Prof. Jang-Ung Park (박장웅) Chapter 2. Current Flow & Capacitance Prof. Jang-Ung Park (박장웅) http://wearable.unist.ac.kr

Current, Electric Field, Voltage Electric field : E = - grad V = -V Electric field strength : The direction of electric field : from positive potential to negative. Electric current : the flow of electric charge (electron / hole) when electric field is applied. I (coulombs / second) (C / s) = qnvdA q: the charge on electrons (-1.610-19C) n: the number of electrons per unit volume vd: the drift velocity A : area J: current density (= I / A)

Electrical Conductivity () In the macroscale (Ohm’s law), In the quantum scale, : Because ions are attached to the lattice sites, ions have no net translational motion.  Negligible contribution to the current. : The current is due to the drift motion of the conduction electrons under electric field. steady-state force to conduction electron :  dv/dt=0 vd: average drift velocity m*: effective mass of electron : relaxation time E: electric field strength : mobility force exerted by E field friction force due to the collision

Electrical Conductivity ()  drift current: relaxation time ()??  vth: thermal velocity l: distance between two successive collisions (mean free path) The thermal energy absorbed by electrons is converted to kinetic energy: vth: ~ 105 m/s vd: 10-2 m/s - 104 m/s  Comparison between vd and vth

High-Field Effects (hot carrier effects) In Ohm’s law, vd: average drift velocity m*: effective mass of e- : relaxation time E: electric field strength vr: ~ 106 m/s vd ~ thermal velocity (vth) vth: ~ 105 m/s (due to the lattice scattering) high-field effect (Ohm’s law is not valid) : used to maximize vd (device speed) Movie (the temperature of the current CPU processors > 350oC)

Sheet Resistance (Rs)  Integrated circuits are composed of thin films of various materials, and it is convenient to define the resistance of a thin conductive sheet as sheet resistance. unit of Rs : “/square” or “/” ( = L/W) Measurement of R and Rs [ two point probe method ] : The contact resistance btw the sample and probes are included in the measured, total resistance value. : When we don’t know the contact resistance, it is difficult to find the resistance of the sample.

Contact Resistance (Rcontact) Measurement of Rcontact [ Transfer length method using two point probe ] sample L metal probe contact interface : Rcontact is independent on L. : Values of Rtotal at different L are measured using two probes. Rtotal 2Rcontact L

Sheet Resistance (Rs) Measurement of R and Rs [ four-point probe method ] sample : Because voltage probes are connected in parallel to current probes, sample’s resistance is directly measured without considering the contact resistance. For a very thin layer (S » t), For R=V/2I, (k =  / ln2 = 4.53)

Diffusion and Drift of Carriers; Built-in Fields Diffusion processes The net motion of electrons due to diffusion is in the direction of decreasing electron concentration. : not dependent on the carrier concentration but the carrier gradient dn/dx (minority carriers can determine J). Dn: diffusion constant of electron Dp: diffusion constant of hole If an electric field is present in addition to the carrier gradient, drift diffusion

Diffusion and Drift of Carriers; Built-in Fields If an electric field is present in addition to the carrier gradient, (at Room Temperature) : Einstein Relation