7. dopant diffusion 1,2 2013 microtech
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This document discusses dopant diffusion, which is the process of introducing controlled amounts of chemical impurities into a semiconductor lattice. Dopant diffusion is used to form source, drain, base, and emitter regions in semiconductor devices. The document covers various diffusion techniques and parameters, including diffusion sources, solid solubility limits, Fick's laws of diffusion, analytical solutions to the diffusion equations, design of diffused layers, and an example design calculation for a boron diffusion process.
![Introduction
Depth
• For a non-uniformly doped layer,
ρs =
ρ
xj
=
1
q n x()−NB[ ]
0
xj
∫ µn x()[ ]dx
(3)
• Sheet resistance can be experimentally measured by a four
point probe technique.
• Doping profiles can be measured by SIMS (chemical) or
spreading R (electrical).
• Generally doping levels need to increase and xJ values need to
decrease as the devices are scaled.](https://image.slidesharecdn.com/7-140603091355-phpapp01/85/7-dopant-diffusion-1-2-2013-microtech-8-320.jpg)
7. dopant diffusion 1,2 2013 microtech
- 2. DOPANT DIFFUSION 1. To form source and drain regions in MOS devices and also to dope poly-Si gate material. 2. Used to form base regions, emitters, and resistors in bipolar devices. Process by which controlled amount of chemical impurities are introduced into semiconductor lattice.
- 3. Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani
- 4. Various ways of introducing dopants into silicon by diffusion have been studied with the goals: • Controlling dopant concentration • Total dopant concentration • Uniformity of the dopant • Reproducibility of the dopant profile Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani Important Parameters of Diffusion
- 5. Basic Concepts • Placement of doped regions (main source/drain, S/D extensions, threshold adjust) determine many short-channel characteristics of a MOS device. • Resistance impacts drive current. • As device shrinks by a factor K, junction depths should also scale by K to maintain same e –field patterns (assuming the voltage supply also scales down by the same factor). • Gate doping affects poly-depletion and limits how the gate voltage controls the channel potential. Rcontact Rsource Rext Rchan Rpoly Silicide VG VS VD Sidewall Spacers xJ xW
- 6. Channel Doping Requirement: Projections (NTRS RoadMap) Year of 1st DRAM Shipment 1997 1999 2003 2006 2009 2012 Min Feature Size (nm) 250 180 130 100 70 50 DRAM Bits/Chip 256M 1G 4G 16G 64G 256G Minimum Supply Voltage (volts) 1.8- 2.5 1.5-1.8 1.2- 1.5 0.9-1.2 0.6-0.9 0.5-0.6 Gate Oxide Tox Equivalent (nm) 4-5 3-4 2-3 1.5-2 <1.5 <1.0 Sidewall Spacer Thickness xW (nm) 100-200 72-144 52-104 20-40 7.5-15 5-10 Contact xj (nm) 100-200 70-140 50-100 40-80 15-30 10-20 xj at Channel (nm) 50-100 36-72 26-52 20-40 15-30 10-20 Drain Ext Conc (cm-3 ) 1x1018 1x1019 1x1019 1x1020 1x1020 1x1020
- 7. Introduction R = ρ ρS = ρ/xj xja) b) • The resistivity of a cube is given by J =nqv =nqµε= 1 ρ ε ∴ρ= ε J Ωcm (1) • The sheet resistance of a shallow junction is R = ρ xj Ω/Square ≡ρS (2)
- 8. Introduction Depth • For a non-uniformly doped layer, ρs = ρ xj = 1 q n x()−NB[ ] 0 xj ∫ µn x()[ ]dx (3) • Sheet resistance can be experimentally measured by a four point probe technique. • Doping profiles can be measured by SIMS (chemical) or spreading R (electrical). • Generally doping levels need to increase and xJ values need to decrease as the devices are scaled.
- 9. Two Step Diffusion • Diffusion is the redistribution of atoms from regions of high concentration of mobile species to regions of low concentration. It occurs at all temperatures, but the diffusivity has an exponential dependence on T. • Predeposition : doping often proceeds by an initial predep step to introduce the required dose of dopant into the substrate. • Drive-In : a subsequent drive-in anneal then redistributes the dopant giving the required junction depth
- 10. Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani
- 11. Impurity Sources for Boron Diffusion Impurity Source State at Room Temp Source Temp Range Impurity Conc Range Advantages Boron Nitride Solid Kept along with wafers High and low Very clean process. Requires activation Boric Acid Solid 600-1200o C High and low Readily available and proven source Boron Tribromide Liquid 10-30o C High and Low Clean system. Good control over impurity Methyl Borate Liquid 10-30o C High Simple to prepare and operate Boron Trichloride Gas Room Temperature High and Low Accurate control of gas concentration Diborane Gas Room Temperature High and Low Accurate control of gas concentration, but highly toxic
- 12. Impurity Sources for Phosphorus Diffusion Impurity Source State at Room Temp Source Tem. Range Concentra- tion Range Advantages Red Phosphorus Solid 200-300o C < 1020 cm-3 Low surface concentration Phosphorus Pentoxide Solid 200-300o C > 1020 cm-3 Proven source for high concentration Phosphorus Oxychloride Liquid 2-40o C High and low Clean system Good control over wide range conc. Phosphorus Tribromide Liquid 170o C High and low Clean system Phosphine Gas Room Temperature High and low Accurate control by gas monito- ring, highly toxic
- 13. Oxidation and Diffusion Furnace Stack, Wafer Loading Boron Predeposition Boron Drive-in Phosphorus Predeposition Phosphorus Drive-in SEPARATE FURNACES FOR EACH IMPURITY TYPE Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani
- 14. Diffusion vs Ion Implantation Advantages Problems Ion Implantation and Annealing Solid/Gas Phase Diffusion Room temperature mask No damage created by doping Precise dose control Batch fabrication 1011 - 1016 atoms cm-2 doses Accurate depth control Implant damage enhances diffusion Usually limited to solid solubility Dislocations caused by damage may cause junction leakage Low surface concentration hard to achieve without a long drive-in Implant channeling may affect profile Low dose predeps very difficult
- 15. Dopant Solid Solubility • Maximum conc.of a dopant that can be dissolved in Si under equilibrium conditions without forming a separate phase is termed as solid solubility. . As P Sb Sn Ga Al B SolidSolubility(atomscm-3) 1022 1020 1021 1019 Temperature(ÞC) 800 900 1000 1100 1200 1300
- 16. • Dopants may have an “electrical” solubility that is different than the solid solubility defined in previous slide. • One example - As4V – electrically inactive complex. V Si As As+ Dopant Solid Solubility
- 17. Dopant Diffusion t1 t2 Concentration F=-DdC/dx Distance Concentration • Macroscopic dopant redistribution is described by Fick’s first law, which describes how the flux (or flow) of dopant depends on the concentration gradient. F =−D ∂C ∂x (4)
- 19. Analytical Solution of Fick’s Law ( ) ( ) ( ) ( ) constQdxtxctc dxt0,dc0,xxc ===∞ =≠= ∫ ∞ ,,0, ,0/00, The solution to Fick’s Second Law for these conditions is a Gaussian centered at x =0 Gaussian solution in infinite medium: Consider a fixed dose Q introduced as Delta function at the origin: Drive in (7)
- 21. 2. Gaussian Solution : Constant Source Near A Surface: Analytic Solutions of Fick’s Laws • This is similar to the previous case except the diffusion only goes in one direction. • Dopant dose Q introduced at the surface. • Can be treated as an effective dose of 2Q being introduced in a virtual infinite medium. DeltaFunction DoseQ (Initial Profile) Imaginary DeltaFunction DoseQ Diffused Gaussian Virtual Diffusion x 0 (8)
- 22. Analytic Solutions of Fick’s Laws 3.Error Function Solution : Infinite Source: • The infinite source is made up of small slices each diffusing as a Gaussian. C x,t( )= C 2 πDt ∆xi exp− x −xi( ) 2 4Dti=1 n ∑ (9) • The solution which satisfies Fick’s second law is C(x,t) = C 2 1−erf x 2 Dt =CS erfc x 2 Dt (10) C ² x Dose C² x Initial Profile Diffused Profile xi x 0 Dose CΔx Δx Boundary conditions: C=0 at t=0 for x> 0 C=C at t=0 for x< 0
- 23. Analytic Solutions of Fick’s Laws Important consequences of error function solution: • Symmetry about mid-point allows solution for constant surface concentration to be derived. • Error function solution is made up of a sum of Gaussian delta function solutions. • Dose beyond x = 0 continues to increase with annealing time. . 0 0.2 0.4 0.6 0.8 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 t=9*t 0 t=4*t 0 Initial t=t 0 erf(x/2¦Dt) X(Unitsof2¦Dt 0 )
- 24. Analytic Solutions of Fick’s Laws 4. Error Function Solution: Constant Surface Concentration: • Just the right hand side of the figure on previous slide C x,t( )=CS erfc x 2 Dt (11) • Note that the dose is given by Q = CS 0 ∞ ∫ 1−erf x 2 Dt = 2CS π Dt (12) • Diffusion through Gas ambient
- 25. Intrinsic Dopant Diffusion Coefficients • Intrinsic dopant diffusion coefficients are found to be of the form: D =D0 exp −EA kT (13) Si B In As Sb P Units D0 560 1.0 1.2 9.17 4.58 4.70 cm2 sec-1 EA 4.76 3.5 3.5 3.99 3.88 3.68 eV • Note that ni is very large at process temperatures, so "intrinsic" actually applies under many conditions. • Note the "slow" and "fast" diffusers. Solubility is also an issue in choosing a particular dopant.
- 26. Effect of Successive Diffusions • If a dopant is diffused at temperature T1 for time t1 and then is diffused at temperature T2 for time t2, the total effective Dt is given by the sum of all the individual Dt products. Dteff =Dt =D1∑ t1 +D2t2 +..... (14) • The Gaussian solution only holds if the Dt used to introduce the dopant is small compared with the final Dt for the drive-in; i.e. if an initial delta function approximation is reasonable.
- 27. Design of Diffused Layers • Eqn. (3) has been numerically integrated for specific cases (erfc and Gaussian). • Example of Irvin’s curves, in this case for P type Gaussian profiles. 1 10 100 Effective Conductivity (ohm-cm)-1 SurfaceConcentration(cm-3) CB=1015 CB=1017 CB=1014 CB=1016 CB=1018 1020 1019 1018 1017
- 28. Design of Diffused Layers • We can now consider how to design a boron diffusion process (say for the well or tub of a CMOS process), such that: P P WellN Well ρS =900 Ω/square xj =3 µm NBC =1x1015 cm-3 (substrate concentration)
- 29. Design of Diffused Layers • The average conductivity of the layer is σ _ = 1 ρSxj = 1 (900Ω/sq)(3×10−4 cm) =3.7 Ω⋅cm( ) −1 • From Irvin’s curve we obtain CS ≈4×1017 /cm3 • We can surmise that the profile is Gaussian after drive-in. ∴CBC = Q πDt exp − xj 2 4Dt =CS exp − xj 2 4Dt so that Dt = Xj 2 4ln Cs Cbc = 3x10−4 ( ) 2 4ln 4x1017 1015 =3.7x10−9 cm2
- 30. Design of Diffused Layers • If the drive-in is done at 1100 ˚C, then the boron diffusivity is D =1.5×10−13 cm2 sec−1 • The drive-in time is therefore tdrive−in = 3.7×10−9 cm2 1.5×10−13 cm2 / sec =6.8 hours • Given both the surface concentration and Dt, the initial dose can be calculated for this Gaussian profile. Q =CS πDt =4×1017 ( )π()3.7×10−9 ( )=4.3×1013 cm−2 • This dose could easily be implanted in a narrow layer close to the surface, justifying the implicit assumption in the Gaussian profile that the initial distribution approximates a delta function.
- 31. Design of Diffused Layers • If a gas/solid phase predeposition step at 950˚C were used, then B solid solubility at 950 ˚C is B diffusivity is 2.5×1020 cm−3 4.2×10−15 cm2 sec−1{ • The dose for an erfc profile is Q = 2Cs π Dt • So that the time required for the predeposition is tpre−dep = 4.3×1013 2.5×1020 2 π 2 2 1 4.2×10−15 =5.5sec Check: ( ) ( )914 107.3103.2 − − − ×<<× indrivepredep DtDt
- 32. Four Point Probe: Characterization When t << s, as in the case of diffused or implanted layer, Sheet Resistance Resistivity=
- 34. Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani Junction Depth Measurements by Grooving and Staining
- 35. Spreading Resistance Technique to Get Impurity Profiles within Transistor Regions (Destructive Technique) Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani