Lecture 7 Drift and Diffusion Currents Reading: Notes and Anderson 2 sections 3.1-3.4
Ways Carriers (electrons and holes) can change concentrations Current Flow: Drift: charged article motion in resonse to an electric field. Diffusion: Particles tend to sread out or redistribute from areas of high concentration to areas of lower concentration Recombination: Local annihilation of electron-hole airs Generation: Local creation of electron-hole airs
Drift Direction of motion: Holes move in the direction of the electric field (from + to -) Electrons move in the oosite direction of the electric field (from - to +) Motion is highly non-directional on a local scale, but has a net direction on a macroscoic scale - + Instantaneous velocity is extremely fast Direction of net motion Average net motion is described by the drift velocity, v d with units cm/second Net motion of charged articles gives rise to a current
Drift Electric Field [V/cm] Current Density J [A/cm 2 ] Area A - Electron Motion + Hole Motion Given current density J (I=J x Area) flowing in a semiconductor block with face area A under the influence of electric field E, the comonent of J due to drift of carriers is: J Drift = q v d and J n Drift = q n v d Hole Drift current density Electron Drift current density
Drift At low electric field values, J = qµ E and J n = qnµ n E µ is the mobility of the semiconductor and measures the ease with which carriers can move through the crystal. [µ]=cm 2 /V-Second Thus, the drift velocity increases with increasing alied electric field. More generally, for Silicon and Similar Materials the drift velocity can be emirically given as: v d = µ E o µ oe 1 + vsat β 1 β µ oe vsat when when where v sat is the saturation velocity E E 0
Drift Drift Velocity [cm/sec] ~µ o E v sat Silicon and similar materials E [V/cm]
Drift Designing devices to work here results in faster oeration v eak Drift Velocity [cm/sec] ~µ o E GaAs and similar materials v sat E [V/cm]
Drift Mobility µis the mobility of the semiconductor and measures the ease with which carriers can move through the crystal. [µ]= cm 2 /V-Second µ n ~1360 cm 2 /V-Second for Silicon @ 300K µ ~460 cm 2 /V-Second for Silicon @ 300K µ n ~8000 cm 2 /V-Second for GaAs @ 300K µ ~400 cm 2 /V-Second for GaAs @ 300K µ = n, q τ Where <τ> is the average time between article collisions in the semiconductor. m * n, Collisions can occur with lattice atoms, charged doant atoms, or with other carriers.
Resistivity and Conductivity Ohms Law States: J=σE=E/ρ where σ =conductivity [1/ohm-cm] and ρ=resistivity [ohm-cm] Adding the electron and hole drift currents (at low electric fields), J = J Drift + J n Drift = q(µ n n+ µ )E Thus, σ = q(µ n n+ µ ) and ρ=1/[q(µ n n + µ )] But since µ n and µ change very little and n and change several orders of magnitude: σ ~= qµ n n for n-tye with n>> σ ~= q µ for -tye with >>n
Do not confuse Resistance and Resistivity or Conductance and Conductivity Area A [cm 2 ] Length L [cm] Resistance to current flow along length L (I.e. the electric field is alied along this samles length). R=ρL/A or in units, [ohm-cm][cm]/[cm 2 ]=[ohms]
Energy Band Bending under Alication of an Electric Field Energy Band Diagrams reresent the energy of an electron. When an electric field is alied, energies become deendent on their osition in the semiconductor. If only energy E g is added, then all energy would go to generating the electron and hole air. No energy left for electron/hole motion. (I.e the electron only has otential energy, and no kinetic energy). If energy E>E g is added, then the excess energy would allow electron/hole motion. (Kinetic energy). KE of electrons = E-E c for E>E c KE of holes = E v -E for E<E v
Energy Band Bending under Alication of an Electric Field Elementary hysics says that PE = -qv, where PE = otential energy, q=electron charge and V=electrostatic otential But we can also say that PE = E c -E arbitrary fixed Reference or Elementary hysics says that V = 1 q E E = = 1 q ( ) E c E arbitrary dv dx de dx E = V in or one Thus, 1 de = q dx fixed direction = c v 1 q reference de dx i If an electric field exists in the material, the conduction, valence and intrinsic energies will vary with osition!
Energy Band Bending under Alication of an Electric Field
Diffusion Nature attemts to reduce concentration gradients to zero. Examle: a bad odor in a room. In semiconductors, this flow of carriers from one region of higher concentration to lower concentration results in a diffusion current.
Diffusion Ficks law describes diffusion as the flux, F, (of articles in our case) is roortional to the gradient in concentration. F = D η whereη is the concentration and D is the diffusion coefficient Derivation of Ficks Law at htt://users.ece.gatech.edu/~gmay/ece3040 lecture #8 For electrons and holes, the diffusion current density (flux of articles times -/+q) can thus, be written as, J Diffusion = qd or J n Diffusion = qd n n Note in this case, the oosite sign for electrons and holes
Total Current Since... J and J n = J = and J = J J n + Drift Drift J n + J + J n Diffusion Diffusion = qµ E qd n = qµ ne + qd n n