A 3-μm n-type epitaxial layer (Nd=10^16 cm^-3) is grown on a p-type Si substrate. Areas of the

step 1 In this problem let us first calculate the value of D. So D is equal to D0 exponential minus Ea

A 3-μm n-type epitaxial layer (Nd=10^16 cm^-3) is grown on...

A $3-\mu \mathrm{m}$ n-type epitaxial layer $\left(N_{d}=10^{16} \mathrm{~cm}^{-3}\right)$ is grown on a p-type Si substrate. Areas of the $\mathrm{n}$ layer are to be junction isolated (see Fig. 9-11a) by a boron diffusion at $1200^{\circ} \mathrm{C}\left(D=2.5 \times 10^{-12} \mathrm{~cm}^{2} / \mathrm{s}\right)$. The surface boron concentration is held constant at $10^{20} \mathrm{~cm}^{-3}$ (see Prob. 5.2). (a) What time is required for this isolation diffusion? (b) How far does an Sb-doped buried layer $\left(D=2 \times 10^{-13} \mathrm{~cm}^{2} / \mathrm{s}\right)$ diffuse into the epitaxial layer during this time, assuming the concentration at the substrate-epitaxial boundary is constant at $10^{20} \mathrm{~cm}^{-3}$ ?

A $3-\mu \mathrm{m}$ n-type epitaxial layer $\left(N_{d}=10^{16} \mathrm{~cm}^{-3}\right)$ is grown on a p-type Si substrate. Areas of the $\mathrm{n}$ layer are to be junction isolated (see Fig. 9-11a) by a boron diffusion at $1200^{\circ} \mathrm{C}\left(D=2.5 \times 10^{-12} \mathrm{~cm}^{2} / \mathrm{s}\right)$. The surface boron concentration is held constant at $10^{20} \mathrm{~cm}^{-3}$ (see Prob. 5.2).
(a) What time is required for this isolation diffusion?
(b) How far does an Sb-doped buried layer $\left(D=2 \times 10^{-13} \mathrm{~cm}^{2} / \mathrm{s}\right)$ diffuse into the epitaxial layer during this time, assuming the concentration at the substrate-epitaxial boundary is constant at $10^{20} \mathrm{~cm}^{-3}$ ?

Key Concepts

Fick's Laws of Diffusion

In semiconductor processes, Fick’s laws govern the movement of dopant atoms under a concentration gradient. They describe how and at what rate atoms diffuse through the semiconductor material, which is critical for predicting dopant profiles and the resulting electrical characteristics after diffusion processes.

Diffusion Coefficient

The diffusion coefficient, often denoted as D, quantifies the rate at which dopants like boron or antimony diffuse within a semiconductor material. It is highly temperature dependent and is central to calculating how far and how fast the dopant atoms can penetrate the substrate or epitaxial layer during thermal processing.

Constant Source Diffusion

In constant source diffusion, the concentration of dopant atoms at the surface is maintained at a fixed level throughout the process. This boundary condition leads to unique dopant profiles, typically described by complementary error functions, and is essential for achieving precise junction depths and isolation in integrated circuits.

Epitaxial Layers

Epitaxial layers are thin, single-crystal layers deposited on a semiconductor substrate. Their controlled doping and thickness allow for the fabrication of high-performance devices by providing tailored electrical characteristics, and they act as the active region in many modern semiconductor structures.

Junction Isolation

Junction isolation is a technique used in semiconductor device fabrication to electrically separate different regions on a chip. This is achieved by creating reverse-biased p-n junctions through selective diffusion of dopants, ensuring that individual devices operate independently without interference from neighboring components.

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