Research Paper

1. Research Paper

2. Chapter 7:DOPANT DIFFUSION

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

4. Introduction • 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 • 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 • 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 • This is valid if the doping is uniform throughout the junction • 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 • 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

11. 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. • 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 • This is a major problem in very shallow junctions

13. Basic Concepts

14. Basic Concepts • 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. • 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. As P 1021 As P Impurity concentration, N (atoms/cm3 ) B 1020 Sb Solubility limit Electrical active 1019 900 1000 1100 1200 Temperature ( o C ) Solubility Limit

17. Solubility Limit • Surface concentrations can be high. • At 1100oC: • B: 3.3 x 1020 cm-3 • P: 1.2 x 1021 cm-3 • 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 • 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

21. 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)

22. Fick’s Laws • 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. • 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 • Concentration of diffusing impurities is linear over distance • This was the solution for the flow of oxygen from the surface to the Si/SiO2 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 • The dose is

26. Solutions To Fick’s Second Law • Complimentary error function (erfc) is defined as erfc(x) = 1 - erf(x) • 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. c0 Impurity concentration, c(x) c ( x, t ) D3t3 > D2t2 > D1t1 1 2 3 cB Distance from surface, x Solutions To Fick’s Second Law • This solution models short diffusions from a gas-phase or liquid phase source • Typical solutions have the following shape

28. Solutions To Fick’s Second Law • 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 • The surface concentration is given by:

29. c01 c ( x, t ) c02 Impurity concentration, c(x) D3t3 > D2t2 > D1t1 c03 1 2 3 cB Distance from surface, x Solutions To Fick’s Second Law • Limited source diffusion looks like