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**Lecture #6 OUTLINE Carrier scattering mechanisms Drift current**

Conductivity and resistivity Relationship between band diagrams & V, e Read: Section 3.1

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**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

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**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

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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

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**Mobility Dependence on Doping**

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

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**Temperature Effect on Mobility**

EE130 Lecture 6, Slide 6

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** 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

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**Conductivity and Resistivity**

Jn,drift = –qnvdn = qnne Jp,drift = qpvdn = qppe Jdrift = Jn,drift + Jp,drift = e =(qnn+qpp)e Conductivity of a semiconductor is qnn + qpp Resistivity 1 / (Unit: ohm-cm) EE130 Lecture 6, Slide 8

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**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

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**Electrical Resistance**

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

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**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

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**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

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**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

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**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

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**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

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

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**Carrier Drift (Band Diagram Visualization)**

Ec Ev EE130 Lecture 6, Slide 17

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**Summary = qnn + qpp 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 = qnn + qpp EE130 Lecture 6, Slide 18

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