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Electrons can move more freely in semiconductors than in insulators, but not as easily as in conductors As shown in Figure 29-4b, the energy gap between the valence band and the conduction band is approximately 1 eV How does the structure of a semiconductor explain its electronic characteristics Atoms of the most common semiconductors, silicon (Si) and germanium (Ge), each have four valence electrons These four electrons are involved in binding the atoms together into the solid crystal The valence electrons form a filled band, as in an insulator, but the forbidden gap between the valence and conduction bands is much smaller than in an insulator Not much energy is needed to pull one of the electrons from a silicon atom and put it into the conduction band, as illustrated in Figure 29-5a Indeed, the gap is so small that some electrons reach the conduction band as a result of their thermal kinetic energy alone That is, the random motion of atoms and electrons gives some electrons enough energy to break free of their home atoms and wander around the silicon crystal If an electric field is applied to a semiconductor, electrons in the conduction band move through the solid according to the direction of the applied electric field In contrast to the effect in a metal, the higher the temperature of a semiconductor, the more able electrons are to reach the conduction band, and the higher the conductivity An atom from which an electron has broken free is said to contain a hole As shown in Figure 29-5b, a hole is an empty energy level in the valence band The atom now has a net positive charge An electron from the conduction band can jump into this hole and become bound to an atom once again When a hole and a free electron recombine, their opposite charges neutralize each other.

Figure 29-5 Some electrons in semiconductors have enough thermal kinetic energy to break free and wander through the crystal, as shown in the crystal structure (a) and in the bands (b)

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

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

Now let s move on to the fun part: drawing the curve itself. We ll use preprocessor #defines to establish values for colors and line widths, making it easier to spot them and change them in order to tweak the appearance. Add these lines somewhere near the top of CurveView.m:

Identify the knowns and unknowns Known:

Unknown:

( N1 )(M )( 1 )(145

1010 free e /cm3 for Si)

By examining the query explain plan for this query, you can see the benefit of using indexes in queries The query on the CustomerID column only took 0077 millisecond, compared to the 0258 millisecond for the query sorting the result set on a non-key value While these values do not look all too much different, remember this example was for a table with only five records If instead this table had five million records, these values would be multiplied many times over, creating quite a performance hit As you use the EXPLAIN command, you may notice that sometimes the database engine does not do things you expect it to do Usually, the database engine keeps track of new database objects, such as table indexes, and utilizes them in the query explain plan Sometimes, however, you must force the database engine to re-evaluate how to execute a query The ANALYZE SQL command (different from the ANALYZE parameter in the EXPLAIN command) tells the database engine to re-examine all database objects The table owner can use the ANALYZE command along with the table name to force PostgreSQL to re-examine the table and reset any query explain plans set for the table:

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

#define #define #define #define #define #define #define #define #define CP_RADIUS 0.1 CP_DIAMETER (CP_RADIUS*2) BACKGROUND_COLOR [NSColor whiteColor] GRID_STROKE_COLOR [NSColor lightGrayColor] GRID_FILL_COLOR [NSColor colorWithCalibratedWhite:0.9 alpha:1.0] CURVE_COLOR [NSColor blackColor] LINE_TO_CP_COLOR [NSColor darkGrayColor] CP_GRADIENT_COLOR1 [NSColor lightGrayColor] CP_GRADIENT_COLOR2 [NSColor darkGrayColor]

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

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