ENSC 324 HOMEWORK #2 Fall 2015

DUE: **Monday **October 19, 2015 at **2 PM **(note new time!)

Please note that unless you show work in the derivations and solutions you will get no credit for the

answers. Obviously copied answers from study partners or other sources, etc., will also receive no credit.

Please do all parts of all eight problems. *It is suggested that you make a copy of your homework *before

turning it in in case it cannot be returned before Exam 2 (solution key will be provided).

Problem #1

In a particular sample of n-type silicon, the Fermi energy level varies linearly with distance over a short

range. At x=0, the difference between the Fermi level and the intrinsic Fermi level is 0.4 eV. At x=10-3

cm, the same difference is only 0.15eV. The electron diffusion coefficient is 25 cm2/s.

a) Write an expression for the Fermi level with respect to the intrinsic fermi level versus distance.

b) What is the electron concentration versus distance?

c) What is the electron diffusion current density at x=0, and at x=5 x 10−4 cm?

Problem #2

A rectangular bar shaped silicon semiconductor resistor with a cross-sectional area of 100 μm2,

and a length of 0.1 cm, is doped with a concentration of 5 x 1016 cm−3 arsenic atoms (and no

acceptors). Let *T *= 300 K. A bias of 5V is applied across the length of the silicon resistor.

a) Calculate the current in the resistor.

b) Repeat part *a*) if the length is reduced by 0.01 cm.

c) What is the drift current in parts *a*) and *b*)?

Problem #3

Assume we have silicon with typical mid-range doping levels of donors (no acceptors) at 300K. Assume

that the mobility for electrons is limited by lattice scattering and has a temperature dependence of

approximately T-3/2. Determine the electron mobility at: a) T=200K; b) 400K.

Problem #4

A silicon bar has a length of *L *= 0.1 cm and a cross-sectional area of *A *= 10−4 cm2. The

semiconductor is uniformly doped with phosphorous at a level 5 x 1016 cm−3 (no other doping).

A voltage of 5 V is applied across the length of the material which is at T=300K. The minority

carrier lifetime is 3 x 10−7 s. For *t *< 0, the semiconductor has been uniformly illuminated with

light, producing a uniform excess carrier generation rate of *g*‘ = 5 x 1021 cm−3 s−1. At *t *= 0, the

light source is turned off. Determine the current in the semiconductor as a function of time for -∞

≥*t *≥ ∞.

Problem #5

An n-type GaAs semiconductor at 300 K is uniformly doped with donors (no acceptors) at a

level of 5 x 1015 cm−3 (mid level doping). The minority carrier lifetime is 5 x 10−8 s. A light

source is turned on at *t *= 0 generating excess carriers uniformly at a rate of *g*‘ = 4 x 1021 cm−3 s−1.

There is no external electric field.

a) Determine the excess carrier concentrations versus time over the range 0 ≤ *t *≤ ∞.

b) Calculate the conductivity of the semiconductor versus time over the same time period as

part (*a*).

Problem #6

Consider a bar of p-type silicon material at T=300K that is homogeneously doped to a value of 3

x 1015 cm−3 (ND=0), which may be considered mid level doping. The applied electric field is

zero. A light source is incident on the end of the semiconductor on one end (where x = 0, with x

increasing into the silicon bar). The excess carrier concentration generated at x = 0 is 1013 cm−3.

The lifetimes for electrons and holes are 0.5 μs and 0.1 μs, respectively.

a) Calculate the steady-state excess electron and hole concentrations as a function of

distance into the semiconductor.

b) Calculate the electron diffusion current density as a function of x.

Problem #7

Calculate the position of the quasi-Fermi level with respect to the intrinsic level for the following silicon

crystal that is steadily illuminated with an excess carrier generation rate of 1021 /cm3S:

NA = 1016 /cm3 , ND = 0

τn0 = τp0 = 1 μS

Problem #8

A silicon sample at 300K has the following impurity concentrations: ND = 1015 /cm3 and NA = 0 . The

equilibrium recombination rate is Rp0 = 1011 cm−3 s−1. A uniform generation rate produces an excess

carrier concentration of 1014 /cm3 .

a) What is the excess carrier lifetime?

b) By what factor does the total recombination rate increase?

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.