Condensed Matter in a Nutshell

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Mark Carter
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1 PHYS 342/555 Condensed Matter in a Nutshell Instructor: Dr. Pengcheng Dai Professor of Physics The University of Tennessee (Room 407A, Nielsen, ) (Office hours: TR 1:10PM-2:00 PM) Lecture room 314 Nielsen Chapter 8: More Band structure and Semiconductors Lecture in pdf format will be available at: p Dai/PHYS 342/555 Spring

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38 Pentavalent impurities Impurity atom with 5 valence electrons produce n-type semiconductors by contributing extra electrons. Trivalent impurities Impurity atoms with 3 valence electrons produce p-type semiconductors by producing a "hole" or electron deficiency. Dai/PHYS 342/555 Spring 2012 Chapter 8-38

39 The addition of pentavalent impurities such as antimony, arsenic or phosphorous contributes free electrons, greatly increasing the conductivity of the intrinsic semiconductor. Phosphorous may be added by diffusion of phosphine gas (PH3). Dai/PHYS 342/555 Spring 2012 Chapter 8-39

40 The addition of trivalent impurities such as boron, aluminum or gallium to an intrinsic semiconductor creates deficiencies of valence electrons, called "holes". It is typical to use B 2 H 6 diborane gas to diffuse boron into the silicon material. Dai/PHYS 342/555 Spring 2012 Chapter 8-40

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42 Semiconductor Current Both electrons and holes contribute to current flow in an intrinsic semiconductor. Dai/PHYS 342/555 Spring 2012 Chapter 8-42

43 Depletion Region When a p-n junction is formed, some of the free electrons in the n-region diffuse across the junction and combine with holes to form negative ions. In so doing they leave behind positive ions at the donor impurity sites. Dai/PHYS 342/555 Spring 2012 Chapter 8-43

44 P-N Energy Bands For a p-n junction at equilibrium, the fermi levels match on the two sides of the junctions. Electrons and holes reach an equilibrium at the junction and form a depletion region. The upward direction in the diagram represents increasing electron energy. That implies that you would have to supply enery to get an electron to go up on the diagram, and supply energy to get a hole to go down. Dai/PHYS 342/555 Spring 2012 Chapter 8-44

45 P-N Energy Bands To reverse-bias the p-n junction, the p side is made more negative, making it "uphill" for electrons moving across the junction. The conduction direction for electrons in the diagram is right to left, and the upward direction represents increasing electron energy. Dai/PHYS 342/555 Spring 2012 Chapter 8-45

It can then move from vacancy to vacancy leftward toward the positive terminal, which could be described as the hole moving right.

46 -N Energy Bands To forward bias the p-n junction, the p side is made more positive, so that it is "downhill" for electron motion across the junction. An electron can move across the junction and fill a vacancy or "hole" near the junction. It can then move from vacancy to vacancy leftward toward the positive terminal, which could be described as the hole moving right. The conduction direction for electrons in the diagram is right to left, and the upward direction represents increasing electron energy. Dai/PHYS 342/555 Spring 2012 Chapter 8-46

higher energy than the holes in the p-type material.

47 When the p-n junction is forward biased, the electrons in the n-type material which have been elevated to the conduction band and which have diffused across the junction find themselves at a higher energy than the holes in the p-type material. They readily combine with those holes, making possible a continuous forward current through the junction. Dai/PHYS 342/555 Spring 2012 Chapter 8-47

Forward Biased Conduction The forward current in a p-n junction when

n-type material moving leftward across the junction and combining with

Electrons can then proceed further leftward by jumping from hole to

48 Forward Biased Conduction The forward current in a p-n junction when it is forward-biased (illustrated below) involves electrons from the n-type material moving leftward across the junction and combining with holes in the p-type material. Electrons can then proceed further leftward by jumping from hole to hole, so the holes can be said to be moving to the right in this process. Dai/PHYS 342/555 Spring 2012 Chapter 8-48

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