ECE-305: Fall 2017 Metal Oxide Semiconductor Devices

Transcription

1 C-305: Fall 2017 Metal Oxide Semiconductor Devices Pierret, Semiconductor Device Fundamentals (SDF) Chapters (pp , ) Professor Peter Bermel lectrical and Computer ngineering Purdue University, West Lafayette, IN USA Bermel C 305 F17 1

2 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

3 MOSFTs S G D source silicon drain SiO 2 gate electrode (Texas Instruments, ~ 2000) gate oxide OT ~ 1.1 nm channel ~ 20 nm 3

4 Basic Configuration of a MOSFT Gate Source n+ n+ n+ Drain y Substrate (p) Bermel C 305 F17 4

5 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

6 MOSFT (off) V D 0 n + -Si L I V G < V D = 0 T n + -Si p-si Bermel C 305 F17 6

7 MOSFT (on) V D 0 n + -Si L I V G > V D > 0 T n + -Si p-si Bermel C 305 F17 7

8 MOSFT and MOS C n + -Si n + -Si p-si MOS capacitor 8

9 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

10 oxide scaling: reaching its limits Bermel C 305 F17 10

11 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

12 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

13 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

14 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

15 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

16 example: Aluminum metal and p-type Si N A = 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 = V FS - V q = 0.2 V bi = -f ms = V Bermel C 305 F17 16

17 the band diagram C qv bi F i F V f M metal Bermel C 305 F17 17

18 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

19 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

20 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

21 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

22 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

23 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

24 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

25 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

26 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

27 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

28 MOS capacitor (accumulation) V G < 0 p-si V G < 0 r > 0 p 0 > N Ā Bermel C 305 F17 30

29 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

30 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

31 band bending in an MOS device Flat band Accumulation Depletion Inversion Fig. 16.6, Semiconductor Device Fundamentals, R.F. Pierret 33

32 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

33 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

34 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

35 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

36 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

37 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

38 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

39 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

40 electric field (semiconductor) ( x) S P S =? W x 1) 1 2 SW = f S Bermel C 305 F17 42

41 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 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

42 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

43 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

44 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

45 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

46 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

47 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

48 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

49 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

50 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

51 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

52 example Assume n+ poly Si gate 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

53 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 = F/cm 2 Q B = 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 = V Bermel C 305 F17 55

54 example (cont) Q n = -C ox ( V G - V T ) Q n = C/cm 2 Q n q = C/cm 2 OX = - Q S = - Q + Q n B k ox e 0 k ox e 0 ( 2f B ) OX = V/cm Bermel C 305 F17 56

55 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

56 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