Topic
2: How do point defects change electronic properties?
Overview
Point defects, specifically solutes, are intentionally introduced
into semiconductors for the changes they induce in electronic
properties. This can be to “donate” conduction electrons (“n”-type
doping) or the “accept” valence electrons that introduces holes
(“p”-type doping). This is described via defect reactions, where a
dopant changes its charge state by interacting with electrons or holes,
causing “ionization,” and resulting in different concentrations of the
charge states of the dopant in a semiconductor, depending on the
ionization energy, Fermi energy and temperature. Some donors / acceptors
are shallow, where they are nearly fully ionized and contribute
electrons / holes that increase mobility; while other donors / acceptors
are deep centers that act as traps or recombination sites that limit
electron / hole lifetimes or reduce carrier concentrations. In addition,
dopants can have multiple states in the bandgap, allowing it to donate
or accept multiple electrons!
Dopants are useful not just for the changes in electronic properties
they induce in a semiconductor, but also the ease with which they can be
introduced in a controllable manner.
Reading
For this topic, you will want to read some of review articles about
dopants in semiconductors.
- “The electronic structure of impurities and other point defects in
semiconductors.” Sokrates T. Pantelides, Rev. Mod. Phys.
50, 797-858 (1978): doi:10.1103/RevModPhys.50.797,
Sections I-VI
- “Point defects and dopant diffusion in silicon.” P. M. Fahey, P. B.
Griffin, and J. D. Plummer. Rev. Mod. Phys.
61, 289-384 (1989): doi:10.1103/RevModPhys.61.289,
Sections I-VI
Team assignment
The European Union, fresh off eliminating
lead from solder, has now decided that phosphorus can no longer be
used in electronic devices. Putting aside questions
about the wisdom of a widespread ban on phosphorus, your team is
immediately concerned about the best possible replacement to manufacture
n-doped Si, if P would no longer be available.
- What dopant(s) would you suggest for production of n-doped Si in
devices?
- What would you consider to be the biggest challenge in processing
with your suggested replacement?
Prelecture questions
- In a crystal the concentration of electrically neutral vacancies is
described by a law of mass action \([\text{V}^\times] = A\;\exp(-\Delta
G_\text{v}/k_\text{B} T)\). These vacancies can act as acceptors,
and the concentration of ionized vacancies is given by \[[\text{V}'] =
\frac{[\text{V}_\text{t}]}{1+g^{-1}\exp(
[E_\text{A}-E_\text{F}]/k_\text{B} T )}\] where \(E_\text{A}\) is the acceptor energy level,
\(E_\text{F}\) is the Fermi energy, the
total concentration \([\text{V}_\text{t}] =
[\text{V}^\times] + [\text{V}']\), and the degeneracy \(g=2\). When the Fermi energy \(E_\text{F}\) is moved by the addition of
substitutional dopants, how does the total vacancy concentration change?
Assume no interaction between dopants and vacancies, so \(E_\text{F}\) is shifted independently of
everything else.
- Estimate the ionization energy and the “size” of the electron
wavefunction for a shallow donor using a hydrogen-like model in a
semiconductor with an effective mass \(m^* =
0.3 m_\text{e}\) and a dielectric constant of \(\epsilon = 10\epsilon_0\) compared with the
vacuum dielectric constant \(\epsilon_0\).
Suggested background
These may help you think about the papers and questions raised; you
may want to look beyond these, too.
- Ibach, H. and Lueth, H. Solid-State Physics. (Springer
Berlin Heidelberg: Berlin, Heidelberg, 2010). doi:10.1007/978-3-540-93804-0.
Chapter 12 covers semiconductors, doping, and much more.
- Chapter 4, “Deep Centers in Semiconductors” by H. Feichtinger, from
Handbook of
Semiconductor Technology (2000). (you may also find some of the
other chapters helpful)
- “Charged point defects in semiconductors.” Edmund G. Seebauer and
Meredith C. Kratzer. Mater. Sci. Eng. R 55,
57-149 (2006): doi:10.1016/j.mser.2006.01.002
- Course
webnotes:
- Slides (on Google Drive):
- Semiconductors
- Electronic Structure of Defects
Discussion: Sept. 17-19, 2024