DFT AND RELATED MODELING OF POST-SILICON VALENCE 4 MATERIALS: SiC AND Ge

Abstract

Though silicon (Si) is in many ways the material of choice for many electronic

applications due in part to its mature processing technology, its intrinsic properties

are not always suited for every challenge. Specialized high power and high temper-

ature devices benefit from using semiconductors with a larger band-gap and higher

thermal conductivity such as silicon carbide (SiC). Additionally, the 1.1eV bandgap

of Si makes it unable to effectively absorb infrared photons so a material with a

smaller bandgap, like germanium (Ge), is more suited to the task.

Currently SiC power transistors are commercially available but suffer from

poor channel mobility due to interface roughness which limits their performance.

To predict the maximum theoretically achievable mobility for different crystallo-

graphic interfaces I developed a novel technique for extracting an atomic-roughness

scattering rate from an arbitrary atomic surface. The term atomic-roughness here

means an interface purely due to the variation of atom species and position without

the presence of a crystallographic miscut due to epitaxial growth considerations.

I used Density Functional Theory (DFT) to obtain a perturbation potential from

which I can calculate a scattering rate. This scattering rate can then be used in a

Monte Carlo simulation to predict mobility for a given field configuration.

In addition to SiC’s low channel mobility, SiC p-type dopant species also ex-

hibit an abnormally large ionization energy compared to its n-type dopants and

to the primary dopants in many other semiconductors. This fact can cause is-

sues such as unexpectedly high resistance regions at lower operating temperatures

- causing the need to dope at significantly higher concentration. To characterize

the incomplete ionization fraction p/N A , I first gathered nearly all existing pub-

lished data on the ionization energy of aluminum (Al) in 4H-SiC and created an

empirical concentration-dependent model of this function. Then I put together a

physics-based model of the entire acceptor and valence band system and used my

concentration-dependent ionization energy as an input to predict p/N A . I verify my

physics-based model result against a separate experimental dataset derived from

nearly-exhaustive literature measurements of Hall mobility and resistivity. Finally,

I transform fully temperature-dependent result of p/N A from a complex numerical

computation to a more easily implementable parameterized function with the use

of a genetic algorithm.

The remaining part of my work was performed on Germanium which has

interesting application in short-wave infrared imaging due its 0.66eV indirect and

0.85 eV direct bandgaps, which corresponds closely to the peak illumination of

the “night glow” at 0.75 eV. Optical devices greatly benefit from direct gap band

structures to increase photon absorption and emission efficiency. Though Ge is an indirect gap material, it can be alloyed with a direct gap material, namely tin (Sn),

to transition it to a direct gap material at a certain molar fraction. Through DFT

calculations I investigate the nature of this transition and determine theoretically

the minimum molar fraction needed to achieve a direct bandgap.