EE216.W2010.Lecture3

EE216.W2010.Lecture3 - Lecture 3 Carrier Transport in...

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1/11/10 1 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Lecture 3. Carrier Transport in Semiconductors Carrier concentrations: charge neutrality, low- T , high- T Thermal equilibrium: thermal velocity Drift velocity – Mobility, mean free path, and scattering mechanisms – Velocity saturation Drift current density and resistivity EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe From A. S. Grove, Wiley, 1967.
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1/11/10 2 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Fermi Levels in Extrinsic Si From charge neutrality Density of ionized donors is simply that of the donor levels not occupied by electrons as they have gone to the conduction band: Density of ionized acceptors is acceptor levels occupied by electrons to create holes in the valence band: n + N a = p + N d + N d + = N d 1 f D ( E ) ( ) = N d 1 + e E f E d ( ) / kT N a = N a f D ( E ) = N a 1 + e E a E f ( ) / kT In a homogeneous (semi)-conducting medium any net space charge is instantly (within a few ps) neutralized by the movement of carriers ('dielectric relaxation'). EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Solve for N d + , N a - , n, p and E f . If E a << E f << E d , then n + N a = p + N d also np = n i 2 (13) N d + N d N a N a n = 1 2 N d N a ( ) 2 + 4 n i 2 + N d N a ( ) Ρ Σ ΢ Τ Φ Υ N d N a for N d N a ( ) >> n i , n - type Si n = N c e E c E f ( ) / kT = N c e E c E i ( ) / kT e E i E f ( ) / kT = n i e E i E f ( ) / kT E f = E i + kT ln n n i by rearranging the terms (15) (14)
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1/11/10 3 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe (16) (17) (18) p = 1 2 N a N d ( ) 2 + 4 n i 2 + N a N d ( ) Ρ Σ ΢ Τ Φ Υ N a N d for N a N d ( ) >> n i , p - type Si p = n i e E f E i ( ) / kT E f = E i kT ln p n i EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe The 60 mV (or meV) Rule Utility : estimate the Fermi level from the doping concentration … assuming non-degeneracy, room temperature and thermal equilibrium, of course E f = E i + kT n n i E f = E i + (26 meV )(2.3) log 10 n n i E f = E i + 59.9 meV log 10 n n i E f E i + 60 meV log 10 n n i
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1/11/10 4 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Band gap and Fermi level variation with temperature and doping concentration At high temperatures, n i >> | N d - N a | ; n, p n i EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe At low temperatures, freezeout of the dopants ( i.e ., not sufficient thermal energy to free the electrons or holes) becomes important. The density of ionized dopants can be
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This note was uploaded on 06/05/2010 for the course EE 216 taught by Professor Harris,j during the Fall '09 term at Stanford.

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EE216.W2010.Lecture3 - Lecture 3 Carrier Transport in...

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