EE216.W2010.Lecture4

EE216.W2010.Lecture4 - Lecture 5. Generation and...

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1 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Lecture 5. Generation and Recombination • Recombination and generation processes in semiconductors • direct recombination, low-level injection case Auger and indirect recombination • Current continuity equation (CHH sec. 4.7) • Low-level injection case - steady-state solutions - transient solutions • Surface recombination EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Carrier Generation and Recombination At any T > 0K, a few electrons (10 10 in Si, 10 6 in GaAs) in the valence band gain sufFcient energy to jump into the conduction band. This leaves behind holes. However, there must be a counterbalancing process or we would end up with an inFnite number of electrons and holes-- Recombination. In thermal equilibrium G th = R th and n = p = n i for intrinsic semiconductors E E G R th th c v
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2 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Suppose we shine light on the semiconductor with E = h ν > Ε g so that extra electrons can be excited into the conduction band. E E E g c v h > ν n = n i + Δ n p = n i + Δ p n , p > n i Ϋ ά Ϊ έ Ϊ (INJECTION) Will recombination increase? EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe If light is shined on an extrinsic semiconductor, e.g., n-type ( N d = 10 15 cm -3 ), what happens? D D 2 N n : Level High N n : Level Low / Δ << Δ Δ + Δ + p N n p n N n D i D The mathematics for high level injection are quite complex, hence only low level injection will be discussed here. However, many devices do operate at high level injection. Equilibrium Low Level High Level Injection Injection
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3 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Direct (Band to Band) Recombination Under thermal equilibrium, generation and recombination are not zero , but in balance G o = R o = K p o n o (" o " indicates equilibrium values) where K is a constant. Suppose excess carriers are generated at a rate of G L (e.g., due to incident light) R = K p n = K (p o + Δ p)(n o + n) E E c v n electrons p holes Light EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe where p = p - p o = excess hole concentration n = n - n o = excess electron concentration What will happen if the source of perturbation is removed? The concentration will return to its equilibrium value through recombination of carriers, p p G R thermal i p p p dt dp τ Δ = = 0
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4 EE 216 Principles and Models of Semiconductor Devices (Winter 2010) K. C. Saraswat and R. T. Howe Excess carriers, given time, will recombine to establish thermal equilibrium. The manner in which this process takes place is of fundamental importance to the operation of semiconductor devices.
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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.Lecture4 - Lecture 5. Generation and...

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