Applied Quantum Mechanics for Electrical Engineers Workshop II Energy Band Model and Doping

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1 Applied Quantum Mechanics for Electrical Engineers Workshop II Energy Band Model and Doping 95 pts Objective: Explore the effect of doping on the energy band diagram and the carrier concentration. Instructions: Make sure that your Java software is up to date in order to avoid simulation delays. I. Doping Models Examine the structure of silicon from the course website. Notice that the atoms inside the cubic structure form bonds with one of the nearest corner atoms and with three of the nearest face atoms. Thus, every Si atom has four neighbors. When one of the Si atoms is replaced by another element, we call this doping. Doping of semiconductor materials is performed during processing and/or fabrication and results in a p-type or n-type material. A p-type material will have more hole carriers than electrons, and an n-type material will have more electron carriers compared to holes. The periodic chart organizes elements into groups with similar valence electrons, and it can be used to determine what type of semiconductor results after doping. If the element is doped or replaced by an element to the left, the dopant is an Acceptor and the semiconductor is p-type. If the element is doped or replaced by an element to the right, the dopant is a Donor and the semiconductor is n-type. Explore the Semiconductor Doping tool on nanohub (https://nanohub.org/resources/semidop) and then complete the following models in order to fully understand what happens to the material during doping. A. Sketch a bond model of Si that has been doped with Ga before Ga is ionized. Place the dopant in the center and include four nearest Si neighbors in your sketch. B. Use your sketch in part A to re-draw a bond model of Si that has been doped with Ga after Ga is ionized.

2 C. Sketch a bond model of Si that has been doped with Sb before Sb is ionized. Place the dopant in the center and include four nearest Si neighbors in your sketch. D. Use your sketch in part C to re-draw a bond model of Si that has been doped with Sb after Sb is ionized. Place the dopant in the center and include four nearest Si neighbors in your sketch.

3 II. Effect of Doping on the Energy Band Diagram The energy band diagram is a critical tool used to understand the device physics of all devices such as solar cells, transistors, infrared detectors, etc. It is important to compare the energy band diagram to the bond model in order to understand what is happening in the lattice (bond model) and compare this to the energy of electrons and holes during carrier activity (energy band diagram). The energy band model represents the energy of electrons and holes with respect to the conduction energy level (E c ), the valence energy level (E v ), and two reference energy levels, intrinsic energy level (E i ) and Fermi energy level (E F ). The energy levels E i and E F are used to represent the level of doping in the material. The intrinsic energy level (Ei) is always placed at the center between the valence and conduction bands. When the Fermi energy level (E F ) is placed below the intrinsic energy level (E i ), the energy band diagram represents a p-type semiconductor. When E F is placed above Ei, the energy band diagram represents an n-type semiconductor. Explore the Effect of Doping on Semiconductors tool on nanohub (https://nanohub.org/resources/dopingsilicon) and then complete the following tasks. A. Sketch the energy band model of Si that has been doped with Ga before Ga is ionized. Label the energy levels (E c, E v, E i, E A and E F ). B. Use your sketch in part A to re-draw the energy band model of Si that has been doped with Ga after Ga is ionized. Label the energy levels (E c, E v, E i, E A and E F ). C. Sketch the energy band model of Si that has been doped with Sb before Sb is ionized. Label the energy levels (E c, E v, E i, E D and E F ).

4 D. Use your sketch in part C to re-draw a bond model of Si that has been doped with Sb after Sb is ionized. Label the energy levels (E c, E v, E i, E D and E F ). E. Using the Effect of Doping on Semiconductors tool on nanohub, set the Donor doping (N D ) to zero, Acceptor doping (N A ) to /cm 3, and the temperature to 300K. Copy and paste the resulting simulation in the space below. Calculate the carrier concentrations for holes and electrons and then label the number of electrons (n), holes (p), and Acceptor atoms (N A ) on your diagram. F. What happens to the number of holes in the valence band (p), the number of electrons in the conduction band (n), and the Fermi energy level (E F ) when the Acceptor atoms (N A ) are increased? Holes in the valence band: Electrons in the conduction band: Fermi energy level:

5 G. Reset the parameters to those specified in part E. Increase the temperature from 300K to 550K, and indicate what happens to the number of holes in the valence band (p), the number of electrons in the conduction band (n), and the Fermi energy level (E F ). What do you notice when you compare the number of holes Holes in the valence band: Electrons in the conduction band: Fermi energy level: Copy and paste the Carrier Concentration vs Temperature plot from the simulation in the space Below and describe what is happening in the semiconductor as the temperature increases. Explanation:.

6 III. Effect of Doping on the Carrier Concentration Calculate the carrier concentration values for the doping and temperature conditions included in the Table below and then compare your values to simulated values using the Carrier Concentration tool (https://nanohub.org/resources/carrierconc) on nanohub. Material T, K N A, cm -3 N D, cm -3 Sim n i, cm -3 Si Si Ge x10 17 GaAs Ge Sim Sim Graph p, cm -3 n, cm -3 n i, cm -3 Calc Calc p, cm -3 n, cm -3

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