In this chapter, you will learn about: carrier transport in semiconductors, diffusion of carriers, diffusion processes, diffusion and recombination, continuity equations, einstein relation.
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: 5 Diffusion of Carriers v v Diffusion Processes Diffusion and Recombination v v Continuity Equations v Einstein Relation Kwangwoon University Nasim Zafar Semiconductor device lab Semiconductor Devices Carrier Diffusion: Introduction: Ø When excess carriers are created nonuniformly in a semiconductor, a “concentration gradient” results due to this nonuniformity of the carrier densities in the sample. This concentration gradient, for electrons and holes, will cause a net motion of the charge carriers from the regions of high density to the regions of low carrier density. This type of carrier motion is called Diffusion and represents an important charge transport process in semiconductors Ø Thus, the charge carriers in a semiconductor diffuse, due to the concentration gradient by random thermal motion and under going scattering from: Ø The lattice vibrations and Ø Ionized Impurity atoms Carrier Diffusion: Introduction: v When excess Carrier Diffusion: Introduction: v Thus, the charge carriers in a semiconductor diffuse, due to the concentration gradient by random thermal motion and under going scattering from: vThe lattice vibrations and vIonized Impurity atoms Carrier Diffusion: How can we produce a concentration gradient in a semiconductor? Ø By making a semiconductor or metal contact. Ø By illuminating a portion of the semiconductor with light, (next slide) As the carriers diffuse, a diffusion current flows. The force behind the diffusion current is due to the random thermal motion of the carriers dn dP Ø dx = kT dx Photo Generation and Diffusion: Current mechanisms Drift Current Diffusion Current photons P = nkT dP dn = kT dx dx dn dP = dx kT dx Contact with a metal Photo Generation and Diffusion: Ø By shining light, electronhole pairs can be produced when the photon energy>Eg. Ø The increased number of electronhole pairs will move toward the lower concentration region, until they reach their equilibrium values. Ø So there is a net number of the charge carriers crossing per unit area per unit time, which is called flux Ø Units: [Flux] = m2 – S1 Diffusion Flux : Fick’s first law Diffusion Flux ∞ Concentration Gradient dn/dx dn Flux = − Dn dx [Flux] = m2 – S1 v v D = vth l , [ D] = m2/S D measures the ease of carrier diffusion in response to a concentration gradient D limited by vibrations of lattice atoms and ionized dopant impurities Diffusion Flux : v For Electrons: Fn = Dn dn/dx v For Holes: Fp = Dp dp/dx Dn = electron diffusion coefficient Dp = hole diffusion coefficient Einstein Relationship: Ø Einstein relation relates the two independent current mechanicms of mobility µ with diffusion D. µn = qτn/mn* Dn = kTτn/mn* ½ m*v2 = ½ kT Dn = v2τn = l2/τn Einstein Relation: Dn kT = µn q and Dp kT = µp q for electrons and holes Constant value at a fixed temperature cm sec = volt cm V − sec kT = 25 mV q kT ( J / K ) ( K ) = = volt q C at room temperature Diffusion Current Density: J Diffusion current density = charge x carrier flux Total Current: Ø Diffusion Current within a semiconductor consists of: i hole component and ii electron component Ø Total Current flowing in a semiconductor is the sum of: i drift current and ii diffusion current: Diffusion Current Densities: [ Flux ] = m−2 − s −1 D = ν thl , [ D ] = m s The current densities for electrons and holes dn � dn � J n = −q � − Dn �= qDn dx � dx � for electrons dp � dp � J p = +q � − Dp = − qD p � dx dx � � for holes � � � � J = A m �n , p � � � Total Current Density: When both electric field and the concentration gradient are present, the total current density, for the electron, is given as: dn J n = qµ n nE + qDn dx dp J p = q µ p pE − qD p dx J total = J n + J p Summary Ø Current flowing in a semiconductor consists of drift and diffusion components: J tot qp qn n E qDn pE dn dp qD p dx dx Ø Mobility and Conductivity are highly temperature dependent Ø Generation and Recombination processes were discussed Nasim Zafar 18 Summary Resistivity formula qp p qn n J drift J n | diff Jp Jn J n | drift J p |drift q dn qDn and J p | diff dx J p|drift J n |drift J p|diff J n |diff nn pp Drift current density E dp qDp dx qpE ( )qDp qnE dn qDn dx dp dx Diffusion current density Total hole and electron current density J = Jn + Jp Total current density 19 ... Carrier Transport in Semiconductors Lecture No: 5 Diffusion of Carriers v v Diffusion Processes Diffusion and Recombination v v Continuity Equations v Einstein Relation Kwangwoon University Nasim. .. Mobility and Conductivity are highly temperature dependent Ø Generation and Recombination processes were discussed Nasim Zafar 18 Summary Resistivity formula qp p qn n J drift J n | diff Jp Jn J n | drift J p |drift... q for electrons and holes Constant value at a fixed temperature cm sec = volt cm V − sec kT = 25 mV q kT ( J / K ) ( K ) = = volt q C at room temperature Diffusion Current Density: J Diffusion current density = charge x carrier flux