Fundamentals of Nanoelectronics Prof. Supriyo Datta ECE 453 Purdue University 08.23.2004 Lecture 1: Energy Level Diagram Ref. Chapter 1.1 Network for Computational Nanotechnology 00:00 Transistors Field Effect Transistor ID S O U R C E VD VG Gate INSULATOR D R A I N L CHANNEL z INSULATOR x • Denote the channel length as ‘L’ • Since the source and drain regions are very good conductors it is the resistance of the channel region that limits the current and determines how much current will flow through the device when voltage is applied. Please do note that as the devices are getting smaller the parasitic resistances in the contacts become important compared to the channel resistance but that’s something we can ignore to start with. • We are interested in the current that flows from Source to Drain,I D (perpendicular to the cross section of the channel). In the absence of good fabrication, leakage current (in the z direction) can exist in the insulator due to VG. This current increases as the insulator thickness is reduced and is problematic for nano-scale FET’s. • There are two types of current-voltage characteristics: One is I D as a function of drain voltage when a constant gate voltage is applied. The other is I D as a function of gate voltage when a constant drain voltage is applied. We are mostly interested in the first one. 05:06 Transistor: I vs. V curves Drain Current I in Amperes 8 x 10 Drain Current I in Amperes -4 6 7 -4 VG =0.5V 5 VD = 0.5V 6 x 10 4 5 3 4 3 VT 2 2 VG = 0.025V VD = 0.025V 1 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Gate Voltage, Vg in volts Æ 0 0 0.2 0.4 0.6 Drain Voltage, Vd in volts Æ What is the physics behind these curves? 09:00 Transistor Scaling: 19602003 1 μm = 103 nm 100 μm 10 μm Microelectronics 1 μm 100 nm 10 nm Nanoelectronics 1 nm 1960 2003 How far will transistor scaling go? 19:02 Energy Level Diagram How do we understand the I-V characteristics? • Begin by understanding the band diagram which describes the energy levels in the device e.g. in silicon. (See right) • But how do we know that these energy levels form bands and where they are? • Experimentally, filled levels are determined from Photoemission Spectroscopy (PES) S + hν Æ S+ + e- (hv should be big enough to knock out an electron; typically hν > 5eV for semiconductors) • Empty levels determined from Inverse Photoemission Spectroscopy (IPE) S + e-Æ S-+ hν 0eV Vacuum Level -3eV -5eV -9eV 29:00 Fermi Energy 0eV E Filled Conduction Band (CB) EF EF Empty 0 ½ 1 Valence Band (VB) f0(E - EF) Fermi Function: f0(E) = 1/ (e E / kBT + 1) 33:54 Gate Bias Fermi energy (or electrochemical potential) is held fixed by source and drain reservoirs Channel energy levels with Channel energy levels with VG = 0 Empty States VG > 0 Vacuum Level Empty States μ Filled States VG = 0 VG < 0 μ Filled States • Apply a positive gate voltage and • Apply a negative gate voltage and band energy levels move down. band energy levels move up. 39:20 Gate Bias & Conduction ID V- Small Fixed VD V+ VG • V-, the negative bias activation voltage, depends on how far the Fermi energy is from the valence band • V+, the positive bias activation voltage, depends on how far the Fermi energy is from the conduction band 46:50 A Simple Energy Level Scenario 0eV Peaks occur where EF crosses an energy level due to an applied VG bias Small Fixed VD E1 E2 E3 E5 E4 ID E4 EF E5 VG E3 E2 E1 What if we had a carbon nano-tube or a hydrogen molecule? Answer: Different energy levels but same basic story.