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.
The diffusivity determined experimentally over a range of diffusion temperatures can be expressed as :
\(D=D_{0}\exp\left(-\dfrac{E}{RT}\right)\)
Diffusivity follows the Arrhenius law — option 3:
\(D=D_{0}\exp\left(-\dfrac{E}{RT}\right)\)
Why the exponent must be negative. A dopant atom moves only by surmounting an energy barrier — it must break free of its lattice site or wait for a vacancy. The fraction of atoms with enough thermal energy to do so is the Boltzmann factor \(e^{-E/RT}\), which rises as T rises because the exponent becomes less negative. Option 1's positive exponent would make D fall with temperature, and its argument \(RT/q\) is a voltage rather than a dimensionless ratio in any case.
Why the exponent must be dimensionless. Both E and RT are energies per mole, so their ratio is a pure number, as an exponent must be. Option 2 divides \(D_{0}\), a diffusivity, by an energy, and option 4 divides an energy by a temperature — neither is dimensionless, so both fail before any physics is considered.
How the constants are measured. Taking logarithms turns the law into a straight line:
\(\ln D=\ln D_{0}-\dfrac{E}{R}\left(\dfrac{1}{T}\right)\)
Plotting \(\ln D\) against \(1/T\) gives a slope of \(-E/R\) and an intercept of \(\ln D_{0}\). This Arrhenius plot is exactly how the tabulated values for each dopant are obtained — which is what the question means by "determined experimentally over a range of diffusion temperatures".
| Symbol | Meaning |
|---|---|
| D0 | Pre-exponential factor — the extrapolated diffusivity at infinite temperature |
| E | Activation energy, typically 3 – 4 eV in silicon |
| R | Gas constant (or k, with E in eV per atom) |
How steep the dependence is. With \(E\approx3.5\) eV, a rise from 1000 °C to 1100 °C — less than 8 % in absolute temperature — multiplies D by roughly a factor of ten. This is why diffusion furnaces are controlled to within a degree, and why the junction depth \(x_{j}\propto\sqrt{Dt}\) is set far more sensitively by temperature than by time.
Hence, the correct expression is D = D0 exp(−E/RT).
Similar Questions
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 :
Arrange the following in ascending order based on their diffusivity :
(A) Boron
(B) Arsenic
(C) Antimony
(D) PhosphorusChoose the most appropriate answer from the options given below :
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 :
The idea of using diffusion techniques was disclosed in patent by Pfann in the year :
Fick's second law of diffusion in one dimensional form can be expressed as :
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 :
Match the following :
List - I List - II (a) Lift - off (i) Fick's Equation (b) Dry Etching (ii) PMMA (Poly Methyl Methacrylate) (c) Lithography (iii) Bombardment of Plasma (d) Diffusion (iv) Structures of Target Material on the Surface of Substrate Codes :
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 ?
Important Questions from Semiconductor Process Flow
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:
Arrange the given process steps in sequence for self-aligned gate formation.
A. Thermal oxidation to grow gate oxide.
B. Polysilicon deposition
C. Photolithography using gate mask
D. Etching of polysilicon and oxide
E. Source/drain diffusion
Choose the correct answer from the options given below:
- Match the LIST-I with LIST-IIChoose the correct answer from the options given below:
LIST-I LIST-II A. Shallow trench isolation (STI) I. Low static power dissipation B. Junction isolation II. High static power dissipation C. CMOS technology III. High component density D. Bipolar IC technology IV. Low component density Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Impurity diffusion in semiconductor essentially needs very high temperature.
Reason R: Diffusivity of impurity atoms is negligibly small at room temperature.
In the light of the above statements, choose the most appropriate answer from the options given below
- In particle beam lithography, the resolution depends upon :
