2. Carrier Modeling 3. Carrier Action Chapter 3. Carrier Action  Drift( 표동 )  Diffusion  Recombination and Generation  Equations of State  Supplemental Concepts 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Drift - Changed particle motion in response to an applied electric field ※ Thermal motion → Random scattering → No net motion of group n electrons/cm 3 If E x applied, -qE x on each electron where P x : Total momentum of the group …………….. ① 3. Carrier Action

2. Carrier Modeling 3. Carrier Action · · · · · · · · ② The rate of decrease in N(t) at any time t where t -1 : constant of proportionality t :mean free time between scattering events N(t) : # of electrons not collide by time t N o : # of electrons at t = 0 · · · · · · · · ③ 3. Carrier Action

2. Carrier Modeling 3. Carrier Action Differential change in P x by collision in time dt where = Probability that any electron has a collision in the time interval dt collision ········· ④ From ④ & ①, sum of acc. & dec. = 0 for steady state ① + ④ = 0 ········· ⑤ 3. Carrier Action

2. Carrier Modeling 3. Carrier Action average momentum per electron net drift velocity current density : # of electrons crossing a unit area per unit time n × (v X ) multiplied by (-q) ampere/cm 2 = Coulomb/electrons · electron/cm 3 · cm 2 /s ⑦ → ⑧ ········· ⑥ ········· ⑦ ········· ⑧ where 3. Carrier Action

2. Carrier Modeling 3. Carrier Action Conductivity Mobility : average particle drift velocity per unit electric field For both electrons and holes, current density, J X 3. Carrier Action

2. Carrier Modeling 3. Carrier Action  Resistivity 3. Carrier Action

2. Carrier Modeling 3. Carrier Action for n-type semiconductor for p-type semiconductor 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ The Hall Effect F = q (E + v×B) In y-direction, To maintain a steady state required ········· ② ·················· ① 3. Carrier Action

2. Carrier Modeling 3. Carrier Action 1. Hall effect : establishment of the electric field E y 2. Hall voltage : V AB = E y W From J x = -qn where R H : Hall coefficient 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Invarience of the Fermi level at equlibrium No discontinuity or gradient can arise in the equilibrium Fermi level E F at the boundary such that electrons can move in two materials. (Junction) 3. Carrier Action

2. Carrier Modeling 3. Carrier Action Figure 5-7 Properties of an equilibrium p-n junction : (a) isolated, neutral regions of p-type and n-type material and energy bands for the isolated regions; (b) junction, showing space charge in the transition region W, the resulting electric field E and contact potential V 0, and the separation of the energy bands. 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action  At thermal equilibrium No current → No net charge transport → No net transfer of energy ⇒ Electrons from 2 to 1 = Electrons from 1 to 2 Let N 1 (E) : density of states at energy E in material 1 N 2 (E) : density of states at energy E in material 2 f 1 (E) : probability of a state being filled at E in material 1 f 2 (E) : probability of a state being filled at E in material 2 Rate of electrons move from 1 to 2 = # of filled states in material 1 × # of empty states in material 2 Rate from 2 to 1 3. Carrier Action

2. Carrier Modeling 3. Carrier Action → At equilibrium ① = ② 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Photoconductive Devices -Change resistance when exposed to light - Some photoconductors respond from impurity levels → photons less than band gap energy - Optical sensitivity : optical generation rate g op - Photoconductivity change 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Diffusion of carriers ※ Two basic processes of current conduction 1. diffusion : due to a carrier gradient 2. drift : in an electric field ※ Diffusion : net motion of the carriers from regions of high carrier concentration to regions of low carrier concentration → charge transport process 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Diffusion Processes ※ After a mean free time, half the molecules at the edge will move into the volume and half will move out of the volume until the molecules are uniformly distributed. 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ※ Mean free path ※ Net # of electrons passing x o from left to right in one mean free time : where A : area perpendicular to x ※ Electrons in segment(1) to the left of x o in Fid 4-13b. : Equal chances of moving left or right → in a mean free time, one-half of them into segment(2) 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ※ Rate of electrons flow in the +x direction per unit area (electron flux density ) 3. Carrier Action

2. Carrier Modeling 3. Carrier Action Since x at the center of (1) & (2) where D n : Electron diffusion coefficient = [cm 2 /s] → Net motion of electrons due to diffusion : Direction of decreasing electron concentration 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ※ The diffusion current crossing a unit area (current dinsity) = particle flux density x charge of carrier 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Hot-Point Probe Measurement 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Band Bending 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Diffusion and Drift of Carriers : Built-in Fields ※ If E-field applied 1. Drift component 2. Diffusion component drift diffusion 3. Carrier Action

2. Carrier Modeling 3. Carrier Action  Total current density 3. Carrier Action

2. Carrier Modeling 3. Carrier Action where V : potential ···· ① where E i = -qv Electron → downhill 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ※ At equilibrium Fermi level : not vary with x ① = ② ⇒ Einstein Relation 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Optical Absorption ※ Absorption of incident photons by the material for measuring the band gap energy of a semiconductor ※ Photons with energies greater than the band gap energy : absorbed Photons with energies less than the band gap energy : transmitted 3. Carrier Action

2. Carrier Modeling 3. Carrier Action (a) Initially has more energy than conduction band (b) Loses energy to the lattice in scattering events until eq. velocity ⇒ Electrons and holes created by this absorption process : excess carriers : conductivity (c) Recombination ※ Photon with 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ※ Photons with : Transmitted : Negligible absorption : IR & red transmitted : IR & all visible transmitted 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ※ Absorption coefficient Degradation of the intensity ∝ intensity remaining where α : absorption coefficient [cm -1 ] where I t : intensity of light transmitted l : sample thickness 3. Carrier Action

2. Carrier Modeling 3. Carrier Action For E[eV] & λ[ ㎛ ]  E=1.24/λ 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Luminescence ※ Luminescence : Light emission property ※ Types of luminescence 1.Photoluminescence : By photon absorption 2. Cathodluminescence : By high energy electron bombardment 3. Electroluminescence : By the introduction of current 3. Carrier Action

2. Carrier Modeling 3. Carrier Action 1. Photoluminescence ▪ Fluorescence - Direct recombination of EHP - Fast process - Mean life time ≤ s ▪ Phosphorescence - Emission continues for seconds or minutes after excitation removed. - Slow process → phosphors direct level (impurity) in the band gap - Capture (trap) electrons 3. Carrier Action

2. Carrier Modeling 3. Carrier Action (a) Photon hν 1 >E g : creating an EHP : excitation (b) Give up energy to the lattice by scattering (c) Electron trapped by impurity level E t (d) Thermally re-excited to the conduction band (e) Direct recombination : hν 2 ▪ Delay of time (1) Probability of thermal re-excitation (d) is small : long (2) Several trips between the trap and the conduction band 3. Carrier Action

2. Carrier Modeling 3. Carrier Action Example 4-1 A 0.46 μm - thick sample of GaAs is illuminated with monochromatic light of hν = 2eV. The absorption coefficient α is 5X10 4 cm -1. The power incident on the sample is 10 mW. (a) Find the total energy absorbed by the sample per second (J/s). (b) Find the rate of excess thermal energy given up by the electrons to the lattice before recombination (J/s). (c) Find the number of photons per second given off from recombination events, assuming perfect quantum efficiency. 3. Carrier Action

2. Carrier Modeling 3. Carrier Action Solution ) 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action 2. Cathodluminescence - Excitation by energetic electrons : CRT 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Carrier lifetime and photoconductivity ▪ Excess electrons and holes → Increasing conductivity ▪ Photoconductivity : excess carriers by optical excitation recombination process 3. Electroluminescence : LED ▪ Electric current → The injection of minority carrier into regions where they recombine with majority carriers → Emission of recombination radiation 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Direct recombination 1. Direct recombination - Excess population of electrons and holes decays electrons falling from the conduction band to empty states (holes) in the valance band. - Spontaneously : probability of EHP recombination is constant in time. 2. Rate of decay of electrons at any time t ∝ # of electrons and holes remaining at time t ▪ Net rate of change recombination rate thermal generation rate 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Recombination - Generation ※ Recombination A process whereby electrons and holes are annihilated or destroyed ※ Generation A process whereby electrons and holes are created 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Momentum Consideration ※ Photons : Absorption or emission of light ※ Phonons : Lattice vibration quanta ※ Band-to-band recombination in an indirect semiconductor : Emission or absorption of photon and phonon 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Indirect recombination n o, p o : Carrier concentrations under equilibrium conditions n, p : Carrier concentrations under arbitrary conditions Δn = n - n o Δp = p - p o N T :Number of R-G centers/cm 3 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ※ Low-level injection At equilibrium state for n-type for p-type material 3. Carrier Action

2. Carrier Modeling 3. Carrier Action minority carrier lifetime for holes in n-type material for holes in p-type material Generally, 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Continuity Equations ※ Carrier Action Drift Diffusion Indirect/Direct thermal recombination Indirect/Direct generation etc. ⇒ Change in the carrier concentrations with time. 3. Carrier Action

2. Carrier Modeling 3. Carrier Action Continuity Equations F px + (x) F px + (x+dx) x x+dx dz dy F px + (x) : hole-particle flux ( holes/cm 2 sec) 3. Carrier Action

2. Carrier Modeling 3. Carrier Action The net increase in the number of holes per unit time The net increase in the number of holes per unit time in the differential volume element devide by dxdydz For electron, (1) (2) 3. Carrier Action

2. Carrier Modeling 3. Carrier Action (3) (4) Taking the divergence of Eq.(3) and (4), and substituting back into the continuity equation of (1) and (2), we obtain (5) (6) 3. Carrier Action

2. Carrier Modeling 3. Carrier Action In equation (5) Change vector equation!!! 3. Carrier Action

2. Carrier Modeling 3. Carrier Action (3.44a) (3.44b) (3.45a) (3.45b) 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Minority carrier diffusion equations ※ Simplifying assumptions (1)The particular system under analysis is one-dimensional : all variations are at most a function of just one coordinate (say the x-coordinate) (2) The analysis is limited or restricted to minority carriers. (3) E≈0 in the semiconductor or regions of the semiconductor subject to analysis. (4) The equilibrium minority carrier concentrations are not a function of position. In other words, n o, p 0 = const. (5) Low-level injection conditions prevail. (6) Indirect thermal recombination-generation is the dominant thermal R-G mechanism. (7) There are no "other processes" except possibly photogeneration, taking place within the system. 3. Carrier Action

2. Carrier Modeling 3. Carrier Action for minority carriers 3. Carrier Action

2. Carrier Modeling 3. Carrier Action if not subject to illumination Equilibrium electron concentration : never a function of time 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ※ Minority carrier diffusion equations 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action Step 1. Review informations Si T = 300K N D = /cm 3 G L = 10 17/ cm 3 -sec equilibrium conditions for t<0 Examples) A uniformly donor doped silicon maintained at room temperature is suddenly illuminated with light at time t=0. Assuming N D =10 15 /cm 3. τp=10 -6 sec, and a light-induced creation of electrons and holes Per cm 3 -sec throughout the semiconductor, determine Δp n (t) for t>0. 3. Carrier Action

2. Carrier Modeling 3. Carrier Action Step 2. Characterize the system under equilibrium conditions at RT for Si Step 3. Analyze the problem qualitatively Δp n =0 for t<0 due to equilibrium condition. Δp n : increase from t=0 due to light → increase indirect thermal recombination rate → holes are eliminated by recombination ⇒ steady state : created carrier by light = annihilated carrier by indirect thermal recombination For low-level injection 3. Carrier Action

2. Carrier Modeling 3. Carrier Action Step 4. Perform quantitative analysis 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Diffusion length ⇒ L p and L n represent the average distance minority carriers can diffuse into a sea of minority carriers before being annihilated 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Quasi-Fermi Levels ⇒ Energy levels to specify the carrier concentrations inside a semiconductor under nonequilibrium conditions 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ⇒ Carrier concentration : Changed ⇒ Nonequilibrium conditions by the use of quasi-Fermi levels F N, F P 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Device Fabrication ※ Oxidation : SiO 2 -an insulator in a number of device structures -a barrier to diffusion during device fabrication Si + O 2 → SiO 2 Si + 2H 2 O → SiO 2 + 2H 2 dry oxidation wet oxidation 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Diffusion -introducing dopant atoms into a semiconductor lattice ∙ predeposition : diffusion employing a liquid source ∙ drive - in : already-introduced impurities driven deeper into the semiconductor at higher diffusion temperature after predeposition after drive-in 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Ion Implantation 3. Carrier Action

2. Carrier Modeling 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Lithography 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Epitaxial Growth 1.epitaxial growth, epitaxy - the growth of a thin crystal layer on a wafer of a compatible crystal - growing crystal layer maintains the crystal structure and orientation of the substrate -the technique of growing an oriented single-crystal layer on a substrate wafer 3. Carrier Action

2. Carrier Modeling 3. Carrier Action -lattice mismatching : lattice structure and lattice constant a. -pseudomorphic : if the mismatch is only a few percent and the layer is thin, the epitaxial layer grows with a lattice constant in compliance with that of substrate in compression or tension along the surface plane as its lattice constant adapts to the substrate. 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Thin-Film Deposition -Evaporation (thermal, e- beam) -Sputtering (DC, RF) -CVD (APCVD, LPCVD, PECVD) -MBE (Molecular Beam Epitaxy) -PLD (Pulsed Laser Deposition) 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Evaporation 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ Sputtering DC Sputtering : depositing conducting material RF Sputtering : depositing insulating material 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ MBE 3. Carrier Action

2. Carrier Modeling 3. Carrier Action ◆ CVD (Chemical Vapor Deposition) - APCVD or CVD : atmospheric pressure - LPCVD : low-pressure - PECVD : plasma-enhanced process 3. Carrier Action