SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

Appendix B BOLTZMANN TRANSPORT THEORY Transport of electrons in solids is the basis of many modern technologies. The Boltzmann t ...

518 APPENDIX B. BOLTZMANN TRANSPORT THEORY n(r) Position Time t = 0 r =δtvk n(r) Position Time t =δt δtvk r Figure B.1: At timet ...

B.1. BOLTZMANN TRANSPORT EQUATION 519 B.1.2 External Field-Induced Evolution offk(r) ................ The crystal momentumkof th ...

520 APPENDIX B. BOLTZMANN TRANSPORT THEORY Substituting for the partial time derivatives due to diffusion and external fields we ...

B.1. BOLTZMANN TRANSPORT EQUATION 521 Substituting these terms and retaining terms only to second-order in electric field (i.e., ...

522 APPENDIX B. BOLTZMANN TRANSPORT THEORY t =τ f(k) t = 0.5 τ t = 0 k= 0 k Figure B.2: This figure shows that at timet=0, the d ...

B.1. BOLTZMANN TRANSPORT EQUATION 523 eτE h fk 0 0 ) eτE h f^0 k)– Figure B.3: The displaced distribution function shows the eff ...

524 APPENDIX B. BOLTZMANN TRANSPORT THEORY Elastic Collisions Elastic collisions represent scattering events in which the energy ...

B.1. BOLTZMANN TRANSPORT EQUATION 525 φ θ' θ α x y z k E k' Figure B.4: Coordinate system illustrating a scattering event. in th ...

526 APPENDIX B. BOLTZMANN TRANSPORT THEORY This weighting factor(1−cosα)confirms the intuitively apparent fact that large-angle ...

B.2. AVERAGING PROCEDURES 527 The perturbation in the distribution function is gk = −∂f^0 ∂Ek τvk·eE ≈ f^0 kBT vk·eE (B.40) If w ...

528 APPENDIX B. BOLTZMANN TRANSPORT THEORY semiconductors. For most scattering processes, one finds that it is possible to expre ...

Appendix C DENSITY OF STATES In semiconductor devices we use the effective mass approximation to describe the properties of elec ...

530 APPENDIX C. DENSITY OF STATES Periodic boundary conditions are shown in figure C.2b. Even though we focus our attention on a ...

APPENDIX C. DENSITY OF STATES 531 2 π L kx ky 2 π L Figure C.2:k-Space volume of each electronic state. The separation between t ...

532 APPENDIX C. DENSITY OF STATES per electron state is(^2 Lπ)^3. Therefore, the number of electron states in the region between ...

APPENDIX C. DENSITY OF STATES 533 ky kx kz –k k 2 dk = k space between k and k + dk k 2 πk dk = area between circles with radii ...

534 APPENDIX C. DENSITY OF STATES N(E) N(E) E–1/2 1D system E (a) E1/2 N(E) 3D system E E^0 2D system E (b) (c) V 0 V 0 V 0 Figu ...

Appendix D IMPORTANT PROPERTIES OF SEMICONDUCTORS The data and plots shown in this Appendix are extracted from a number of sourc ...

536 APPENDIX D. IMPORTANT PROPERTIES OF SEMICONDUCTORS Material Structure Lattice Constant Density (Å) (gm/cm^3 ) C Diamond 3.56 ...