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Solid State Electronic Devices

Ben G. Streetman, Sanjay Kumar Banerjee

Chapter 8

Optoelectronic Devices - all with Video Answers

Educators

Chapter Questions

04:05

Problem 1

For the p-i-n photodiode of Fig. $8-7,($ a) explain why this detector does not have gain: (b) explain how making the device more sensitive to low light levels degrades its speed; (c) if this device is to be used to detect light with $\lambda=0.6 \mu \mathrm{m}$, what material would you use and what substrate would you grow it on?

Averell Hause
Averell Hause
Carnegie Mellon University
03:52

Problem 2

We make a quantum well by sandwiching a 60 ? layer of GaAs $\left(E_{z}=1.43 \mathrm{eV}\right)$ between AlAs with a bandgap of $2.18 \mathrm{eV}$. We can assume two-thirds of the bandgap difference appear as conduction band discontinuity, and the rest in the valence band. The electron and hole effective masses in GaAs are $0.067 \mathrm{~m}_{0}$ and $0.5 \mathrm{~m}_{0}$, respectively. If we make an LED out of this heterostructure, what is the lowest energy photon that can be emitted from this GaAs layer? If we make a photodetector out of this, what is the longest wavelength that can be detected? You can assume the infinite potential well approximation for this calculation. How many confined states can you have in the conduction and valence bands in the GaAs layer? Qualitatively sketch the electron and hole probability density functions for these states. How far from the heterointerfaces is the hole most likely to be in the second excited state?

Manish Jain
Manish Jain
Numerade Educator
03:54

Problem 3

For a Si solar cell, the dark saturation current is $2 \mu \mathrm{A}$ and the short circuit current is $150 \mathrm{~mA}$. When it is optically illuminated, the optically generated current is $0.1 \mathrm{~mA}$. Find the corresponding voltage at current of $100 \mathrm{~mA}$.

Subash Charan
Subash Charan
Numerade Educator
01:39

Problem 4

For a Si photoconductor of length $5 \mu \mathrm{m}$, doped $\mathrm{n}$ -type at $10^{15} \mathrm{~cm}^{-3}$, calculate the change in current density when we shine light on the photoconductor under the following circumstances: We create $10^{20}$ electron-hole pairs $/ \mathrm{cm}^{3}-\mathrm{s}$ and carrier-recombination lifetimes, $\tau=0.1 \mu$ s. The applied voltage is $2.5 \mathrm{~V}$ across the photoconductor's length. How about if we increase the voltage to $2500 \mathrm{~V} ?$ The electron and hole mobilities are $1500 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$ and $500 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$,
respectively, in the ohmic region for electric fields below $10^{4} \mathrm{~V} / \mathrm{cm}$. For higher fields, electrons and holes have a saturation velocity of $10^{7} \mathrm{~cm} / \mathrm{s}$.

Chai Santi
Chai Santi
Numerade Educator
02:30

Problem 5

A Si solar cell with a dark saturation current $I_{\mathrm{th}}$ of $5 \mathrm{nA}$ is illuminated such that the short-circuit current is $200 \mathrm{~mA}$. Plot the $I-V$ curve for the cell as in Fig. $8-6$. (Remember that $I$ is negative, but is plotted positive as $I_{r .}$ )

Lucas Finney
Lucas Finney
Numerade Educator
01:48

Problem 6

What is the main limiting factor in increasing the efficiency of a solar cell?

Ajay Singhal
Ajay Singhal
Numerade Educator
01:54

Problem 7

A major problem with solar cells is internal resistance, generally in the thin region at the surface, which must be only partially contacted, as in Fig. $8-5$. Assume that the cell of Prob. $8.5$ has a series resistance of $1 \Omega$, so that the cell voltage is reduced by the $I R$ drop. Replot the $I-V$ curve for this case and compare with the cell of Prob. $8.5$.

Jilin Wang
Jilin Wang
Boston University
01:39

Problem 8

(a) Why must a solar cell be operated in the fourth quadrant of the junction $I-V$ characteristic?
(b) What is the advantage of a quaternary alloy in fabricating LEDs for fiber optics?
(c) Why is a reverse-biased GaAs p-n junction not a good photodetector for light of $\lambda=1 \mu \mathrm{m}$ ?

Penny Riley
Penny Riley
Numerade Educator
02:15

Problem 9

A Si solar cell $2 \mathrm{~cm} \times 2 \mathrm{~cm}$ with $I_{\mathrm{th}}=32 \mathrm{nA}$ has an optical generation rate of $10^{18} \mathrm{EHP} / \mathrm{cm}^{3}-$ s within $L_{p}=L_{n}=2 \mu \mathrm{m}$ of the junction. If the depletion width is $1 \mu \mathrm{m}$, calculate the short-circuit current and the open-circuit voltage for this cell.

Chai Santi
Chai Santi
Numerade Educator
03:10

Problem 10

The maximum power delivered by a solar cell can be found by maximizing the $I-V$ product.
(a) Show that maximizing the power leads to the expression
$$
\left(1+\frac{q}{k T} V_{\operatorname{mp}}\right) e^{q v_{-1} / k T}=1+\frac{I_{\text {sc }}}{I_{\text {th }}}
$$
where $V_{\mathrm{mp}}$ is the voltage for maximum power, $I_{\mathrm{sc}}$ is the magnitude of the shortcircuit current, and $I_{\mathrm{d}}$ is the thermally induced reverse saturation current.
(b) Write this equation in the form $\ln x=C-x$ for the case $I_{\mathrm{sc}}>I_{\mathrm{th}}$, and $V_{\mathrm{mp}}: k T / q .$
(c) Assume a Si solar cell with a dark saturation current $I_{\mathrm{th}}$ of $1.5 \mathrm{n} \mathrm{A}$ is illuminated such that the short-circuit current is $I_{\mathrm{sc}}=100 \mathrm{~mA}$. Use a graphical solution to obtain the voltage $V_{\mathrm{mp}}$ at maximum delivered power.
(d) What is the maximum power output of the cell at this illumination?

Chai Santi
Chai Santi
Numerade Educator
03:07

Problem 11

For a solar cell, Eq. $(8-2)$ can be rewritten
$$
V=\frac{k T}{q} \ln \left(1+\frac{I_{\mathrm{sc}}+I}{I_{\mathrm{th}}}\right)
$$
Given the cell parameters of Prob. 8.10, plot the $I-V$ curve as in Fig. $8-6$ and draw the maximum power rectangle. Remember that $I$ is a negative number but is plotted positive as $I_{r}$ in the figure. $I_{\mathrm{th}}$ and $I_{\mathrm{sc}}$ are positive magnitudes in the equation.

Ahmed Ali
Ahmed Ali
Numerade Educator
04:16

Problem 12

Solar cells are severely degraded by unwanted series resistance. For the cell described in Prob. 8.7, include a series resistance $R$, which reduces the cell volt-
age by the amount $I R$. Calculate and plot the fill factor for a series resistance $R$ from 0 to $5 \Omega$, and comment on the effect of $R$ on cell efficiency.

Jayashree Behera
Jayashree Behera
Numerade Educator
02:35

Problem 13

During the absorption spectra measurement of an unknown semiconductor material, the peak of the spectra appears around $364 \mathrm{~nm}$. What is the band gap of the device and what material is this? If the majority carrier in that material will be able to move with $5 \times 105 \mathrm{~cm} / \mathrm{sec}$ velocity, what will be the carrier mass for that material?

Dading Chen
Dading Chen
Numerade Educator
01:20

Problem 14

A semiconductor material of band gap $1.2 \mathrm{eV}$ is used to make a device. At what wavelength it will emit radiation? Is the emitted radiation in the optical range? From these, can you predict the band gap nature of the semiconductor material under observation?

Narayan Hari
Narayan Hari
Numerade Educator
00:46

Problem 15

The degenerate occupation of bands shown in Fig. 8-19 helps maintain the laser requirement that emission must overcome absorption. Explain how the degeneracy prevents band-to-band absorption at the emission wavelength.

Dading Chen
Dading Chen
Numerade Educator
01:54

Problem 16

Assume that the system described by Eq. $(8-7)$ is in thermal equilibrium at an extremely high temperature such that the energy density $\rho\left(v_{12}\right)$ is essentially infinite. Show that $B_{12}=B_{21}$.

Manik Pulyani
Manik Pulyani
Numerade Educator
View

Problem 17

The system described by Eq. (8-7) interacts with a blackbody radiation field whose energy density per unit frequency at $\nu_{12}$ is
$$
\rho\left(v_{12}\right)=\frac{8 \pi h v_{12}^{3}}{c^{3}}\left[e^{k v_{d} / k T}-1\right]^{-1}
$$
from Planck's radiation law. Given the result of Prob. $8.16$, find the value of the ratio $A_{21} / B_{12}$.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:02

Problem 18

In a compound $\mathrm{Al}_{*} \mathrm{Ga}_{1 \cdot \mathrm{x}}$ As material, calculate the energy band gap for the $\mathrm{AL}$ concentration of $0.40$ using linear interpolation method at $300 \mathrm{~K}$ temperature. Calculate the minimum carrier concentration $\mathrm{n}=\mathrm{p}$ for population inversion in AlGaAs at $300 \mathrm{~K}$ if the intrinsic carrier concentration is $2.1 \times 10^{3} / \mathrm{cm}^{3}$

Aadit Sharma
Aadit Sharma
Numerade Educator
04:32

Problem 19

In a Si base long p'n diode, the excess hole distribution due to optical excitation becomes
$$
\delta p\left(x_{n}\right)=\left[p_{n} \cdot\left(e^{a V K T}-1\right)-g_{o p}, \frac{L_{p}^{2}}{D_{p}}\right] \cdot e^{-x_{n} / L_{p}}+g_{o p}, \frac{L_{p}^{2}}{D_{p}}
$$
Suppose for such a device acceptor concentration is $10^{18} / \mathrm{cm}^{3}$, diffusion coefficient for holes is $10.36 \mathrm{~cm}^{2} / \mathrm{sec}$, mobility for holes is $400 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{sec}$, carrier lifetime = $10 \mathrm{~ns}$ and applied bias is $0.7 \mathrm{~V}$. Due to uniform illumination, $10^{20} / \mathrm{cm}^{3}$ EHP is generated. Now calculate the excess hole distribution for this long diode at a distance of twice the diffusion length from the junction at the $\mathrm{n}$ side.

Chai Santi
Chai Santi
Numerade Educator