6.7: Problems
- Page ID
- 19300
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)6.1. Rank the materials from smallest energy gap to largest energy gap:
- Indium arsenide, InAs
- Aluminum arsenide, AlAs
- Gallium arsenide, GaAs
6.2. The energy level diagram for a silicon pn junction is shown in the figure below. Part of the device is doped with Ga atoms, and part of the device is doped with As atoms. Label the following:
- The valence band
- The conduction band
- The energy gap
- The n-type region
- The p-type region
- The depletion layer
- The part of the device doped with Ga
- The part of the device doped with As
6.3. The figure in the previous problem shows the energy level diagram for a semiconductor pn junction.
(a) If this pn junction is used in an LED, what will be the wavelength in nm of the light emitted by the LED?
(b) If this pn junction is used as a solar cell, what range of wavelengths of light will be absorbed by the solar cell?
6.4. A semiconductor is used to make an LED that emits red light at \(\lambda\) = 630 nm.
(a) Find the energy gap in eV of the semiconductor.
(b) Find the energy in joules of a photon emitted.
(c) Find the energy in joules for Avogadro constant number of these photons.
6.5. The figure below shows the energy level diagram for a gallium arsenide LED.
(a) Find the energy gap.
(b) Find the energy of a photon emitted by the LED.
(c) Find the frequency in Hz of a photon emitted by the LED.
6.6. Use Fig. 6.2.6 to answer this question.
(a) Suppose you would like to make an LED that emits red light with a wavelength of 650 nm. Suggest three possible semiconductor materials that could be used.
(b) Suppose you would like to make a layered solar cell using layers of the following materials: InP, \(\text{In}_{0.5}\text{Ga}_{0.5}\text{As}\), and \(\text{AlAs}_{0.5}\text{Sb}_{0.5}\), Which layer would be on top, in the middle, and on the bottom of the device, and why?
6.7. Use Fig. 6.2.6 to answer this question.
(a) Find the energy gap of \(\text{InP}_{0.1}\text{As}_{0.9}\) in the units of joules.
(b) If \(\text{InP}_{0.1}\text{As}_{0.9}\) is used to make an LED, find the expected frequency, in Hz, of the photons emitted. (c) Would it be better to make a solar cell out of gallium phosphide or indium phosphide? Why?
6.8. A solar panel produces an average power of 800 W. The panel is in a location which receives an average of \(0.07 \frac{W}{cm^2}\) of optical energy from the sun. Assume the panel has an eciency of 9%.
(a) Calculate the surface area of the solar panel in units \(m^2\).
(b) Calculate the average amount of energy (in eV) produced in one week.
6.9. A solar panel has an area of \(50 m^2\), and it produces an average of 4 kW of power. The panel is in a location which receives an average of \(0.085 \frac{W}{cm^2}\) of optical energy from the sun. Calculate the efficiency of the panel.