Lecture 3 - MIT

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Spring 2007Lecture 31Lecture 3Semiconductor Physics (II)Carrier TransportOutline Thermal Motion Carrier Drift Carrier DiffusionReading Assignment:Howe and Sodini; Chapter 2, Sect. Spring 2007Lecture 321. Thermal Motion Undergo collisions with vibrating Si atoms (Brownian motion) Electrostatically interact with each other and with ionized (charged) dopantsIn thermal equilibrium, carriers are not sitting still:Characteristic time constant of thermal motion: mean free time between collisions c collison time[s]In between collisions, carriers acquire high velocity:vth thermal velocity[cms 1].... but get nowhere! Spring 2007Lecture 33Characteristic length of thermal motion: mean free path[cm] =vth cPut numbers for Si at room temperature: c 10 13svth 107cms 1 mFor reference, state-of-the-art production MOSFET:Lg m Carriers undergo many collisions as they travel through Spring 2007Lecture 342. Carrier DriftApply electric field to semiconductor:E electric field[V cm-1] net force on carrierF = qEBetween collisions, carriers accelerate in the direction of the electrostatic field:v(t)=a t= qEmn, Spring 2007Lecture 35But there is (on the average) a collision every cand the velocity is randomized:The average net velocity in direction of the field:v =vd= qE2mn,p c= q c2mn,pEThis is called drift velocity[cm s-1]Define: n,p=q c2mn,p mobility[cm2V 1s 1]Then, for electrons:and for holes:vdn= nEvdp= pEnet velocityin direction of fieldtime Spring 20

• Undergo collisions with vibrating Si atoms (Brownian motion) • Electrostatically interact with each other and with ionized (charged) dopants In thermal equilibrium, carriers are not sitting still: Characteristic time constant of thermal motion: ⇒mean free time between collisions τc …

  Vibrating