Question

Problem 2 (20 pts) A scanning tunneling microscope employs a small sharp conducting tip that is brought into close proximity of a material, as TIP shown in the figure at right. The vacuum region between the tip and the sample acts as a potential barrier because the electrons in the material have a lower potential than in free space (work functions of the materials). Therefore, the current across the vacuum is proportional to the transmission probability T approximated by a square barrier. In this problem you will show that the current changes by several arders of magnitude over a distance of a few tenths of a nanometer making this a highly sensitive instrument. electons Sample Vacuum く16 pts) Determine the ratio of the current for a tip sample separation of d-02 nm to that with d-05 nm. The electron energy is E-100 meV and the barrier potential is Ve seV. Hint I: Td-0.2 m/Tid-0.5 nm) a) b) (4 pts) Repeat for d-0.5 nm and d-0.8 nm. Hint 2: See equation 13.18 from the lecture 13 notes. Extra Credit (5 pts): Plot Tus d over the interval 0.01nmsd so.8 nm

Answer 1

From the given data here the scanning tunneling microscope from the given figure electrons sample the electron energy is 100 mev and this is = 100 times 10^7 eV. = > 0.1 eV and the barrier potential is and barrier potential and electron energy difference (V_0 - E) = (5 - 0.1) eV. = 4.9 eV V_0 - t = 4.9 times 1.6 times 10^-1 Joule and the current and portability of transmission current is directly proportionality to probability of Therefore I_1 alpha T tau = e^-2 yd. where squareroot 2m/k^2 (-E) \r\n and the formula for ratio to the diameters d_1 and d_2 d_1 = 0.02 m d_2 = 0.5 nm then I_2y/I_2 = T_2/T_2 = e^-2t d_1/e^-2y d_2 = > e^- (d_1 - d_2) here we need to determine the ratio at currents y = squareroot 2m/K^2 (V_0 - E) = squareroot 2 times 9.1 times 10 times 9.5 times 1.6 times 10^-19/(1.059 times 10^-34)^2 = > squareroot 2 times