[2/10/11 ver.]
EE 5340 - Semiconductor Device Theory
Due
April 19, 2011
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Project
Assignment
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All
project solutions should be submitted on 8.5" x 11" paper with a
cover sheet attached. The project report
should be stapled only in the upper left-hand corner and no other cover or
binder or folder should be used. The
cover sheet should include (1) your name, (2) the project title, (3) the course
name and number, and (4) your e-mail address.
The report should include clearly marked sections on (a) purpose of the
project and the theoretical background, (b) a narrative explaining how you did
the project, (c) answers to all questions asked in the project assignment, and
(d) a list of references used in the order cited in the report (the reference
number should appear in the report each time the reference is used). All
figures and tables should be clearly marked with a figure or table number and
caption. The caption and labels on the
figures should make the information in the figure comprehensible without
reading further in the text of the report.
Auxiliary information (such as SPICE data outputs, etc.) should be
included in appropriate Appendices at the end of the report. Be sure to describe exactly how all results
were obtained, giving enough information for anyone who understands EE 5340 to
repeat your work. All work submitted must be original. If derived from another source, a full
bibliographical citation must be given.
(See all of Notes 5 and 6 in the syllabus.) Click solution.pdf. to download a pdf file copy. Use
the IEEE style sheet to write project report (plus cover sheet and auxiliary
information). For further information, see http://ieee.org/documents/TRANS-JOUR.doc and http://ieee.org/publications_standards/publications/authors/authors_journals.html.
Using
SPICE to Verify a Thermometer Design Using a Diode
Introduction: A p-n
junction diode can be used to generate a voltage which can be converted to
temperature. The SPICE parameter values for IS, XTI, N, IKF, RS, ISR, NR and
TNOM provide a sufficiently complete model to verify this concept and design
the circuit to obtain the requisite temperature dependent voltage.
A.
For a diode model with SPICE parameters
identified above, with applied voltage v_{A} and forward
current i_{D},
it can be shown that the junction temperature, T_{j} is (approximately)
given by the function defined in (1) as T_{jA}.
The
constant k is Boltzmann’s constant,
and q is the magnitude of the
electron charge. The “min” subscript notation is taken to mean the minimum
value observed for the derivative of v_{A} as a function of ln(i_{D}). By definition,
TEMP is the SPICE global simulation parameter for the junction temperature of
the diode modeled with the parameters above. TNOM is the temperature at which
the parameters have been determined. At the condition thus described, the diode
state is specified as i_{D,min}, v_{A,min}.
1.
Using the SPICE diode equations, derive
the above approximation. For simplicity, assume that the parameters
IS, IKF and ISR are temperature independent. In all cases, assume 300 mV
< v_{A}
< 1 V.
a.
Do the derivation for v_{A,min}
in terms of the SPICE parameter values, finding the value of v_{A,min}
for which T_{jA},
as defined in (1), best approximates TEMP = T_{j}. In other words,
derive the equation for v_{A,min} in terms of IS and ISR, etc., which
gives the minimum for the logarithmic derivative expressed in (1).
i.
Find the value v_{A,min}
in the limit of RS > 0, and IKF ŕ
∞. (Note that setting IKF = 0 in a SPICE simulation has the effect IKF ŕ ∞.)
ii.
Or find
the value v_{A,min}
in the limit of RS = 0, and IKF < i_{D}(v_{A}=1V)
b.
Express your conclusion in the form of a
plot of (T_{jA}
- T_{j})
vs. IS/ISR, in terms of values of
IKF/IS or i_{D}(v_{A}=1V)×RS/(1V).
B.
Derive theoretical calculations for IS,
IKF, RS and ISR as a function of process parameters (N_{d},
N_{a}, etc.) for a diode which will minimize the error function (T_{jA} - T_{j}).
Assume that N=1, NR=2 and XTI=3. Further, assume the diode is made with either
a p+ diffusion into an n-type (phosphorous doped) wafer, or an n+ diffusion
into a p-type (boron doped) wafer, and that the thickness of the wafer is 700
µm. For simplicity, assume the diode chip will be 100 µm by 100 µm, and that
the one-dimensional diffusion current theory applies at the depletion regions
boundaries. Assume the diffusion is 1 µm deep. For minority carrier mobility,
assume the same value that Muller and Kamins give for
majority carrier mobility. For minority carrier recombination rates, apply the
results given in M. E. Law, E. Solley, M. Liang, and
D. E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion
Length, and Mobility,” IEEE Electron Device Lett.,
vol. 12, pp. 401-403, 1991.
1.
You may assume that all that you need do
is to choose the doping concentration and doping type of the lightly doped
wafer. You should give a justification for making this assumption.
2.
Report the values of IS, IKF, RS, ISR
you calculate for the best diode.
3.
Using SPICE simulation, calculate the
values of (T_{jA}
- T_{j})
using the values reported in B.2. Report these values for the simulation
temperature range for T_{j}
of -40 C < TEMP < 100 C.
4.
Report this result in a graph of (T_{jA} - T_{j})
vs. T_{j} = TEMP.
5.
Identify the SPICE parameter most
responsible for error parts B.4 and B.5.
6.
Verify the correctness of the
theoretical values of v_{A} derived in A.1.a. Discuss reasons why
the values of v_{A} you observed in the simulations of B.3
are different than the theoretical values you predicted.
C.
A simple thermometer circuit can be made
by using a 9 V source, V, in series
with a resistor and a diode.
1.
Using the diode parameters you derived
in B.2, determine the values of the resistor, R, that at T=300 K will give
2.
Using the value of R from (2) in the
circuit thus defined, plot the value of v_{A} as a function of TEMP for the range -40
C < TEMP < 100 C.
3.
Will this function serve as a voltage to
temperature conversion? Report the computation that will be required to convert
these voltage values to a Celsius temperature scale?