Page 49 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

DOPING SEMICONDUCTORS 31

100 r

10

Intrinsic Extrinsic
diffusion diffusion

0.01 0.1 1 10 100
NIN i (T)

Figure 2.17 Relationship between the diffusion coefficient and doping concentration of a charge
carrier in a semiconducting material

independent of dopant concentration when the doping concentration is low. However,
when the doping concentration exceeds some temperature-dependent characteristic value,
called the intrinsic carrier concentration [N i (T)], the diffusion coefficient becomes
dependent on dopant concentration. When D is independent of dopant concentration, the
diffusion process is called intrinsic diffusion, whereas when D is dependent on the doping
concentration, the diffusion process is called extrinsic diffusion (Figure 2.17). In intrinsic
diffusion the dopant diffusion profiles are complementary error functions as given by
Equation (2.22); however, extrinsic diffusion profiles are somewhat complex and deviate
from the basic linear theory. Instead, more complex models or empirical lookup tables
are used to predict the diffusion depth.
The diffusion coefficients of commonly used dopants are considerably smaller in silicon
dioxide than in silicon. Hence, while doping silicon, silicon dioxide can be used as an
effective diffusion barrier or mask. Typical diffusion coefficients in the oxide at ~900 °C
-19 2 -18 2
are 3 x 10 cm /s for boron and 10 cm /s for phosphorus. This is to be contrasted
with diffusion coefficients at ~900 °C for the same dopants in silicon that are on the order
2
of 10 -14 cm /s.

2.5.2 Ion Implantation

Ion implantation is induced by the impact of high-energy ions on a semiconductor
substrate. Typical ion energies used in ion implantations are in the range of 20 to 200 keV