Formation of films over solid surfaces


Liquid He-II can creep along solid surfaces in the form of high mobile film generally known as "Rollin" (also called as Rollinsimon) film.

The properties of film were investigated by Daunt and Mendelsohn.

If a tube containing Helium-II is placed in Helium-II bath

a) If liquid level inside tube is less, flow of liquid takes place from bath to tube.
b) Flow from tube to bath.
c)  Liquid inside the tube creeps out along surface of tube collects at its bottom in form of drops and falls into bath till tube becomes empty.

Thus liquid He-II seems to defy gravity by creeping out of containing vessel by coating the walls with a thin film of the liquid.

What is Sputtering?



If a surface is bombarded with an energetic particle it is possible to cause ejection of surface atoms. This process is called sputtering. These ejected atoms could be condensed on to a substrate to form a thin film; this process can be realized by forming positive ions of heavy neutral gas such as Argon gas and bombarding the surface of target material by making the surface of cathode in an electrical circuit.

Basic Principle
When a charged particle strikes a surface a variety of interactions are possible. The most important reactions are shown in figure.

(a) Ejection of neutral atoms of surface material.

(b) Ejection of small no of charger atoms of surface material.

(c) Ejection of free electrons, the no. of free electrons usually greaker than io for each arriving incident ion.





Observed points

1) The first major effect in this method is that the neutral ejected atoms can be collected on a suitably placed substrate to form a film.

2) The second most important effect is that the electrons ejected can be accelerated from target cathode to a suitably anode.

3) On the way to anode they can cause for their ionization which helps to enhance sputtering head.

a) Cathode to Anode spacing : 15 cm

b) Pressure: 10-2 Torr.

Summary of observed salient features

i) The sputtering yield defined as the average no. of atoms ejected from target per incident ion, increases with increasing energy of incident ion.

ii) Also depends on atomic weight of target.

iii) Sputtering threshold exist within 5eV and 25ev for most of materials. Yield increased rapidly beyond the threshold shows some linearity in beginning and then approaches saturation.

iv) The yield depends on angle of incidence. It increases approximately as cosent angle between normal to the target surfaces and beam direction.


v) The yield as a function of atomic number of target displays an unduality behavior.


vi) The yield is rather in sensitive to target temperature.

vii) The ejected atoms have considerable energy. The distribution is Maxwellian.

viii) With increasing bombarding energy, the peak of curve shifts slightly towards high energy.

ix) The peak energy of ejected atoms increases with angle of ejection. However a decrease occurs for large angles greater than angle of ejection.

x) The ejected particles are considerably single atoms however in case of copper or silver at high energies some percent of ejected particles, clusters consists of two or three atoms.

xi) The ejected atoms will be in excited state and show characteristic recombination light emission.

Advantages
sputtering offers many advantages over other deposition techniques such as

1) You can get film of multi component material such as Alloys.

2) Irrespective of melting point, refractive materials films can also be prepared.

3) Insulating materials.

4) Good adhesion

5) Low temperature epitaxy

6) Thickness uniformity over large plane of areas.

Limitations

i) The source material must be available in sheet form.

ii) Deposition rates are usually less than 2000 per minute.

iii) Substrate material should be cooled.

THEORY OF SPUTTERING

1) Transfer of energy

2) Transfer of momentum

3) Radiation

 
The hot spot of evaporation theory yield at experimental evidence. Later developments showed that sputtering is not an energy transfer but rather a momentum transfer process. It considers sputtering as resulting of double or triple collisions of ion with in lattice atoms followed by its back reflection by lattices.

More sophisticated theories consider the sputtering as essentially a radiation damage phenomenon. Accordingly the incident ion displaces a no. of atoms (knocks on) during its passage thru material and thus loses its energy. Some fraction of knocked – on atoms will diffuse to surface and emerge as sputtering atoms.

The Knocked on atoms may also have sufficient energy to produce additional atoms which contribute to total sputtering yield.

The exact details of interaction of an ion with target atom depends on

a) Target atom

b) Momentum Transfer

c) Collision means free path.

Different Kinds of Sputtering techniques:

1) Glow discharge sputtering

2) Reactive sputtering

3) Bias sputtering

4) Triode sputtering

5) Ion beam sputtering

6) RF sputtering


CATHODIC SPUTTERING
The deposition of metal film by sputtering form a cathode by glow discharge method was first observed by groove.

The ejection of atoms from cathode surface by impinging of energetic positive ions of noble gases such as helium, argon, neon, krypton at a reduced pressure under high dc voltage gives rise to sputtering phenomenon.

It is now possible to make various resistive, semiconducting, superconducting and magnetic films by this technique in better way.

If the process doesn’t involve any chemical reaction between bombarding gas ions and the cathode is known as Physical sputtering.

On the other hand, some reactions are involved then it is termed as Reactive sputtering.

Both the types of sputtering are carried out in poor vacuum and are known as high pressure sputtering.



The mechanism of process involves a momentum-transfer between the impinging energetic ions and cathode surface atoms as a result of which physical removal of atoms takes place.

Sputtering yield increases with the energy and mass of bombarding ions and also with decrease of angle of incidence to the target. A minimum energy is required to start the sputtering process. Sputtered atoms have much higher energies than those of the thermally evaporated ones. Sputtering yield also decreases with large increases of ion energy because of deeper penetration of ions or neutrals inside the lattice.

Sputtering is also accompanied by the emission of secondary electrons from cathode surface. Auger transitions (radiation less) also take place along with emission of secondary electrons.

TUNNEL DIODE - DETAILED EXPLANATION



We know that a conventional PN Diode is doped by impurity atoms in the concentration 1 part in 108 . With this order of doping, there exists a potential barrier of order 5 microns which restrains the flow of majority carriers to the side of where they constitute minority carriers.
If the concentration of impurity is greatly increased, (by about 1000 times) in a PN Junction diode then the potential barrier width reduces from order of 5 microns to less than 100 A0  . This thickness is only about one-fiftieth of wavelength of visible light. And thus the devices characteristics are completely changed.

“Esaki” introduced a new device, and it is names as “Tunnel diode” as it uses the phenomenon of “Tunneling”.

“A Tunnel diode is a high conductivity two terminal P-N diode doped heavily about 1000 times higher than a conventional diode”.

The heavy doping produces following effect:
(i)                  Width of Depletion layer is reduced.
(ii)                Reverse breakdown voltage reduces to a very small scale.
(iii)               It produces a negative resistance section on V-I Character





From above fig, Tunnel diode is an excellent conductor in Reverse direction i.e when it is Reverse biased.For as soon as forward bias is applied, significant current is produced. The current quickly reaches its peak value ’Ip’ when the applied forward voltage reaches a value ` Vp’.
At the peak current ‘Ip’ corresponding to voltage ‘Vp’, the slope dI/dV of characteristic is zero.

This current variation in the vicinity of origin is due to quantum mechanical tunneling of electrons through narrow space charge region of the Junction.
When ‘V’ is increased beyond ‘Vp’, the current decreases. As a consequence, the dynamic conductance
g = dI/dV is negative. The current reduces to its minimum value ‘Iv’ (valley current) at ‘Vv” (valley voltage).

Tunnel diode exhibits ‘ Negative resistance characteristic’ between Ip & Iv.

At valley voltage Vv at which I=Iv, The conductance is again zero, and beyond this point the resistance becomes and remains positive.

At the so called peak forward voltage ‘Vf’ the current again reaches the value ‘Ip’ and for larger voltages the current increases beyond this value.

SYMBOL:
Standard circuit symbol for a Tunnel diode is given by
 
 Uses of a Tunnel diode:-
Γ¨         For currents whose values are between ‘Iv’ and ‘Ip’, the curve is triple valued, because each current can be obtained at three different applied voltages. It is this multi valued featured which makes Tunnel Diode useful in “Pulse and Digital circuitry”.
       
     It can be used as a very high speed switch. Since Tunneling takes place at speed of light, the transient response is limited only by a shunt capacitance (Junction Plus stray wiring capacitance) and peak driving current switching times of order of  a nano second are reasonable, and times as low as 50 pico sec have been obtained.

       Tunnel diode can be used as a very high frequency (microwave) oscillator.

Manufacturing of Tunnel diodes:
Γ¨        The most Common commercially available tunnel diodes are made from “Germanium” or “Gallium Arsenide”. It is difficult to manufacture a silicon tunnel diode with a high ratio of peak to valley current Ip/Iv.
Γ¨      
      The below table summarizes important static characteristics of these devices. The voltage values are almost independent of current rating.

Ge
Ga AS
Si
Ip/Iv……
Vp,V….
Vv,V…..
Vf,F…….
8
0.055
0.35
0.50
15
0.15
0.50
1.10
3.5
0.065
0.42
0.70


Note:
  • Gallium Arsenide has highest ratio Ip/Iv and lagest voltage swing Vf-Vp ⩯͌ 1.0 V as against 0.45V for Ge.
  • The peak current ‘Ip’ is determined by impurity concentration (resistivity) and Junction area.
  •  The peak point (Vp, Ip) which is in tunneling region is not a very sensitive function of Temperature.
  • The temperature coefficient of ‘Ip’ may be positive or negative depending upon impurity concentration and operating temperature, but temperature coefficient of ‘Vp’ is always negative.
  • Valley point ‘Vv’ which is affected by injection current is temperature sensitive. ‘Iv’ increases rapidly with temperature.
  •  Tunnel diodes are found to be several orders of magnitudes less sensitive to nuclear radiation than are transistors.

ADVANTAGES OF TUNNEL DIODE
  •   Low cost, Low Noise, simplicity
  •   High speed, environmental immunity, low power
 DISADVANTAGES
  • Low output – voltage swing
  • Fact that is a two terminal device, as there is no isolation between input & output and this leads to serious circuit design difficulty.
  • Transistors are preferred for switching times longer than several nano seconds.

Law of Conservation of Energy

Energy when considered in all its forms, is automatically conserved. The total amount of energy remains numerically constant in time (although some of energy may swap from one form to other).

Whenever one object exerts a force on another object - either a pull or push. Physics can introduce a Potential Energy (or other form of energy) such that a Law of Conservation of Energy holds.

This is ofcourse, a remarkable property of nature, not just a sign of Physicists ingenuity.

What is Fluid?

Substances capable of flowing are fluids. They don't have their own shape and they take shape of containing vessel. Fluid undergoes shear deformation continuously till force acts on it.

Liquid is a incompressible fluid as they are difficult to compress for practical purpose so they have definite volume. Gas is a compressible fluid. Their volume varies with temperature & pressure.

If we talk of ideal fluid then that fluid should not have Viscosity, Surface Tension and compressibility. But in nature all fluids have one or all properties depending on condition so they are called real or practical fluids. Hence they pose certain amount of resistance when set in motion.

Differences between Ionic, Covalent, Metallic & Vanderwall Bonds


What are Hydrogen Bonds?

This bond may be considered as a special type of dipole bond, but it is one that is considerably stronger. It occurs between molecules in which one end is a hydrogen atom. When a hydrogen atom is covalent bonded  to a relatively large atom such as Nitrogen, Oxygen or Fluorine a powerful permanent dipole is set up.


This is because the electron cloud tends to become concentrated around that part of molecule containing the Nitrogen, Oxygen and Fluorine Nucleus, thus leaving the positively charged Hydrogen Nucleus relatively unprotected.  


Consequently a strong permanent dipole is created that can bond to other similar dipoles with a force near that involved in the ionic bond.


 A good example of Hydrogen bond is water molecule.