Lecture #6

1. Lecture #6 OUTLINE Carrier scattering mechanisms Drift current Conductivity and resistivity Relationship between band diagrams & V, e Read: Section 3.1

2. Mechanisms of Carrier Scattering • Dominant scattering mechanisms: • 1. Phonon scattering (lattice scattering) • 2. Impurity (dopant) ion scattering Phonon scattering mobility decreases when T increases:  = q / m EE130 Lecture 6, Slide 2

3. Impurity Ion Scattering Boron Ion Electron _ - - + Electron Arsenic Ion There is less change in the electron’s direction of travel if the electron zips by the ion at a higher speed. EE130 Lecture 6, Slide 3

4. Matthiessen's Rule • The probability that a carrier will be scattered by mechanism i within a time period dt is where ti is the mean time between scattering events due to mechanism i  The probability that a carrier will be scattered within a time period dt is EE130 Lecture 6, Slide 4

5. Mobility Dependence on Doping Total Doping Concentration NA + ND (cm-3) EE130 Lecture 6, Slide 5

6. Temperature Effect on Mobility EE130 Lecture 6, Slide 6

7. Drift Current vdtA = volume from which all holes cross plane in time t pvdt A = # of holes crossing plane in time t q pvdt A = charge crossing plane in time t qpvd A = charge crossing plane per unit time = hole current  Hole current per unit area J = qpvd EE130 Lecture 6, Slide 7

8. Conductivity and Resistivity Jn,drift = –qnvdn = qnne Jp,drift = qpvdn = qppe Jdrift = Jn,drift + Jp,drift = e=(qnn+qpp)e Conductivity of a semiconductor is   qnn + qpp Resistivity  1 /  (Unit: ohm-cm) EE130 Lecture 6, Slide 8

9. Resistivity Dependence on Doping For n-type material: p-type For p-type material: n-type Note: This plot does not apply for compensated material! EE130 Lecture 6, Slide 9

10. V I _ + W t homogeneously doped sample L Resistance (Unit: ohms) where r is the resistivity Electrical Resistance EE130 Lecture 6, Slide 10

11. Example 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 EE130 Lecture 6, Slide 11

12. Example: Dopant Compensation 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 EE130 Lecture 6, Slide 12

13. Example: Temperature Dependence of r Consider a Si sample doped with 1017cm-3 As. How will its resistivity change when the temperature is increased from T=300K to T=400K? Solution: The temperature dependent factor in  (and therefore ) is n. From the mobility vs. temperature curve for 1017cm-3, we find that n decreases from 770 at 300K to 400 at 400K. As a result,  increases by EE130 Lecture 6, Slide 13

14. Potential vs. Kinetic Energy electron kinetic energy Ec increasing electron energy increasing hole energy Ev hole kinetic energy Ec represents the electron potential energy: EE130 Lecture 6, Slide 14

15. Electrostatic Potential, V N- • The potential energy of a particle with charge -q is related to the electrostatic potential V(x): EE130 Lecture 6, Slide 15

16. Electric Field,e N- • Variation of Ec with position is called “band bending.” EE130 Lecture 6, Slide 16

17. Carrier Drift (Band Diagram Visualization) Ec Ev EE130 Lecture 6, Slide 17

18. Summary • Carrier mobility varies with doping • decreases w/ increasing total concentration of ionized dopants • Carrier mobility varies with temperature • decreases w/ increasing T if lattice scattering is dominant • decreases w/ decreasing T if impurity scattering is dominant • The conductivity of a semiconductor is dependent on the carrier concentrations and mobilities • Ec represents the electron potential energy Variation in Ec(x)  variation in electric potential V Electric field • E - Ec represents the electron kinetic energy  = qnn + qpp EE130 Lecture 6, Slide 18