11 - ECE331 Carriers in Semiconductors From the preceding...

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1 Lu ECE331 From the preceding discussion we expect that there should be NO free carriers in a semiconductor crystal at ZERO temperature * This is since ALL electrons are involved in bonding and are therefore unable to carry an electrical current * EQUIVALENTLY we may understand this to be due to the fact that the valence electrons FILL the valence band completely It is well known from BAND THEORY that the net momentum in a FULL band is always ZERO Carriers in Semiconductors BOND PICTURE OF SILICON AT ZERO TEMPERATURE ALL ELECTRONS ARE INVOLVED IN BONDING BAND PICTURE OF SILICON AT ZERO TEMPERATURE … THE VALENCE BAND IS FILLED WITH ELECTRONS E Bot E v E c E Top Lu ECE331 If a bond in the crystal is BROKEN however a “ FREE” electron is created that may carry electrical current * In terms of the energy BAND picture this corresponds to EXCITING an electron from the valence band into the CONDUCTION band In this sense we see that the energy required to break the bond is simply equal to the GAP energy E g The energy required to break the bond may be supplied by THERMAL energy at FINITE temperatures Carriers in Semiconductors BOND PICTURE OF SILICON AT FINITE TEMPERATURE … ELECTRONS ARE LIBERATED WHEN BONDS BREAK BAND PICTURE OF SILICON AT FINITE TEMPERATURE … ELECTRONS ARE EXCITED INTO THE CONDUCTION BAND - E Bot E v E c E Top
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2 Lu ECE331 Electrons are NOT the only charge carriers in a semiconductor at finite temperatures! * Excitation of an electron into the conduction band leaves a void or HOLE in the valence band * In the BONDING model we picture the hole as carrying an electrical current when an electron HOPS from a nearby bond to FILL the original hole By completing the initially broken bond in this manner ANOTHER bond is broken and we can think that the POSITIVE hole has MOVED to a new position Concept of Holes 1 2 1 2 INITIALLY A BOND IS BROKEN IN REGION 1 BUT THEN AN ELECTRON HOPS FROM REGION 2 TO 1 . .. THIS COMPLETES THE ORIGINALLY BROKEN BOND BUT AT THE SAME TIME BREAKS A BOND IN REGION 2 Lu ECE331 Within the framework of the BAND model we picture the hole as the EMPTY state that is left behind in the VALENCE band when an electron is excited into the conduction band * The hole carries CURRENT through the lattice when an electron moves from an occupied state in the valence band to fill the initial hole This process leaves behind ANOTHER empty state in the valence band so that the hole appears to have changed energy state In the language of band theory a current flow may occur in the presence of holes since the net momentum in the valence band is NO LONGER zero Concepts of Holes E Bot E v E c E Top E Bot E
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11 - ECE331 Carriers in Semiconductors From the preceding...

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