Presentation on theme: "The story so far.. The first few chapters showed us how to calculate the equilibrium distribution of charges in a semiconductor np = ni2, n ~ ND for n-type."— Presentation transcript:
1 The story so far..The first few chapters showed us how to calculate theequilibrium distribution of charges in a semiconductornp = ni2, n ~ ND for n-typeThe last chapter showed how the system tries to restore itselfback to equilibrium when perturbed, through RG processesR = (np - ni2)/[tp(n+n1) + tn(p+p1)]In this chapter we will explore the processes that drive the systemaway from equilibrium.Electric forces will cause drift, while thermal forces (collisions)will cause diffusion.ECE 663
2 Drift: Driven by Electric Field vd = mEElectric field(V/cm)Velocity(cm/s)Mobility(cm2/Vs)EWhich has higherdrift?x
10 Ohm’s Law Jn = E/rn Jp = E/rp L E = V/L I = JA = V/R A R = rL/A (Ohms) driftJp = E/rpLE = V/LI = JA = V/RR = rL/A (Ohms)AVWhat’s the unit of r?
11 So mobility and resistivity depend on material properties (e. g. m So mobility and resistivity depend on material properties (e.g. m*) and sample properties (e.g. NT,which determines t)Recall 1/t = svthNT
12 Can we engineer these properties? What changes at the nanoscale?
30 In Equilibrium, Fermi Level is Invariant e.g. non-uniform dopingECE 663
31 Einstein Relationship m and D are connected !!Jn Jn = qnmnE + qDndn/dx = 0diffdriftn(x)= Nce-[EC(x) - EF]/kT = Nce-[EC -EF - qV(x)]/kTdn/dx = -(qE/kT)nDn/mn = kT/qqnmnE - qDn(qE/kT)n = 0ECE 663
32 Einstein Relationship mn = qtn/mn*Dn = kTtn/mn*½ m*v2 = ½ kTDn = v2tn = l2/tnECE 663
33 So… We know how to calculate fields from charges (Poisson) We know how to calculate moving charges(currents) from fields (Drift-Diffusion)We know how to calculate chargerecombination and generation rates (RG)Let’s put it all together !!!ECE 663
48 In summary While RG gives us the restoring forces in a semiconductor, DD gives us the perturbing forces.They constitute the approximate transport eqns(and will need to be modified in 687)The charges in turn give us the fields throughPoisson’s equations, which are correct (unless weinclude many-body effects)For most practical devices we will deal with MCDEECE 663