Advanced Semiconductor Fundamentals Chapter 6 Carrier Transport Chapter

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Chapter 6 Carrier Transport Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport DRIFT Definition-Visualization Drift is charge-particle motion in response to an applied electric field. The probability that a particle experience collision during time dt: If there are n(t) particles, Collision becomes less with time. Number of particles experience a collision during dt. Average time, Mean free time Mean free path Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport In steady-state, carriers drifts at a constant drift velocity by balancing between acceleration by electric field and deceleration by collision. Total momentum at t acceleration, deceleration, Momentum change due to collision during dt Average momentum per electron, In 3 -D, 1 -D expression for electron for hole Where are conductivity effective masses. Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Two effective masses of carrier The density of states effective mass for electrons and holes is given by, The conductivity (or mobility) effective mass for electrons and holes is given by, Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Drift Current The formal definition of current, In vector notation, similarly, Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Mobility The carrier mobility varies inversely with the amount of scattering taking place within the semiconductor. To theoretically characterize mobility it is therefore necessary to consider the different types of scattering events that can take place inside a semiconductor. (i) (iii) (iv) (v) Phonon (lattice) scattering Ionized impurity scattering Scattering by neutral impurity atoms and defects Carrier-carrier scattering Piezoelectric scattering For the typically dominant phonon and ionized impurity scattering, single-component theories yield, respectively, to first order where Matthiessen’s Rule Noting that each scattering mechanism gives rise to a “resistance-to-motion” which is inversely proportional to the component mobility, and taking the “resistance” to be simply additive (analogous to a series combination of resistors in an electrical circuit), one obtains Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Doping/Temperature Dependence The Si carrier mobility versus doping and temperature plots presented respectively in Figs 6. 5 and 6. 6 were constructed employing the empirical-fit relationship where All other quantities are fit parameters that exhibit a temperature dependence of the form where Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport from first order theory Experimental values for lightly doped Si, for electron for hole Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport For Ga. As, Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport High-Field/Narrow-Dimensional Effects Under low electric field Velocity Saturation under high electric field A = 0. 8 Td = 600 K Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Intervalley Carrier Transfer For Ga. As ellipsoidal constant energy surface spherical constant energy surface = 0. 29 e. V Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport for nondegenerated semiconductor where Te is an electron temperature For temperature higher than this, the upper valley has a higher density of states occupied. The total conductivity for carriers in the two set of valleys, Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport (-)function also, where for Ga. As. Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Assuming that the electron temperature increases linearly with electric field, simple transcendental equation Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport So that negative differential conductivity sets when as little as 15 % of the electrons transferred to the upper valleys. Read “Ballistic transport/velocity overshoot”. Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Related Topics Resistivity/Conductivity or In a homogeneous material, resistivity conductivity, for n-type semiconductor for p-type semiconductor Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Sheet Resistance Four-point probe technique 1) For thick sample (s << t) At probe 1, where D t I In spherical coordinate system Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport At probe 4, I where : thickness correction factor Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport 2) For thin sample (s >> t) At probe 1, where D t I At probe 4, In cylinderical coordinate system Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals where Chapter 6. Carrier Transport : size correction factor : same as before summary i) If t >> s and D >> s, ii) If the condition for t >> s and D >> s is not satisfied, iii) In most cases, t << s and D >> s, Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Hall Effect Lorenz force in the sample assuming p-type, Lorenz force in y-direction must be balanced under steady state. Moreover, Hall coefficient, for p-type for n-type Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport With measurable quantity, If VH is given in volts, w in cm, B in gauss, I in amps, and RH in cm 3/coul. The resistance of the bar is just VA/I. The Hall mobility, More exacting analysis gives, for p-type Hall factor for n-type The relationship between hall mobility and drift mobility Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Anisotropic Conductivity The equations, so far, for the mobility, conductivity, and Hall constant are applicable for electrons in spherical band minima. The situation is somewhat more complicated, when the carrier transport in an ellipsoidal minima. transverse longitudinal The total current density is therefore, Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport This can also be put in the form, “anisotropic conductivity” y x Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals ky Chapter 6. Carrier Transport kx For example, Si: Concentration of electron in each minima is n/6. kz When the electric field in x-direction, the total current in the x-direction Similar expressions can be obtained for y- and z-directions and for any electric field. Compare with the expression for the conductivity, : conductivity mobility : conductivity effective mass scalar quantity Isotropic conductivity The current and the electric field are always in the same direction. Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport DIFFUSION Definition-Visualization Diffusion Current SIMPLIFYING ASSUMPTIONS: Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Consider the p-type semiconductor bar of cross-sectional area A and the steady-state hole concentration gradient shown in the figure. Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Finally, introducing (exact three dimensional analysis leads to ) In three dimension, The hole and electron diffusion coefficient with standard unit of cm 2/sec. Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Einstein Relationship Consider a nununiformly doped semiconductor under equilibrium conditions, as shown below. under equilibrium condition Nonzero electric field is established inside nonuniformly doped semiconductors under equilibrium conditions. where generalized form of Einstein relationship Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport In the nondegenerate semiconductor, Einstein relationship for electrons Similar argument for holes, Einstein relationship for holes (Home work) Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport EQUATIONA OF STATE Current Equations Carrier Currents : total particle current at steady state Dielectric Displacement Currents The change in polarization may be viewed as given rise to a nonparticle current, the dielectric displacement current. Ex) Current flow through a capacitor under a. c. and transient conditions For a linear dielectric, : total current under a. c. and transient conditions Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Quasi-Equilibrium and Quasi-Femi Energies For nondegenerate semiconductors, equilibrium due to perturbation nonequilibrium with small perturbation Carrier distributions remain almost unchanged from the equilibrium distributions even when small perturbation applied to the semiconductor. This is referred to the quasi-equilibrium and the Fermistatistics developed at equilibrium still can be used with quasi -Fermi energies, FN and FP, at quasi-equilibrium. Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Differentiating the nonequilibrium carrier concentration, where Ohm’s law Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Continuity Equations By introducing, and noting the particle divergence, Jung-Hee Lee @ Nitride Semiconductor Device Lab.

Advanced Semiconductor Fundamentals Chapter 6. Carrier Transport Minority Carrier Diffusion Equations Minority carrier diffusion equations Jung-Hee Lee @ Nitride Semiconductor Device Lab.