Charge Trapping Model (CTM) for IGZO Memristors

A physics-based compact model for simulating interface-type resistive switching in metal/IGZO Schottky diode memristors. This model captures the bottom electrode (BE) charge trapping mechanism that modulates the Schottky barrier height.

Physical Model

The CTM implements interface-type resistive switching based on charge trapping at the metal/oxide interface:

Schottky Barrier Modulation

Following Mikheev et al. (2014), the barrier height is modulated by interface trapped charge:

$$\Phi_{B,0} = \Phi_M - \chi$$

$$\Delta\Phi_{max} = \frac{q \cdot n_0 \cdot h \cdot x}{\varepsilon_0 \cdot \varepsilon_r}$$

Where:

• $\Phi_M$ = metal work function (eV)
• $\chi$ = semiconductor electron affinity (eV)
• $n_0$ = trap density (m⁻³)
• $h$ = interaction radius (m)
• $x$ = charge centroid distance (m)

The SBH varies between:

• HRS (Q=0): $SBH_{max} = \Phi_{B,0} + \Delta\Phi_{max}$
• LRS (Q=1): $SBH_{min} = \Phi_{B,0} - \Delta\Phi_{max}$

Asymmetric SET/RESET Kinetics (V3)

Direction-based time constants capture asymmetric trapping/detrapping dynamics:

$$\tau_{set}(V) = \tau_{0,set} \cdot \frac{F_{ref}}{F} \cdot e^{\gamma |V|}$$

$$\tau_{reset}(V) = \tau_{0,reset} \cdot \frac{F_{ref}}{F} \cdot e^{\gamma |V|}$$

Where $F = n_0 \cdot h^2 \cdot x$ is the dimensionless trap factor.

Current Transport

Thermionic emission with image-force barrier lowering:

$$I = A \cdot A^* \cdot T^2 \cdot \exp\left(-\frac{q(\Phi_B - \Delta\Phi_{IFL})}{kT}\right)$$

Streamlit Application

The model is implemented as an interactive Streamlit web application (be_trap_physics_model_v3.py).

Running the App

streamlit run be_trap_physics_model_v3.py

Features

• Interactive parameter control: Adjust material properties, device geometry, and trapping kinetics in real-time
• Material presets: Pre-configured parameters for W/IGZO, Pd/IGZO, and Mo/IGZO interfaces
• Physics validation: Automatic detection of unphysical parameter combinations (e.g., negative SBH)
• Visualization:
  • Linear and semilog I-V characteristics
  • SBH, charge state, and effective tau evolution
  • Two-cycle hysteresis loops
• Data export: Download simulation results as CSV

Adjustable Parameters

Category	Parameters
Materials	Metal work function (Φ_M), semiconductor affinity (χ)
Device	Oxide thickness, permittivity, device area, series resistance
Trapping	Trap density (n₀), interaction radius (h), charge centroid (x)
Kinetics	τ₀_set, τ₀_reset, voltage acceleration (γ), V_scale
Simulation	Max voltage, sweep rate, time step, temperature

Connection to Thesis

This model is discussed in Chapter 3: Compact Modelling of Interface-Type Memristors of the thesis "Interface-Engineered Memristors for Neuromorphic Computing." It provides the theoretical framework for understanding experimental I-V characteristics of IGZO-based memristors fabricated at Cambridge.

The physics implemented here—interface charge trapping modulating a Schottky barrier—represents a non-filamentary switching mechanism distinct from traditional conductive filament-based RRAM.

Dependencies

streamlit
numpy
pandas
scipy
plotly

References

• Mikheev, E. et al. (2014). Resistive switching and its suppression in Pt/Nb:SrTiO₃ junctions. Nature Communications, 5, 3990.