Example

1. Example • Design a B diffusion for a CMOS tub such that s=900/sq, xj=3m, and CB=11015/cc • First, we calculate the average conductivity • We cannot calculate n or  because both are functions of depth • We assume that because the tubs are of moderate concentration and thus assume (for now) that the distribution will be Gaussian • Therefore, we can use the P-type Gaussian Irvin curve to deduce that

2. Example • Reading from the p-type Gaussian Irvin’s curve, CS4x1017/cc • This is well below the solid solubility limit for B in Si so we may conclude that it will be driven in from a fixed source provided either by ion implantation or possibly by solid state predeposition followed by an etch • In order for the junction to be at the required depth, we can compute the Dt value from the Gaussian junction equation

3. Example • This value of Dt is the thermal budget for the process • If this is done in one step at (for example) 1100 C where D for B in Si is 1.5 x 10-13cm2/s, the drive-in time will be • Given Dt and the final surface concentration, we can estimate the dose

4. Example • Consider a predep process from the solid state source (as is done in the VT lab course) • The text uses a predep temperature of 950 oC • In this case, we will make a glass-like oxide on the surface that will introduce the B at the solid solubility limit • At 950 oC, the solubility limit is 2.5x1020cm-3 and D=4.2x10-15 cm2/s • Solving for t

5. Example • This is a very short time and hard to control in a furnace; thus, we should do the predep at a lower temperature • In the VT lab, we use 830 – 860 oC • Does the predep affect the drive in? • There is no affect on the thermal budget because it is done at such a “low” temperature

6. DIFFUSION SYSTEMS • Open tube furnaces of the 3-Zone design • Wafers are loaded in quartz boat in center zone • Solid, liquid or gaseous impurities may be used • Common gases are extremely toxic (AsH3 , PH3) • Use N2 or O2 as carrier gas to move impurity downstream to crystals

7. Exhaust Slices on carrier Platinum source boat burn box and/or scrubber Quartz diffusion tube Quartz diffusion boat Valves and flow meters O2 N2 SOLID-SOURCE DIFFUSION SYSTEMS

8. Exhaust Slices on carrier Burn box and/or scrubber Quartz diffusion tube Valves and flow meters N2 O2 Liquid source Temperature- controlled bath LIQUID-SOURCE DIFFUSION SYSTEMS

9. Exhaust Slices on carrier Burn box and/or scrubber Quartz diffusion tube Valves and flow meter To scrubber system N2 O2 Dopant gas Trap GAS-SOURCE DIFFUSION SYSTEMS

10. o - + ¾ ¾ ¾ ® + + 900 C 2 CH O B 9 O B O 6 CO 9 H O 3 2 2 3 2 2 3 + ¬ ¾ ® + 2 B O Si SiO 4 B 2 3 2 - + ¾ ¾ ® + 4 POCl 30 2 P O 6 Cl 3 2 2 5 2 + ¬ ¾ ® + 2 P O 5 Si SiO 4 P 2 5 2 - + ¬ ¾ ® + 2 As O 3 Si 3 SiO 4 As 2 3 2 - + ¬ ¾ ® + 2 Sb O 3 Si 3 SiO 4 Sb 2 3 2 DIFFUSION SYSTEMS • Typical reactions for solid impurities are:

11. Rapid Thermal Annealing • An alternative to the diffusion furnaces is the RTA or RTP furnace

12. Rapid Thermal Anneling • Absorption of IR light will heat the wafer quickly (but not so as to introduce fracture stresses) • It is possible to ramp the wafer at 100 oC/s • Because of the thermal conductivity of Si, a 12 in wafer can be heated to a uniform temperature in milliseconds • 1 – 100 s drive or anneal times are possible • RTAs are used to diffuse shallow junctions and to anneal radiation damage

13. Rapid Thermal Annealing

14. Concentration-Dependent Diffusion • When the concentration of the doping exceeds the intrinsic carrier concentration at the diffusion temperature • We have assumed that the diffusion coefficient, D, is dependent of concentration • In this case, we see that diffusion is faster in the higher concentration regions

15. Concentration-Dependent Diffusion • The concentration profiles for P in Si look more like the solid lines than the dashed line for high concentrations (see French et al)

16. Concentration-Dependent Diffusion • We can still use Fick’s law to describe the dopant diffusion • Cannot directly integrate/solve the differential equations when D is a function of C • We thus must solve the equation numerically

17. Concentration-Dependent Diffusion • It has been observed that the diffusion coefficient usually depends on concentration by either of the following relations

18. Concentration-Dependent Diffusion • B has two isotopes: B10 and B11 • Create a wafer with a high concentration of one isotope and then diffuse the second isotope into this material • SIMS is used to determine the concentration of the second isotope as a function of x • The experiment has been done using many of the dopants in Si to determine the concentration dependence of D

19. Concentration-Dependent Diffusion • Diffusion constant can usually be written in the formfor n-type dopants and for p-type dopants

20. Concentration-Dependent Diffusion • It is assumed that there is an interaction between charged vacancies and the charged diffusing species • For an n-type dopant in an intrinsic material, the diffusivity is • All of the various diffusivities are assumed to follow the Arrhenius form

21. Concentration-Dependent Diffusion • The values for all the pre-exponential factors and activation energies are known • If we substitute into the expression for the effective diffusion coefficient, we findhere, =D-/D0 and=D=/D0

22. Concentration-Dependent Diffusion

23. Concentration-Dependent Diffusion •  is the linear variation with composition and  is the quadratic variation • Simulators like SUPREM include these effects and are capable of modeling very complex structures