ELEG 867 Nanotechnology
Homework #7 - due Monday, 12 November 2001

1. Design a quantum well infrared photodetector (QWIP) for operation at the optical fiber communication wavelength of 1.55 mm, using n-type GaAs quantum wells and AlGaAs barriers. Select your quantum well width so that the electron transition from the n=1 state to the n=2 state absorbs the designed energy, using the GaAs effective electron mass of m* = 0.07 m_o, and refractive index n = 3.4. Calculate your subband energies for n=1,2 using the approximation of infinitely high barriers, even though in practice the upper level will be equal with the continuum at the top of the barrier. Calculate the 2-dimensional absorption coefficient a_2D per quantum well, assuming a broadening G that is 10 % of your transition energy. Also calculate the oscillator strength, the momentum matrix element and the spatial matrix element. How many quantum wells are needed to absorb 90 % of the incident light intensity, neglecting absorption in the barrier layers and the contacts?

2. Calculate the optical force on one atom in a lithography system, based on atom-optics, that is used to deposit metal lines with a period of 200 nm for an integrated circuit. In a simple model of atomic polarizabilty due to electron motion, the polarizabilty a (not to be confused with the absorption coefficient as in the above problem) is given by a = e²/mw_a² , where w_a is the angular frequency of the atomic resonance. Use the equations given in class to calculate the stimulated dipole force on one atom from a laser of the appropriate wavelength with a peak intensity of 1 MW/cm², that decreases from peak to zero intensity over a space of 100 nm.

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