1. MSE-630 Dopant Diffusion Topics: Doping methods Resistivity and Resistivity/square Dopant Diffusion Calculations -Gaussian solutions -Error function solutions

2. MSE-630 As devices shrink, controlling diffusion profiles with processing and annealing is critical in acquiring features down to 10-20 nm Schematic of a MOS device cross section, showing various resistances. X j is the junction depth in the table above As devices shrink, controlling the depth of the gate channel becomes critical

3. MSE-630 Deposition Methods Chemical Vapor Deposition Evaporation -Physical Vapor Deposition -Sputtering Ion Beam Implantation

4. MSE-630 Vapor Deposition: Chemical (CVD) In Chemical Vapor Deposition (CVD) a reactive gas is passed over the substrate to be coated, inside of a heated, environmentally controlled reaction chamber. In this case (right) CH4 gas is introduced to create a diamond-like coating

5. MSE-630 Vapor Deposition: Physical (PVD) Physical Vapor Deposition (PVD) may be from evaporation or sputtering. Sometimes a plasma is used to create high energy species that collide with target (right)

6. MSE-630 Sputtering

7. MSE-630 Ion beam implantation gives excellent control over the predeposition dose and is the most widely used doping method

8. MSE-630 Ion beam implantation It can cause surface damage in the form of sputtering of surface atoms, surface roughness and changes in the crystal structure. Though these defects can be removed by annealing, annealing also results in a high degree of dopant diffusion.

9. MSE-630

10. Resistivity and Sheet Resistance From Ohm’s Law:  J =  Where J = current density (A/cm 2 )  = electric field strength (V/m)  =resistivity (  cm) Thus  =  /J In semiconductors, the doped regions have higher conductivity than the sheet as a whole. We are interested in the depth of the junction, x j. The resistance we measure is that of a square of any dimension with depth x j, or R =  /x j  /square ≡  s for uniform doping. For variable doping:

11. MSE-630

12. Solid solubility Sometimes dopants cluster around vacancies and other point defects, as above, becoming electrically neutral. As a result, effective level of doping may be lower than equilibrium values in the adjacent figure

13. MSE-630 Diffusion Models Fick’s 1 st law: F = -D dC/dx Fick’s 2nd law:  C/  t =  F/  x = (F in – F out )/  x dC/dt = D d 2 C/dx 2

14. MSE-630 Diffusion in Silicon In general, diffusivity is given by: D = D o exp(-E a /kT) Where E a = activation energy ~ 3.5 – 4.5 eV/atom k = 8.61x10 -5 eV/atom-K This applies to intrinsic conditions. Dopant levels (N D, N A ) need to be less than the intrinsic carrier density, n i as shown in the graph

15. MSE-630

16. Gaussian Solution in an Infinite Medium

17. MSE-630

18. Gaussian Diffusion near a Surface

19. MSE-630 Error-Function solution in an Infinite Medium

20. MSE-630 Error-Function solution near a Surface This solution assumes the concentration C is at the solid solubility limit and is infinite The dose, Q, is calculated by summing the concentration:

21. MSE-630

23. Effect of successive diffusion steps If diffusion occurs at constant temperature, where the diffusivity is constant, then the effective thermal budget, Dt is: (Dt) eff = D 1 t 1 +D 1 t 2 +…D 1 t n If D is not constant, then time is increased by the ratio of D 2 /D 1, or (Dt) eff = D 1 t 1 +D 1 t 2 (D 2 /D 1 )+…D 1 t n (D n /D 1 )

24. MSE-630