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Solid State Devices - Assignments 2010

In my teaching philosophy, homework is primarily for learning, with evaluation left primarily to exams. The upside of this view is that I will be free to provide a bit of help with the homework.

But how will this be rectified with the fact that homework scores will contribute to your final grade?

First, I will weigh homework as only 20% of the final grade.

Second, while I will allow you to discuss homework with others, when you begin to write down (or type in) your own personal answers, I will require - pledged under UVA's Honor Code - that you start with a blank page. That is, at that point, all prior sources of information from others must be closed down / hidden / erased. To put it another way, I don't care exactly how or from whom you learn the material - as long as THEN using the textbook, my lecture notes and your personal class notes (only!), you can proceed to solve the assigned problems. (But note that this homework policy does NOT extend to exams where consultation with others remains strictly prohibited).

To the specifics: This class has a compressed schedule. But I know that some of you may have simultaneous job commitments. To deal with these conflicting demands, and after consultation with professors who've taught similarly compressed classes, I have decided on the following:

HOMEWORK:

Each week there will be two assignments. These will be due on Monday and Thursday mornings by 9 AM (meaning, I assume, that most of you will will do the work on Wednesday and Sunday evenings).

For the Thursday assignment, I will hold a live online homework discussion session at 5pm Wednesday evening. I will not give you the answers, but I will work with you to identify the key bits of knowledge and to point you in the right direction. At least I will do that if you actively participate in the discussion (if you sit online silently, I reserve the right to do the same).

I will not provide the same assistance for the assignments due on Mondays. That is because I want those assignments to serve as your weekly self-test as to whether you are keeping up with the class. If these assignments give you trouble, seek help immediately (this is not a class to fall behind in)!

TESTS:

There will be a midterm exam (given in lieu of homework assignments) covering material up to and including basic diodes. We complete that material by class hour 20 (i.e. Monday July 26). But to allow for some homework experience with the material, l assign that midterm over the following week of August 2-9.

The final exam will be due a full week after the last homework assignment (on Friday August 27th).

Due1
Assignment2
Solutions3
Thursday - July 8
1.1 - (number per cell = "owned by cell", i.e. fractional atoms for those shared with other cells)
1.2 - part a only
1.11 - (sketch by showing where the planes intercept the x,y,z axes, similar to figure 1.21)
1.19 - part a only
1
     
Monday - July 12
NOTE: Recurring theme for this assignment is that you learn more by writing down a derivation than you do by simply reading it:



AND book problems:

2.5 - (in other words, what wavelength of light will supply the energy specified)
2.6 - parts a & d only
2.29 - part a only (see note at beginning of this assignment)
2
     
Thursday - July 15

Note: Despite what your calculator may say, "0" is not an acceptable answer to any of these problems. So you might want to check this link on how to handle small numbers in general, or this link on how to handle small numbers in Mathcad

2.29 - part b for a = 4 Å only
2.31 - part a only (should read INTO rather than beyond the barrier)

3.13
3.42 - do only for Si

3
     
Monday - July 19

Note: From book (and recent lectures), for both no and po we have TWO expressions based on EF (eqns. 4.11 & 4.19 as well as later 4.39 & 4.40)

4.8
4.12 - do only for Si and only for 300K (yes, 300 - because it is then interesting to compare this problem on "intrinsic" Si with the near intrinsic result of problem 3.42)
4.18
4.29

4
     
Thursday - July 22
NOTE 1: The addition of carriers (via addition of ionizing acceptors or donors) will change the conductivity. But the changes are not quite proportional to doping because as ions are added, scattering increases and mobility falls. So to zero in an a desired conductivity value you either have to: 1) Iteratively calculate the effects of changed doping and mobility upon conductivity; 2) Or simply use the reciprocal of the value read off a resistivity chart (where doping effects upon mobility are already taken into account).

NOTE 2: Some textbook figures are unreadably small (5.3, 5.4) or have errors (5.7). See instead:
Silicon mobility and resistivity, GaAs and Ge resistivity, Velocity vs. Electric Field.

5.2 - a/b/c (but not part d which is unrealistic)
5.6 - (see note above concerning fig 5.7)
5.8 - part b only
5.27 - (denominator of exponential should really be "22.5 microns")
5.33 - (exponential should be α x)

Note: Last two problems assume D (and thus mobility) is not a function of doping. This will ONLY be the case for a semiconductor with light doping (<1 x 1016/cm3) where lattice scattering dominates.

5
     
Monday - July 26

MATHCAD REQUIRED FOR THIS (AND SUBSEQUENT) ASSIGNMENTS

6.1
6.5
6.19
6.20 - but calculate ONLY the electron diffusion currents at the points specified.

6
     
Thursday - July 29
7.8

8.8
8.11 parts a, b, c (part d is not required) - EXCEPT CHANGE THE DOPING LEVELS TO:
Na = 5 x 1017/cc, and Nd = 1 x 1017/cc
7
     
Monday - August 2
9.2, 9.15, 9.25, 9.29

See note above beginning of problem 9.1 pertaining to values of A to use for this problem set.

Metal-semiconductor barriers can be either: 1) Computed from work function & affinity tables 9.1 and 9.2 OR 2) Read from measured barrier data, figure 9.5.

Results are slightly different because the first approach does not account for possible contaminants or atomic charge rearrangements at real metal-semiconductor interfaces.

Neaman's solutions to problems 9.2 and 9.25 use the tables, but his solution to problem 9.15 uses the measured barrier data figure (!#%@!).

For this class, YOU can use either technique as long as you WRITE DOWN which you have chosen (i.e. "from tables 9.1 & 9.2" vs. "from data fig. 9.5")!
8
 
 
 
Thursday - August 5
No assignment due today to give you more time to work on the midterm (below)
 
     
Monday - August 9
Midterm Exam (covering material through class hour 20 = diodes)
 
     
Thursday - August 12
For this assignment (and subsequent tests) you can ignore recombination INSIDE of the junction depletion regions. This means that the book's JR => 0, and the parameter δ => 1

10.1

10-john: A SILICON NPN bipolar transistor (@ 300K) has the following characteristics:

Total Emitter Thickness:

Total Base Thickness:

Total Collector Thickness:

1 micron
1 micron
248 microns

Emitter doping:

Base Doping:

Collector Doping:

Nd = 1018/cm3
Na = 1017/cm3
Nd = 1016/cm3

Minority carrier lifetimes in all three layers = 10-6 seconds

The following voltages are applied to the transistor: VBE = 0.5 Volts, VCB = 5 Volts

a) What are the "effective widths" of the emitter, base and collector layers?

b) What are the minority carrier diffusion lengths in the emitter, base and collector?

c) What are the current densities crossing the emitter-base junction (JnE and JpE)?

d) What is the recombination current density in the base layer (JRB)?

e) What is the common emitter current gain of this transistor at these voltages (b)?
9
     
Monday - August 16
11.1 Note, these are plots of the NET charge (i.e. he does not show charges that are perfectly balanced by opposite charges)

11.2 - Do only part #a, only for Si - as you cannot successfully make a GaAs or Ge MOSFET!

11.4 - Do using tables 9.1 & 9.2 and positions of Fermi level in semiconductor (idealized view)

11.4 - REPEAT problem 11.4 using figure 11.15 (real MOS data that includes the effect of non-ideal charge at interfaces)

11.6 - Do parts a and b only for Qss = 1010/cm2, i.e. the case (i) value of Qss
10
     
Thursday - August 19
11.31, 11.36, 11.39 (in 11.39 part b, I believe it should be VSG = 5 volts)
11
 
 
 
Due date August 30 Final Exam  
     

1) By 9 am on the indicated date, homework must be submitted in pdf format via the UVA Collab website (CLICK HERE)

2) Problem numbers refer to those in the Neaman class textbook (exception is problems I've invented which I identify as jcb . . .)

3) After the assignment's due date I will post online solutions to the problems (but not to the exams)