NNSE618-L7-DOS-statistics

NNSE618-L7-DOS-statistics - 1 Lecture contents Density of...

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NNSE 618 Lecture #7 1 Lecture contents Density of states Distribution function Statistic of carriers Intrinsic Extrinsic with no compensation Compensation
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NNSE 618 Lecture #7 2 Density of states Problem: Calculate number of states per unit energy per unit volume z z z y y y x x x n L k n L k n L k 2 2 2 Large 3D box (L is large, n is large) with Born-von Karman Boundary Conditions: ikr Ae 3D : 2D : 1D :   3 2 V N x L z L y L Free electron approximation: ) , , ( ) , , ( z y x z y L x x 0 L x V(x) x V 0   z y x z y x z y x n n n L L L k k k 3 2   2 2 S N 2 kL N Number of states:
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NNSE 618 Lecture #7 3 Density of states m k V E 2 2 2 0 In the interval k to k+ k number of states : 2 kL N 3D :      2 1 0 2 1 V E m k In the interval E to E+dE number of states per unit “volume” (spin included): 2D : 1D : m k k E 2   3 2 V N   2 2 2 2 kL k N   3 3 2 2 4 kL k N 2 ) ( m E N   2 1 0 2 1 2 ) ( V E m E N E N V E N 1 ) (   2 1 0 3 2 2 3 2 ) ( V E m E N
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NNSE 618 Lecture #7 4 Density of states and dimensionality From Singh, 2003
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NNSE 618 Lecture #7 5 Density of states in 3D Valence band density of states (calculations) Effective mass density of states   2 1 0 3 2 2 3 * 2 ) ( V E m E N 3D density of states * * c dos m m Conduction band DOS mass in G point:   3 1 * 3 * 2 * 1 3 2 * m m m m c dos Conduction band DOS mass in indirect gap semiconductors: Valence band DOS mass :   3 2 2 / 3 * 2 / 3 * * lh hh dos m m m
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NNSE 618 Lecture #7 6 Intrinsic n-type p-type Carrier concentrations n and p Fermi-Dirac distribution function, f(E) Density of states, N(E) f(E) 1.0 0 E C N(E)     dE E f E N top C E E General: N(E), f(E) and carrier concentrations
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NNSE 618 Lecture #7 7 Filling the empty bands: Distribution function ) ( ) ( ) ( E f E N E n c Electron concentration at the energy E (Density of states) x (distribution function): Electrons (Fermi particles) follow Fermi-Dirac statistics. Fermi-Dirac distribution function:
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This note was uploaded on 11/07/2011 for the course NNSE 618 taught by Professor Sergeoktyabrsky during the Spring '11 term at SUNY Albany.

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NNSE618-L7-DOS-statistics - 1 Lecture contents Density of...

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