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1. k*p method and Kane model: Starting from Bloch wave function derive k*p Hamiltonian. Retain S and Px,Py,Pz basis functions at k=0 with Ec and Ev as corresponding energies. Derive k*p Hamiltonian in this basis retaining only one non vanishing matrix element coupling S conduction orbital with 3 p orbitals. Plot conduction and valence bands as a function of k assuming Kane P parameter eq. 1eV and Energy gap of 2eV.
2. Light and heavy holes: Construct basis functions as eigen functions of total angular momentum J=L+S where L=1 is angular momentum and S=1/2 is electron spin. Classify your states into heavy and light holes and a spin split-off band. Use four J=3/2 hole functions to write Luttinger - Kohn Hamiltonian for holes. Consider a hole with J=3/2 on a disk with radius R=300A, height H=120A and infinite confining potential. Use Luttinger-Kohn parameters for SiGe from attached paper Rego et al. Construct Luttinger spinors and compute energy spectrum of a hole.
3. Strain and elastic energy:
i) Introduce displacement field.
Ii) Define strain tensor.
Iii) Compute total energy.
A 20 x microscope objective is designed for use in a microscope with a 17 cm tube length. The objective is marked NA = 0.45. What is the diameter of the objective lens
compute the angular spread of the light. Note: For simplicity, Figure P21.62 shows a single ray of one color.
What is the polarization mismatch factor for two linearly polarized antennas whose polarization vectors are mismatched by an angle of 35°?
An object has a kinetic energy of 279 J and a momentum of magnitude 24.3 kg·m/s. Find the speed and the mass of the object
For the capacitor network shown in the following figure, the potential difference across ab is 240 V. (Let C1 = 25 nF, C2 = 80 nF.) Find the total charge stored in this network. Find the charge on each capacitor.
what is the net force exerted by these two charges on a third charge 50.5 placed between and at -1.230 ? your answer
Calculate the hydrostatic difference in blood pressure between the brain and the foot in a person of height 1.75 m
When a resistor is connected across the terminals of an acgenerator (111 V) that has a fixed frequency, there is a current of0.351 A in the resistor. When an inductor is connected across theterminals of the same generator, there is a current of 0...
An old hunting weapon was a rock on the end of a string. The hunter would swing the rock in horzontal circles and then throw it. If the rock had a mass of 2 kg and the 2 m long string breaks when the tension is 60N.
An airplane is flying at 175km/hr on a headwind of 45 degrees. The wind is blowing from 300 degrees at 45 km/hr. Find the direction and magnitude of the plane's velocity
A ball is thrown upward with an initial velocity of 12.0 m/s at an angle of 50.0 deg above the horizontal. find the ball's greatest height above the ground
Point charges q1=- 4.00nC and q2=+ 4.00nC are separated by a distance of 3.60mm, forming an electric dipole. Find the magnitude of the electric dipole moment
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