# In order to understand how the potential and charge

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Unformatted text preview: in. –  ID increases ~ linearly with input voltage (VG), because the carrier concentration in the channel is proportional to (VG-VTH) In order to understand how MOSFET design parameters affect MOSFET performance, we first need to understand how a MOS capacitor works... EE105, Fall 2013 Lecture 15 – Slide 8 Prof. Ming C. Wu 4 MOS Capacitor §༊  A metal-oxide-semiconductor structure can be considered as a parallel-plate capacitor, with the top plate being the positive plate, the gate insulator being the dielectric, and the p-type semiconductor substrate being the negative plate. §༊  The negative charges in the semiconductor (for VG &gt; 0) are comprised of conduction electrons and/or acceptor ions. §༊  In order to understand how the potential and charge distributions within the Si depend on VG, we need to be familiar with electrostatics... EE105, Fall 2013 Lecture 15 – Slide 9 Prof. Ming C. Wu Gauss’s Law ∇⋅E = ρ ε ρ is the net charge density ε is the dielectric permittivity à༎ If the magnitude of electric ﬁeld changes, there must be charge! §༊  In a charge- free region, the electric ﬁeld must be constant. §༊  Gauss’ Law equivalently says that if there is a net electric ﬁeld leaving a region, there must be posiNve charge in that region: ∫ E ⋅ dS = EE105, Fall 2013 Q ε Lecture 15 – Slide 10 The integral of the electric field over a closed surface is proportional to the charge within the enclosed volume Prof. Ming C. Wu 5 Gauss’s Law in 1- D ∇⋅E = dE ρ = dx ε ρ dx ε x ρ ( x' ) E ( x) = E ( x0 ) + ∫ dx ' ε x dE = 0 §༊  Consider a pulse charge distribuNon: ρ ( x) 0 Xd x E ( x) 0 − qNA x Xd Lecture 15 – Slide 11 EE105, Fall 2013 Prof. Ming C. Wu ElectrostaNc PotenNal §༊  The electric ﬁeld (force) is related to the potenNal (energy): dV E=− dx ⇒ d 2V ( x) ρ ( x) =− 2 dx ε –  N...
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## This note was uploaded on 01/22/2014 for the course EE 105 taught by Professor King-liu during the Fall '07 term at University of California, Berkeley.

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