Set 5 Web Solutions LC

8/22/2019 Set 5 Web Solutions LC

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P3000 LON-CAPA Set 5 Sample Solutions

1. pn Junction Zero Voltage From Neamen Sect. 5.2. Consider a uniformly-doped

Germanium pn junction with doping concentrations N_a = 3.71017

cm^-3 and N_d =

1.31017

cm^-3. Calculate the built-in potential barrier, V_bi, at T = 300 K. Enter your

answer in volts. Assume that the intrinsic electron concentration for Germanium at 300 Kis n_i = 2.271013

cm^-3.

Cor r ect , comput er get s: 4. 75e- 01

Calculate the built-in potential barrier, V_bi, for the same junction at T = 337.5 K. Enter

your answer in volts. To calculate the intrinsic electron concentration for Germanium at

337.50 K, you can assume that the effective densities of states for the conduction bandand valence band, respectively, at this temperature are N_c = 1.2410

19cm^-3 and N_v =

7.161018

cm^-3) and that the band gap is E_g = 0.66 eV.



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2. pn Junction Reverse Voltage: From Neamen Sect. 5.3. A silicon one-sided n+p

junction is biased at V_R = 9.0 V. Its temperature is 307.0 K. By what factor does thejunction capacitance increase if the acceptor concentration in the p region increases by a

factor of 5.0. You can assume that the built-in potential barrier, V_bi, does not change

significantly and that, for a n+p one-sided junction, that the donor concentration N_d on

the n side is much greater than the acceptor concentration N_a on the p side (i.e. that N_d>> N_a).

Corr ect , comput er gets: 2. 24e+00

We can test the assumption that the change in the built-in potential barrier, V_bi, is small

compared to V_R. For the n+p one-sided junction described in the previous question,

calculate the change in the built-in potential barrier, V_bi, when the acceptorconcentration in the p region is increased by a factor of 5.0. Enter your answer in volts.



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3. pn Junction Reverse Voltage:

From Neamen Sect. 5.3. A Germanium pn junction at 291.5 K has the doping profile

shown. Because N_d


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Calculate the width, x_p, of the p-type part of the depletion region for the junction

described in the previous question at zero bias. Enter your answer in cm.


Calculate the applied bias, V_R, required in order for the n-type part of the depletion

region, x_n, to increase to 1.8810-4

cm. Enter your answer in volts.


Hint: To do this problem, you need to take the difference of two numbers that are veryclose to each other. In order for your answer to be accurate to 3 significant figures, you

need to be sure that your intermediate calculations are done to about 5 significant figures.


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4. Rectifying Junction:. Consider a Nickel Schottky diode at 300 K formed on n-type

Germanium doped at N_d = 4.201016

cm^-3. The work function for Nickel is phi_m =5.15 V (i.e. e*phi_m = 5.15 eV). The electron affinity for Germanium is chi=4.13 V (i.e.

e*chi = 4.13 eV). Determine the theoretical barrier height, phi_B0, for the Schottky

barrier and enter your answer in volts.


Calculate the potential difference, phi_n, between the conduction band edge and theFermi energy. Enter your answer in volts. You can assume that the effective density of

states in the conduction band is N_c = 1.041019

cm^-3).


Hint: Be careful with units!

Calculate the built-in potential barrier, V_bi. Enter your answer in volts.


Hint: For a Schottky barrier, the built-in potential barrier depends on the ideal Schottky

barrier and on phi_n.


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Calculate width, x_n, of the space charge region for a reverse bias of V_R = 5.0 V. Enter

your answer in cm. For Germanium the relative permittivity or dielectric constant is16.00.


Calculate magnitude of the maximum electric field in the space charge region for a

reverse bias of V_R = 5.0 V. Enter your answer in V/cm. For Germanium the relativepermittivity or dielectric constant is 16.00.



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5. Forward Applied Bias: From Neamen Sect. 5.5. The reverse saturation current

density in a pn junction diode is 5.0010-12

A/cm^2 at 300 K. The cross-sectional area ofthe pn junction diode is 8.5010

-4cm^2. What is the forward bias voltage necessary to

achieve a current of 1.00 mA? Enter your answer in volts.


Now consider a Schottky barrier diode with a reverse saturation current density of

7.0010-8

A/cm^2. For this diode, the current of 1.00 mA is a obtained with a forward

bias voltage that is 0.250 V less than the bias voltage that you found for the pn junction inthe previous question. What is the cross sectional area of the Schottky barrier diode?

Enter your answer in cm^2.



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6. Metal-Semiconductor Ohmic Contacts: From Neamen Sect. 5.6. A metal-

semiconductor ohmic contact is formed by depositing a layer of Aluminum, for which thework function is phi_m = 4.28 V, on n-type Silicon for which the electron affinity is 4.01

V and the bandgap is 1.12 eV. Assume that no interface states exist at the junction and

that the temperature is 300 K. Determine the doping concentration, N_d, so that no space

charge region exists at the junction for zero bias. You can do this by finding the potentialdifference,phi_n, between the conduction band edge and the Fermi energy and then using

this to calculate the donor concentration. For Silicon, the effective density of conduction

band states, N_c, at 300 K is N_c = 2.801019

cm^-3. Enter your answer in cm^-3.


What is the potential barrier height seen by electrons moving from the metal into the

semiconductor? Enter your answer in V.


Hint: Be careful with units!

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Set 5 Web Solutions LC