1. Research Paper

2. Chapter 7: DOPANT DIFFUSION

3. DOPANT DIFFUSION Introduction Introduction Basic Concepts Basic Concepts –Dopant solid solubility –Macroscopic view –Analytic solutions –Successive diffusions –Design of diffused layers Manufacturing Methods Manufacturing Methods

4. Introduction Main challenge of front-end processing is the accurate control of the placement of active doping regions Main challenge of front-end processing is the accurate control of the placement of active doping regions Understanding and control of diffusion and annealing is essential to obtaining the desired electrical performance Understanding and control of diffusion and annealing is essential to obtaining the desired electrical performance –If the gate length is scaled down by 1/K (K>1) ideally the dimensions of all doped regions should also scale by 1/K to maintain the same electric field patterns  With the same field patterns, the device physics remains the same except that the device is faster because of the shorter channel

5. Introduction There is a continuous drive to reduce the junction depth with each new technology generation There is a continuous drive to reduce the junction depth with each new technology generation –We need high activation levels to reduce parasitic resistances of the source, drain and extensions  Activation level is the ratio of the concentration of the electrically active impurities to total concentration of impurities

7. Introduction The sheet resistance is given by The sheet resistance is given by –This is valid if the doping is uniform throughout the junction If it is not, the expression becomes If it is not, the expression becomes

9. Introduction The challenge is to keep the junctions shallow and yet keep the resistance of the source and drain small to maximize drive current The challenge is to keep the junctions shallow and yet keep the resistance of the source and drain small to maximize drive current –These are conflicting requirements  It is extremely difficult to obtain high concentration of impurities in the material without the impurity concentration extending deep into the semiconductor.

10. NTRS Projections Note particularly the projected junction depth Note particularly the projected junction depth

11. Planar process has dominated all methods for creating junctions since 1960 Planar process has dominated all methods for creating junctions since 1960 The fundamental change in the past 40 years has been how the “predep” has been done. The fundamental change in the past 40 years has been how the “predep” has been done. –Predep (predeposition) controls how much impurity is introduced into the wafer  In the 1960s, this was done by solid state diffusion from glass layers or by gas phase diffusion  By the mid-1970s, ion implantation became the method of choice –Its only drawback is radiation damage

12. In ion implantation, damaged-enhanced diffusion allows for significant diffusion of dopants In ion implantation, damaged-enhanced diffusion allows for significant diffusion of dopants –This is a major problem in very shallow junctions

13. Basic Concepts

14. The desired dopants (P, As, B) have only limited solid solubility in Si The desired dopants (P, As, B) have only limited solid solubility in Si –The solubility increases with temperature –Some dopants exhibit retrograde solubility (where the solubility decreases at elevated temperatures) precipitates form when concentration is above solid solubility limit. precipitates form when concentration is above solid solubility limit. – When combined in precipitates (or clusters) the dopants do not contribute donors or acceptors (electrons or holes) –The dopant is not electrically active

15. Dopant Solubility in Si

16. Solubility Limit 10 21 10 20 10 19 900 1000 1100 1200 Temperature ( o C ) Sb B P As P Solubility limit Electrical active Impurity concentration, N (atoms/cm 3 )

17. Solubility Limit Surface concentrations can be high. Surface concentrations can be high. –At 1100 o C:  B:3.3 x 10 20 cm -3  P:1.2 x 10 21 cm -3 At high temperatures, impurities cluster without precipitating and have limited electrical activity At high temperatures, impurities cluster without precipitating and have limited electrical activity

19. III-V dopants have limited solubility in Si

20. Diffusion Models The macroscopic view describes the overall motion of the dopant profiles The macroscopic view describes the overall motion of the dopant profiles –It predicts the motion of the profile by solving a differential equation subject to certain boundary conditions The atomistic approach is used to understand some of the very complex mechanisms by which dopants move in Si The atomistic approach is used to understand some of the very complex mechanisms by which dopants move in Si

21. Fick’s Laws Diffusion is described by Fick’s Laws. Diffusion is described by Fick’s Laws. Fick’s first law is: D = diffusion coefficient Conservation of mass requires (This is the continuity equation) Conservation of mass requires (This is the continuity equation)

22. Fick’s Laws Combining the continuity equation with the first law, we obtain Fick’s second law: Combining the continuity equation with the first law, we obtain Fick’s second law:

23. Solutions to Fick’s Laws depend on the boundary conditions. Solutions to Fick’s Laws depend on the boundary conditions. Assumptions Assumptions –D is independent of concentration –Semiconductor is a semi-infinite slab with either  Continuous supply of impurities that can move into wafer  Fixed supply of impurities that can be depleted

24. Solutions To Fick’s Second Law The simplest solution is at steady state and there is no variation of the concentration with time The simplest solution is at steady state and there is no variation of the concentration with time –Concentration of diffusing impurities is linear over distance This was the solution for the flow of oxygen from the surface to the Si/SiO 2 interface in the last chapter This was the solution for the flow of oxygen from the surface to the Si/SiO 2 interface in the last chapter

25. Solutions To Fick’s Second Law For a semi-infinite slab with a constant (infinite) supply of atoms at the surface For a semi-infinite slab with a constant (infinite) supply of atoms at the surface The dose is The dose is

26. Solutions To Fick’s Second Law Complimentary error function (erfc) is defined as erfc(x) = 1 - erf(x) Complimentary error function (erfc) is defined as erfc(x) = 1 - erf(x) The error function is defined as The error function is defined as –This is a tabulated function. There are several approximations. It can be found as a built-in function in MatLab, MathCad, and Mathematica

27. Solutions To Fick’s Second Law This solution models short diffusions from a gas-phase or liquid phase source This solution models short diffusions from a gas-phase or liquid phase source Typical solutions have the following shape Typical solutions have the following shape c0c0 cBcB Distance from surface, x 1 2 3 D 3 t 3 > D 2 t 2 > D 1 t 1 Impurity concentration, c(x) c ( x, t )

28. Solutions To Fick’s Second Law Constant source diffusion has a solution of the form Constant source diffusion has a solution of the form Here, Q is the does or the total number of dopant atoms diffused into the Si Here, Q is the does or the total number of dopant atoms diffused into the Si The surface concentration is given by: The surface concentration is given by:

29. Solutions To Fick’s Second Law Limited source diffusion looks like Limited source diffusion looks like c ( x, t ) c 01 c 02 c 03 cBcB 12 3 Distance from surface, x D 3 t 3 > D 2 t 2 > D 1 t 1 Impurity concentration, c(x)