An n-type Ge sample is used in the Haynes–Shockley experiment shown
in Fig.4–20.The length of the sample is 1 cm, and the probes (1) and (2) are separated by 0.95 cm. The battery voltage $E_{0}$ is 2 V. A pulse arrives at point (2)0.25 ms after injection at (1);the width of the pulse Δt is 117 μs. Calculate the hole mobility and diffusion coefficient, and check the results against the Einstein relation.

Question

An n-type Ge sample is used in the Haynes–Shockley experiment shown
in Fig.4–20.The length of the sample is 1 cm, and the probes (1) and (2) are separated by 0.95 cm. The battery voltage[latex]E_{0}[/latex]is 2 V. A pulse arrives at point (2)0.25 ms after injection at (1);the width of the pulse Δt is 117 μs. Calculate the hole mobility and diffusion coefficient, and check the results against the Einstein relation.

Accepted Answer

[latex]\mu_{p} =\frac{V_{d} }{ℰ} =\frac{0.95/(0.25 imes 10^{-3})}{2/1}=1900 cm^{2}/(V-s)[/latex]

[latex]D_{p}=\frac{(\Delta x)^{2}}{16t_{d} }=\frac{(\Delta t L)^{2}}{t^{3}_{d} }[/latex]

[latex]=\frac{(117 imes 0.95)^{2} imes 10^{-12}}{16(0.25)^{3} imes 10^{-9}} =49.4 cm^{2} s[/latex]

[latex]\frac{D_{p} }{\mu _{p} } =\frac{49.4}{1900} =0.026=\frac{kT}{q}[/latex]

Question 4.5: An n-type Ge sample is used in the Haynes–Shockley experimen...

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