Chapter 7: DOPANT DIFFUSION

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

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

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)

Introduction

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

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

NTRS Projections Note particularly the projected junction depth

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

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

Basic Concepts

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

Dopant Solubility in Si

Solubility Limit Solubility and electrical activity of impurities in Si 1021 1020 1019 900 1000 1100 1200 Temperature ( o C ) Sb B P As Solubility limit Electrical active Impurity concentration, N (atoms/cm3 )

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

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

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)

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)

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

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

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

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

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 )

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

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)

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 0 0.5 1 1.5 2 2.5 3 3.5 Normalized distance from surface,

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

Diffusion Coefficient Typical diffusion coefficients in silicon

Diffusion Of Impurities In Silicon Arrhenius plots of diffusion in silicon 1400 1300 1200 1100 1000 Temperature (o C) 10-9 10-10 10-11 10-12 10-13 10-14 0.6 0.65 0.7 0.75 0.8 0.85 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 0.6 0.7 0.8 0.9 1.0 1.1 1200 1100 1000 900 800 700 Li Cu Fe Au

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

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

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

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

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

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

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

Junction Formation Junction Depth Lateral Diffusion

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

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

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

Irvin’s Curves

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

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

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

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

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

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

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)

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

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

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

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

- + 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: - + ¾ ® ¬ 2 9 6 4 30 5 3 900 CH O B CO H Si SiO POCl P Cl As Sb o C

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

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

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

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

Rapid Thermal Annealing

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

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)

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

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

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

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

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

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

Concentration-Dependent Diffusion

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