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Semiconductor Conduction band E 1 eV Forbidden gap
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Valence band
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Figure 29-4 Compare the valence and conduction bands in an insulator (a) and in a semiconductor (b) Compare these diagrams with the one shown in Figure 29-2
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Atom core e Electron Hole e Free electron
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Conduction band e
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The electron, however, has left behind a hole at its previous location Thus, as in a game of musical chairs, the negatively charged, free electrons move in one direction and the positively charged holes move in the opposite direction Pure semiconductors that conduct as a result of thermally freed electrons and holes are called intrinsic semiconductors Because so few electrons or holes are available to carry charge, conduction in intrinsic semiconductors is very low, making their resistances very high
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Fraction of Free Electrons in an Intrinsic Semiconductor Because of the thermal kinetic energy of solid silicon at room temperature, there are 145 1010 free electrons/cm3 What is the number of free electrons per atom of silicon at room temperature
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Si Si Si e Si Si Si Electron Hole Si Si Si e Free electron Si Atom core
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Analyze the Problem
Identify the knowns and unknowns Known:
233 g/cm3 M 2809 g/mol NA 602 1023 atoms/mol For Si: 145 1010 free e /cm3
Unknown:
free e /atom of Si
Solve for the Unknown
free e atom
( N1 )(M )( 1 )(145
1010 free e /cm3 for Si)
2809 g 1 mol
1 mol 602 1023 atoms
1 cm3 233 g
145 1010 free e cm3
290 10 13 free e /atom of Si or, roughly 1 out of 3 trillion Si atoms has a free electron
Substitute NA 602 1023 atoms/mol, M 2809 g/mol, 233 g/cm3, 3 Si free e /cm 145 1010 free e /cm3
Evaluate the Answer
Are the units correct Using dimensional analysis confirms the correct units Is the magnitude realistic In an intrinsic semiconductor, such as silicon at room temperature, very few atoms have free electrons
Math Handbook
Operations with Scientific Notation pages 842 843
6 In pure germanium, which has a density of 523 g/cm3 and an atomic mass of 726 g/mol, there are 225 1013 free electrons/cm3 at room temperature How many free electrons are there per atom 7 At 2000 K, silicon has 189 105 free electrons/cm3 How many free electrons are there per atom at this temperature What does this temperature represent on the Celsius scale 8 At 1000 K, silicon has 923 10 10 free electrons/cm3 How many free electrons are there per atom at this temperature What does this temperature represent on the Celsius scale 9 At 2000 K, germanium has 116 1010 free electrons/cm3 How many free electrons are there per atom at this temperature 10 At 1000 K, germanium has 347 free electrons/cm3 How many free electrons are there per atom at this temperature
29 Solid-State Electronics
Doped Semiconductors
The conductivity of intrinsic semiconductors must be increased greatly to make practical devices Dopants are electron donor or acceptor atoms that can be added in low concentrations to intrinsic semiconductors Dopants increase conductivity by making extra electrons or holes available The doped semiconductors are known as extrinsic semiconductors n-type semiconductors If an electron donor with five valence electrons, such as arsenic (As), is used as a dopant for silicon, the product is called an n-type semiconductor Figure 29-6a shows a location in a silicon crystal where a dopant atom has replaced one of the silicon atoms Four of the five As valence electrons bind to neighboring silicon The fifth electron is called the donor electron The energy of this donor electron is so close to the conduction band that thermal energy can easily move the electron from the dopant atom into the conduction band, as shown in Figure 29-7a Conduction in n-type semiconductors is increased by the availability of these extra donor electrons to the conduction band p-type semiconductors If an electron acceptor with three valence electrons, such as gallium (Ga), is used as a dopant for silicon, the product is called a p-type semiconductor When a gallium atom replaces a silicon atom, one binding electron is missing, creating a hole in the silicon crystal, as shown in Figure 29-6b Electrons in the conduction band can easily drop into these holes, creating new holes Conduction in p-type semiconductors is enhanced by the availability of the extra holes provided by the acceptor dopant atoms, as shown in Figure 29-7b Both p-type and n-type semiconductors are electrically neutral Adding dopant atoms of either type does not add any net charge to a semiconductor Both types of semiconductor use electrons and holes in conduction Only a few dopant atoms per million silicon atoms are needed to increase the conductivity of semiconductors by a factor of 1000 or more Silicon is doped by putting a pure silicon crystal in a vacuum with a sample of the dopant material The dopant is heated until it is vaporized, and the atoms condense on the cold silicon The dopant diffuses into the silicon on warming, and a thin layer of aluminum or gold is evaporated onto the doped crystal A wire is welded to this metal layer, allowing the user to apply a potential difference across the doped silicon
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