Semiconductor: Solid-source Diffusion

[mbrmbrg]

Homework Statement

You use the solid diffusion source wafers PH-950 from St. Gobain (see data sheet on TSquare, Diffusion Chapter) to form phosphorous-doped resistors in a p-type wafer with a background doping concentration of 1015 cm-3. According to the data sheet, a 60-min predeposition at 925°C should yield a sheet resistance of 10 Ω/sq. and a junction depth of approx. xj = 1.3 μm.

(a) Verify these numbers by calculating (and plotting) the doping profile ND(x), the junction
depth xj, and the sheet resistance. Assume that the surface concentration reaches the solid
solubility at the pre-deposition temperature.

(b) What thickness must a masking oxide have to locally prevent P-diffusion?

Homework Equations

$$C(x,t)=C_serf\left\frac{x}{2\sqrt{Dt}}\right$$

$$D=D_0^{-E_a/kT}+D_0_-^{-E_a_-/kT}+D_0_--^{-E_a_--/kT}$$

The Attempt at a Solution

See attached

Briefly, I'm trying to plot concentration as a function of x, so I solved for D and plugged everything into the equation for C(x,t), with t=3600s. However, that returns an answer that the concentration > 0 only when the depth is < 0.19um. As the manufactuer claims a junction depth of 1.3um, I assume I did something very, very wrong.

 

[phyzguy]

1.3 micron sounds awfully deep for those parameters. Are you sure you have the manufacturers specs right? Maybe the 1.3 micron Xj is after a subsequent drive-in? I think you did the calculations correctly for what you were given

 

[mbrmbrg]

Oh, dear. The manufacturer's specs are stated in the problem, and I checked it on the graphs the manufacturer gives out. Sounds unreasonable, but that's what they say, and I can't imagine they'd get away with such an egregious error. I must be making a mistake somewhere...

To clarify, the wafers have a background doping concentration of 10¹⁵ cm^-3. (I lost formatting when I copied and pasted.) Either way, though, I'm still getting a ridiculously small junction depth.