1. A planar silicon diode is designed as follows: p+ - n junction, with junction depth of 0.5µm from the surface of the wafer, fabricated in an 21micron thick layer of lightly doped silicon (this layer ends 21 microns from the surface) over a very heavily doped silicon substrate (this is the thick silicon substrate). Doping: p+ - 10¹⁸
n - 10¹⁵
n+ substrate - large, you can assume 10¹⁸ but it doesn't matter.
Lifetimes: t_p = t_n = 10^-7 sec
T = 300K

a. What is the breakdown voltage of the diode, ignoring 3-dimensional effects? (refer to figures in Sze Ch. 2, figures 26, 29, 35. (on web site))

b. What is the breakdown voltage of a square diode of the same doping, (shape as viewed from above) 0.1 cm x 0.1 cm in dimension? (Refer to Fig. 9, Ch. 2, Sze. (on web site))

c. What is the breakdown voltage of a circular diode, again of the same doping, 0.1 cm in diameter?

2. a. Considering only one-dimensional effects, does the onset of series resistance effects, or high injection effects, occur first in this diode? (diode from previous problem, one-dimensional analysis) Estimate the onset of high injection effects as the voltage at which p_n at x_n = n_no. Estimate the onset of series resistance effects by computing the resistivity of the bulk semiconductor, and determining the voltage at which the current is half of that predicted by the ideal diode equation. Examine each effect separately, assuming no other non-ideal effects. T = 300K.

3. What will the reverse current be at -50V, including generation in the depletion layer, if the traps are located midgap, E_T' = E_i? How does this compare with J_s? T= 300K.

4. Given the attached measured I-V data for a silicon diode, area = 2.24 X 10^-3 cm^-2. Note that the data points start at -5 V and 3.766e-11 (signs not shown). One - and one + sign indicate where the applied voltage changes from negative to positive. A seperate, better data file is attached.

a. Are the forward I-V characteristics dominated by recombination or diffusion currents? (This may not have a clear-cut answer - explain. Comparing the slope with that expected from diffusion or recombination-dominated behavior will be useful.)

b. Identify the portion of the forward characteristics where high injection and series resistance effects are important.

c. What is the diffusion dominated saturation current? Again this may not have a clear answer, but think about it and do your best!!

d. Assuming that if traps are important, that they are located midgap, is the reverse current what you would predict from the forward characteristics? (Several approaches to this part of the problem are possible, but there is not clear answer. Some simple calculations and discussion should be sufficient).

5 3.766E 11
4.941 3.534E 11
4.882 3.428E 11
4.823 3.353E 11
4.764 3.317E 11
4.705 3.28E 11
4.646 3.245E 11
4.587 3.21E 11
4.528 3.18E 11
4.469 3.151E 11
4.41 3.122E 11
4.351 3.092E 11
4.292 3.053E 11
4.233 3.027E 11
4.174 2.996E 11
4.115 2.962E 11
4.056 2.935E 11
3.997 2.909E 11
3.938 2.88E 11
3.879 2.848E 11
3.82 2.822E 11
3.761 2.795E 11
3.702 2.77E 11
3.643 2.736E 11
3.584 2.712E 11
3.525 2.684E 11
3.466 2.659E 11
3.407 2.633E 11
3.348 2.604E 11
3.289 2.573E 11
3.23 2.545E 11
3.171 2.514E 11
3.112 2.482E 11
3.053 2.451E 11
2.994 2.424E 11
2.935 2.394E 11
2.876 2.359E 11
2.817 2.329E 11
2.758 2.295E 11
2.699 2.257E 11
2.64 2.229E 11
2.581 2.2E 11
2.522 2.169E 11
2.463 2.136E 11
2.404 2.106E 11
2.345 2.077E 11
2.286 2.042E 11
2.227 2.001E 11
2.168 1.969E 11
2.109 1.938E 11
2.05 1.901E 11
1.991 1.858E 11
1.932 1.822E 11
1.873 1.786E 11
1.814 1.748E 11
1.755 1.711E 11
1.696 1.674E 11
1.637 1.636E 11
1.578 1.599E 11
1.519 1.559E 11
1.46 1.52E 11
1.401 1.478E 11
1.342 1.435E 11
1.283 1.39E 11
1.224 1.346E 11
1.165 1.303E 11
1.106 1.261E 11
1.047 1.205E 11
.988 1.159E 11
.929 1.114E 11
.87 1.07E 11
.811 1.02E 11
.752 9.68E 12
.693 9.14E 12
.634 8.61E 12
.575 8.06E 12
.516 7.53E 12
.457 6.97E 12
.398 6.37E 12
.339 5.76E 12
.28 5.12E 12
.221 4.48E 12
.162 3.75E 12
.103 2.95E 12
- .044 1.74E 12
+.015 1.07E 12
.074 1.157E 11
.133 5.818E 11
.192 3.051E 10
.251 1.962E 09
.31 1.5397E 08
.369 1.26E 07
.428 7.08E 07
.487 2.071E 06
.546 3.93E 06
.605 6.039E 06
.664 8.274E 06
.723 1.059E 05
.782 1.295E 05
.841 1.536E 05
.9 1.778E 05

5. 5.19, text. Note that the diffusion capacitance at zero or reverse bias is negligable. Assume the semiconductor is Si and use fig. 3.11, 3.21 and 3.23 as in the example to get the lifetime and calculate the saturation current. Also note that the p and n curves in 3.21 and 3.23 are swapped. In both cases, the top curve corresponds to holes. Another note: Example 5.5 has an incorrect number. It is 37fF rather than 53fF.

6. 5.21, text.

7. 5.22, text.

8. Use spice to simulate the circuit in Figure S2.14. Use the 1n4002 diode first, then try the 1n914 diode.

Hints: For the 1n4002 diode with the circuit shown, and a 5 V pulse, an on time of 10 microseconds with a total simulation time of 40 microseconds works well.

A student version of PSpice is available on the course web site. Other versions are available on the College of Engineering computer network.

a. What is different in the response between the two diodes. (you may have to change simulation times to really see this)

b. Try to figure out what the difference in the device is from the difference in the model parameters in Spice. You may have to do a little digging for the definition of parameters. To find the parameters in PSpice, click on the diode of interest (the 1n4002, for example), then go to Edit > Model > Edit Instance Model (Text). You will be able to read the parameters. There are many references for the meaning of the spice parameters, and the most important ones are covered in our text.