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**Circuit Modeling of Non-volatile Memory Devices**

M. Sadd and R. Muralidhar Introduction to NVM Capacitor sub-circuit and sense model Extensions: Program/Erase, 2-bit storage, reliability

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**NVM operates with processes that normally cause failure: Example **

NVM Process Failure Mode Fe-RAM Ferro-Electric Hysteresis Vt instability in High-k dielectrics SONOS Charge Trapping in gate stack Fixed Charge instability Floating Gate NVM HCI Programming/ Tunnel Erase Stress-induced trap creation and charging Need to model effects that are minimized in most other devices!

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**Flash Cell Over-view Flash Cell most common type of NVM:**

Control Gate ONO Layer Floating Gate Tunnel Oxide The memory becomes “Flash” when organized in an array with “block” erase: NOR Array:

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**Flash Cell Operations Operation: Sense Program Erase Retention**

Model Needs to describe: Variable Threshold voltage HCI or Tunneling Tunneling Charge loss

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**Flash Sense Operation Memory senses the Vt shift from stored charge:**

Basic sense circuit:

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Flash Sense Model Simple Approach Separate models for program/erase Vt More flexible sub-circuit:

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**QFG ~ Cmos Vfg + Cfs Vfg + Cfd(Vfg- Vd) + Ccg(Vfg-Vcg)**

Flash Sense Model Charge stored on floating node: QFG ~ Cmos Vfg + Cfs Vfg + Cfd(Vfg- Vd) + Ccg(Vfg-Vcg) Define coupling ratios: g = Ccg/ (Ccg + Cmos + Cfd+ Cfs) d = Cfd/ (Ccg + Cmos + Cfd+ Cfs) Then, VT ~ -QFG/Ccg+ (1/ g ) VT,FG + (d / g ) Vd Charge of floating node shifts Vt Drain coupling to floating gate introduces “DIBL” Typically g = and d ~ 0.1

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**Sense Model: Extraction**

Vd Vg Extract base MOSFET model by accessing floating gate Compare to bit-cell to obtain coupling capacitances Vg Vd Requires comparison of two devices subject to mis-match errors Extraction with bit-cell alone (e.g. ref) requires erase or program model

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**Flash Sense Model: Use Model may only be used for transient simulation**

Example: Generating an Id-Vg curve Ramp Drain from 0 to Vd Ramp Gate from 0 to Vg Compute Idrain Idrain vs. Vgate Ramp slow enough that transient currents (C dV/dt) ~ 0 Not restrictive: Model used mainly for timing

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**Flash Sense Model: DC Model**

May build a DC Flash model: Solve for Floating node potential for capacitor sub-circuit model See: Y. Tat-Kwan, et. al. IEDM Tech Dig. p. 157 (1994) L. Larcher, et. al. IEEE Trans. Elec. Dev., 49 p. 301(2002) Voltage source sets Vfg such that charge QFG is conserved

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**Flash Program/Erase Model**

Time scales: Read ~ 10 ns Program ~ 1 s Erase ~ 100 ms Retention ~ 10 Years Read tightest timing, so most need for circuit simulation Program/Erase May need a circuit model (multi-level storage) Most models add non-linear resistor or current source:

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**Charge-Trapping NVM Scaled NVM devices charge trapping in a layer of:**

Nitride (SONOS): Nano-crystals: Advantages: Reliability (resistant to defects) Reduced program/erase voltage Avoids drain coupling “DIBL”

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**Charge-Trapping NVM: 2 Bit Storage**

Two bits may be stored: One each above source or drain: For large Vd charge over source barrier affects charge more than over drain A simple circuit model: Two reads (forward & reverse) can store 4 states: Forward Vt Reverse Vt State High 11 Low 10 01 00

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**Reliability Model Non-linear current source model charge loss:**

Integrate in log(t) dQ/d(log(t)) = t dQ/dt = t Itunnel(V) May calculate long-time loss: Physics of charge loss (tunneling) is lumped into the non-linear current source

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**Summary Capacitor sub-circuit foundation for flash model**

Appropriate for timing simulation May be augmented to model: Program and erase Reliability (charge loss or gain) Device asymmetry (2-bit storage)

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