1. Chapter 7: DOPANT DIFFUSION

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

3. 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 works the same as before, except that it is faster because of the shorter channel

4. Introduction
Thus, there is a continuous drive to reduce the junction depth with each new technology generation
However, the diffusion cycles often become the limiting factor in junction depth
We need high activation levels to reduce parasitic resistances of the source, drain and extensions (see Figure 1)

5. Introduction

6. 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

8. 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
The NTRS has set goals for shallow junctions

9. NTRS Projections
Note particularly the projected junction depth

10. Basic Concepts
Since 1960, the planar process has dominated all methods for creating junctions
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 (and remains) the method of choice
Its only drawback is radiation damage

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

12. Basic Concepts

13. Basic Concepts
The desired dopants (P, As, B) have only limited solid solubility in Si
The solubility increases with temperature
Except, some dopants exhibit retrograde solubility (where the solubility decreases at elevated temperatures)
If we dope above the solubility limit, precipitates form. When combined in precipitates (or clusters) the dopants do not contribute donors or acceptors (electrons or holes)
The dopant is not electrically active
We therefore need to know the maximum amount of dopant that we can put in Si and maintain electrically active donors and acceptors

14. Dopant Solubility in Si

15. Solubility Limit Solubility and electrical activity of impurities
in Si
1021
1020
1019
Temperature ( o C ) Sb B P As
Solubility limit
Electrical active
Impurity concentration, N (atoms/cm3 )

16. Solubility Limit III-V dopants have limited solubility in Si
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

17. Diffusion Models
We can discuss diffusion from a macroscopic or a microscopic point of view
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
We will solve the macroscopic part first

18. 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)

19. Fick’s Laws
Combining the continuity equation with the first law, we obtain Fick’s second law:
Solutions depend on the boundary conditions. We have assumed D is independent of concentration
Assume a semi-infinite slab with
Continuous supply (Models diffusion of impurities in wafer)
Fixed supply (Models ion implantation of impurities in wafer)

20. Solutions To Fick’s Second Law
The simplest solution is when there is a steady state and there is no variation of the concentration with time
In this case
This steady-state solution shows that the concentration 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

21. Solutions To Fick’s Second Law
There are two other solutions of interest
The text breaks these into two sub-solutions each; one for an infinite slab and one for a semi-infinite slab
We will examine only the latter as they approach real conditions

22. Solutions To Fick’s Second Law
For a semi-infinite slab with a constant (infinite) supply of atoms at the surface
The dose is x c (x , t) = c
erfc o 2 Dt

23. Solutions To Fick’s Second Law
In this solution, the complimentary error function (erfc) is defined as erfc(x)=1-erf(x)
The error function is defined as
This is a tabulated function. It also has several decent approximations, and is usually found as a built-in function in MatLab, MathCad, and Mathematica

24. Solutions To Fick’s Second Law
This solution models diffusion from a gas-phase or liquid phase source
Typical solutions look like c0 cB
Distance from surface, x 1 2 3
D3t3 > D2t2 > D1t1
Impurity concentration, c(x)
c ( x, t )

25. Solutions To Fick’s Second Law
Constant source diffusion, as is performed for example with ion implantation, 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 2 Q x - c (x , t) = e 4 Dt p Dt

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

27. Comparison Of Models
Comparison of constant source and continuous source models 1
10-1
exp( ) 2
10-2
erfc( )
Value of functions
10-3
10-4
10-5
10-6
Normalized distance from surface,

28. Diffusion Coefficient
Probability of a jump is
Diffusion coefficient is proportional to jump probability

29. Diffusion Coefficient
Typical diffusion coefficients in silicon

30. Diffusion Of Impurities In Silicon
Arrhenius plots of diffusion in silicon
Temperature (o C)
10-9
10-10
10-11
10-12
10-13
10-14
Temperature, 1000/T (K-1) Al Ga
B,P In As Sb
Diffusion coefficient, D (cm2/sec)
10-4
10-5
10-6
10-7
10-8 Li Cu Fe Au

31. Diffusion Of Impurities In Silicon
We recall that the intrinsic carrier concentration in Si is about 7 x 1018/cc at 1000 C
Thus, if NA and ND are <ni, the material will behave as if it were intrinsic; there are many practical situations where this is a good assumption
The solutions we have given will be valid so long as the concentrations are low enough so that the material is intrinsic at the diffusion temperature

32. Diffusion Of Impurities In Silicon
Note that the dopants cluster into “fast” diffusers (P, B, In) and “slow” diffusers (As, Sb)
As we develop shallow devices, slow diffusers are becoming very important
Note that B is the only p-type dopant that has a high solubility; therefore, it is very hard to make shallow p-type junctions with this fast diffuser
We will also find that the theories given here break down as we go to higher concentrations of dopants

33. Successive Diffusions
To create devices, we must successively diffuse n- and p-type dopants
There are many high temperature steps and all preceding impurities can move as succeeding dopant or oxidation steps are performed
The effective Dt product is
There is no difference between doing diffusion in one step or in several steps at the same temperature
If we now increase the time of step 2 by the ratio D2/D1

34. Successive Diffusions
The actual distribution is given by
Di , ti = diffusion coefficient and time for ith step
We need to bear in mind that, as will be seen later, D may be a function of more than T; thus these results will not hold å Dt = D t
tot i i i

35. Junction Formation
When diffuse n- and p-type materials, we create a pn junction
When [donor]=[acceptor], the semiconductor material is compensated and we create a metallurgical junction
At metallurgical junction the material behaves intrinsic
We can calculate the position of the metallurgical junction for those systems for which our analytical model is a good fit

36. p-type Gaussian diffusion
Junction Formation
Formation of a pn junction by diffusion
Impurity
concentration
N(x) N0 NB
(log scale) xj
p-type Gaussian diffusion
(boron)
n-type silicon
background
Distance from surface, x
Net impurity
|N(x) - NB |
N0 - NB
p-type
region
n-type region

37. Junction Formation x Dt N = 2 erfc
The position of the junction for a fixed source diffused impurity in a constant background is given by
The position of the junction for a continuous source diffused impurity is given by x Dt N j B = 2 ln x Dt N j B = - 2 1
erfc

38. Junction Formation
Junction Depth
Lateral Diffusion

39. Design and Evaluation
There are three parameters that define a diffused region
The surface concentration
The junction depth
The sheet resistance
These parameters are not independent
Irvin developed a relationship that describes these parameters very well
Consider the equation for sheet resistance

40. Irvin’s Curves
In designing processes, we need to use all available data
We need to determine if one of the analytic solutions applies
For example,
if the surface concentration is near the solubility limit, perhaps the continuous (erf) solution applies
If we have a low surface concentration, perhaps the fixed (Gaussian) solution applies

41. Irvin’s Curves
If we describe the dopant profile by either the Gaussian or the erf model, we can evaluate the integral
The surface concentration becomes a parameter in this integration
By rearranging the variables, we find that the surface concentration and the product of sheet resistance and the junction depth are related by the definite integral of the profile
There are four separate curves to be evaluated; one pair using either the Gaussian or the erf function, and the other pair for n- or p-type materials (because the mobility is different for electrons and holes)
Typical examples are shown on the following slide

42. Irvin’s Curves

43. Irvin’s Curves
An alternative way of presenting the data may be found if we set eff=1/sxj

44. 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

45. 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

46. 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
This is easy to deposit by ion implantation

47. Example
Let us also look at doing it by predep from the solid state (as is done in the VT lab course)
The text uses a predep temperature of 950 C
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 C, the solubility limit is 2.5x1020cm-3 and D=4.2x10-15 cm2/s
Solving for t

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

49. DIFFUSION SYSTEMS Use open tube furnaces of the 3-Zone design
Wafers are mounted in quartz boat in center zone
Use solid, liquid or gaseous impurities for good reproducibility
Use N2 or O2 as carrier gas to move impurity downstream to crystals
Common gases are extremely toxic (AsH3 , PH3)

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

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

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

53. DIFFUSION SYSTEMS
Al and Ga diffuse very rapidly in Si; B is the only p-dopant routinely used
Sb, P, As are all used as n-dopants

54. - + ¾ ® ¬ 2 9 6 4 30 5 3 CH O B CO H Si SiO POCl P Cl As Sb
DIFFUSION SYSTEMS
Typical reactions for solid impurities are: - + 2 9 6 4 30 5 3
900 CH O B CO H Si
SiO
POCl P Cl As Sb o C

55. PRODUCTION DIFFUSION FURNACES
Commercial diffusion furnace showing the furnace with wafers (left) and gas control system (right). (Photo courtesy of Tystar Corp.)

56. PRODUCTION DIFFUSION FURNACES
Close-up of diffusion furnace with wafers.

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

58. Rapid Thermal Anneling
In this system, we try to heat the wafer quickly (but not so as to introduce fracture stresses)
RTAs usually use infrared lamps and heat by radiation
It is possible to ramp the wafer at 100 C /sec
Such devices are used to diffuse shallow junctions and to anneal radiation damage
In such a system, for the thermal conductivity of Si, a 12 in wafer can be heated to a uniform temperature in milliseconds
Therefore, 1 – 100 s annealing times are very reasonable

59. Rapid Thermal Annealing

60. Concentration-Dependent Diffusion
If the concentration of the doping exceeds the intrinsic carrier concentration at the diffusion temperature, another effect occurs
We have assumed that the diffusion coefficient, D, is independent of concentration
This is not valid if the concentration of the diffusing species is greater than the intrinsic carrier concentration
In this case, we see that diffusion is faster in the higher concentration regions

61. 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)

62. Concentration-Dependent Diffusion
If we define the diffusivity to be a function of composition, then we can still use Fick’s law to describe the dopant diffusion
Usually, we cannot directly integrate/solve the differential equations when D is a function of C
We thus must solve the equation numerically

63. Concentration-Dependent Diffusion
It has been observed that the diffusion coefficient usually depends on concentration by either of the following relations
Look, for example, at the diffusion of P in Si observed by French et al
How do we obtain information about the concentration dependence of diffusivity?
There is a lovely experiment done with B

64. Concentration-Dependent Diffusion
B has two isotopes: B10 and B11
We create a wafer with a high concentration of one isotope (say B10) and then we diffuse the second isotope into this material
We use SIMS to determine the concentration of B11 as a function of distance
This gives us the diffusion of B as a function of the concentration of B
These experiments have been done for a great many of the dopants in Si

65. Concentration-Dependent Diffusion
We find that the diffusivity can usually be written in the form for n-type dopants and for p-type dopants

66. Concentration-Dependent Diffusion
The superscripts are chosen because we believe the interaction is 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 of the Arrhenius form

67. Concentration-Dependent Diffusion
The values for all the pre-exponential factors and activation energies are known (see next Table)
If we substitute into the expression for the effective diffusion coefficient, we find here, =D-/D0 and =D=/D0

68. Concentration-Dependent Diffusion

69. Concentration-Dependent Diffusion
Expressed this way,  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