Chapter 3 Program Charge Effect on Random Telegraph Noise Amplitude in
3.5 P/E Cycle Dependence of RTN
The RTN amplitude versus the drain current in the first three P/E cycles in FG flash is shown in Fig. 3.6. The result shows program-state and erase-state have the same RTN characteristics and implies that program charges in a FG do not alter current percolation paths caused by substrate dopants and no P/E cycle dependence.
The first three P/E cycles in SONOS flash is shown in Fig. 3.7. The program-state
2 2
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RTN amplitude varies from cycle to cycle, suggesting that random program charges play an important role in current percolation paths. The measured RTN waveforms and the Id -Vg for SONOS flash are shown in Fig. 3.8 and the waveforms of the first two program-state are shown in Fig. 3.9. Two-level current switching is observed in both erase and program-states, showing that RTN arises from a single interface trap and no additional traps are created during P/E cycles. As a result, we affirm that the variation of RTN amplitude from cycle to cycle is attributed to different program charge percolation paths, not additional trap creation.
3-6 3D Atomistic Simulation of RTN
To evaluate percolation effect on RTN, we performed a 3D atomistic simulation [12] for FG and SONOS cells. The first step is establishing a flash cell for both FG and planar SONOS and then placing random discrete dopants in substrate and defining a site of an interface trap inside bottom oxide layer.
We need to consider two individual states: trapping and detrapping when simulating RTN amplitude. The first one with nothing is placed at the interface trap standing for emission trap state in RTN phenomenon lets us extract an IV curve, and the second on with an electron charge is put in the interface trap symbolizing occupation trap state lets us extract another IV curve. Once we get the two IV curve, we can simulate the relative RTN amplitude by calculating ΔId/Id. So, the simulation of erase state RTN amplitude can be achieved by following the procedure above.
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When simulating program state RTN amplitude, two different program charge storage characteristics in FG and SONOS flash have to be taken into account respectively. In FG cell simulation, program charges have a continuous distribution and an equi-potential condition in a FG is obtained in the simulation. Besides, in a SONOS cell, nitride program charges are randomly placed. So again, the simulation of program state RTN amplitude can also be accomplished by the same method. Fig.
3.10 is our simulation flow chart for reference.
Fig. 3.11 shows our simulated RTN amplitude versus the drain current in a FG cell. The program and erase-state RTN are measured in three P/E cycles. The RTN amplitudes are all the same in three P/E cycles, in agreement with our measured result.
Fig. 3.12 shows the simulation result in a planar SONOS cell. Ten different sets of random program charges with a similar program-state Vt are simulated. In all simulations no matter it is program-state or erase-state, a fixed placement of random substrate dopants and interface trap is used. The simulation shows that program-state RTN has a wide spread in amplitudes since each set of program charges results in a different current percolation path, the large variation of program-state RTN amplitude can be realized.
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Fig. 3.1 An illustration of two different program charge storage characteristic resulting distinct outcome of percolation path. Continuous distribution in FG flash and random discrete distribution in SONOS flash
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Fig. 3.2 RTN amplitude versus drain current in a FG flash cell at two program window : 1V, 2V. The drain voltage in measurement is 0.7V and the gate voltage is varied.
10 -7 10 -6 0
10 20 30 40
R T N Am pl it ude
, Δ
I d /I d (%)
Drain Current (Amp)
Floating gate cell
Prog. state Ers. state
(ΔV t =1V)
(ΔV t =2V)
W/L = 0.11mm/0.09mm
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Fig. 3.3 RTN amplitude versus drain current in a SONOS flash cell at two program window : 0.8V, 1.5V. The drain voltage in measurement is 0.7V and the gate voltage is varied.
R T N Am pl it ude
, Δ
I d /I d (%)
Drain Current (Amp)
Prog. state Ers. state
W/L = 0.09mm/0.08mm
10 -7 10 -6 0
10 20 30 40
(ΔV
t=0.8V) (ΔV
t=1.5V)
Planar SONOS cell
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Fig. 3.4 Measured program-state RTN amplitude versus erase-state RTN amplitude in 40 FG flash cells. The RTN amplitude is measured at Id=500nA @Vd=0.7V. The device dimension is W/L=0.11μm/0.09μm. The program window is 1V or 2V.
0 10 20 30 40 0
10 20 30 40
P ro g. St at e R T N A m pl it ude
, Δ
I d /I d (%)
Erase State RTN Amplitude, ΔI d /I d (%)
40 Floating Gate cells
Prog. ΔV t =1V Prog. ΔV t =2V Slope=1
I d =500nA
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Fig. 3.5 Measured program-state RTN amplitude versus erase-state RTN amplitude in 60 planar SONOS cells. The RTN amplitude is measured at Id=500nA @Vd=0.7V.
The SONOS cells have W/L=0.09μm /0.08μm, a 2.8nm tunnel oxide, a 6nm SiN and a 6nm top oxide.
0 10 20 30 40 0
10 20 30 40
P ro g. S ta te R T N Am p li tu d e,
Δ I /I (%) d d
Erase State RTN Amplitude, ΔI d /I d (%)
60 Planar SONOS Cells
Slope=1
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Fig. 3.6 RTN amplitude versus drain current in a FG flash cell in three P/E cycles.
The Vt window is 1V. The drain voltage in measurement is 0.7V and the gate voltage is varied.
Ers. state Prog. state
P/E cycle
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Fig. 3.7 RTN amplitude versus drain current in a SONOS cell in three P/E cycles. The Vt window is 1V. The drain voltage in measurement is 0.7V and the gate voltage is varied.
Ers. state Prog. state
P/E cycle
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Fig. 3.8 Measured RTN waveform and Id versus Vg plot (a) in erase-state and (b) in program-state of a SONOS cell. Electron trapping at an interface trap is manifested by a current discontinuity in the Id-Vg plot
1.95 2.00 2.05 2.10
0.0
1.95 2.00 2.05 2.10
0.0
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Fig. 3.9 The waveform of two-level RTN current switching is observed in erase-state and 1st and 2nd program-state.
2.00 2.05 2.00 2.05 2.10
1.95 2.00 2.05 2.10 Dr a in Cu rr en t (μ A)
0.2 1.95 0.3 0.4 0.5
0.2 0.3 0.4 0.5
1
stP/E 2
ndP/E
erase state program state
Time (sec) Time (sec)
Dr a in Cu rr en t (μ A)
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Fig. 3.10 Simulation flow chart of our 3D atomistic simulation for RTN amplitude at program state and erase state for both FG flash and planar SONOS flash.
interface trap dopant
program charge
Random Dopants
Equi-Potential Distribution in a FG
Random and Discrete Program Charges
RTN Relative Amplitude (ΔI
d/I
d) Calculation
Program StateErase State
Flash Cells
Planar SONOS Floating Gate
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Fig. 3.11 Simulated RTN amplitude versus drain current in a FG flash cell.
Program-state and erase-state have the same placement of substrate random dopants.
The RTN trap is placed in the middle of the device.
10 -8 10 -7 10 -6 0
10 20 30 40 50 60
R T N Am pl it ude
, Δ
I d /I d (%)
Drain Current (Amp) Floating Gate (simulation)
Prog. state
Erase state
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Fig. 3.12 Simulated RTN amplitude versus drain current in a planar SONOS cell.
Program-state and erase-state have a fixed placement of substrate dopants. Ten different sets of random program charges are simulated. An RTN amplitude due to number fluctuation is calculated with continuous substrate doping and program charges.
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