In this chapter, you will learn about: Thermal generation/excitation, optical generation/excitation, particle bombardment and other external sources.
COMSATS Institute of Information Technology Virtual campus Islamabad Dr. Nasim Zafar Electronics 1 EEE 231 – BS Electrical Engineering Fall Semester – 2012 Carrier Transport in Semiconductors Lecture No: 4 v v Drift and Mobility Conductivity and Resistance v Continuity Equations v Einstein Relation Kwangwoon University Nasim Zafar Semiconductor device lab Semiconductor Devices Introduction: Ø In the first few lectures we discussed and calculated the equilibrium distribution of charges in a semiconductor n.p = ni2, n ~ ND for ntype Ø last lecture showed how the system tries to restore itself back to equilibrium when perturbed, through R G processes R = (n p ni2)/[tp(n+n1) + tn(p+p1)] Ø In this lecture we will explore the processes that drive the system away from equilibrium Nasim Zafar Introduction: The carrier transport or the mechanisms which cause charges to move in semiconductors can be classified into two categories. Both these mechanisms will be discuss in this lecture. The two mechanisms are: Ø Drift: DriftMotion under an applied electric field Ø Nasim Zafar diffusion: DiffusionMotion due to the concentration The Drift Motion Nasim Zafar An Applied Electric Field Across: ntype Si + V - E n – type Si Vd V L e- Electric field Electron movement Current flow Current carriers are mostly electrons Nasim Zafar + V - An Applied Electric Field V E L Across: Ptype Si p– type Si hole Vd Electric field Hole movement Current flow Current carriers are mostly holes Nasim Zafar The Thermal Velocity: Ø Ø For free charge carriers the thermal energy and the thermal velocity is given by: From classical thermal physics, KE * m v th 2 kT or Ø v th 3kT * m 107 cm/s in Si where vth is the thermal velocity, which is the average velocity of carriers due to thermal excitation The Concept of Driftunder an applied Electric Field: Random scattering events (RG centers) The electric field gives a net drift, superposed on top Nasim Zafar The Concept of Driftunder an Electric Field: Ø If an electric field, Ex, is applied along the xdirection to the Si sample, each electron will experience a net force qEx from F = qE the field, given by: Ø This force may be insufficient to alter, appreciably, the random thermal motion of an individual electron, however, there is a net motion of the group in the xdirection Ø When electrons collide with the lattice and impurity atoms, Carrier Mobility qτ µ= * m Thus: me* mh* in general m ; n − type * e m ; p − type * h Nasim Zafar 15 Carrier Mobility : Ø There are the two basic types of scattering mechanisms that hinder mobility. Thus the mobility has two components: Impurity interaction component Lattice interaction component Nasim Zafar 16 Lets Solve a Problem: Ø Ø Calculate the velocity of an electron in an ntype silicon sample due to its thermal energy at room temperature and due to the application of an electric field of 1000 V/m across the Silicon sample Vth = ? Vd = ? V th = RT = 300 K E = 1000 V / m me* = 1.18 m0 µ = 0.15 m /(V − s ) 3kT � V = 1.08 x 10 m / sec th ∗ m Vd = µ E � Vd = 150 m / sec Nasim Zafar 17 Temperature Dependence of Mobility Nasim Zafar 18 Variation of mobility with temperature At high temperatures L component becomes significant L decreases when temperature increases L C1 T T C1 is a constant It is called as a power law T −1.5 Carriers are more likely scattered by the lattice atoms Nasim Zafar 19 Variation of mobility with temperature At low temperatures I I component is significant decreases when temperature decreases I C2 T Nasim Zafar C2 is a constant 20 Mobility and Scattering: Lattice and Impurity Ø Ø Lattice vibrations: due to temperature Ionized impurity scattering: slow moving carriers are easily affected by a charged ion Net Mobility 1 i i ~i l Temperature Dependence of Mobility T T Low temperature High temperature 1 = + µT µ L µ I ln( ) µL I Peak depends on the density of impurities ln( T ) Nasim Zafar 22 Current Density and Conductivity Nasim Zafar 23 Conductivity and Resistance Ø The semiconductor bar contains both electrons and holes, the conductivity is given by • • • Ø Ø Electric field Current Hole motion Electron motion The resistance of the bar is given L L by: R wt wt Where ρ is the resistivity I Electron motion Ohm’s Law drift Jn = E/ρn drift Jp = E/ρp E = V/L L A I = JA = V/R V R = ρ L/A (Ohms) Nasim Zafar 25 Current Density and Conductivity Ø In a semiconductors, both electrons and holes conduct current: J p ,drift qp E J n ,drift J tot ,drift J p ,drift J tot ,drift q( p Ø p J n ,drift p n n qp p qn( qp )E qn p n E qn E n The conductivity is: – Unit: mho/cm Nasim Zafar 26 E) n E Resistivity and Conductivity drift Jn = σnE ρ = 1/σ drift Jp = σpE – Unit: ohmcm σn = nqµn = nq2τn/mn* σp = pqµp = pq2τp/mp* σ = σn + σp Nasim Zafar 27 Mobility and Drift Current drift Jn = qnv = qnµnE (A/cm2) drift Jp = qpv = qpµpE µn = qτn/mn* µp = qτp/mp* Nasim Zafar 28 Summary Ø The peak of the mobility curve depends on the number density of ionized impurities. Ø Highly doped samples will therefore cause more scattering, and have a lower mobility, than low doped samples. Ø Mobility and resistivity depend on the material properties like m* and sample properties (e.g. NT, which determines τ) Ø This fact is used in high speed devices called High Electron Mobility Transistors (HEMTs) where electrons are made to Nasim Zafar move in undoped material, with the resulting high 29 ... this lecture. The two mechanisms are: Ø Drift: DriftMotion under an applied electric field Ø Nasim Zafar diffusion: DiffusionMotion due to the concentration The Drift Motion Nasim Zafar. .. An Applied Electric Field Across: ntype Si + V - E n – type Si Vd V L e- Electric field Electron movement Current flow Current carriers are mostly electrons Nasim Zafar + V - An Applied Electric Field V... area of the semiconductor Nasim Zafar n : number of charge carriers per unit volume q : charge of t he electron 14 Carrier Mobility qτ µ= * m Thus: me* mh* in general m ; n − type * e m ; p − type * h Nasim Zafar