ECE 440
Homework IV
Fall 2009
Print your name and netid legibly. Show all work leading to your answer clearly
and neatly. Staple multiple pages.
1. A Si bar is 0.2 cm long and 200 µm2 in cross-sectional area. Find the current at 300
K with 10 V applied to (a) the Si bar is doped with 1x1017 /cm3 gallium and (b) the Si
bar is doped with 1x1017 /cm3 gallium and 2x1017 /cm3 arsenic. Refer to Fig. 3-23 or
the mobility chart posted online.) (c) The silicon sample is grounded at x=0 and
biased at +10 V at x=0.2 cm. Draw the corresponding energy band diagram for case
(a).
2. How long does it take for an average electron to drift 0.2 mm donors under an
electric field of 100 V/cm for: (a) pure Si and (b) Si doped with 6x10 16 /cm3 donors at
an electric field of 100 V/cm? Repeat if the electric field is change to 10 5 V/cm.
Assume that the electron effective mass mn*=0.26 mo.
3. Consider a silicon sample at 300 K. Assume that the electron concentration varies
linearly with distance. At x=0, the electron concentration is n(0). At x=10 µm, the
electron concentration is n(10µm)= 5x1014 /cm3. If the electron diffusion coefficient,
assumed constant, is Dn =30 cm2/sec, determine the electron concentration at x=0
for the following two diffusion current densities: (a) the diffusion current density is
found to be Jndiff = + 0.9 A/cm2 and (b) Jndiff = - 0.9 A/cm2.
4. Drift and Carrier Mobility Simulation. We will use the following tool:
http://nanohub.org/resources/semi
The tool explores the Drift and Diffusion concepts we have learned in class.
Please answer the following at room temperature (300K) unless otherwise
stated. and Select Experiment #1: Apply Bias Only in the tool.
Hint: Extract the low field mobility from the I-V Curve.
a. ) Now, let us consider an intrinsic Si, Ge and GaAs slab of length 0.5um:
i) Compare the electron mobility of the 3 materials if each sample is
doped with donor concentration ND =1x1016 /cm3. Repeat for hole
mobility with NA = 1x1016 /cm3. How do your results compare to the
mobility values shown in appendix III.
ii) Refer to Figure 3-23 (Streetman). Explain why mobility varies with
doping concentration.
b. ) Let us consider an intrinsic Si slab of length 0.1um at room temperature
iii) Dope the semiconductor with NA = 1x1014 /cm3 and Generate vd
(cm/sec) vs E (V/cm) curves for holes using log-scale. Repeat for
electron with ND = 1x1014 /cm3. What is the saturation velocity for each
case? At what fields can we still use low-field mobility?
iv) Extract electron (μn) and hole (μp) mobility values from the figure
generated above.