Junction Formation The position of the junction for a limited 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

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, the continuous (erf) solution may be applied If we have a low surface concentration, the limited source (Gaussian) solution may be applied

Irvin’s Curves If we describe the dopant profile by either the Gaussian or the erf model 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

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

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

Example Consider a predep process from the solid state source (as is done in the VT lab course) The text uses a predep temperature of 950 oC 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 oC, 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 predep at a lower temperature In the VT lab, we use 830 – 860 oC 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 Open tube furnaces of the 3-Zone design Wafers are loaded in quartz boat in center zone Solid, liquid or gaseous impurities may be used Common gases are extremely toxic (AsH3 , PH3) Use N2 or O2 as carrier gas to move impurity downstream to crystals

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 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

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

Rapid Thermal Anneling Absorption of IR light will heat the wafer quickly (but not so as to introduce fracture stresses) It is possible to ramp the wafer at 100 oC/s Because of the thermal conductivity of Si, a 12 in wafer can be heated to a uniform temperature in milliseconds 1 – 100 s drive or anneal times are possible RTAs are used to diffuse shallow junctions and to anneal radiation damage

Rapid Thermal Annealing

Concentration-Dependent Diffusion When the concentration of the doping exceeds the intrinsic carrier concentration at the diffusion temperature We have assumed that the diffusion coefficient, D, is dependent of 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 We can still use Fick’s law to describe the dopant diffusion 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

Concentration-Dependent Diffusion B has two isotopes: B10 and B11 Create a wafer with a high concentration of one isotope and then diffuse the second isotope into this material SIMS is used to determine the concentration of the second isotope as a function of x The experiment has been done using many of the dopants in Si to determine the concentration dependence of D

Concentration-Dependent Diffusion Diffusion constant can usually be written in the form for n-type dopants and for p-type dopants

Concentration-Dependent Diffusion It is assumed that there is an interaction 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 assumed to follow the Arrhenius form

Concentration-Dependent Diffusion The values for all the pre-exponential factors and activation energies are known 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  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