EE 5621

PROBLEM SET 2

S. G. Burns

Due: Wednesday,  29 September 2021

 

Note 1:  The following problems require using the data and curves from the text and embedded in the class PowerPoints:

Note 2:  Also recall the erfc and Gaussian graphs. I have attempted to simplify algebra and arithmetic.  Not all problems are one-liners, but reasonably close.

1.   Assume a linear donor doping profile defined by  as sketched.  The substrate is doped at NA = 1 x 1017cm-3.

 

 

 

 

 

 

 


(a)                        Compute a value for the junction depth, xj.

(b)                       What is the resultant dose, Qo?  [You can make your algebraic life easier by utilizing the

          linear nature of the assumed doping profile! and knowing how to compute the area of a triangle!

(c)         This predeposition step is now capped and we proceed with a limited source diffusion for time  t1 and temperature T1. 

During the time, t1, used for this finite (limited source) drive diffusion, the surface concentration will (INCREASE,

REMAIN THE SAME, DECREASE), the junction    depth, xj, will (INCREASE, REMAIN THE SAME,         DECREASE),

and the dose, Qo will (INCREASE, REMAIN THE SAME, DECREASE).   Circle your choices.

(d)                       Suppose the finite (limited) source diffusion in Part (c) was done at temperature T2, where T2> T1 and the time remains

            the same.  Comparing to the results from Part (c), the surface concentration would              be (LOWER, ABOUT THE

            SAME), the junction depth, xj, would be (DEEPER,  ABOUT THE SAME, NOT AS DEEP), and the dose, Qo would be

           (LARGER, ABOUT THE SAME, SMALLER)  Circle your choices.

2.                Now let’s work with a bit more complicated doping profile function.  Assume that an infinite source   profile of boron

doping can be      approximated by an exponential of the form .  Assume the n-type   substrate is doped at ND = 1017 cm-3. 

(a)   Sketch the diffusion profile.  You will need to find a reasonable value for from the curves in the    PPTs

(b)  Compute the junction depth in μm.

(c ) Compute a value for the dose, Qo, with correct units.  Although you can use MATLAB or MATHEMATICA for the integration, the exponential function closed form by-hand solution is probably much quicker.  Whichever you use, show the problem graphical set up.

3.      A bit of a plug-and-chug Assume a p-doped substrate where NA = 1 x 1016 cm-3 .  From an infinite As source

         ND = 1 x 1019 cm-3, compute the junction     depth, xj, for one hour and a two hour diffusion at 1100°C. 

4.     Compare the impurity concentration at 1μm with that of the surface concentration for a 1 hour and 2 hour diffusion of boron

        into an n-type substrate at 1100°C  To have some consistency in your solutions, use D=3.5 x 10-13 cm2/sec.

Using graphs from class notes, answer the following for oxidations:

5.      Oxidation Analysis

          (a)     How long to grow a 200Å  SiO2 gate dielectric at 1000°C.  For this, assume a dry oxidation.  Discuss several  reasons       why this dry oxidation is           preferable to a wet oxidation.

          (b)    How long to grow a 0,3 μm   SiO2 masking layer at 1000°C.  For this, use assume a wet  oxidation.  Discuss several      reasons why this wet oxidation is preferable to a dry oxidation.