Generation and Recombination-Introduction to Microelectronic Circuits-Lecture 18 Slides-Electrical Engineering, Slides of Microelectronic Circuits

Download Generation and Recombination-Introduction to Microelectronic Circuits-Lecture 18 Slides-Electrical Engineering and more Slides Microelectronic Circuits in PDF only on Docsity! 1 Lecture 18, Slide 1EECS40, Fall 2003 Prof. King Lecture #18 OUTLINE – Generation and recombination – Charge-carrier transport in silicon – Resistivity as a function of doping Reference Texts on reserve in Engr. Library • Howe & Sodini Chapter 2.1: Pure semiconductors Chapter 2.2: Generation, recombination, thermal equilibrium Chapter 2.3: Doping Chapter 2.4: Carrier Transport Chapter 2.6: IC Resistors • Schwarz and Oldham Chapter 13: Semiconductor Devices Lecture 18, Slide 2EECS40, Fall 2003 Prof. King Generation • We have seen that conduction (mobile) electrons and holes can be created in pure (intrinsic) silicon by thermal generation. – Thermal generation rate increases exponentially with temperature T • Another type of generation process which can occur is optical generation – The energy absorbed from a photon frees an electron from covalent bond • In Si, the minimum energy required is 1.1eV, which corresponds to ~1 µm wavelength (infrared region) • Note that conduction electrons and holes are continuously generated, if T > 0 2 Lecture 18, Slide 3EECS40, Fall 2003 Prof. King Recombination • When a conduction electron and hole meet, each one is eliminated. The energy lost by the conduction electron (when it “falls” back into the covalent bond) can be released in 2 ways: 1. to the semiconductor lattice (vibrations) “thermal recombination” semiconductor is heated 2. to photon emission “optical recombination” light is emitted • Optical recombination is negligible in Si. It is significant in compound semiconductor materials, and is the basis for light-emitting diodes and laser diodes. Lecture 18, Slide 4EECS40, Fall 2003 Prof. King Generation and Recombination Rates • The generation rate is dependent on temperature T, but it is independent of n and p : • The recombination rate is proportional to both n and p: • In steady state, a balance exists between the generation and recombination rates. • A special case of the steady-state condition is thermal equilibrium: no optical or electrical sources opticalthermal GTGG += )( )(2 Tnnp i= )( TfnpRG =⇒= npR ∝ 5 Lecture 18, Slide 9EECS40, Fall 2003 Prof. King Electrical Conductivity σ When an electric field is applied, current flows due to drift of mobile electrons and holes: EqnnvqJ nnn µ=−= )(electron current density: hole current density: EqppvqJ ppp µ=+= )( total current density: pn pnpn qpqn EJ EqpqnJJJ µµσ σ µµ +≡ = +=+= )( conductivity Lecture 18, Slide 10EECS40, Fall 2003 Prof. King (Units: ohm-cm) Electrical Resistivity ρ pn qpqn µµσ ρ + =≡ 11 for n-type mat’l nqnµ ρ 1≅ for p-type mat’l pqpµ ρ 1≅ Note: This plot does not apply for compensated material (doped with both donors and acceptors) 6 Lecture 18, Slide 11EECS40, Fall 2003 Prof. King Consider a Si sample doped with 1016/cm3 Boron. What is its resistivity? Answer: NA = 1016/cm3 , ND = 0 (NA >> ND p-type) p ≈ 1016/cm3 and n ≈ 104/cm3 Example [ ] cm 4.1)450)(10)(106.1( 11 11619 −Ω=×= ≅ + = −− ppn qpqpqn µµµ ρ From µ vs. ( NA + ND ) plot Lecture 18, Slide 12EECS40, Fall 2003 Prof. King The sample is converted to n-type material by adding more donors than acceptors, and is said to be “compensated”. Consider the same Si sample, doped additionally with 1017/cm3 Arsenic. What is its resistivity? Answer: NA = 1016/cm3, ND = 1017/cm3 (ND>>NA n-type) n ≈ 9x1016/cm3 and p ≈ 1.1x103/cm3 [ ] cm 10.0)700)(109)(106.1( 11 11619 −Ω=××= ≅ + = −− npn qnqpqn µµµ ρ Example (cont’d) 7 Lecture 18, Slide 13EECS40, Fall 2003 Prof. King R ≅ 2.6Rs Sheet Resistance Rs Rs is the resistance when W = L t R W LR Wt LR ss ρρ ≡⇒== (Unit: ohms/square) R = Rs/2 R = 2Rs R = 3Rs • The Rs value for a given layer in an IC technology is used – for design and layout of resistors – for estimating values of parasitic resistance in a circuit R = Rs Metallic contacts Lecture 18, Slide 14EECS40, Fall 2003 Prof. King At high electric fields, the average velocity of carriers is NOT proportional to the field; it saturates at ~107 cm/sec for both electrons and holes: Velocity Saturation