SCLC Tutorial: Quick start — simulate space-charge limited current

🐝 Under construction: This section is being written and will be updated soon 15/09/2025

Band diagrams illustrating: (a) a standard device with electron and hole contacts and built-in potential; (b) SCLC electron-only transport with aligned conduction band and blocked valence band; (c) SCL hole-only transport with aligned valence band and blocked conduction band. — (a) Standard device with electron + hole contacts. (b) SCLC — electron transport only. (c) SCL — hole transport only.

Space-charge limited current (SCLC) is the transport regime where injected carriers dominate and the current is limited by their motion through the film, not by generation. In an ideal, trap-free device, the current density follows the Mott–Gurney law: $ J = \frac{9}{8}\,\varepsilon\,\mu\,\frac{V^2}{L^3} $, with dielectric constant $ \varepsilon $, mobility $ \mu $, voltage $ V $, and thickness $ L $. SCLC measurements (often using hole-only or electron-only diodes) are widely used to extract mobility and assess trap effects. In this quick start, you will configure an SCLC structure, run a JV sweep, locate the J ∝ V² region, and see how traps or thickness shift the curve and the extracted mobility.

In ?? we compare contact configurations that control which carriers can enter the device. In panel (a) the standard structure has electron- and hole-selective contacts, creating a built-in potential and allowing both electrons and holes to be injected/extracted. By adjusting the contact energetics or adding/selecting transport/blocking layers, you can enforce single-carrier injection: in panel (b) an electron-only device (SCLC) is formed by providing low barriers to the conduction band at both contacts while blocking the valence band (hole injection), and in panel (c) a hole-only device (SCL) is formed by aligning the valence band at both contacts while blocking the conduction band (electron injection). Compared to the standard device in (a), the single-carrier cases (b,c) suppress recombination and force current to be governed by space-charge-limited transport, which is ideal for extracting carrier mobility and contact effects.

Step 2: Create a new simulation

Start OghmaNano from the Windows Start menu. The main OghmaNano window will appear as shown in ??.

OghmaNano new simulation window showing device categories including perovskite cells, OLEDs, OFETs, GaAs demos, ray tracing, and FDTD examples — The *New simulation* window provides a library of device types and example projects. Double-clicking a category opens preconfigured simulations — for example, the **Perovskite cells** folder highlighted here.

OghmaNano perovskite solar cell examples list showing preconfigured MAPbI₃ device, Perovskite solar cell, and a CELIV example template — Within the *Perovskite cells* category you can choose from several pre-built device structures, including a **MAPbI₃** example, a generic **Perovskite solar cell**, and a dedicated **CELIV example**. For this tutorial, select the CELIV template to explore how OghmaNano simulates charge extraction transients.

For a trap-free space-charge-limited current (SCLC), the Mott–Gurney law is

$$ J = \frac{9}{8}\,\varepsilon \mu \frac{V^2}{L^3} $$

Rearranging for the mobility:

$$ \mu = \frac{8}{9} \cdot \frac{J L^3}{\varepsilon V^2} $$

Substituting the known values:

$ L = 100~\text{nm} = 1.0\times10^{-7}~\text{m} \;\;\Rightarrow\;\; L^3 = 1.0\times10^{-21}~\text{m}^3 $
$ \varepsilon_r = 3.0 $, $ \varepsilon_0 = 8.85\times10^{-12}~\text{F·m}^{-1} $, so $ \varepsilon = 2.656\times10^{-11}~\text{F·m}^{-1} $
$ V = 1.0~\text{V} $
$ J \approx 1.0\times10^{3}~\text{A·m}^{-2} $

Now:

$$ \mu = \frac{8}{9} \cdot \frac{ (1.0\times10^{3})(1.0\times10^{-21}) } { (2.656\times10^{-11})(1.0^2) } = 3.35\times10^{-8}~\text{m}^2\text{V}^{-1}\text{s}^{-1} $$

Or in cgs units:

$$ \mu \approx 3.35\times10^{-4}~\text{cm}^2\text{V}^{-1}\text{s}^{-1} $$