Homework Assignments EEL 4351 Fall 2004

Homework QM Nanodevices assignments Fall 2012

1. Quiz on September 19 (UG and G students) at the beginning of class: HW set 1; 2.1, 2.3, 2.5, 2.6, 2.16, 2.19. Note that on pg 31 below eq. 2.3 the units of max.T are meter.Kelvin not millikelvin.

2. Quiz on October 10 (UG and G students) at the beginning of class on the material of HW set 2: 2.1 The channel of a modern n-channel MOSFET could have a length of 90 nm (y-axis, Source-Drain spacing), width of 1 m (x-axis), with an electron confinement under the SiO2/Si interface of 100 Angstrom (z-axis).Using stationary boundary conditions in the x and z-direction and periodic bc in the y- direction, calculate the 3 lowest electron energy levels E using EC for potental energy. Express your answers in eV and use mn*= 0.3 x mo with mo = 9.11x10-31 kg. Also draw a picture of the 3D k-space associated with this device. 2.2 Calculate the required thickness [in x-direction] of a silicon wafer in nm to create an 0.2 eV energy difference between the two lowest Enx energy states, -31 use mn*= 0.3 x mo with mo = 9.11x10 kg. Assume the y and z-direction infinitely long. 2.3 What is the wavelength of the photon produced by an electron dropping from the higher to the lower state calculated in 2.2? 2.4 Derive an expression for the electron density of a 2D system in terms of the DoS and Fermi level EF. Simplify it for low temperature if EF lies between E1 and E2, and below E1.

3. Quiz on October 24 (UG and G students) at the beginning of class on the material of HW set 3: book hw problems 4.13 [answer E1=1.3eV, E2=2.9eV], 4.14 [answer mn*= 8 x m0], and 4.15 [answer i. mn*=8.1 x mo, ii. mn*=-7.2 x mo, iii.mn*=+/- infinity]. Note that this time we require you to hand in a paper copy of your computer code for solving problem 4.15 to earn 5 out of 20 quiz points. Only original, individual work will be accepted at the time of the quiz. The remaining 15 quiz points can be earned by answering the quiz questions which will cover the details of the hw solution process.

4. Due November 14. No quiz but a hardcopy of your homework solution needs to be handed in at the beginning of class for credit. Of course only original and individual work will be accepted. Problem Statement: Design the width and the minimum mol fraction x of an AlxGa1-xAs/GaAs/ AlxGa1-xAs Quantum Well Infrared Photodetector (QWIP) device such that it is able to detect infrared radiation of 10 m wavelength (night vision, skin thermography application. Note that 10 m is the peak blackbody radiation wavelength at about T=300K). Design the QWIP such that it has 2 confined energy levels E1 and E2 (p.153 Singh, fig. 5.3) in the conduction band with the difference between E2 and E1 corresponding to the incoming photon energy and E2 aligning with the barrier height. Use

m*=0.067 mo, assume that 60% of the EG shows up in the conduction band, and employ the theory of graphical solution explained on page 151 of Singh’s book. Show graphs, arguments, equations, etc. in your handed-in work. Box your answers and explain your steps and use of equations clearly so that your work can be followed by others.

5. Quiz 5 [last] on November 28 in class based on book problems 5.1 [use mass values specified in problem 5.2], 5.2, 5.5.