5.5: Problems
- Page ID
- 18969
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)5.1. Suppose that you are using a piece of semiconductor as a Hall effect device to measure a magnetic field. You supply a DC current through the device. You would like to replace the piece of semiconductor with another one that will give a larger output for the same external magnetic field. List two ways you can change the piece of semiconductor so that the output would increase. (Specify both the property and whether it would need to be increased or decreased.)
5.2. A piece of p-type semiconductor is used as a Hall effect device. The device has a thickness of \(d_{thick} = 1 mm\). It is placed in an external magnetic field of \(|\overrightarrow{B}| = 10^{-5} \frac{Wb} {cm^2}\). A Hall voltage of \(5 \mu V\) is measured when a current of \(3 mA\) is applied. Calculate \(p\), the charge (hole) concentration in units \(\frac{1}{cm^3}\).
5.3. A Hall effect device is used to measure the strength of an external magnetic field. The device is oriented in the way described in Fig. 5.1.1. It is made from a cube of p-type silicon with hole concentration \(5 \cdot 10^{15} cm^{-3}\) where the length of each side of the cube is \(1 mm\). A current of \(3 mA\) is applied through the device. The voltage measured across the device is \(2.4 mV\). Find the strength of the external magnetic flux density, \(|\overrightarrow{B}|\).
5.4. A Hall effect device is used to measure the strength of an external magnetic field. The device is oriented in the way described in Fig. 5.1.1. It is made from a material of length \(l = 3 mm\), width \(w = 0.5 mm\), and thickness \(d_{thick} = 0.5 mm\). It has a hole concentration of \(p = 10^{20} m^{-3}\). In an experiment, the devices was placed in an external magnetic field of \(|\overrightarrow{B}| = 2.5 \frac{Wb}{m^2}\) and a voltage of \(9 mV\) was measured. What current was used in the experiment?
5.5. Two expressions were given for the Hall resistance:
\(R_H = \frac{B_z}{qp} \cdot \frac{w}{l \cdot d_{thick}}\) and \(R_H = \frac{h}{q^2n}.\)
Show that both expressions have the units of ohms.