Charge Density in MOS

1

OXIDE AND INTERFACE TRAPPED CHARGES, OXIDE THICKNESS

CHAPTER 6

2

6.1 INTRODUCTION

3

INTRODUCTION

Charges and their location for thermally oxidized silicon.

“Deal triangle” showing the reversibility of heat treatment effects on Qf.

(1) Interface trapped charge (Qit, Nit, Dit)

(2) Fixed oxide charge (Qf, Nf)

(3) Oxide trapped charge (Qot, Not)

(4) Mobile oxide charge (Qm, Nm)

4

6.2 FIXED, OXIDE TRAPPED, AND MOBILE OXIDE CHARGE

5

Cross section and potential band diagram of an MOS capacitor.

6

Capacitance-Voltage Curves

Qs=Qp+Qb+Qn+Qit

7

Capacitances of an MOS capacitor for various bias conditions as discussed in the text.

8

In order for the inversion charge to be able to respond, Jscr = qniW/τg J≦ d = CdVg/dt

W in μm, tox in nm, τg in μs

9

is the dimensionless semiconductor surface electric field. Us=φs/kT, UF=qφF/kT

= ±1

is the intrinsic Debye length

10

11

dd stands for deep depletion

12

Low-frequency (lf), high-frequency (hf), and deep-depletion (dd) normalized SiO2-Si capacitance-voltage curves of an MOS-C; (a) p-substrate NA= 1017 cm-3, (b) n-substrate ND = 1017 cm-3, tox= 10nm, T=300K.

13

Effect of sweep direction on the hf MOS-C capacitance on an p-substrate, (a) entire C-VG curve, (b) enlarged portion of (a) showing the dc sweep direction; f=1 MHz.

(a) (b)

14

Flatband Voltage

There is a built-in potential at epi-sub. junction

normalized CFB

15

CFB/COX versus NA as a function of tox for the SiO2 -Si system at T=300K.

16

Schematic illustration of an MOS-C with finite gate doping density, showing gate depletion for positive gate voltage.

17

Low-frequency and high-frequency capacitance-voltage curves for various n+ polysilicon gate doping densities. The lowest Chf curve is for ND (gate) =1018 cm-3. Substrate NA =1016 cm-3, tox =10nm.

18

Capacitance Measurement

Simplified capacitance measuring circuit.

for RG<<1 and (ωRC)2<<RG

From the in-phase and out of phase component G and C can be determined.

19

Block diagram of circuits to measure the current and charge of an MOS capacitor.

(a) (b)

20

CF is the feedback capacitance.

Low Frequency : Current-Voltage

Low Frequency : Charge-Voltage

21

Ideal (line) and experimental (point) MOS-C curves. NA =5×1016 cm-3, tox=20nm, T=300K, CFB/Cox=0.77.

22

Fixed Charge

23

Gate-Semiconductor Work Function Difference

Potential band diagram of a metal-oxide-semiconductor system at flatband.

24

Potential band diagram of (a) n+ polysilicon-p substrate, and (b) p+ polysilicon-n substrate at flatband.

25

26

Oxide Trapped Charge

Flatband voltage of polysilicon-SiO2-Si MOS devices as a function of oxide thickness.

27

Work function difference as a function of doping density for polysilicon-SiO2 MOS devices.

28

29

Mobile Charge

Drift time for Na, Li, K, and Cu for an oxide electric field of 106 V/cm and tox =100 nm.

30

31

C-VG curves illustrating the effect of mobile charge motion.

32

CIf and Chf measured at T=250OC. The mobile charge density is determined from the area between the two curves.

33

6.3 INTERFACE TRAPPED CHARGE

34

Low-Frequency (Quasi-static) Method

• Semiconductor band diagram illustrating the effect of interface traps; (a) V=0, (b) V>0, (c) V<0. Electron-occupied interface traps are indicated by the small horizontal heavy lines and unoccupied traps by the light lines

35

Theoretical ideal (Dit=0) and Dit ≠0 (a) hf , (b) If and (c) experimental lf C-V curves.

(a)

(b)

(c)

36

CS=Cb+Cn

37

High- and low-frequency C-VG curves showing the offset △C/Cox due to interface traps.

38

Interface trapped charge density from the hf curve and the offset C/C△ ox.

39

Conductance Method

G CitGpCp

(a) (b) (c)

Rit

Cox Cox

GmCm Cit

RitCS

Cox

rS

(d)

Gt

(a) MOS-C with interface trap time constant τit=RitCit , (b) simplified circuit of (a),

(c) measured circuit, (d) including series rs resistance and tunnel conductance Gt.

40

41

Gp/ω versus ω for a single level, a continuum and experimental data. For all curves: Dit =1.9×109 cm-2 eV-1, τit=7×10-5s.

42

Interface trapped charge density versus energy from the quasi-static and conductance methods. (a) (111) n-Si, (b) (100) n-Si.

43

High-Frequency Methods

Gray-Brown method:The hf capacitance is measured as a function of temperature.

Terman method:

44

Charge Pumping Method

Circuit diagram and energy bands for charge pumping measurement. The figures are explained in the text.

45

(d) (e)(c) (f)

46

47

Bilevel chare pumping waveforms.

48

MOSFET Qcp versus frequency

Dit=7×109cm-2eV-1

49

Trilevel charge pumping waveform and corresponding band diagrams.

50

(a) Icp as a function of tstep showing τe at the point where Icp begins to saturate.

(b) insulator trap density versus insulator depth from the insulator/Si interface for Al2O3 and SiO2.

51

52

Interface trap density as a function of energy through the band gap for various measurement techniques. Reprinted with permission

53

Charge pumping current versus base voltage for two voltage pulse

heights before and after gate leakage current correction. tox=1.8nm, f=1kHz.

54

MOSFET Subthreshold Current Method

55

MOSFET subthreshold characteristic.

56

MOSFET substhreshold characteristics before and after stress.

57

Band diagram for (a) VG =VMG (φs=ψF) (a) VG =VT (φs 2ψ≒ F).

58

59

DC-IV

(a) DC-IV measurement set-up. (b) surface space charge region for different gate bias.

60

With the surface in strong inversion or accumulation, the recombination rate is low. The rate is highest with the surface in depletion.

)kT2/qVexp(snqAI BSriGB

itthor Nv)2/(s

If charge is injected into oxide, leading to a VT shift, ID will also shift. ΔID→ΔVT→ΔQot

61

IB before and after stress.

62

6.4 OXIDE THICKNESS

63

C-V Measurements

Assume:

1. The interface trap capacitance is negligible in accumulation at 100kHz to 1MHz.2. The differential interface trap charge density

between flatband and accumulation is negligible.3. The oxide charge density is negligible.4. Quantum effects are negligible.

64

C-V Measurements

65

1/C versus 1/(VG-VFB) for two oxide thicknesses. Data adapted from Ref. 101.

66

(a) MOSC equivalent circuit with tunnel conductance and series resistance. (b) parallel and (c) series equivalent circuit .

D=Gp/ωCp.

67

• Measurement error dependence on device area and oxide thickness. The two-frequency measured capacitance is in error less than 4% in the shaded region. At higher frequencies the D=1.1 border shifts to thinner oxides. Adapted from ref. 109

68

I-V Measurements

Eox is the oxide electric field and A and B are constants. AJ FN

)E/Bexp(AEJ ox2oxFN

)E

))/qV1(1(Bexp(C

q

kT

t

AVJ

ox

5.1Box

2ox

Gdir

Both currents are very sensitive to oxide thickness.