Nanoelectronics Topics Moore s Law Inorganic nanoelectronic devices Resonant tunneling Quantum dots Single electron transistors Motivation for molecular electronics The review article Overview of Nanoelectronic Devices by David Goldhaber- Gordon et al. is available on the course website.
1,000,000 100,000 10,000 1,000 100 10 K 8086 80286 Moore s Law 1 Billion Transistors Pentium III Processor Pentium II Processor Pentium Pro Processor Pentium Processor i486 Processor i386 Processor 1 75 80 85 90 95 00 05 10 15 The Number of of Transistors Per Chip Will Double Every 18 18 Months Source: Intel
Benefits of scaling Reducing the size of the transistors makes them faster and keeps the power consumption reasonable. Putting more transistors in a circuit enables more computation. Integrating several chips into one improves reliability. Cost per transistor goes down.
How long will Moore s Law continue? Billions of dollars will be spent to make sure that improvement of silicon chips stay on the curve predicted by Moore, but there are some serious obstacles that must be overcome.
Expected obstacles With very small channels, carriers could tunnel all the way across, even when there isn t supposed to be any current. Paul Packan, Science 285 (1999) p. 2079.
Interconnects 0.13µm Cu Interconnects The speed of circuits is starting to be limited by the RC time constant of the interconnects rather than the switching speed of the transistors. R is being reduced by using Cu instead of Al. C is being reduced by using a low-k dielectric, such as nanoporous silica, to insulate the wires from each other. From Craig Barrett (Intel)
Other obstacles The resolution of lithography must go below 100 nm. Heat must be dissipated. Fabrication plants are costing billions of dollars. As daunting as the problems are, my bet is that the silicon industry will find ways to solve them for at least 7 more years and maybe much longer. The focus of this course is not how to push silicon (or germanium) technology forward, but how to make new devices with non-traditional fabrication techniques. We will look at candidates for post 2010 circuits.
Nanoelectronics Smaller devices will be made for all the reasons just given. When the devices become smaller than 100 nm in size, quantum mechanical effects such as energy quantization and tunneling will become important. These effects could be a problem, but they could be turned into an advantage.
Confinement quantizes the energy levels If V O = infinite, then E k = 2π = = λ nπ L 2 2 2 2 h k h π n = 2 2m 2mL 2 For small L, the spacing between energy levels is larger. Coldren, Corzine, Diode Lasers, 1995.
Quantum wells (Electrons confined in one-dimension) Energy AlGaAs GaAs AlGaAs Distance Electrons are confined in one dimension and free in the other. A common method for making quantum wells is to use epitaxial methods to deposit alloys with varying composition onto a substrate.
Quantum dots (artificial atoms) Electrons are confined in all three dimensions. The energy levels are discreet, so these quantum dots are much like atoms. Review Article A.P. Alivisatos, Semiconductor Clusters, Nanocrystals, and Quantum Dots, Science 271 (1996) p. 933.
M.G. Bawendi et al. JACS 115 (1993) 8706. Nanocrystals The absorption and emission spectra depend on the nanocrystal size.
David Goldhaber-Gordon Artificial atom made with a gated 2DEG A sheet of electrons is confined to the interface between the GaAs and the AlGaAs because there is a potential well there. When a negative voltage is applied to the gate electrodes (shown on top), electrons are repelled underneath. This can be used to create a puddle of electrons shown in the center. The size of the puddle can be varied by adjusting the gate bias.
Resonant tunneling diode (RTD) Goldhaber-Gordon et al. Proc. of IEEE, 85 (1997) p. 521.
Comments on the previous slide Electrons can tunnel across the barrier if it is less than approximately 10 nm thick and there is a state with the same energy level for it to tunnel into. In this schematic, the source and drain are doped semiconductors. Their energy levels are closely spaced because they are relatively large. The spacing between the energy levels in the island is large because the island is small. ε = difference in the energy levels that is found by solving Schrodinger s equation for the potential well. U = charging energy that arises from repulsion between an extra electron in the island and those that are already there.
Goldhaber-Gordon et al. Proc. of IEEE, 85 (1997) p. 521. Operation of an RTD Negative differential resistance: di/dv < 0
Goldhaber-Gordon et al. Proc. of IEEE, 85 (1997) p. 521. Resonant tunneling transistor In (b), the energy level of the quantum well is not in resonance with the source, so very little current flows through the device. In (c), a bias has been applied to the gate electrode to lower the energy levels in the quantum well. The first empty level is in resonance with the source, so electrons can tunnel into. From there, they can tunnel into empty levels in the drain.
Comparison of quantum devices Resonant tunneling devices ε >> U Confinement in only 1 or 2 dimensions causes ε to be large. The lack of confinement in the other 1 or 2 dimensions lets the charges spread out, which keeps U small. Quantum dots Electrons are confined in all three dimensions. ε and U are both significant. Single-electron transistors True SETs are usually made of metals and tend to be larger than quantum dots. The wavelength of the electrons is small, so ε is small.
Single electron transistor at constant V G. Source-drain current V DS The Coulomb energy needed to put an extra electron in a quantum dot is U. The I vs V DS curve is a Coulomb staircase. The current jumps up when there is enough extra energy to have one more electron in the dot at at time. U
Source-drain conductance Single-electron transistor (SET) V G Conductance = di/dv DS The Coulomb blockade prevents the flow of charge. Electrons hop across one at a time Electrons can hop across two at a time.
Conductance versus gate voltage in an SET T = 60 mk. Conductance = di/dv DS with V DS near zero. Marc Kastner, Artificial Atoms Physics Today, Jan. 1993 p. 24.
SET made from a CdSe nanocrystal The gap is approximately 10-nm wide. There can be several nanocrystals in the gap, but the one that comes closest to the electrodes carries almost all of the current. The heavily doped silicon wafer is used as a gate electrode. The 5.5-nm-diameter nanocrystals are connected to the Au electrodes with 1,6- hexanedithiol, which forms a 1.2-nm-thick barrier. Alivisatos, McEuen et al., Nature 389 (1997) p. 699.
Alivisatos, McEuen et al., Nature 389 (1997) p. 699. IV characteristics of a CdSe-nanocrystal SET T = 4.2 K
Alivisatos, McEuen et al., Nature 389 (1997) p. 699. Coulomb diamonds When the conductance is plotted in gray scale as a function of gate voltage and source-drain voltage, there are white diamond shaped regions where the conductance is zero. The plots show how the Coulomb gap varies with gate voltage.
Using quantum devices in circuits MOSFETs are only two-state devices (They are either on or off) Quantum devices are multi-state devices. Since they have more functionality than MOSFETs, it is possible that computation could be performed with a smaller number of transistors.
Drawbacks and obstacles to nanoelectronic devices In the RTDs the current does not drop to zero in between peaks. The current is very sensitive to the source-drain voltage and the gate voltage. It could be hard to make stable circuits. The devices only show their quantum effects at low temperature because kt must be less than U or ε. The tunneling current is very sensitive to the width of the barrier. The current depends sensitively on the energy levels, which vary substantially with small changes in the size of the potential well.
Motivation for using organic devices Every molecule has exactly the same dimensions. Very small devices can be made, so U and ε can be larger than kt at room temperature. Moles of molecules can be made at low cost. Maybe circuits can be made inexpensively using self-assembly techniques.
Arieh Aviram, Mark Ratner, Chem. Phys. Lett. 29 (1974) p. 277. The beginning of molecular electronics Insulating bridge electron acceptor (p-type) electron donor (n-type) In 1974 Aviram and Ratner predicted that molecules with a donor and acceptor would behave like a pn junction.
A donor-acceptor junction
Forward bias Electrons can easily tunnel Holes can easily tunnel across this barrier. across this barrier. Electrons can tunnel from B to C if there are holes in C. Current flows.
Reverse bias Electrons can t tunnel into D. Very little current flows.
Goldhaber-Gordon et al. Proc. of IEEE, 85 (1997) p. 521. Proposed resonant tunneling in a conjugated molecule A potential problem is that it could be hard to line up energy levels in the source, island and drain since the source and drain have a limited number of energy levels.
How can we make these molecular electronic devices?