ECE 305: Fall 2016 MOSFET Energy Bands Professor Peter Bermel Electrical and Computer Engineering Purdue University, West Lafayette, IN USA pbermel@purdue.edu Pierret, Semiconductor Device Fundamentals (SDF) Chapter 17 (pp. 611-616) 11/7/2016 1
Example: 32 nm N-MOS technology 11/7/2016 2
summary Given the measured characteristics of a MOSFET, you should be able to determine: 1. on-current: I ON 2. off-current: I OFF 3. subthreshold swing, S 4. drain induced barrier lowering: DIBL 5. threshold voltage: V T (lin) and V T (sat) 6. on resistance: R ON 7. drain saturation voltage: V DSAT 8. output resistance: r o 9. transconductance: g m Our goal is to understand these device metrics. 11/7/2016 3
understanding MOSFETs 0 V GS > V T V D n-si n-si p-si To understand any semiconductor device, we should first draw an Energy Band Diagram. 11/7/2016 4
normal to the channel DV OX f S E i E F E FM Si E V 5 metal x 11/7/2016 5
equilibrium E-band diagram: 3 separate pieces 0 V GS 0 n-si n-si p-si E F E F E F E V E V source channel drain 11/7/2016 6
E V source channel drain equilibrium E-band diagram: 3 separate pieces E F E F E F EV 1) Equilibrium: Fermi level is constant 2) Changes in electrostatic potential, change the electron s energy. E V ( y) = 0 - qf ( y) ( y) = E V 0 - qf ( y) 11/7/2016 7
putting the 3 pieces together (equilibrium) E F E V source channel drain E V y ( y) = 0 - qf y ( ) ( x) = E V 0 - qf ( y) 11/7/2016 8
final result: one semiconductor with 3 regions E Now, what effect does a gate voltage have? E F E V source channel drain E V ( y) = 0 - qf ( y) ( y) = E V 0 - qf ( y) 9
equilibrium energy band diagram A positive gate voltage will increase the electrostatic potential in the channel and therefore lower the electron energy in the channel. 0 V GS 0 n-si n-si p-si x 11/7/2016 10
the transistor as a barrier controlled device E V G low gate voltage E F E F V D = V S = 0 source channel drain 11/7/2016 11 y
the transistor as a barrier controlled device E V G low gate voltage E = -qv F n source channel drain 11/7/2016 12 F n y high drain voltage
the transistor as a barrier controlled device E V G high gate voltage E = -qv F n source 11/7/2016 13 F n y high drain voltage
effect of gate voltage first V G E low gate voltage = 0 - qf s E F high gate voltage y 11/7/2016 14
Now add a small drain voltage V G E What if we apply a small positive voltage to the drain? 1) The Fermi level in the drain is lowered. y F n 2) The conduction band is lowered too, but the electron density stays the same. constant electric field substantial electron density 15
how transistors work 2007 N-MOSFET V GS V GS (Courtesy, Shuji Ikeda, ATDF, Dec. 2007) 11/7/2016 16
understanding DIBL I D ( ma mm) threshold voltage V T ( ) V DS V DS = V DD I ON V DS = 0.05 V V GS V TSAT V TLIN V DD 11/7/2016 17
log 10 I D ( ma mm) understanding DIBL transfer characteristics: V DS = V DD I ON V DS = 0.05 V DIBL º DV GS DV DS ( mv V) V GS V TSAT V TLIN V DD 11/7/2016 18
understanding DIBL E V G DIBL F n F n ( low V DS ) source channel drain F n ( high V DS ) 11/7/2016 19
understanding DIBL 0 V GS V DS > 0 n-si E y n-si p-si 11/7/2016 20
2D energy band diagrams 0 V GS > V T V D n-si n-si p-si x y We have been discussing energy band diagrams from the source to the drain along the top of the Si, but more generally, we should look at the 2D energy band diagram. 11/7/2016 21
2D energy band diagram on n-mosfet a) device b) equilibrium (flat band) c) equilibrium (f S > 0) d) non-equilibrium with V G and V D > 0 applied F N 22 S.M. Sze, Physics of Semiconductor Bermel ECE 305 Devices, F16 1981 and Pao and Sah.
limits to barrier control: quantum tunneling 4) 3) 2) 1) 11/7/2016 23 from M. Luisier, ETH Zurich / Purdue
conclusions A MOSFET can be understood by connecting the MOS band diagram with the source and drain across the channel A MOSFET (and most transistors) are barriercontrolled devices A high gate voltage lowers the barrier to current flow, thus increasing current (as seen in the transfer characteristics) Drain-induced barrier lowering (DIBL) is caused by an asymmetric barrier band diagram 11/7/2016 24