1Carrier Transport and Access carrier phenomenaµ Drift and Diffusion Currents Chapter-4 ¸HW#5 solution23Mobile Charge Carriers in Semiconductors• Three primary types of carrier action occur inside a semiconductor:– Drift: charged particle motion under the influence of an electric field.–Diffusion: particle motion due to concentration gradient or temperature gradient.– Recombination-generation (R-G)Carrier MotionCarrier DynamicsElectron DriftHole DriftElectron DiffusionHole Diffusion4.1 Carrier Drift Direction of motion¾ Holes move in the direction of the electric field. (⊕F\)¾ Electrons move in the opposite direction of the electric field. (\F⊕)¾ Motion is highly non-directional on a local scale, but has a net direction on a macroscopic scale.¾ Average net motion is described by the drift velocity, vd[cm/sec].¾ Net motion of charged particlesgives rise to a current.Instantaneous velocity is extremely fastDescribe the mechanism of the carrier drift and drift current due to an applied electric field.4.1 Drift Drift of CarriersElectric FieldDrift of electron in a solidThe ball rolling down the smooth hill speeds up continuously, but the ball rolling down the stairs moves with a constant average velocity.µ[cm2/Vsec] : mobility4Random thermal motion.Combined motion due to random thermal motion and an applied electric field.4.1 Drift Schematic path of an electron in a semiconductor.EECarrier Scattering• Mobile electrons and atoms in the Si lattice are always in random thermal motion.– Electrons make frequent collisions with the vibrating atoms• “lattice scattering”or “phonon scattering”– increases with increasing temperature– Average velocity of thermal motion for electrons: ~107cm/s @ 300K• Other scattering mechanisms:– deflection by ionized impurity atoms– deflection due to Coulombic force between carriers• “carrier-carrier scattering”• only significant at high carrier concentrations• The net current in any direction is zero, if no electric field is applied.12345electronThe motion of an electron in a solid under the influence of an applied field.Energy-band representation of the motion, indicating the loss of energywhen the electron undergoes a collision.4.1 Drift inside a solidEDriftRandom thermal motion.Combined motion due to random thermal motion and an applied electric field.5Carrier Drift• When an electric field (e.g. due to an externally applied voltage) is applied to a semiconductor, mobile charge-carriers will be accelerated by the electrostatic force. This force superimposes on the random motion of electrons:12345electron• Electrons drift in the direction opposite to the electric fieldÆ current flows Because of scattering, electrons in a semiconductor do not achieve constant acceleration. However, they can be viewed as quasi-classical particles moving at a constant average drift velocity vd4.1 Drift Conduction process in an n-type semiconductor Thermal equilibrium Under a biasing condition4.1 DriftGiven current density J ( I = J x Area ) flowing in a semiconductor block with face area A under the influence of electric field E, ρ is volume density, the component of J due to drift of carriers is:Hole Drift Current DensitydpvpqJvJdrfdrfd⋅⋅==Electron Drift Current DensitydnvneJ drf⋅⋅−=anddpdrfvpeJvJdrfd⋅⋅==ρDrift At Low Electric Field Values,EpeJpDriftp⋅⋅⋅=µEneJnDriftn⋅⋅⋅=µand¾µ[cm2/V·sec] is the “mobility” of the semiconductor and measures the ease with which carriers can move through the crystal. ¾ The drift velocity increases with increasing applied electric field.:EnpqJJJnpDriftnDriftpdrf⋅+=+= )(µµ6Electron and hole mobilities of selected intrinsic semiconductors (T=300K)Si Ge GaAs InAsµn (cm2/V·s) 1350 3900 8500 30000µp (cm2/V·s) 480 1900 400 500 sVcmV/cmcm/s2⋅=µhas the dimensions of v/ :Electron and Hole Mobilities Example • Consider a Si sample at 300K with doping concentration of Na=0 and Nd=1016cm-3. Asume electron and hole mobilities given in table 4.1. Calculate the drift current density if the applied electyric filed is e=35/cm.EX 4.1• Consider a GaAs sample at 300K with doping concentration of Na=0 and Nd=1016cm-3. Assume electron and hole mobitities given in table 4.1. Calculate the drift current density if the applied electric filed is E=10V/cm.74.1.2: Mobility effectsF = (-e) = moaF = (-e)= mn*awhere mn* is the electron effective massIn vacuum In semiconductorF = m n*dvd/dt =-eEυd=etE/mn*•µp≡ [eτcp/ mp*] is the hole mobilityCarrier Mobility|vd| = eτmn/ mn* =µn•µn≡ [eτcn/ mn*] is the electron mobilitySimilarly, for holes:|vd| = eτmp/ mp* ≡µp a) Find the hole drift velocity in an intrinsic Si sample for = 103V/cm.b) What is the average hole scattering time?Solution:a)b)Example: Drift Velocity Calculationvd= µnqmmqppmppmppµττµ**=⇒=Mean Free Path• Average distance traveled between collisionsmpthvlτ=EX 4.2Using figure 4.3 determine electron and hole nobilities.8EX 4.2Using figure 4.3 determine electron and hole mobilities in (a) Si for Nd=1017cm-3,Na=5 x 1016cm-3and (b) GaAs for Na=Nd=1017cm-3Ex 4.2 Effect of Temperature on MobilityTemperature dependence of mobility with both lattice and impurity scattering.¾ A carrier moving through the lattice encounters atoms which are out of their normal lattice positions due to the thermal vibrations.¾ The frequency of such scattering increases as temperature increases.At low temp. lattice scattering is less important.¾ At low temperature, thermal motion of the carriers is slower, and ionized impurity scattering becomes dominant.¾ Since the slowing moving carrier is likely to be scattered more strongly by an interaction with charged ion.¾ Impurity scattering events cause a decrease in mobility with decreasing temperature.As doping concentration increase, impurity scattering increase, then mobility decrease.Mobility versus temperatureMobility versus temperature Effect of Temperature on Mobility¾ Electron mobility in silicon versus temperature for various donor concentrations. ¾ Insert shows the theoretical temperature dependence of electron mobility.9¾µ[cm2/Vsec] is the “mobility” of the semiconductor and measures the ease with which carriers can move through the crystal.  Mobilityµn~ 1360 cm2/Vsec for Silicon @ 300Kµp~ 460 cm2/Vsec for Silicon @ 300Kµn~ 8000 cm2/Vsec for GaAs @ 300Kµp~ 400