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Dopant Diffusion

Dopant Diffusion. Topics: Doping methods Resistivity and Resistivity/square Dopant Diffusion Calculations -Gaussian solutions -Error function solutions. As devices shrink, controlling diffusion profiles with processing and annealing is critical in acquiring features down to 10-20 nm.

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Dopant Diffusion

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  1. Dopant Diffusion • Topics: • Doping methods • Resistivity and Resistivity/square • Dopant Diffusion Calculations • -Gaussian solutions • -Error function solutions

  2. As devices shrink, controlling diffusion profiles with processing and annealing is critical in acquiring features down to 10-20 nm Schematic of a MOS device cross section, showing various resistances. Xj is the junction depth in the table above As devices shrink, controlling the depth of the gate channel becomes critical

  3. Deposition Methods • Chemical Vapor Deposition • Evaporation • -Physical Vapor Deposition • -Sputtering • Ion Beam Implantation

  4. Vapor Deposition: Chemical (CVD) In Chemical Vapor Deposition (CVD) a reactive gas is passed over the substrate to be coated, inside of a heated, environmentally controlled reaction chamber. In this case (right) CH4 gas is introduced to create a diamond-like coating

  5. Vapor Deposition: Physical (PVD) Physical Vapor Deposition (PVD) may be from evaporation or sputtering. Sometimes a plasma is used to create high energy species that collide with target (right)

  6. Sputtering

  7. Ion beam implantation gives excellent control over the predeposition dose and is the most widely used doping method

  8. Ion beam implantation It can cause surface damage in the form of sputtering of surface atoms, surface roughness and changes in the crystal structure. Though these defects can be removed by annealing, annealing also results in a high degree of dopant diffusion.

  9. Resistivity and Sheet Resistance • From Ohm’s Law: rJ = e • Where J = current density (A/cm2)e = electric field strength (V/m)r=resistivity (W-cm) • Thus • r = e/J In semiconductors, the doped regions have higher conductivity than the sheet as a whole. We are interested in the depth of the junction, xj.The resistance we measure is that of a square of any dimension with depth xj, or R = r/xjW/square ≡ rs for uniform doping. For variable doping:

  10. Solid solubility Sometimes dopants cluster around vacancies and other point defects, as above, becoming electrically neutral. As a result, effective level of doping may be lower than equilibrium values in the adjacent figure

  11. Diffusion Models Fick’s 1st law: F = -D dC/dx Fick’s 2nd law: DC/Dt = DF/Dx = (Fin – Fout)/Dx dC/dt = D d2C/dx2

  12. Diffusion in Silicon In general, diffusivity is given by: D = Doexp(-Ea/kT) Where Ea = activation energy ~ 3.5 – 4.5 eV/atom k = 8.61x10-5 eV/atom-K This applies to intrinsic conditions. Dopant levels (ND, NA) need to be less than the intrinsic carrier density, ni as shown in the graph

  13. Gaussian Solution in an Infinite Medium

  14. Gaussian Diffusion near a Surface

  15. Error-Function solution in an Infinite Medium

  16. Error-Function solution near a Surface The dose, Q, is calculated by summing the concentration: This solution assumes the concentration C is at the solid solubility limit and is infinite

  17. Effect of successive diffusion steps If diffusion occurs at constant temperature, where the diffusivity is constant, then the effective thermal budget, Dt is: (Dt)eff = D1t1+D1t2+…D1tn If D is not constant, then time is increased by the ratio of D2/D1, or (Dt)eff = D1t1+D1t2(D2/D1)+…D1tn(Dn/D1)

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