University of Texas Arlington
Department of Electrical Engineering
Nanotechnology – Microelectromechanical Systems
Ph.D. Diagnostic Examination
Spring 2015
To be filled by the student
Question
#
1
2
3
To be filled by the graders
Check to have this question
graded. Check only 2.
Grade
Grade
TOTAL:
GRADE OUT of 100:
1
Average
1.
(50 pts)
The newly discovered, mythical semiconductor “utaium” has a cubic crystal symmetry. The E-k
relationship is shown in the figure below. The conduction Bands “A” and “B” have the same
energy minima Ec.
Conduction Band A
Ec
Conduction Band B
Ev
Valence Band
L
[111]

[100]
X
Given the following inverse effective mass tensor data measured by cyclotron resonance at 4 K.
Conduction Band A
Conduction Band B
0.5 0 0 
mo 

  0 0.5 0 
m*
 0 0 0.5
0.1 0 0 
mo 
 0 6 0 
m* 
 0 0 6 
mo=9.1 x 10-31 kg
Assuming parabolic constant energy surfaces at the band minima to:
a) Draw the constant energy surface(s) for electrons near the conduction band minima in k-space.
b) Determine the effective mass for electrons in each conduction band ( bands A and B) which have
minima at the same energy Ec.
c) Determine the overall average density of states effective mass for the entire conduction band mn*.
2
Note: Volume of a prolate spheroid is 4 ab where 2a and 2b are the lengths of the major and minor axes
3
respectively of the rotated ellipse.
2
sol
3
2.
(50 pts)
Given the iso-etch curves for the HNA silicon isotropic etch system below
a. Calculate the etch rate for a etchant solution of 60:20:20 HF:HNO3:HC2H3O2.
b. Repeat if the diluent is DI water.
sol
a. 330 µm/min
b. 11.5 µm/min
4
3.
(50 pts)
A one-hour dry oxidation at 1000 °C is followed by a 5-hour wet oxidation at 1100 °C. Calculate
the oxide thickness after each step for a <100> wafer.
sol
5