Diffusion a very important process in IC
- 1. Course :IC Fabrication & VLSI Course Code : ECL 3130 B.Tech 6th Sem ECE Session : Jan-May 2023 Course Co-ordinator : Dr.Anil Kumar Bhardwaj Assistant Professor School of ECE Shri Mata Vaishno Devi University Diffusion
- 2. Diffusion
- 3. Overview • Introduction • Basic Diffusion Process • Diffusion Equation Source: Fundamentals of Semiconductor Fabrication SM SZE
- 4. • Diffusion and ion implantation are the two key processes to introduce a controlled amount of dopants into semiconductors and to alter the conductivity type. • Figure compares these two techniques and the resulting dopant profiles. In the diffusion process, the dopant atoms are introduced from the gas phase of by using doped-oxide sources. • The doping concentration decreases monotonically from the surface, and the in-depth distribution of the dopant is determined mainly by the temperature and diffusion time. • Generally speaking, diffusion and ion implantation complement each other. For instance, diffusion is used to form a deep junction, such as an n-tub in a CMOS device, while ion implantation is utilized to form a shallow junction, like a source / drain junction of a MOSFET. Introduction to Diffusion
- 6. Comparison of (a) diffusion and (b) ion implantation for the selective introduction of dopants into a semiconductor substrate.
- 7. Diffusion An example of the chemical reaction for phosphorous diffusion using a liquid source is 4POCl3 + 3O2 2P2O5 + 6Cl2 The P2O5 forms a glass on silicon wafer and is then reduced to phosphorous by silicon. 2P2O5 + 5 Si 4P + 5SiO2 The phosphorous is released and diffuses into the silicon and Chlorine is vented.
- 8. • Boron is the most common p-type impurity in silicon, whereas arsenic and phosphorus are used extensively as n- type dopants. • These three elements are highly soluble in silicon with solubilities exceeding 5 x 1020 atoms / cm3 in the diffusion temperature range (between 800o C and 1200o C). • These dopants can be introduced via several means, including solid sources (BN for B, As2O3 for As, and P2O5 for P), liquid sources (BBr3, AsCl3, and POCl3), and gaseous sources (B2H6, AsH3, and PH3). • Usually, the gaseous source is transported to the semiconductor surface by an inert gas (e.g. N2) and is then reduced at the surface. Diffusion
- 9. Schematic diagram of a typical open-tube diffusion system
- 10. • For diffusion in gallium arsenide, the high vapour pressure of arsenic requires special methods to prevent the loss of arsenic by decomposition or evaporation. • These methods include diffusion in sealed ampules with an overpressure of arsenic and diffusion in an open tube furnace with a doped oxide capping layer (e.g Silicon nitride) • Most of the studies of p-type diffusion have been confined to use of zinc in the forms of Zn-Ga-As alloys and ZnAs2 for the sealed ampule approach or ZnO-SiO2 for the open-tube approach. • The n-type dopants in gallium arsenide include selenium and tellurium.
- 11. Diffusion Equation • Diffusion in a semiconductor can be visualized as the atomic movement of the dopant in the crystal lattice by vacancies or interstitials. • There is a finite probability that a host atom can acquire sufficient energy to leave the lattice site and to become an interstitial atom thereby creating a vacancy. • When a neighboring impurity migrates to the vacancy site, the mechanism is called vacancy diffusion. • If an interstitial atom moves from one place to another without occupying a lattice site the mechanism is interstitial diffusion.
- 12. (a): Diagram to show vacancy diffusion in a semiconductor. (b): Diagram to show interstitial diffusion in a semiconductor. Source : http://web.eng.gla.ac.uk/groups/sim_centre/courses/diffusion/diff_3.html
- 13. Models of atomic diffusion mechanisms for a two-dimensional lattice, with a being the lattice constant: (a) Vacancy mechanism. (b) Interstitial mechanism.
- 14. Diffusion Equation • The basic diffusion process of impurity atoms is similar to that of charge carriers. Let F be the flux of dopant atoms traversing through a unit area in a unit time, and • where D is the diffusion coefficient, C is the dopant concentration, and x is the distance in one dimension. • The equation imparts that the main driving force of the diffusion process is the concentration gradient, ∂C/ ∂x. • In fact, the flux is proportional to the concentration gradient, and the dopant atoms will diffuse from a high-concentration region toward a low-concentration region.
- 15. Diffusion Equation • The basic diffusion process of impurity atoms is similar to that of charge carriers. Let F be the flux of dopant atoms traversing through a unit area in a unit time, and • where D is the diffusion coefficient, C is the dopant concentration, and x is the distance in one dimension. • The equation imparts that the main driving force of the diffusion process is the concentration gradient, ∂C/ ∂x. • In fact, the flux is proportional to the concentration gradient, and the dopant atoms will diffuse from a high-concentration region toward a low-concentration region.
- 16. Diffusion Equation • The negative sign on the right-hand-side of states that matters flow in the direction of decreasing dopant concentration, that is, the concentration gradient is negative. • According to the law of conservation of matter, the change of the dopant concentration with time must be equivalent to the local decrease of the diffusion flux, in the absence of a source or a sink.
- 17. Diffusion Equation • When the concentration of the dopant is low, the diffusion constant at a given temperature can be considered as a constant and can be written as: • This equation is referred to as Fick's Second Law of Diffusion.
- 18. Diffusion Equation • Figure on next slide shows the measured diffusion coefficients for low concentrations of various dopant impurities in silicon and gallium arsenide. • The logarithm of the diffusion coefficients plotted against the reciprocal of the absolute temperature yield a straight line in most of the cases, implying that over the temperature range, the diffusion coefficients can be expressed as:. where Do denotes the diffusion coefficient extrapolated to infinite temperature and Ea stands for the Arrhenius activation energy.
- 19. Diffusion coefficient (also called diffusivity) as a function of the reciprocal of temperature for (a) silicon and (b) gallium arsenide. Fast moving species Slow moving species
- 20. For interstitial diffusion, Ea is related to the energy required to move a dopant atom from one interstitial site to another. The values of Ea are between 0.5 to 1.5 eV in both Si and GaAs. For vacancy diffusion, Ea is related to both the energies of motion and formation of vacancies. Hence, Ea for vacancy diffusion is larger than that for interstitial diffusion and is usually between 3 to 5 eV.
- 21. Diffusion Profiles • The diffusion profile of dopant atoms is dependent on the initial and boundary conditions. • Solution of equation have been obtained for various simple conditions, including constant-surface-concentration diffusion and constant-total- dopant diffusion. • In the first scenario, impurity atoms are transported from a vapour source onto the semiconductor surface and diffuse into the semiconductor wafer. • The vapour source maintains a constant level of surface concentration during the entire diffusion period. • In the second situation, a fixed amount of dopant is deposited onto the semiconductor surface and is subsequently diffused into the wafer.
- 22. Constant Surface Diffusion • The initial condition at t=0 is C (x,0) = 0 Which states that the dopant concentration in the host semiconductor is initially zero. • The boundary condition are C(0, t) = Cs and C(∞, t) = 0 • where Cs is the surface concentration (at x = 0) which is independent of time. • The second boundary condition states that at large distances from the surface, there are no impurity atoms. • The solution of the Fick’s diffusion equation that satisfies the initial and boundary conditions is given by:
- 26. Diffusion profiles. (a) Normalized complementary error function (erfc) versus distance for successive diffusion times. (b) Normalized Gaussian function versus distance for successive times. Constant Surface Diffusion
- 27. Constant Total Dopant • A fixed (or constant) amount of dopant is deposited onto the semiconductor surface in a thin layer, and the dopant is subsequently diffused into the semiconductor. • The initial condition at t = 0 is again C(x, 0) = 0. The boundary conditions are: where S is the total amount of dopant per unit area. The solution of the diffusion equation satisfying the above conditions is: This expression is the Gaussian distribution, and the dopant profile is displayed in Figure
- 28. Normalized concentration versus normalized distance for the erfc and Gaussian functions.
- 29. Constant Total Dopant (contd..)
- 30. Influencing factors for diffusion • Diffusing species: Interstitial atoms diffuse easily than substitutional atoms. • Again substitutional atoms with small difference in atomic radius with parent atoms diffuse with ease than atoms with larger diameter. • Temperature: It is the most influencing factor. Their relations can be given by the following Arrhenius equation • where D0 is a pre-exponential constant, Q is the activation energy for diffusion, R is gas constant (Boltzmann’s constant) and T is absolute temperature.
- 31. Influencing factors for diffusion • From the temperature dependence of diffusivity, it is experimentally possible to find the values of Q and D0. • Lattice structure: Diffusivity is high for open lattice structure and in open lattice directions. • Presence of defects: The other important influencing factor of diffusivity is presence of defects. Many atomic/volume diffusion processes are influenced by point defects like vacancies, interstitials. • Apart from these, dislocations and grain boundaries, i.e. short-circuit paths as they famously known, greatly enhances the diffusivity.
- 33. Evaluation of Diffused Layers
- 34. Junction depth measurement by grooving and staining.
- 35. Evaluation of Diffused Layers (contd..) • In case if R0 is much larger than a and b, then • The junction depth is the position where the dopant concentration equals the substrate concentration CB or C (xj) = CB • Thus, if the junction depth and CB are known, the Cs and the impurity distribution can be calculated, provided the diffusion profile.
- 36. Thank You