Notes Chapter L8 (page 149-166). L8 101816 ECE 4243/6243 Fall 2016 UConn F. Jain Notes Chapter L8 (page 149-166). Reference: G. Hanson, Nanoelectronics, Prentice Hall 1. Tunneling probability in potential barriers, resonant tunneling barriers 2. Coulomb Blockade and Single Electron Transistors. 3. Material selection for devices

Tunneling through a potential barrier: (page 150) nGaAs/AlGaAs/nGaAs Region 1 V=0 Region 2 = - k22Ψ2(x)----------------(7) Fig. 1. A potential barrier in the conduction band of nGaAs/AlGaAs/nGaAs system.

Tunneling Probability (p. 153)

Channel to Gate tunneling in FETs Channel to floating gate tunneling in Nonvolatile flash Source to Drain tunneling in sub-10nm FETs

Double Barrier Tunneling: Resonant Tunneling :p. 154

Now we have 5 regions (3, 4 and 5 from the finite single potential well). Also we know solutions in region 1 and 5from the single barrier. The solution in the 5 regions leads to the following transmission coefficient

Coulomb Blockade Ref:: Hanson’s TEXT Book, Chapters 6 and 7 Resonant Tunneling, Coulomb Blockade and Single Electron Transistors I. Potential Barrier: First we learn to solve the Schrödinger Equation for a potential barrier. Equation 6.15 shows that there is a finite probability of finding a particle (electrons if the barrier is in the conduction band or holes if the barrier is in the valence band) beyond the barrier. The resonance in T(E) occurs at [a replaces L]. a ( or L barrier width)= n (l2/2) = np/k2 Eq. 6.24 Textbook In the barrier, the two left moving waves (reflected from the two walls/barriers) cancel each other. CASE I: E<Vo and barrier width a is quite large, The tunneling probability T exponentially decreases exp[-2aa]. Here, a = [2me (Vo-E)/(h/2p)2]1/2 Eq. 6.27 For example, for a 0.2eV barrier, at incident energy E=0.01eV, the T values are 8.86x10-3 and 1x10-4, respectively for barrier width a of 1nm and 2nm.

Coulomb Blockade Ref:: Hanson’s TEXT Book, Chapters 6 and 7 Resonant Tunneling, Coulomb Blockade and Single Electron Transistors I. Potential Barrier: First we learn to solve the Schrödinger Equation for a potential barrier. Equation 6.15 shows that there is a finite probability of finding a particle (electrons if the barrier is in the conduction band or holes if the barrier is in the valence band) beyond the barrier. The resonance in T(E) occurs at [a replaces L]. a ( or L barrier width)= n (l2/2) = np/k2 Eq. 6.24 Textbook In the barrier, the two left moving waves (reflected from the two walls/barriers) cancel each other. CASE I: E<Vo and barrier width a is quite large, The tunneling probability T exponentially decreases exp[-2aa]. Here, a = [2me (Vo-E)/(h/2p)2]1/2 Eq. 6.27 For example, for a 0.2eV barrier, at incident energy E=0.01eV, the T values are 8.86x10-3 and 1x10-4, respectively for barrier width a of 1nm and 2nm.

Single electron transistor: Circuit Model

Stored energy in 3 capacitors

Device design parameters

LED Design Design parameters: Operating wavelength, single (green, red, blue) or multi-color white light LEDs Optical power output, expected external and wall conversion efficiency, Cost.: Preferred packaging, (epoxy dome), Operating wavelength: Material selection

Material Selection Point A: Project GaAs-A-InAs curve on the horizontal O-C-2 line. Find the fraction OC/O2 = 0.528 C2/O2 = 0.472. Therefore, at point A the composition is Ga0.472In0.528As.

Material Selection

Material Selection for Engineering Devices

LED Design Index of refraction for ternary semiconductors 4.7. Refractive Index as a funciton of semiconductor composition This section provides information on the index of refraction for semiconductors we use for visible or infrared sources. The compositional dependence of refractive index in the case of AlxGa1-xAs is given by[1] (22) and for InxGa1-xAsyP1-y[2] [1]H.C. Casey Jr. & M.B. Panish, Heterostructure Lasers Part A: Fundamental Principles, Academic Press, 1978, Chapter 2 [2]G.H.Olsen et al, Journal of Electronic Materials, vol 9, pp. 977-987, 1980.