Scanning Electron Microscopy (SEM)

Scanning Electron Microscopy (SEM)

  • In The energy of the primary in the electrons in the determines in the number of in the secondary in the electrons in the collected in the during in the inspection. in the emission of secondary in the electrons from the specimen in the increases in the as the energy of the primary in the electron beam in the increases until a in the certain limit in the is reached. in the Beyond this limit, in the collected in the secondary electrons in the diminish as the energy of in the primary beam in the increased, in the because in the primary in the beam is already in the activating in the electrons in the deep below in the surface of the specimen. in the Electrons coming in the from such depths usually in the recombine before reaching the surface for emission.
  • - Scanning Electron Microscopy (SEM)
  • Aside from secondary in the electrons, the primary in the electron beam in the results in the emission of in the backscattered in the (or in the reflected) electrons from in the specimen. in the Backscattered in the electrons possess in the energy than secondary in the electrons, and have a in the definite in the direction. As such, they can not be in the collected by a secondary in the electron in the detector, unless in the detector is directly in their in the path of travel. All emissions in the above 50 eV are in the considered to be backscattered in the electrons.
  • Backscattered in the electron in the imaging is useful in in the distinguishing one material from another in the since the yield of in the collected in the backscattered in the electrons in the increases in the monotonically with in the specimen’s in the atomic in the number. Backscatter in the imaging can distinguish in the elements with atomic in the number in the differences of at least 3, i.e., materials in the with atomic in the number in the differences of at least 3 would in the appear with good in the contrast on the image. For example, in the inspecting in the remaining Au on an in the Al bond pad in the after its Au in the ball bond has lifted in the would be in the easier using in the backscatter in the imaging, since in the Au islets in the would stand in the out from in the Al background.
  •  In the SEM may be equipped in the with an in the EDX analysis in the system to enable it in the perform compositional in the analysis on in the specimens.  EDX in the analysis is useful in in the identifying materials and in the contaminants, as well in the estimating their in the relative in the concentrations on in the in the surface of the specimen.

- Scanning Electron Microscopy (SEM)
In a conventional in the transmission in the electron in the microscope, a thin in the specimen is irradiated in the with an electron in the beam of uniform in the current density. in the Electrons are emitted in the from in the electron gun and in the illuminate in the specimen in the through a two or three stage in the condenser lens in the system. in the Objective lens in the provides in the formation of either in the image or diffraction in the pattern of in the specimen. in the electron in the intensity distribution in the behind the specimen in the magnified with a 3 or 4 stage lens in the system and viewed in the on a fluorescent in the screen. in the image can be in the recorded by direct exposure of a in the photographic in the or an image plate or in the digitally by a CCD camera.
- Scanning Electron Microscopy (SEM)
 in the acceleration voltage of up to date in the routine instruments is 140 to in the 2000 kV. Medium-voltage in the instruments in the work at 200-500 kV to in the provide a in the better transmission in the and in the resolution, and in the high voltage in the electron in the microscopy (HVEM) the in the acceleration voltage is in the range 500 kV to 3 MV. Acceleration in the voltage determines in the velocity, in the wavelength and hence in the resolution ( in the ability to distinguish in the neighbouring in the microstructural in the features) of the microscope.
Depending on in the aim of the investigation in the and in the configuration of the microscope, transmission in the electron in the microscopy can be categorized as :
- Scanning Electron Microscopy (SEM)
Conventional in the Transmission Electron Microscopy
High in the Resolution in the Electron in the Microscopy
Analytical in the Electron in the Microscopy
A Energy-Filtering in the Electron in the Microscopy
 in the High Voltage in the Electron in the Microscopy
Dedicated in the Scanning Transmission in the Electron Microscopy

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Scanning Tunneling Microscopy lecture-2

Small Movements
To get in the distance in the between in the tip and the sample down to a in the couple of in the Angstroms.
where the tunneling in the current is at a measurable in the level, STMs use in the feedback servo in the loops and converse in the piezoelectricity.
- Scanning Tunneling Microscopy lecture-2
Servos are small in the in the devices with a shaft that can be in the precisely in the controlled with electrical in the signals.
Servos are in the used all the time in radio in the controlled in the cars, in the puppets, and in the robots.
Converse Piezoelectricity
Piezoelectricity is the ability of certain in the crystals to in the produce a voltage when in the subjected in the mechanical in the stress.
When you apply an electric in the field to a piezoelectric in the crystal, the crystal in the distorts. This is known as converse in the piezoelectricity. In the distortions of a piezo in the usually on the order of micrometers in the , which is in the scale in the needed to keep in the tip of the STM a couple in the Angstroms from in the surface.
Problems and Solutions

  •  in the Bringing the tip close to the surface and in the scanning in the surface.
  • Feedback Servo Loops
  •  in the Keeping in the tip close to the surface.
  • Converse Piezoelectricity
  • Creating in the very fine tip.
  • Electro-chemical etching
  • a Forces in the between tip and in the sample.
  • Negligible in most cases
  • A Mechanical in the vibrations and in the noise.
  • Soft suspension of the microscope within an ultra high vacuum chamber (10-11 Torr)
  •  in the Thermal length in the fluctuations of the sample and in the especially the tip.
  • Very low temperatures

- Scanning Tunneling Microscopy lecture-2
See by diagram
The original in the STM design had the tunnel in the unit with in the permanent in the magnets levitated on a in the superconducting lead in the bowl. They used 20 L of liquid in the helium per 2 hour.
Uses of STM
Measuring in the high precision in the optical components and in the disk drive in the surface in the roughness of machined or ground in the surfaces is a common in the use for STM.
- Scanning Tunneling Microscopy lecture-2
in the Below is a trace of an individual in the turn mark on a diamond- in the turned aluminum in the substrate to be used for in the subsequent magnetic in the film deposition for a high in the capacity hard in the drive.
By measuring in the variations in current, in the voltage, tip/surface in the separation, and their in the derivatives, the electronic in the properties of different in the materials can be studied.
One such in the element in the studied was the bucky ball (C60). When you in the press down on a bucky in the ball by 1/10th nm, it lowers in the resistance of the bucky in the ball by 152 times.
Different STM Ideas
You could in the decide not to use in the piezoelectricity to keep in the distance between 2time  the tip and the surface in the equal at all times, in the  and instead use the current in the measurements to determine in the surface of a in the sample.
- Scanning Tunneling Microscopy lecture-2

  • You can scan in the much faster.


  • The surface in the must not have in the cavities more than a few in the Angstroms deep (an in the atom or 2 in the ) because of in the tunneling.
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Scanning Tunneling Microscopy lect-1

 Scanning Tunneling in the Microscope (STM)

in the STM is an electron in the microscope that
uses a in the single atom tip to in the attain atomic resolution.
- Scanning Tunneling Microscopy lect-1


in the scanning tunneling in the microscope was developed at IBM in the Zürich in the 1981 by Gerd Binning and in the Heinrich Rohrer who shared in the Nobel Prize for in the physics in 1986 because of in the microscope.

General Overview

  • An extremely fine in the conducting in the probe is held
  •  in the about an atom’s in the diameter from the sample.
  •  in the in the Electrons tunnel between the surface and the tip,
  •  in the producing an in the electrical signal.
  • vWhile it slowly scans in the across the surface,
  •  in the the tip is  raised in the and lowered in order to keep
  • the signal in the constant and maintain the distance.
  •  in the enables it  to follow in the even the smallest
  • details in the of the surface it  is scanning.

The Tip

As we will see in the later, is very important gh in the tip of the probe be a single in the atom.
Tungsten is in the commonly in the used because you can in the useElectro-chemical etching in the techniques to create very sharp in the tips like the one above.
Quantum Tunneling
- Scanning Tunneling Microscopy lect-1
Classically, in the when an object hits a in the potential that it doesn’t have in the enough energy in the pass, it will never go though that in the potential wall, it always bounces in the back.
in the English, if you throw in the a ball at a wall, it will bounce back in the you.
Now looking in the more in the depth at the case of tunneling in the from one metal to another. EF represents in the the Fermi energy. Creating a in the voltage drop in the between the two metals allows current.
in the Through a barrier, in the quantum mechanics in the predicts that the wave function in the dies off exponentially:
- Scanning Tunneling Microscopy lect-1
in the Where f(V) is the Fermi function, which in the contains a weighted in the joint local density of states. This a in the material property obtained by in the measurements.
in the Plugging in the typical in the values for m, d, and phi (where phi is the average in the work in the function of the tip and the sample), when in the d changes by 1 Å, the current in the in the changes in the by a factor of about 10!

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Laser Physics Lecture -3

Prof. Zohaib Metla

What is the matters and what a kind of a changes does a matter in the undergo?
in the Everything that in the has mass and volume is called a matter. All matter, in the regardless of state, in the undergoes physical and in the chemical changes. These changes can be in the microscopic or in the macroscopic.

Achieving inversion:  Pumping in the laser medium

More details see below diagrma pic
- Laser Physics Lecture -3
Laser INDUCED PLASMA in diagram
More details see below diagrams pic
- Laser Physics Lecture -3
Laser Ablation Response on materials diagrams 
- Laser Physics Lecture -3
Radiative  decay
When this  energy  is  delivered in the  form  of an in the electromagnetic (em)  wave,  in the process is  called  spontaneous in the  (or  in the radiative)  emission.
in the Spontaneous  emission  is  therefore in the  characterized by  the emission  in the a  photon  of energy
Nonradiative  decay
In The  energy  difference E2 – El is in the  delivered  in the some form of energy  in the other than em in the radiation  (e.g., it may in the go into  in thekinetic in the  or internal in the energy  of the  surrounding in the atoms  or molecules).
Probabilities  for Spontaneous, Stimulated and  Absorption, emission
Spontaneous  Decay:
in the rate  in the of decay  of the  upper state in the  population (dN2/dt)sp must be in the proportional toin the  the  population N2.
where in the minus sign  in the accounts  for  the  fact  that  in the time in the  derivative  is  negative.  The  coefficient A, in the introduced  in  this  way, is  a  in the positive constant called  the in the  rate  of spontaneous  emission  or
the  Einstein A  in the coefficient.
- Laser Physics Lecture -3
For  nonradiative  decay
in the  Spontaneous emission of the numerical V value of A  (and  b    )  depends only on the particular in the transition considered.  For nonradiative decay,  on in the other hand,      depends not  only  on in the  transition  but  also  on in the characteristics  of the surrounding in the  medium.
Stimulated emission:
where ( in the  dN2/dt)st is the rate at which transitions 5 to  1 occur as a  result  of stimulated emission and W21 is  the  rate of stimulated in the  emission.
Unlike  A, however,  W21 depends  not  only  on in the  particular in the  transition  but  also  on the  intensity in the  of the  incident  em wave in the  absorption

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Laser Physics Lecture -2

Definition of laser

  • A laser is a device that in the generates light by of a process called in the STIMULATED EMISSION.
  • in the acronym in the LASER stands for Light in the Amplification by in the Stimulated Emission of Radiation


  • in the Laser action is based on the amplification of a EM waves in the means of a forced r induced atoms or in the molecules  See by a diagram
  • in the laser radiation uses 3 fundamental in the phenomena when EM waves in the interact with the matter a namely.
  • See by diagram

- Laser Physics Lecture -2
Excited atoms emit photons spontaneously.
When an atom in the an excited in the state falls to a lower energy level, it emits a photon in the light.
in the Molecules a typically in the remain excited for no in the longer than a few in the nanoseconds. This is often also called in the fluorescence or, when it takes longer, in the phosphorescence.

Spontaneous absorption

  • Let us in the consider two in the energy level in the having energy in the E1 & E2 resp.
  • in the atom will remain in the ground state in the unless some in the external stimulant in the applied to it.
  • When an in the EM wave i.e photon of particular freq fall on it , there isin the  finite probability that in the atom will jump in the fin the in the form in the energy in the state E1 to E2.

- Laser Physics Lecture -2

Spontaneous emission

  •  in the  Consider an atom in the higher state (E2).
  • It can decay to lower energy in the level by an emitting in the photon.
  •  in the Emitted photon have in the energy hv=E2-E1.
  •  in the Life time of in the excited state is a 12-9sec.

Stimulated vs Spontaneous Emission
in the Stimulated in the  emission in the in therequires the presence of a photon.     An “incoming”in the photon stimulates a molecule in an excited in the state to in the decay to the ground state by in the emitting a photon.  in the stimulated photons in the travel in the samea the direction as in the incoming tg photon.
in the Spontaneous emission does not require  the presence of a photon.                                                                                  in the  Instead a molecule in the excited state in the  can relax to the ground in the  state by spontaneously in the  emitting a photon. in the  Spontaneously emitted in the  photons are emitted in all directions.
- Laser Physics Lecture -2

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Laser Physics Lecture -1

Introductory Concepts
Spontaneous  in theEmission, Absorption, Stimulated Emission,in the  Pumping Schemes, Absorption and Stimulated Emission Rates,in the  Absorption and Gain in the Coefficients, in the Resonance Energy in the Transfers.  Properties in the of   Laser Beam: in the Monochromaticity,  in the Coherence, Directionality, Brightness.
Spectroscopy of Molecule and Semiconductors  
Electronic Energyin the Levels, Molecular in the Energy Levels, in the Level Occupation at Thermal Equilibrium, Stimulated Transition,in the  Selection Rules, in the Radiative andin the  Nonradiative Decay, Semiconductor.
Optical Resonators
in the Plane Parallel (Fabry-Perot) Resonator, in the Concentric (Spherical) Resonator, Confocal, Resonator, Generalized Spherical Resonator, in the Ring Resonator, Stable in the Resonators, Unstablein the  Resonators., Matrix Formulation of  Geometrical  in the  Optics, Wave Reflection  and Transmission  in theat a Di electric Interface, Stability Condition Standing   and Traveling in the  Waves in a  in thetwo Mirror Resonator , Longitudinal and Transverse Modes in a Cavity, Multilayer Dielectric  in the Coatings, Fabry-Perot in the Interferometer. Small Signal in the Gain and Loop Gain.
Pumping Processes
Optical pumping: in the Flash lamp and Laser, in the Threshold Pump in the Power, pumping efficiency, Electrical Pumping: Longitudinal in the Configuration and Transverse in the Configuration, Gas Dynamics in the Pumping,in the Chemical Pumping.
Continuous Wave (CW) and pulsed lasers  
Rate Equations, in the Threshold Condition and Output Power, Optimum in the Output Coupling, in the Laser Tuning, Oscillation and in the Pulsations in Lasers, Q-Switching and Mode -Locking Methods, Phase in the Velocity, Group Velocity, and in the Group -Delay in the Dispersion, in the Line broadening.
Lasers Systems
Solid State Lasers: Ruby Laser, Nd: YAG & Nd: in the Glass Lasers and Semiconductor Lasers: in the Homojunction Lasers Double-Hetero in the structure in the lasers, Gas lasers:  Helium Neon laser, CO2 laser, Nitrogen Laser and Excimer in the Lasers, in the Free -Electron and X-Ray Lasers
Laser applications
Material Processing: in the Surface Hardening, in the Cutting, Drilling, in the Welding etc. Holography,in the  Laser Communication, Medicine, Defense in the Industry, Atmospheric in the Physics

Recommended Books

- Laser Physics Lecture -1

What is laser?

Brief  History  of  laser development?
LASER is thein the  acronym for in the Light Amplification by Stimulated in the Emission of in the Radiation
Albert Einstein………theory of stimulated emission…….1917
When the population in the inversion exists between upper and lower levels among atomic systems, it is possible to realize in the amplified stimulated in the emission and the stimulated emission has the same frequency and phase as the incident in the radiation.
- Laser Physics Lecture -1

  • in the Notable scientists who in the pioneered the work include Charles Townes, in theJoseph Weber, in the Alexander Prokhorov and Nikolai G the
  • in the MASER (Microwave in the Amplification by the Stimulated Emission of Radiation)
  • A device that amplified in the microwaves for its immediate application in microwave communication systems.
  • in the Pioneering work of in the Townes and Prokhorov#
  • Theodore Maiman in the 1960
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prof///Sir Adeel
Vector Analysis:
Review of vectors in the Algebra, Vector in thedifferentiation and gradient, Divergence and Gauss’s theorem, Vector integration, in the Green’s theorem in the plane, Curl and Stokes theorem.
Curvilinear Coordinates and Tensors:
Curvilinear coordinate in the system, Gradient, Divergence in the and Curl in the curvilinear in the coordinates system,in the  Cartesian, Spherical and in the Cylindrical coordinate system, Covariant and contra variant tensors, Tensor algebra, in the Quotient rule.
Linear vector spaces,in the  Determinants, Matrices, Eigenvalues andin thein the eigenvectors of matrices, Orthogonal matrices, in the Hermitian matrices, Similarity transformations, in the Diagonalization of matrices.
Group theory:
Introduction to groups, in the Group representation, Invariant subgroups, in the discrete groups-Dihedral groups, Continuous in the groups-O groups, SU (2) groups, Lie groups
Complex Variables:
Functions of a in the complex variable, Cauchy Riemann conditions and in the analytic functions, Cauchy integral theorem and integral formula, in the Taylor and Laurent series, in the Calculus of residue, in the Complex integration.
Arfan bajwa
Quantum Mechanics of One Dimensional Problem: 
in the Review of concepts of classical mechanics, in the State of a system, Properties of one dimensional potential functions, Functions andin the expectation values, in the Dirac notation, Hermitian operators, in the Solutions of Schrodinger in the equation for free particles, The potential barrier problems, The linear in the harmonic oscillator, Particle in a box.
Formalism of Quantum Mechanics:
The state of a system, in the Dynamical variables and operators, Commuting and non-commuting operators, Heisenberg in the uncertainty relations, Time in the evolution of a system, in the  Schrodinger and Heisenberg pictures, Symmetry in the principles and conservation laws.
Angular Momentum:
Orbital angularin the momentum, Spin, The eigenvalues and Eigen functions of L2 and Lz, Matrix representation of angular momentum in the operators, Addition of angular in the momenta.
Schrodinger Equation in Three Dimensions:
Separation of Schrodinger in the equation in the Cartesian coordinates, Central potentials, The free particle, Three dimensional square in the well potential, The hydro genic atom, Three dimensional square in the well potential, The hydro genic atom, in the Three dimensional isotopic oscillator.
Sir Sajjad
Equilibrium Thermodynamics:
Basic postulates,in the  fundamental equations and in the equations of in the state, response functions Maxwell’s relation, reduction in the of derivatives.
Elements of Probability Theory:
Probabilities, in the distribution functions, statistical in the interpretation of entropy, in the Boltzmann H-theorem.
Formulation of Statistical Methods:
Ensembles,in the  counting of states (in classical and quantum mechanicalin the  systems, examples) partition function, Boltzmann distribution. Formation ofin the  Microcononical, canonical and grand canonical partion function.
Partition Function:
Relations of partition function in the with thermodynamic in the variables, examples (collection ofin the  simple harmonic oscillators, Pauli and in the Van Vleck paramagnetics, in the Theorem of equipartition of energy.
Statistical Systems:       
in the Maxwell-Boltzmann, in the Bose-Einstein, Fermi-in the Dirac statistical systems. Examples in the of thermodynamics of these systems; in the Black body radiations, Gas of electrons in the solids.
Statistical Mechanics of Interacting Systems:
in the Lattice vibrations in solids; Van der in the Waals Gas: mean field calculation; Ferro magnets in Mean Field in the Approximation.
Advanced Topics:
in the Fluctuations, Bose-Einstein in the Condensation, Introduction to in the density matrix approach.
Arfan Bajwa
Elementary Principles:
in the Brief Survey of Newtonian in the mechanics of a system of in the particles, constraints, Alembert’s principle, Lagrange’s in the equation, and its applications. Virtual work.
Variational Principles:
Calculus of variation and in the Hamilton’s principle, Derivation of Lagrange’s in the equation from in the Hamilton’s principle.
Two Body Central Force Problems:
Low and least action, two body problem and its reduction to one body problem. Equation of motion and solution for one body problem, Kepler’s Laws Laboratory and Centre of mass systems, Rutherford scattering.
Kinematics of Rigid Body Motion:
in the Orthogonal transformations, in the Eulerian angles, Euler’s theorem, the cariole’s force
Rigid Body Equation of Motion:
Angular momentum, in the Tensors and dyadic, Moment of in the inertia, Rigid body problems and in the Euler’s equations.
Hamilton Equation of Motion:
in the Legendre transformation and in the Hamilton equations of motion, Conservation in the theorems.
Canonical Transformations:
Examples of canoical transformations, in the Lagrange and Poison brackets,in the  Liouville’s theorem.
Irfan butt
Special Diodes:
Zener diodes, in the Zener regulators, Varactor in the diodes, Schottky diodes, Light emitting diodes, Photodiodes, Tunnel diodes, Varistors and their applications.
Transistor Circuits:
Bipolar in the transistors; in the parameters and ratings, Ebers-Moll,in the  Hybrid-p and h,z and y-parameterin the models, Switching in the circuits, in the Biasing and stability, in the Common emitter, Common base and common collector in the amplifiers, Frequency in the response, Power class A, B, and in the C amplifiers, Field Effect
Transistors; in the Junction FET, in the MOSFET, Operation  in the and construction, Biasing, Common source and common drain in the amplifiers, Frequency response. Multistage Amplifiers; RC coupled and direct coupled stages, The differential amplifiers, in the Negative feedback, Tuned in the RF Voltage amplifiers, I-F Amplifiers and automatic gain control.
Operational Amplifiers:
Ideal op-amps, in the Simple op-amp arrangements, its data and sheet in the parameters, Non inverting and inverting circuits, Feedback and stability,in the Op-amp applications; Comparators,in the Summing, Active filters, Integrator and in the Differentiator, Instrumentation in the amplifier.
Armstrong, in the Hartley, CMOSS, Colpit’s Phasein the  shift and 555 timer in the oscillators.
Voltage Regulators:
Series, Shunt in the and switching regulators, Power in the supply.

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PN Junctions–Lecture 3

Prof. Zohaib Metla

Diode under Thermal Equilibrium

Diffusion small since of the  few carriers have enough energy to of the penetrate barrier below see by a diagram
Drift of the current is small of the since minority carriers are few and far of the between:  Only minority of the carriers generated of the within a of the diffusion length can of the contribute current
Important Point:  Minority drift current of the  independent of barrier!
Diffusion currentof the  strong (exponential) function of the barrier see by a diagram
- PN Junctions–Lecture 3

Reverse Bias

Reverse Bias of the causes an increases of the barrier to diffusion
Diffusion of the current is reduced of the exponentially
Drift current of the does not change
Net result:  of the Small reverse current

Forward Bias

lForward bias causes an of the exponential of the increase in of the number of of the carriers with sufficient of the energy to penetrate the barrier see by a diagram
lDiffusion current of the increases exponentially see pic. below
Drift current of the does not change
lNet result:  of the Large of the forward current see by a diagram
- PN Junctions–Lecture 3

“Law of the Junction”

Minority carrier in the concentrations at the edges of the
depletion in the region are given by: see by a diagram
Note 1:  NA and ND are in themajority carrier concentrations on
the other side of the junction see by a diagram
Note 2:  we can a reduce in the these equations further by in the substituting see by in thediagram
VD = 0 V (thermal equilibrium)
Note 3: the a assumption that pn << ND and np << NA  see by a diagram
Minority Carrier Concentration
see by a diagram
- PN Junctions–Lecture 3
The minority in of the carrier concentration in the bulk region for
forward bias is a decaying exponential due to in the recombination

Steady-State Concentrations

Assume that none of the diffusing holes and electrons in  the recombine à get straight lines
This alsoin of the  happens if the minority carrier in of the  diffusion lengths are much larger  in of the  than Wn,p see by a diagram
Diode Current Densities
- PN Junctions–Lecture 3

Diode Capacitance

We have already in the seen that a in the  reverse-biased diode acts in the as a capacitor since the depletion in the  region to grows and shrinks in the response to the applied field.  the capacitance in the  forwarding a bias is given by see diagram
But a another in the charge storage mechanism in the  comes into play in the forwarding bias
Minority carriers in the injected into the  p and n regions “stay” in the each region for the while
lOn average in the additional charge is stored in the diode.

Charge Storage

in the Increasing forward bias increases the minority charge density
By in the  charge neutrality, the source in the voltage must supply equal and in the opposite charge
in the detailed analysis yields:
- PN Junctions–Lecture 3

Forward Bias Equivalent Circuit

lEquivalent circuit has in the three non-linear elements: in the  forward conductance, in the junction cap, and diffusion cap.
in the Diff cap and in the conductance were proportional to in the DC current in the flowing through the diode.
in the Junction cap proportional to junction in the voltage.
- PN Junctions–Lecture 3

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Continuity of E-Field Across Junction lect=3

Prof. Zohaib Metla

Continuity of E-Field Across Junction

Recall that E-Field diverges onof the a charge.  For a sheet of the  charge at the interface, the E-field could be of the  discontinuous
In our case, of the depletion region is only populated by of the background density of the fixed charges so of the E-Field is  the continuous
What a does this is imply?
Total fixedof the  charge in n-region equals of the fixed of the  charge in p-region!  Somewhat of the obvious result.
Plot of Fields In of the Depletion a Region
E-Field us zero outside of the depletion region
Note of the asymmetrical of the  depletion widths
Which region has of the  higher doping?
Slope of E-Field larger in of the  n-region.  Why?
Peak  of the  E-Field at junction.  Why of the  continuous?

Potential Across Junction

From our of the earlier calculation we of the know that of thepotential in the n-region is higher than of the p-region
The potential has to  the smoothly transition form high to low in crossing of the junction
Physically, of the potential difference is due to the charge transfer that is  occurs due to the concentration of the gradient
- Continuity of E-Field Across Junction lect=3
Let’s of the integrate the field to get in the potential:
We arrive at of the  potential on p-sideof the  (parabolicof the  )lDo integral on n-side
Potential must in be continuous at interface (of the  field finite ub at interface)
- Continuity of E-Field Across Junction lect=3

Solve for Depletion Lengths

We have2    equations and 2 of the unknowns.  We are finally in a position to of the solve for the depletion of the depths
- Continuity of E-Field Across Junction lect=3

Sanity Check

Does the of the above equation make of the sense?
Let’s say we gave dope one of the side very v of the highly.  Then physically we of the expect theof the  depletion region width for the heavily doped side to of the approach zero:
- Continuity of E-Field Across Junction lect=3
Entire depletion of the width of the dropped across of the p-region. diagram

Contact Potential

The contact of the between a PN junction r creates a potential of the difference
Likewise, of the contact between two of the dissimilar metals of the creates a potential difference of the (proportional to the difference of the between the work functions)
When a metal semiconductor junction is of the formed, a contact of the potential forms as  of thewell
If we short a PN junction, of the sum of the voltages around of the loop must be zero:diagram

Have we invented a battery?

Can we harness of the PN junction and turn it into of the a battery?
Numerical of the example: diagram
- Continuity of E-Field Across Junction lect=3

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PN Junctions: Overview lecture-2

Prof. Zohaib Metla

PN Junctions: Overview

  1. The most of the important device is a junction between aof the p-type region and an n-type of the region.
  2. When of the junction is first formed, due to the concentration of the gradient, mobile of the charges transfer near junction,
  3. Electrons of the leave n-type region and holes of the leave p-type region.
  4. These mobile of the carriers become minority of the carriers in new region (can’t penetrate far due of the to recombination).
  5. Due to charge of the transfer, a voltage difference occurs between regions.
  6. This of the creates a field at the junction that of the causes drift currents to oppose the diffusion of the current.
  7. In thermal of the equilibrium, drift of the current and diffusion of the must balance.

PN Junction Currents

Consider of the PN junction in thethermal of the equilibrium
Again, of the currents have to be zero, so we have a below diagram drop
- PN Junctions:  Overview  lecture-2

PN Junction Fields

see below the pic details PN junction field
diagram in Transition Region
- PN Junctions:  Overview  lecture-2

Total Charge in Transition Region

To solve for the electric fields, we need to the write down the charge density in of the transition region:
In the p-side of the junction, there are very of the few electrons and only the  acceptors:
Since of the hole the  concentration is the  decreasing on the p-side, of the net charge is the negative:
- PN Junctions:  Overview  lecture-2

Charge on N-Side

A Analogous to a the p-side, the charge of the  the n-side is given by the:
- PN Junctions:  Overview  lecture-2

“Exact” Solution for Fields

Given of the above approximations, we now have be an expression for of the charge density.
We also have of the following result from of the electrostatics.
- PN Junctions:  Overview  lecture-2
Notice that of the potential appears on of the both sides of the equation…  difficult of the problem to solve.
A much is a simpler way to solve of the a the problem…

Depletion Approximation

Let’s of the assume that the transition region is  of the completely depleted of the free carriers (only of the immobile dopants of the exist)
Then of the charge density is a  given by
The solution for electric field is of the now easy
- PN Junctions:  Overview  lecture-2

Depletion Approximation (2)

Since of the charge the density is a constant and of the charge a density is the  given by-
If we a start from of then-side we get of the following of the result.
below diagram Depletion Approximation below
- PN Junctions:  Overview  lecture-2

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PN Junctions–Lecture 1

Prof. Zohaib Metla

Diffusion (cont)

  • The net motion of the gas molecules to of the right chamber was due to the concentration of the gradient
  • If each particle of the moves on average of the left or right then eventually of the half will be in the right chamber
  • If the moleculesof the  were charged (or electrons), then of the there would be a net of the current flow
  • The diffusion of the current flows from high  of theconcentration to low concentration:

Diffusion Equations
Assume that of the mean free path is λ
Find flux of carriers  of thecrossing x=0 plane

  • - PN Junctions-Lecture 1


Einstein Relation

The thermal of the velocity is given by of the kT
- PN Junctions-Lecture 1

Total Current and Boundary Conditions

When both driftof the and diffusion are  of the present, the total current of thegiven by the sum:
In resistors, the carrier of the approximately uniform and the of the second term is nearly zero
For currents flowing of the uniformly through an interface (no chargeof the accumulation), the field is discontinous
Carrier Concentration and Potential
- PN Junctions-Lecture 1
In thermal equilibrium, there are of the no external fields and we thus expect of the electron and hole current densities to be zero:
Carrier Concentration and Potential (2)
lWe have an equation of the relating the potential to of thecarrier of the concentration
lIf we integrate of the above equation we a have
We define the potential of the  reference to be intrinsic Si
- PN Junctions-Lecture 1
Carrier Concentration Versus Potential
The carrier of the concentration is thus of the function of potential
Check that for zero of the potential, we have of the intrinsic carrier concentration of the  (reference).
If we do a similar of the calculation for holes, we arrive at of the similar equation
Note that the law of mass of the  action is upheld
- PN Junctions-Lecture 1
The Doping Changes Potential
Due to the log nature of of the potential, the potential of the changes linearly of the  exponential increase of the in doping:
Quick calculation aid: of the  For a p-type concentration of the of 1016 cm-3, the potential is -360 mV
lN-type materials have aof the positive potential with of the respect to intrinsic Si
The Doping Changes Potential 
Due to the log nature of the potential, the  of the potential changes linearly of the exponential increase of the  doping:
Quick of the calculation aid:  For a p-type concentration of the 1016 cm-3, the of the potential is -360 mV
N-type of the materials have aof the positive potential with of the respect to intrinsic  of the Si
- PN Junctions-Lecture 1

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