C-305: Fall 2017 Metal Oxide Semiconductor Devices Pierret, Semiconductor Device Fundamentals (SDF) Chapters 15+16 (pp. 525-530, 563-599) Professor Peter Bermel lectrical and Computer ngineering Purdue University, West Lafayette, IN USA pbermel@purdue.edu Bermel C 305 F17 1
MOS capacitor 1) MOSFT and MOS capacitors 2) -bands and work functions 3) Band-bending in ideal MOS-C s 4) Accumulation, depletion, inversion 5) Depletion approximation 6) Gate voltage V G metal / heavily doped polysilicon SiO 2 t ox» 1-2 nm p-si Bermel C 305 F17 2
MOSFTs S G D source silicon drain SiO 2 gate electrode (Texas Instruments, ~ 2000) gate oxide OT ~ 1.1 nm channel ~ 20 nm 3
Basic Configuration of a MOSFT Gate Source n+ n+ n+ Drain y Substrate (p) Bermel C 305 F17 4
Background S G D n + n + Strained MOSFT High-k/metal gate MOSFT Sources: IBM J. Res. Dev. Google Images Intel website Bermel C 305 F17 5
MOSFT (off) V D 0 n + -Si L I V G < V D = 0 T n + -Si p-si Bermel C 305 F17 6
MOSFT (on) V D 0 n + -Si L I V G > V D > 0 T n + -Si p-si Bermel C 305 F17 7
MOSFT and MOS C n + -Si n + -Si p-si MOS capacitor 8
MOS capacitor SiO 2 t ox» 1-2 nm V G metal or heavily doped polysilicon p-si or n-si Bermel C 305 F17 9
oxide scaling: reaching its limits Bermel C 305 F17 10
how can we understand MOSFT performance? What characterizes its performance? How can we calculate it? What is the closest analogue that we ve already seen? Bermel C 305 F17 11
MOS capacitor 1) MOSFT and MOS capacitors 2) -bands and work functions 3) Band-bending in ideal MOS-C s 4) Accumulation, depletion, inversion 5) Depletion approximation 6) Gate voltage V G metal / heavily doped polysilicon SiO 2 t ox» 1-2 nm p-si Bermel C 305 F17 12
What we need to do: draw e-band diagram 0 c i F M C c S FM C metal i G» 8.9 ev G = 1.12 ev Si i F V SiO 2 Bermel C 305 F17 V 13
Recall the MS junction 0 F M = 4.08 ev c S = 4.05 ev F S FM C i aluminum FP V Bermel C 305 F17 14
built-in potential 0 F M = 4.08 ev c S = 4.05 ev F S FM C aluminum potential = V bi V bi = -F MS q = -f ms i FS V qv bi = ( FM - FS ) = ( F S - F M ) = -( F M - F S ) = -F MS 15
example: Aluminum metal and p-type Si N A = 10 16 cm -3 ( p 0 = N V e V - FS )/k T B cm -3 F M = 4.08 ev F S = c S + G - ( FS - V ) q æ FS - V = k B T ln è ç N V N A ö ø F S = 4.97 ev ( f ms = F - F M S ) q = - 0.9 V FS - V q = 0.2 V bi = -f ms = + 0.9 V Bermel C 305 F17 16
the band diagram C qv bi F i F V f M metal Bermel C 305 F17 17
MOS e-band diagram 0 c i F M C c S FM C G = 1.12 ev i i metal G» 8.9 ev Si F V SiO 2 Bermel C 305 F17 V 18
MOS e-band diagram 1) Built-in potential is exactly the same. 2) But part of the voltage drop occurs across the semiconductor and part across the oxide. Bermel C 305 F17 19
MOS capacitor 1) MOSFT and MOS capacitors 2) -bands and work functions 3) Band-bending in ideal MOS-C s 4) Accumulation, depletion, inversion 5) Depletion approximation 6) Gate voltage V G metal / heavily doped polysilicon SiO 2 t ox» 1-2 nm p-si Bermel C 305 F17 20
lectrostatics of MOS Capacitor in quilibrium qc i Vacuum level Gate qc s qf m C x Substrate (p) F V Schottky barrier with an interposed dielectric Metal Insulator P-Semiconductor Bermel C 305 F17 21
potential vs. position f( x) V ( metal) = V bi = -f ms = DV ox + DV S f S > 0 f = 0 -x ox 0 x Bermel C 305 F17 22
equilibrium e-band diagram DV ox f S V ( metal) = DV ox + f S C DV S i F V bi = -f ms metal V ( metal) = V bi f ( x) = 0 in the bulk V f ( x = 0) = f S surface potential Bermel C 305 F17 23
equilibrium e-band diagram constant electric field d ( ) dx = r x e C i F V metal V ( metal) = V bi monotonically decreasing electric field 26
equilibrium e-band diagram D ox = D S K ox e 0 ox = K S e 0 S DV OX S = ( 0 + ) K OX ox = K S ox» 3 S S ox DV S C i F V V bi metal Bermel C 305 F17 27
MOS capacitor 1) MOSFT and MOS capacitors 2) -bands and work functions 3) Band-bending in ideal MOS-C s 4) Accumulation, depletion, inversion 5) Depletion approximation V 6) Gate voltage G metal / heavily doped polysilicon SiO 2 t ox» 1-2 nm p-si Bermel C 305 F17 28
MOS capacitor (flat band) V G = 0 r = 0 p-si p 0 = N Ā V G = 0 No metal-semiconductor work function difference Bermel C 305 F17 29
MOS capacitor (accumulation) V G < 0 p-si V G < 0 r > 0 p 0 > N Ā Bermel C 305 F17 30
MOS capacitor (depletion) V G > 0 W p-si 0 < V G < V T r» -qn A p 0 << N Ā Bermel C 305 F17 31
MOS capacitor (inversion) V G > V T W T p-si V G > V T electrons r» -qn A p 0 << N Ā Bermel C 305 F17 32
band bending in an MOS device Flat band Accumulation Depletion Inversion Fig. 16.6, Semiconductor Device Fundamentals, R.F. Pierret 33
what if we had an N-type MOS-C? 1) Can we still achieve the same operating regimes? 2) What similarities should occur across devices in common regimes? 3) What might be different about them? V G metal / heavily doped polysilicon n-si SiO 2 t ox» 1-2 nm Bermel C 305 F17 34
hole density in the bulk depletion: ( p bulk = N A = n i e i( bulk)- F ) k B T qf ( x) f = 0 C p bulk = N A = n i e qf F k B T f S i qf F f F = k BT q ln æ è ç N A n i ö ø W Si F V x Bermel C 305 F17 35
electron density at the surface depletion: ( n surface = n i e F - i ( x=0) ) k B T qf ( x) f = 0 C ( n surface = n i e F - i ( bulk)+qf S ) k B T = n bulk e qf S k B T f S qf F i F n bulk = N A f S = 2f F W Si V x Bermel C 305 F17 36
onset of inversion depletion: qf ( x) f = 0 C f S = 2f F i f F = k BT q ln æ è ç N A n i ö ø W Si qf F F V x Bermel C 305 F17 37
accumulation, depletion, inversion depletion: 0 < f S < 2f F qf ( x) f = 0 f F = k BT q ln æ è ç C N A n i ö ø inversion: f S qf F i f S > 2f F F accumulation: f S < 0 W Si V x Bermel C 305 F17 38
MOS electrostatics: depletion 0 < f S < 2f F Given the surface potential: f S f ( x) f ( 0) C S ( f S ) W ( f S ) Q S ( f S ) = -qn A W ( f S ) What gate voltage produced this surface potential? f F i F V Si W x Depletion approximation for the charge in the semiconductor. Bermel C 305 F17 39
MOS capacitor 1) MOSFT and MOS capacitors 2) -bands and work functions 3) Band-bending in ideal MOS-C s 4) Accumulation, depletion, inversion 5) Depletion approximation 6) Gate voltage V G metal / heavily doped polysilicon SiO 2 t ox» 1-2 nm p-si Bermel C 305 F17 40
space charge density vs. position r ( x) d dx = r K S e 0 = - qn A K S e 0 -x ox 0 W = 0 x -qn A depletion charge Bermel C 305 F17 41
electric field (semiconductor) ( x) S P S =? W x 1) 1 2 SW = f S Bermel C 305 F17 42
surface electric field (semiconductor) d dx = - qn A K S e 0 ( x) S d = - qn A K S e 0 dx P ( 0) ò ( W ) d 1) 2) = - qn A K S e 0 1 2 0 ò W dx SW = f S = qn W A S K S e 0 Bermel C 305 F17 1) 2) 1 2 W SW = f S = qn W A S K S e 0 x 43
final answers (semiconductor) W = S = 2k Se 0 f S qn A 2qN Af S k s e 0 cm V/cm ( x) S 1 2 = qn A S W k S e 0 SW = f S P Q B = -qn A W ( f S ) C/cm 2 Q B ( f S ) = - 2qk s e 0 N A f S C/cm 2 0 < f S < 2f F W What gate voltage produced this surface potential? x 44
gate voltage and surface potential DV OX 0 < f S < 2f F V G = DV OX + f S DV ox = x o ox DV S C i F FM Si V metal V G =? Given the surface potential, what is the gate voltage? 45 Bermel C 305 F17 45
voltage drop across a capacitor V +V C º Q V = K Oe 0 A x o metal = F + + + + + + x o - - - - - - Q A C/cm 2 metal C ox = - Q A V V = - Q A C ox C A º Q A V = K Oe 0 = C ox F/cm 2 x o Bermel C 305 F17 46
relation to gate voltage ox V G = DV ox +f S DV ox = -Q B C OX ( f S ) metal V G -x o S ( x) W V G = - Q B Q B x ( f S ) C ox + f S ( f S ) = -qn A W ( f S ) C ox = K O e 0 Bermel C 305 F17 x o 47
summary W = S = 2k Se 0 f S qn A 2qN Af S k s e 0 Q B = -qn A W f S cm V/cm ( ) C/cm 2 ( x) S S = qn A W k S e 0 1 SW = f S 2 P Q B = - 2qk s e 0 N A f S C/cm 2 V G = - Q B ( f S ) C ox + f S W x 0 < f S < 2f F Bermel C 305 F17 48
MOS electrostatics: inversion f ( x) f ( 0) C f F i f S» 2f F ff Si F V W T é W T = 2K Se 0 ù ê 2f F ë qn ú A û 1/2 Maximum depletion region depth x 49
delta-depletion approximation r metal W T = 2k Se 0 2f F qn A -x o W T Q B = -qn A W T x r = -qn A Q n Bermel C 305 F17 50
delta-depletion approximation ( x) S ( 0) = - Q S K S e 0 ( 0 + ) = - Q B K S e 0 P Bermel C 305 F17 W x 51
MOS electrostatics: inversion f S» 2f F f ( x) f ( 0) V G = - Q S + 2f F C ox C V G = - Q B V T = - Q B ( 2f F ) + Q n C ox ( 2f F ) C ox + 2f F + 2f F f F Si f F i F V Q n = -C ox V G - ( ) V T W T é W T = 2K Se 0 ù ê 2f F ë qn ú A û Bermel C 305 F17 1/2 52 x
MOS capacitor 1) MOSFT and MOS capacitors 2) -bands and work functions 3) Band-bending in ideal MOS-C s 4) Accumulation, depletion, inversion 5) Depletion approximation 6) Gate voltage V G metal / heavily doped polysilicon SiO 2 t ox» 1-2 nm p-si Bermel C 305 F17 53
example Assume n+ poly Si gate 10 18 channel doping t ox = 1.5 nm S G D What is V T? e-field in oxide at V G = 1V? source silicon drain SiO 2 Bermel C 305 F17 54
example (cont.) V G = - Q S ( f S ) C ox + f S f F = k BT q ln æ è ç N A n i ö ø f F = 0.48 V V T = - Q B ( 2f F ) C ox V T = f ms - Q B + 2f F ( 2f F ) C ox + 2f F C ox = K O e 0 x o Q B = -qn A W ( 2f F ) Q B = - 2qk s e 0 N A 2f F C ox = 2.36 10-6 F/cm 2 Q B = -5.71 10-7 C/cm 2 V T = 0.14 V f ms = - k T B q ln æ è ç N A N D n i 2 ö ø f ms = -1.06 V Bermel C 305 F17 55
example (cont) Q n = -C ox ( V G - V T ) Q n = -2.06 10-6 C/cm 2 Q n q = -1.3 1013 C/cm 2 OX = - Q S = - Q + Q n B k ox e 0 k ox e 0 ( 2f B ) OX = 7.3 10 6 V/cm Bermel C 305 F17 56
Notation in SDF Chapter 16 V G means ; i.e. an ideal MOS structure with NO metal-semiconductor work function difference is assumed. Bermel C 305 F17 57
conclusions Introducing an oxide layer between a metal and semiconductor creates a new type of band structure This also allows for a new type of device, known as a metal-oxidesemiconductor field effect transistor (MOSFT) Discussed the primary MOS operational regimes: flat band, accumulation, depletion, and inversion The depletion approximation allows us to calculate the charge distribution and surface potentials of each regime This can then be translated into expressions for the gate voltage thresholds Bermel C 305 F17 58