1. Slide # 1 SPM Probe tips CNT attached to a Si probe tip

2. Slide # Microcantilevers: Mechanical properties 2 Spring constant: Resonant frequency: E: Young’s Modulus I: Moment of inertia L: length, W: width, h: height Rectangular Cantilever: Triangular Cantilever:

3. Slide # Microcantilevers II Cantilever quality factor Q: Quality factor depends on loss mechanisms. Usually the quality factor is ~50 in air. In vacuum, it can go up to several thousand or more. 3 Detection Of Cantilever Deflection: There are 3 common techniques for cantilever detection: (i)Optical detection: commonly used for scanning robe microscopy. This is well suited for a single cantilever, but not suitable for an array of cantilevers (ii)Piezoresistive detection: used for sensing purposes and in integrated circuit applications. Not as sensitive as the (iii)Capacitive detection: used in some transducers. Highly sensitive for short distances, but not for long distances. Ultimately, the resolution of the cantilever deflection is limited by its thermomechanical noise given as

4. Slide # Midterm Review: Important topics Mobility and Hall effect Excitonic effects Photoluminescence for impurity and composition determination Atomic force microscopy modes –Contact –Tapping –Non-contact modes

5. Slide # Problems 1 Calculate the maximum excitonic binding energy for excitons in GaN. Effective masses: 0.2m 0 and 0.75m 0 for electrons and holes. k = 9.5. Calculate the bandgaps of AlN and GaN from 2 PL peak positions given for two compositions: x = 0.11, peak at 340 nm; x = 0.45, peak at 290 nm. What are the two major factors that affect mobility? Choose one of these factors and design a device to reduce the scattering factor drastically Why is small magnetic field used during Hall mobility measurement?

6. Slide # Problems 2 In the force vs. distance curve point out the regions where contact mode and non-contact modes are operated. Sketch the AFM topography image of a perfectly square ridge with vertical edges, with a tip that has a conical shape with half angle of 20 degrees. How does the shape looks like if the tip has a parabolic edge? Mention three major information that you can get from PL. Do you expect PL peak intensity for GaAs and GaN, similar order as for Si and SiC? Explain in detail. For a very pure material, without defects and doping, the lowest energy and most prominent PL peak is observed at 1.40 eV at 4 K. The bandgap of the material is 1.42 eV, and the dielectric constant is 13. The typical donor and acceptor activation energies are 7 meV and 130 meV. Assuming that the momentum relaxation time is 1 ns for both type of carriers, calculate (i) Electron and hole effective masses (ii) Electron and hole mobility values (iii) How would the peak position change with increase in temperature?

7. Slide # Short questions and problems Explain briefly: –Why is scanning capacitance performed in contact mode but potential measurement in non-contact mode –Why is optical phonon scattering only at higher temperature but acoustic scattering at lower temperature –Calculate the low field mobility for GaN if the saturation velocity is 2x10 7 cm/s and the critical electric field is 4x10 5 V/cm. Why does velocity saturate at higher field? –Draw the band diagram for a metal tip and an n-type semiconductor sample, with a surface barrier. Show the change in surface barrier as super bandgap illumination is incident on it. –How does the intensity and peak position of PL peak vary for a quantum well with (a) AlGaAs/GaAs, (b) with AlGaN/GaN