Lecture #19Minority-Carrier Charge StorageDerivation of Charge Control Model(Long Base Diode)Charge Control ModelCharge Control Model for Narrow BaseSummarySlide 8EE130 Lecture 19, Slide 1Spring 2007Lecture #19OUTLINE• pn junctions (cont’d)– Charge control modelReading: Finish Chapter 6.3EE130 Lecture 19, Slide 2Spring 2007Minority-Carrier Charge Storage•When VA>0, excess minority carriers are stored in the quasi-neutral regions of a pn junction:PnnxnPLxpqAdxxpqAQn)( )(NppxpNLxnqAdxxnqAQp)( )(EE130 Lecture 19, Slide 3Spring 2007Derivation of Charge Control Model•Consider a forward-biased pn junction. The total excess hole charge in the n quasi-neutral region is:•The minority carrier diffusion equation is (without GL):•Since the electric field is very small,•Therefore:nxnPdxtxpqAQ ),(pnnPnpxpDtp22xpPPnqDJpnPnpqxJtpq )(EE130 Lecture 19, Slide 4Spring 2007•Integrating over the n quasi-neutral region:•Furthermore, in a p+n junction:•So:nPnpnxnpJxJPxndxpqAdJAdxpqAt1)()(DIFFnPnPPJxJPixAJxAJAJdJAPnp)()()()()(pPDIFFPQidtdQ(Long Base Diode)EE130 Lecture 19, Slide 5Spring 2007Charge Control ModelWe can calculate pn-junction current in 2 ways:1. From slopes of np(-xp) and pn(xn) 2. From steady-state charges QN, QP stored in each excess-minority-charge distribution:pPnPnPQxIxAJτ)()( nNpNQxIτ)( Similarly,0τ)( pPnPPQxAJdtdQEE130 Lecture 19, Slide 6Spring 2007Charge Control Model for Narrow Base•For a narrow-base diode, replace p and/or n by the minority-carrier transit time tr–time required for minority carrier to travel across the quasi-neutral region–For holes on narrow n-side:–Similarly, for electrons on narrow p-side: PNPPptrNnnPnPPPNnnWxnPDWIQWxpqADdxpdqADAJIWxpqAdxxpqAQNn2 τ)()(21)(2, NPntrDW2τ2,EE130 Lecture 19, Slide 7Spring 2007Summary•Under forward bias, minority-carrier charge is stored in the quasi-neutral regions of a pn diode.–Long base:–Short base: PkTqVDiPLeNnqAQA1/2 NkTqVAiNLeNnqAQA1/2 PkTqVAiNWeNnqAQA 121/2 NkTqVDiPWeNnqAQA 121/2EE130 Lecture 19, Slide 8Spring 2007•The steady-state diode current can be viewed as the charge supply required to compensate for charge loss via recombination (long base) or collection at the contacts (short base)–Long base:–Short base:wherepPnNQQIττptrPntrNQQI,,ττPPpPNNnNLDLLDLτ and τNote that NPntrDW2τ2,
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