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SPM Probe tips CNT attached to a Si probe tip Slide # 1 Microcantilevers: Mechanical properties Rectangular Cantilever: Spring constant: Resonant frequency: f res E: Young’s Modulus I: Moment of inertia L: length, W: width, h: height 3EI k 3 L 0.162 E 0.5 h3W k 0.323 0.5 2 L m Wh 3 I 3 L m hLW Triangular Cantilever: 4W 3 Eh W k cos 1 3 3 cos 2 2 L3 b 3 i2 k k fi 0.323 m 2 3 M 1 i 1.875 Slide # 2 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. 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 2 x tm 12 4Qk BTB k0 12 Slide # 3 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 Slide # Problems 1 • Calculate the maximum excitonic binding energy for excitons in GaN. Effective masses: 0.2m0 and 0.75m0 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? bind Eex * 13.6 mred 1 2 n m0 2 1 x EGaN xEAlN Eg , AlGaN 1 y EGaN yE AlN Eg , AlGaN 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? 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 2x107 cm/s and the critical electric field is 4x105 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 Slide #