Read the following passage and answer the questions that follow : Diffusion of impurity atoms in silicon is important in silicon integrated circuit processing. The idea of using diffusion techniques to alter the type of conductivity in silicon or germanium was disclosed in a patent by Pfann. Since then various ways of introducing dopants into silicon by diffusion have been studied with the goal of controlling dopant distribution, total dopant concentration, its uniformity reproducibility, and of processing a large number of device wafers in a batch to reduce the manufacturing cost. The diffusion is used to form bases, emitters and resistors in bipolar devices technology, to form source and drain regions and to dope polysilicon in MOS device technology. Dopant atoms that span a wide range of concentrations can be introduced into silicon in many ways.
Fick's second law of diffusion in one dimensional form can be expressed as :
\(\dfrac{\partial C(x,t)}{\partial t}=\dfrac{\partial}{\partial x}\left[D\dfrac{\partial C(x,t)}{\partial x}\right]\)
Fick's second law is a time derivative on the left and a space derivative twice on the right — option 1:
\(\dfrac{\partial C}{\partial t}=\dfrac{\partial}{\partial x}\left[D\dfrac{\partial C}{\partial x}\right]\)
Where it comes from — two statements combined.
Fick's first law says that flux is driven by a concentration gradient, and flows down it:
\(J=-D\dfrac{\partial C}{\partial x}\)
Continuity says that whatever does not flow out must accumulate:
\(\dfrac{\partial C}{\partial t}=-\dfrac{\partial J}{\partial x}\)
Substituting the first into the second gives the second law directly, and the two minus signs cancel. Seeing this derivation makes the structure inevitable: the left side is a rate of accumulation in time, and the right is the divergence of a flux in space. The two sides must therefore carry different variables, which immediately rules out options 2, 3 and 4 — each of which differentiates twice with respect to the same variable somewhere.
Checking option 1 dimensionally. With C in cm–3 and D in cm2/s:
\(\left[\dfrac{\partial C}{\partial t}\right]=\dfrac{\text{cm}^{-3}}{\text{s}},\qquad \left[\dfrac{\partial^{2}C}{\partial x^{2}}\right]=\dfrac{\text{cm}^{-3}}{\text{cm}^{2}}\)
and multiplying the second by D's cm2/s reproduces the first exactly. None of the other three balances.
Why D is left inside the derivative. If diffusivity is constant the equation simplifies to \(\partial C/\partial t=D\,\partial^{2}C/\partial x^{2}\), whose solutions are the Gaussian and error-function profiles of the previous questions. But D is not always constant: at concentrations above the intrinsic carrier density it becomes concentration dependent through the charged point defects that carry the dopant, so \(D=D(C)\) and the general form must be kept. That is why heavily doped profiles are box-shaped rather than Gaussian.
The same equation governs heat conduction, with temperature in place of concentration — which is why solutions worked out for one field transfer directly to the other.
Hence, the correct expression is option 1.
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Match the following :
List - I List - II (a) Lift OFF (i) Etching (b) Rant's Rule (ii) Crystal Growtd (c) Hydrofluoric acid (iii) Packaging (d) Float zone (iv) Metallisation Codes :
What is the name of adhesion promoter used in case of positive photo resist ?
What is the correct sequence of the following step in the fabrication of a monolithic, bipolar junction transistor ?
1. Emitter diffusion
2. Base diffusion
3. Buried layer formation
4. Epi-layer formationSelect the correct sequence using the codes given below :
When silicon dioxide of thickness d is grown, the Silicon consumed is :
Match List - I with List - II.
List - I List - II (A) Annealing (I) Isolation (B) Sealing (II) Doping (C) Ion implantation (III) Packing density (D) Oxidation (IV) Crystal restoration Choose the correct answer from the options given below :
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(B) Arsenic
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The idea of using diffusion techniques was disclosed in patent by Pfann in the year :
A thin layer of dopant is deposited onto silicon surface with a fixed total amount of dopants QT per unit area. If D is the diffusivity of dopants, then the surface concentration is :
For a diffused layer that forms a p-n junction an average sheet resistance RS is defined and related to junction depth xj, the carrier mobility μ, and impurity distribution C(x) as :
Important Questions from Semiconductor Process Flow
Which one of the following processes is preferred to form the gate dielectric (SiO2) of MOSFETs?
Arrange the following in the correct sequence of steps for MOS fabrication
A. Wafer formation
B. Photolithography
C. Oxidation
D. Gate and source/drain formation
E. Metallization
Choose the correct answer from the options given below:Which of the following statements are true for optical photoresists
A. Solubility of a photo-resist changes on exposure to light in developer solution.
B. Solubility of a photo-resist does not change on exposure to light in developer solution.
C. A negative photo-resist on exposure to light becomes less soluble in developer solution.
D. A positive photo-resist on exposure to light becomes more soluble in developer solution.
Choose the correct answer from the options given below:- In particle beam lithography, the resolution depends upon :
A. For impurity diffusion in semiconductor, concentration gradient is the only essential requirement.
B. Annealing is a mandatory step after ion-implantation.
C. Wet etching is normally anisotropic
D. High temperature is required for the growth of $SiO_2$ because oxidation reaction takes place at high temperature
E. Bird's beak formation is a characteristic of LOCOS isolation
Choose the correct answer from the options given below:
