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how to answer these 3 questions , please show the details and answer

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We set a hypothesis semiconductor A and B with the following material parameters and
fabricate quantum structures as described in Question 1-3
Semiconductor A
Semiconductor B
Band gap (eV)
Electron affinity (eV)
Electron effective mass
0.05 mo
0.10 mo
Hole effective mass
1. (40pt) Firstly, we design double-hetero quantum well structure using the hypothesis
semiconductor A and B.
(a) (10pt) Draw the schematics of energy band diagram for double-hetero quantum well
structure. Find the ionization potential for both semiconductors. Also, find the barrier
heights for electron and hole.
(b) (10pt) What is the maximum of width of semiconductor well layer to observe the electron
confinement effect at 300K and 77K ?
(c) (10pt) Now, we fabricate the quantum well structure with the well width of 6 nm. Find all
the energy eigenvalues for conduction and valence subband levels by graphical methods
(You are required to show the plots)
(d) (10pt) Find the density of the states (DOS, D(E)) (the unit: ev"'nm") for the conduction
band for the above quantum well. Also, Plot the D(E)) for the quantum well structure.
2. (30pt) Here, we fabricate the tunneling, i.e. potential barrier, structure using these
hypothesis semiconductor A and B.
(a) (10pt) Find the transmission coefficient when the barrier width is 0.2nm, Inm, 2nm and
4nm. The energy of incident electron (E) is +0.1 eV.
(b) (10pt) Plot T(E) for the barrier thickness of 2nm, 4nm and 8nm (0 < E<7 eV).
(c) (10pt) Discuss about the condition to exhibit the T =1.


3. (30pt) Next, we fabricate superlattice (SL), tie. periodic structure, using the hypothesis
semiconductor A and B. We set the potential (V 1) with 0 eV for the conduction band
minimum for the well layer of semiconductor. Here, we use the following relation to find allowed energy bands 0: ( —2 s a s 2)= 2cos(k2(a — b))cos(k1b) — Q + :4) sin 0:201 — b))sin(k1b)
1 2 2 E— z E—
Here.k1 = l—g—mii V1) , k2 = —2—mz{fi V2) (3) (lflpt) Plot the E—k dispersion curve (0<E< 50, (K k < n/a) when the superlattice period is
1.2nrn and the well width is 0.8mm. Also, Find the mini band width and mingap at 1" point
for first two bands. Here on must consider the effective mass of the h thesis
semiconductor A and B. (b)(10pt) Drive the equation for density of state, D(E) and plot the D(E) (0<E< 20, the unit: eV" nm'l) for SL structure. Here, we assume the effective mass of the hypothesis
semiconductor A and B are 0.083110. (c)(10pt) Discuss about the condition to form miniband and discrete energy for super lattice.

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