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.  Hole current per unit area J = q p vd
Drift Current
vd t A = volume from which all holes cross plane in time t
p vd t A = # of holes crossing plane in time t
q p vd t A = charge crossing plane in time t
q p vd A = charge crossing plane per unit time = hole current
 Hole current per unit area J = q p vd
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. Electrical ResistanceV + _ L t W I
homogeneously doped sample
where r is the resistivity
Resistance
(Unit: ohms)
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 = (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
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  = qnn + qpp 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