Effect of temperature on ionized impurity scattering:
Lower temperatures lead to lower energy electrons, which scatter more around impurities.
Higher temperatures allow electrons to overcome scattering better.
Combined Effects
Total mobility is influenced by both phonon and ionized impurity scattering:
Total mobility equation:
[ \frac{1}{\mu_{total}} = \frac{1}{\mu_{phonon}} + \frac{1}{\mu_{impurity}} ]
Example Calculation:
Given ( \mu_{phonon} = 400 \text{ cm}^2/ ext{V·s} ) and ( \mu_{impurity} = 500 \text{ cm}^2/ ext{V·s} ), the total mobility is approximately 220 cm²/V·s.
Doping Effects on Mobility
Low Doping: Phonon scattering dominates, high mobility.
High Doping: Ionized impurity scattering dominates, reducing mobility drastically.
Plotting mobility versus doping reveals:
Initial constant mobility due to low ionized impurities.
Mobility decreases significantly at high doping concentrations.
Current Density and Conductivity
Current Density (J):
Defined by equation: ( J = q n \mu E )
Conductivity (σ):
Defined as: ( \sigma = q \mu n )
Relationship with Ohm's Law:
J is proportional to the electric field.
Velocity Saturation
Drift velocity increases linearly with field until saturation point (V_sat).
Physical reasoning:
Increased acceleration leads to higher collision frequency.
Energy gained from the field dissipates to phonons, limiting further acceleration.
Saturation velocity varies among materials:
e.g., Si: ( \sim 2 \times 10^7 \text{ cm/s} )
Diffusion Current
Diffusion: Movement of carriers from high to low concentration.
Flux of Carriers: Dependent on concentration gradient:
( ext{Flux} = -D \frac{dN}{dx} )
Total Diffusion Current:
Combination of both electron and hole diffusion currents:
[ J = q D_n \frac{dN}{dx} - q D_p \frac{dP}{dx} ]
Conclusion
Overview of drift and diffusion currents.
Next class: Discuss relation between drift and diffusion and introduction of Einstein relation.