Microelectronics Processing Diffusion Microelectronics processing - E. FinkmanEliezer Finkman

Doping Thermal diffusion Doping is the process that puts specific amounts of dopants in the wafer surface through openings in the surface layers. Thermal diffusion is a chemical process that takes place when the wafer is heated (~1000 C) and exposed to dopant vapor. In this process the dopants move to regions of lower concentration. Doping Control is critical in MOS device scaling. (Scaling down the gate length requires equal scaling in doping profile) Ion source Thermal diffusion Ion implantation Microelectronics processing - E. FinkmanEliezer Finkman

Comparison of thermal diffusion and ion implantation Microelectronics processing - E. FinkmanEliezer Finkman

Mathematics of diffusion: Fick’s First diffusion law D is thermally activated

Mathematics of diffusion: Fick’s Second diffusion law What goes in and does not go out, stays there C/t = (Fin-Fout)/ x

Fick’s diffusion law F F Concentration independent diffusion equation. Often referred to as Fick’s second law.

Analytic solutions of the diffusion equations: Case of a spike delta function in infinite media (x)

The evolution of a Gaussian diffusion profile Peak concentration decreases as 1/√t and is given by C(0,t). Approximate measure of how far the dopant has diffused (the diffusion length) is given by x=2√Dt which is the distance from origin where the concentration has fallen by 1/e

Carl Friedrich Gauss (1777-1855)

Analytic solutions of the diffusion equations: Case of a spike delta function near the surface The symmetry of the problem is similar to previous case, with an effective dose of 2Q introduced into a (virtual) infinite medium. The solution is thus:

Constant total dopant (number) diffusion: Impurity profile Log scale Linear scale Three impurity profiles carried out under constant total dopant diffusion conditions. Note the reduction in the surface concentration C(0,t) with time, and the corresponding rise in the bulk density.

Analytic solutions of the diffusion equations: Case of an infinite source of dopant

The error function A related function is tabulated: The solution of the diffusion equation from an infinite source is finally:

Constant surface concentration: diffusion depth Log scale Linear scale Plots of C(x,t)/Cs vs diffusion depth x(µm) under constant surface concentration conditions for three different values of √Dt . This could mean either a change of temperature (i.e D(T)) or time, t.

Total number of impurities (predeposition dose) As seen in the figure, the error function solution is approximately triangular. The total dose may be estimated by an area of triangular of height Cs and a base of 2√Dt, giving Q= Cs √Dt. More accurately: = Characteristic distance for diffusion. CS = Surface concentration (solid solubility limit).

Two-step junction formation: (a) Predeposition from a constant source (erfc) (b) Limited source diffusion (Gaussian)

Shallow predep approximation Solution of Drive-in profile: In summary: D1= Diffusivity at Predep temperature t1= Predep time D2= Diffusivity at Drive-in temperature t2= Drive-in time

Two-step junction formation

Temperature dependence of D

Diffusion coefficients (constants) for a number of impurities in Silicon Substitutional Interstitial

Typical diffusion coefficient values Element D0 (cm2/sec) EA(eV) B 10.5 3.69 P As 0.32 3.56

The two principal diffusion mechanisms: Schematic diagrams Vacancy diffusion in a semiconductor. Interstitial diffusion in a semiconductor.

Vacancy Intersticial                                                                

Thermal diffusion – general comments Schematic diagram of a furnace for diffusing impurities (e.g. phosphorus) into silicon. Microelectronics processing - E. FinkmanEliezer Finkman

Rapid thermal annealing a) Concept. b) Applied Materials 300 mm RTP system.

Dopant diffusion sources Gas Source: AsH3, PH3, B2H6 Solid Sources: BN, NH4H2PO4, AlAsO4 Spin-on-glass: SiO2+dopant oxide Liquid source: A typical bubbler arrangement for doping a silicon wafer using a liquid source. The gas flow is set using mass flow controller (MFC). Microelectronics processing - E. FinkmanEliezer Finkman

Junction depth Microelectronics processing - E. FinkmanEliezer Finkman

Sheet resistance The resistance of a rectangular block is: R = ρL/A = (ρ/t)(L/W) ≡ Rs(L/W) Rs is called the sheet resistance. Its units are termed Ω/ . L/W is the number of unit squares of material in the resistor.

Sheet resistance

Irving’s curves: Motivation to generate them Microelectronics processing - E. FinkmanEliezer Finkman

Irving’s curves Microelectronics processing - E. FinkmanEliezer Finkman

Figure illustrating the relationship of No, NB, xj, and Rs Microelectronics processing - E. FinkmanEliezer Finkman

Diffusion of Gaussian implantation profile Q Note: Q is the implantation dose. Microelectronics processing - E. FinkmanEliezer Finkman