Semiconductor Device Physics Lecture 4 Dr Ing Erwin

Semiconductor Device Physics Lecture 4 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress. com 2 President University 0 1 6 Erwin Sitompul SDP 4/1

Chapter 3 Carrier Action Direct and Indirect Semiconductors E-k Diagrams Ec Ec Phonon Photon Ga. As, Ga. N Photon Ev Si, Ge (direct semiconductors) (indirect semiconductors) • Little change in momentum is required for recombination • Momentum is conserved by photon (light) emission President University Ev • Large change in momentum is required for recombination • Momentum is conserved by mainly phonon (vibration) emission + photon emission Erwin Sitompul SDP 4/2

Chapter 3 Carrier Action Excess Carrier Concentrations Deviation from equilibrium values Values under arbitrary conditions Equilibrium values n Positive deviation corresponds to a carrier excess, while negative deviation corresponds to a carrier deficit. n Charge neutrality condition: President University Erwin Sitompul SDP 4/3

Chapter 3 Carrier Action “Low-Level Injection” n Often, the disturbance from equilibrium is small, such that the majority carrier concentration is not affected significantly. n However, the minority carrier concentration can be significantly affected. n For an n-type material n For a p-type material n This condition is called “low-level injection condition”. n The workhorse of the diffusion in low-level injection condition is the minority carrier (which number increases significantly) while the majority carrier is practically undisturbed. President University Erwin Sitompul SDP 4/4

Chapter 3 Carrier Action Indirect Recombination Rate n Suppose excess carriers are introduced into an n-type Si sample by shining light onto it. At time t = 0, the light is turned off. How does p vary with time t > 0? n Consider the rate of hole recombination: NT : number of R–G centers/cm 3 Cp : hole capture coefficient n In the midst of relaxing back to the equilibrium condition, the hole generation rate is small and is taken to be approximately equal to its equilibrium value: President University Erwin Sitompul SDP 4/5

Chapter 3 Carrier Action Indirect Recombination Rate n The net rate of change in p is therefore: where • For holes in n-type material n Similarly, where • For electrons in p-type material President University Erwin Sitompul SDP 4/6

Chapter 3 Carrier Action Minority Carrier Lifetime n The minority carrier lifetime τ is the average time for excess minority carriers to “survive” in a sea of majority carriers. n The value of τ ranges from 1 ns to 1 ms in Si and depends on the density of metallic impurities and the density of crystalline defects. n The deep traps originated from impurity and defects capture electrons or holes to facilitate recombination and are called recombination-generation centers. President University Erwin Sitompul SDP 4/7

Chapter 3 Carrier Action Photoconductor n Photoconductivity is an optical and electrical phenomenon in which a material becomes more electrically conductive due to the absorption of electro-magnetic radiation such as visible light, ultraviolet light, infrared light, or gamma radiation. n When light is absorbed by a material like semiconductor, the number of free electrons and holes changes and raises the electrical conductivity of the semiconductor. n To cause excitation, the light that strikes the semiconductor must have enough energy to raise electrons across the band gap. President University Erwin Sitompul SDP 4/8

Chapter 3 Carrier Action Example: Photoconductor n Consider a sample of Si at 300 K doped with 1016 cm– 3 Boron, with recombination lifetime 1 μs. It is exposed continuously to light, such that electron-hole pairs are generated throughout the sample at the rate of 1020 per cm 3 per second, i. e. the generation rate GL = 1020/cm 3/s. a) What are p 0 and n 0? b) What are Δn and Δp? • Hint: In steady-state (equilibrium), generation rate equals recombination rate President University Erwin Sitompul SDP 4/9

Chapter 3 Carrier Action Example: Photoconductor n Consider a sample of Si at 300 K doped with 1016 cm– 3 Boron, with recombination lifetime 1 μs. It is exposed continuously to light, such that electron-hole pairs are generated throughout the sample at the rate of 1020 per cm 3 per second, i. e. the generation rate GL = 1020/cm 3/s. c) What are p and n? d) What are np product? • Note: The np product can be very different from ni 2 in case of perturbed/agitated semiconductor President University Erwin Sitompul SDP 4/10

Chapter 3 Carrier Action Net Recombination Rate (General Case) n For arbitrary injection levels and both carrier types in a nondegenerate semiconductor, the net rate of carrier recombination is: where • ET : energy level of R–G center President University Erwin Sitompul SDP 4/11

Chapter 3 Carrier Action Continuity Equation n Consider carrier-flux into / out of an infinitesimal volume: Area A, volume A. dx Flow of current JN(x) JN(x+dx) Flow of electron dx President University Erwin Sitompul SDP 4/12

Chapter 3 Carrier Action Continuity Equation • Taylor’s Series Expansion n The Continuity Equations President University Erwin Sitompul SDP 4/13

Chapter 3 Carrier Action Minority Carrier Diffusion Equation n The minority carrier diffusion equations are derived from the general continuity equations, and are applicable only for minority carriers. n Simplifying assumptions: n The electric field is small, such that: • For p-type material • For n-type material n Equilibrium minority carrier concentration n 0 and p 0 are independent of x (uniform doping). n Low-level injection conditions prevail. President University Erwin Sitompul SDP 4/14

Chapter 3 Carrier Action Minority Carrier Diffusion Equation n Starting with the continuity equation for electrons: n Therefore n Similarly President University Erwin Sitompul SDP 4/15

Chapter 3 Carrier Action Carrier Concentration Notation n The subscript “n” or “p” is now used to explicitly denote n-type or p-type material. n pn is the hole concentration in n-type material n np is the electron concentration in p-type material n Thus, the minority carrier diffusion equations are: • Partial Differential President University • Equation (PDE)! The so called “Heat Conduction Equation” Erwin Sitompul SDP 4/16

Chapter 3 Carrier Action Simplifications (Special Cases) n Steady state: n No diffusion current: n No thermal R–G: n No other processes: • Solutions for these common special-case diffusion equation are provided in the textbook President University Erwin Sitompul SDP 4/17

Chapter 3 Carrier Action Minority Carrier Diffusion Length n Consider the special case: n Constant minority-carrier (hole) injection at x = 0 n Steady state, no light absorption for x > 0 n The hole diffusion length LP is defined to be: Similarly, President University Erwin Sitompul SDP 4/18

Chapter 3 Carrier Action Minority Carrier Diffusion Length n The general solution to the equation is: n A and B are constants determined by boundary conditions: n Therefore, the solution is: • Physically, LP and LN represent the average distance that a minority carrier can diffuse before it recombines with a majority carrier. President University Erwin Sitompul SDP 4/19

Chapter 3 Carrier Action Example: Minority Carrier Diffusion Length n Given ND=1016 cm– 3, τp = 10– 6 s. Calculate LP. n From the plot, President University Erwin Sitompul SDP 4/20

Chapter 3 Carrier Action Quasi-Fermi Levels n Whenever Δn = Δp ≠ 0 then np ≠ ni 2 and we are at nonequilibrium conditions. n In this situation, now we would like to preserve and use the relations: n On the other hand, both equations imply np = ni 2, which does not apply anymore. n The solution is to introduce to quasi-Fermi levels FN and FP such that: • The quasi-Fermi levels is useful to describe the carrier concentrations under non-equilibrium conditions President University Erwin Sitompul SDP 4/21

Chapter 3 Carrier Action Example: Quasi-Fermi Levels n Consider a Si sample at 300 K with ND = 1017 cm– 3 and Δn = Δp = 1014 cm– 3. a) What are p and n? • The sample is an n-type b) What is the np product? President University Erwin Sitompul SDP 4/22

Chapter 3 Carrier Action Example: Quasi-Fermi Levels n Consider a Si sample at 300 K with ND = 1017 cm– 3 and Δn = Δp = 1014 cm– 3. 0. 417 e. V c) Find FN and FP? Ec FN Ei FP Ev 0. 238 e. V President University Erwin Sitompul SDP 4/23

Chapter 3 Carrier Action Homework 4 (1/2) n 1. (6. 17) A certain semiconductor sample has the following properties: DN = 25 cm 2/s τn 0 = 10– 6 s DP = 10 cm 2/s τp 0 = 10– 7 s It is a homogeneous, p-type (NA = 1017 cm– 3) material in thermal equilibrium for t ≤ 0. At t = 0, an external light source is turned on which produces excess carriers uniformly at the rate GL = 1020 cm– 3 s– 1. At t = 2× 10– 6 s, the external light source is turned off. (a) Derive the expression for the excess-electron concentration as a function of time for 0 ≤ t ≤ ∞. (b) Determine the value of the excess-electron concentration at (i) t = 0, (ii) t = 2× 10– 6 s, and (iii) t = ∞. (c) Plot the excess electron concentration as a function of time. n Problem 2 on the next slide. President University Erwin Sitompul SDP 4/24

Chapter 3 Carrier Action Homework 4 (2/2) n 2. (4. 38) Problem 3. 24 Pierret’s “Semiconductor Device Fundamentals” Replace the figure on the book with the figure below n Hint: Draw all sketches/ graph using ruler n Deadline: Monday, 10 October 2016. President University Erwin Sitompul SDP 4/25