Fall 2002 6.720J/3.43J Integrated Microelectronic Devices Prof. J. A. del Alamo Octob er 10, 2002 - Quiz #1 Name: General guidelines (please read carefully b efore starting): • Make sure to write your name on the space designated ab ove. • Open book: you can use any material you wish. • All answers should b e given in the space provided. Please do not turn in any extra material. • You have 120 minutes to complete your quiz. • Make reasonable approximations and state them, i.e. low-level injection, extrinsic semicon-ductor, quasi-neutrality, etc. • Partial credit will b e given for setting up problems without calculations. NO credit will b e given for answers without reasons. • Use the symb ols utilized in class for the various physical parameters, i.e. N , τ , E , etc. c • Pay attention to problems in which numerical answers are exp ected. An algebraic answer will not accrue full p oints. Every numerical answer must have the prop er units next to it. Points will b e subtracted for answers without units or with wrong units. In situations with a defined axis, the sign of the result is also part of the answer. • If needed, use the doping-dep endent Si parameters graphed throughout del Alamo’s notes. • If needed, use physical parameters for silicon at ro om temp erature listed in App endix B of del Alamo’s notes. • If needed, use the values of fundamental constants listed in App endix A of del Alamo’s notes. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].1. (10 points) Describ e a semiconductor in which Maxwell-Boltzmann statistics cannot b e used in thermal equilibrium for neither electrons nor holes at ro om temp erature. Explain. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].2. (10 points) Do es the threshold photon energy for carrier generation in a semiconductor dep end on doping? Explain. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].3. (10 points) Consider a Si sample at ro om temp erature whith a dominant trap with a concentration 16 −3 N =10 cm lo cated at E . The electron and hole capture rates for this trap are c = c = t i e h −10 3 10 cm /s. This sample is placed under intense light illumination that causes the carrier concentrations to 17 −3 17 −3 b ecome n =2 × 10 cm and p =10 cm , uniformly in space. Calculate the net recombination rate by as many generation/recombination pro cesses as you can. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].[this page left intentionally blank] Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].4. (40 points) Consider a piece of n-typ e Si in thermal equilibrium at ro om temp erature. In a region defined by 0 ≤ x (µm) ≤ 10, there is a spatially varying electron concentration as sketched b elow. no (cm-3) 1017 n 3 17 −2×10 x −3 (x)= 10 × 10 cm with x in cm o 1016 1015 1014 0 5 10x (µm) a) [10 points] Derive an analytical equation for the minority carrier concentration in space. Quan-titatively sketch the result in a suitable diagram. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].b) [10 points] Derive an analytical equation for the electrostatic p otential in space. Quantitatively sketch the result in a suitable diagram. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].c) [10 points] Derive an analytical equation for the electric field in space. Quantitatively sketch the result in a suitable diagram. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].d) [10 points] Derive an analytical expression for the charge distribution that supp orts this electric field. Quantitatively sketch the result in a suitable diagram. Can this sample b e considered quasi-neutral? Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].� 5. (30 points) The energy band diagram b elow corresp onds to a region of a Si bar at ro om temp er-ature next to a surface (E − E E − E ) under static conditions. The actual semiconductor c fe c F surface is lo cated at x =0. In answering the questions b elow, make whatever assumptions you need to make. State them and justify them clearly. a) (5 points) Circle all the terms that apply to the situation: - thermal equilibrium/out of equilibrium -uniformly dop ed/non-uniformly dop ed -n-typ e/p-typ e -low-level injection/high-level injection/extraction -intrinsic/extrinsic b) (5 points) Estimate the hole current density at x =0 (numerical answer and appropriate sign expected). Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare