Lecture 16: Semiconductors and Doping

Lecture 16: Semiconductors and Doping Summary Semiconductors have this name because their conductivity of electrons lie somewhere between those of insulators and metals. The band gap of a semiconductor, meaning the space between its conduction band and valence band, is larger than that of a metal but smaller than that of an insulator. Initially, the electrons are bound to the lattice (the arrangement of atoms in the solid) and cannot conduct. Their energy states are within the valence band. In order for electrons to conduct, they must obtain enough energy to leave the valence band and enter the conduction band, which involves passing the band gap (forbidden energy states). Two ways in which these initially bound electrons can achieve conduction are via a thermal energy transfer and through doping, which involves introducing impurities (a relatively small number of foreign atoms compared to the number of atoms in the lattice) to increase the density of charge carriers (electrons or holes, the absence of an electron which essentially acts as a positive charge). (Note: there’s a third way we discussed in the last lecture, by kicking electrons above the gap using photons). There are two types of doping, p-type and n-type. P-type doping involves adding impurities with fewer electrons than the atoms in the undoped lattice (i.e. aluminum doped into silicon). P-type doping creates holes. The presence of these holes enables conduction in the lattice and the creation of an acceptor energy level. 38 N-type doping involves adding impurities with more electrons than the atoms in the undoped lattice (i.e. phosphorus doped into silicon). N-type doping introduces additional electrons (negative charge carriers). These electrons have an energy corresponding to the donor level, and are able to conduct with a much smaller addition in energy compared to the electrons in the valence band. Why this matters The entire semiconductor industry is built on ways to dope Si, Ge, GaAs, and other semiconductors with precise amounts of desired impurities, to make n-type and p-type semiconductors which then get put in the billions into a single chip in extremely complicated arrangements. This is how the very first transistor was made, by putting an n-type and p-type semiconductor in contact with one another. You can learn all about the very first transistor in so many great resources (like this short video explanation for example, https://www.youtube.com/watch?v=JBtEckh3L9Q). Here’s a picture of that very first transistor, which doesn’t look like what you’d see on a computer chip today–but it’s the first p-n junction and it opened the door to a revolution. Just to get a little perspective: In 2014 250 billion billion transistors were made, which amounts to a pace of 8 trillion transistors per second. Here’s a chart of what we call Moore’s law, which isn’t a law at all but rather simply what happens when a lot of incredibly smart scientists and engineers work on something for 60 years. Transistors made per year vs. price removed due to copyright restrictions. Speaking of smart, how do we, as humans, do our natural computing? How do the computers we make stack up to the brains we use to make them? You see, Moore’s law looks, and is, impressive, but it’s a measure of computing power, not power consumption. Data centers alone currently account for 3% of global CO2 emissions and estimates are that within 10 years over 20% of all electricity will be consumed by IT. Most of this energy goes into sending current through trillions and trillions of p-type and n-type semiconductors. Just for fun, let’s compare the power consumed by a computer that has the equivalent number of processors as the human brain. A typical adult human brain has about 1011 neurons, or nerve cells, each one connected to about 10,000 other neurons via connectors called synapses, which are the superhighways of information processing in the brain. A brain has a total of around 1014 synapses. With 1 transistor being equivalent to about 10 synapses, we can build a computer as powerful as the brain, or at least with as much computing capacity, with 106 computer chips (each chip packing 10 billion transistors). This would require around 10MW to power. That’s 10,000,000 Watts of power needed to run the artificial brain. In comparison, the human brain runs on about 20 Watts! 39 Photo of model of the first transistor © source unknown. All rights reserved. This content is excluded from our Creative Commons license. For information, see https://ocw.mit.edu/fairuse. The reason I’m making this comparison in our Why This Matters is that the p-n junction and the transistor brought forth an amazing revolution spanning many orders of magnitude. But we’re still short another 6 zeros on power consumption reduction, if we ever want to try to match the brain, for which another revolution is clearly needed. Why this employs Since I brought up the human brain and compared it to computer chips, let’s focus this section on the brain-machine interface. This has been, of course, the subject of many science fiction movies (yes, The Matrix), but it’s also been the focus of many research labs and government programs for at least the past 30 years. This is because of the massive potential in enabling the human-brain interface to help patients with a wide range of neurodegenerative disease. And all of this work has brought us to quite an exciting time in efforts to merge the brain with machines, one in which many new commercial entities are forming. Elon Musk, for example, launched Neuralink a few years ago. This is a pretty exciting company not only because of its initial concept, but also because they have brought in highly talented and interdisciplinary teams of scientists, doctors, and engineers. Many of the people involved in such an effort will need to know about semiconductors and doping, and in this case the serious challenge of creating electronics that are “brain friendly” (take a look at the work of Professor John Rogers, as an example). A number of companies have invested in this area, like Boston Scientific, Abbot, Blackrock Microsystems, CorTec, or NeuroNexus, to name only a few. And government programs are also growing efforts, for example through DARPA or the NIH BRAIN Initiative. Example problems 1. Doping levels in semiconductors typically range from 1013 /cm3 to 1018 /cm3 , depending on the application. In some devices (like transistors) you need several n- and p-type materials with different doping concentrations. Si has a density of 2.328 g/cm3 . What is the ratio of Si atoms to dopant atoms in 1013 /cm3 doping and 1018 /cm3 doping? a) 1013 /cm3 b) 1018 /cm3 40 2. You dope Ge with 2.43mg Mg. a. What kind of doping is this? What charge carriers are introduced? b. How many carriers does each substitution yield? c. Calculate the number of charge carriers created by the addition of 2.43 mg Mg. d. How much Ge should you start with if you want a charge carrier density of 1016/cm3 ? 3. For 13 cm3 of Si, calculate the number of milligrams of B atoms needed in order to have 3.091*10 17 carriers/cm3. Assume that the dopant only substitutionally incorporates into the Si. 41 Solutions 1. To find the ratio between Si atoms and dopant atoms, we need to find the number of Si atoms per cubic cm. This is a straightforward stoichiometry problem: 2.328gSi 1molSi 6.022 × 1023 atomsSi 5 × 1022 atomsSi × × = 3 1cm Si 28gSi 1molSi cm3 Now we take the ratio of Si atoms to dopant atoms, obtaining: a) 5 × 1022 :1013 = 5, 000, 000, 000 : 1 b) 5 × 1022 :1018 = 50, 000 : 1 2. a) p-type doping; holes are introduced b) each substitution yields 2 carriers c) 2.43mg × 10−3 g 1mol × = 10−4 mol mg 24.3g 2 carriers per substitution: 2 × 10−4 mol holes 2 × 10−4 × 6.602 × 1023 = 1.32 × 1020 holes d) 1016 carriers/cm3 = 1.32 × 1020 x x = 1.32 × 104 cm3 Ge 3. p-type: carriers are holes 13cm3 × 3.091 × 1017carriers 1atom 1mol 10.81g 1000mg × × × × = 0.0721mg 3 23 1carrier 6.022 × 10 atoms 1mol 1g 1cm 42