EA Spectroscopy as a series of sensors: Investigating the Impact of Film-Processing Temperature on Mobility in Organic Diodes

Team members

Li Jinhan A0327554Y

Liu Chenyang A0328377R

Idea

We will use EA spectroscopy, which will include optical sensors, electrical sensors, and lock-in amplifiers, among other components as a highly sensitive, non-destructive optical sensing platform to measure the internal electric field modulation response of organic diodes under operating conditions, and to quantitatively extract carrier mobility based on this measurement. By systematically controlling the thin film preparation temperature and comparing the EA response characteristics of different samples, the project aims to reveal the influence of film preparation temperature on device mobility.

Introduction

The performance of organic semiconductor devices (such as organic diodes) is largely limited by the charge transport processes within the thin film, and carrier mobility is one of the key parameters characterizing charge transport capability. Since organic thin films typically exhibit significant morphological and microstructure sensitivity, the film fabrication temperature affects factors such as molecular packing, crystallinity, phase separation behavior, and trapped state density, thereby altering the internal electric field distribution and charge injection/transport efficiency, ultimately manifesting as differences in mobility and device response. Therefore, establishing a characterization method capable of reliably tracking the "process-structure-transport" relationship is crucial for process optimization and device performance improvement.

Theory

Electroabsorption technology is achieved by measuring the change in absorption coefficient after an applied electric field is applied. Under normal incident conditions, the intensity $I$ of light transmitted through the absorbing medium can be calculated using the Lambert-Beer law:

$I=I_0(1-R{)}^2{e}^{-\alpha d}$----------(1)

Where $I_0$ represents the original light intensity of the incident light, $R$ is the reflectivity, $\alpha$ is the absorption coefficient, and $d$ is the thickness of the absorbing medium.

Both $R$ and $\alpha$ are affected by the external electric field, and their $\mathrm{\Delta }I$ changes as follows:

$\mathrm{\Delta }I=-I(\frac{2R}{1-R}\frac{\mathrm{\Delta }R}{R}+d\mathrm{\Delta }\alpha )$----------(2)

Under classical operating conditions, the change in the value of $R$ is negligible. Equation (2) simplifies to:

$\frac{\mathrm{\Delta }I}{I}=-d\mathrm{\Delta }\alpha$----------(3)

From a microscopic perspective, the energy level E(F) of state $⟨i|$ in electric field F is given by the following equation:

$E(F)=E(0)-m_{i}F-\frac{1}{2}(p_{i}F)F$----------(4)

$m_i$ represents the electric dipole moment of this state, and $p_i$ is its polarizability. Therefore, the optical transition energy shift $\mathrm{\Delta }E$ from the initial state to the final state is given by the following equation:

$\mathrm{\Delta }E(F)=-(m_f-m_i)F-\frac{1}{2}(p_f-p_i)F^2$----------(5)

The first term represents the linear energy change caused by the difference in dipole moments between the initial and final states, which cancels out in isotropic solids without permanent dipoles. The second term describes the energy shift caused by the difference in polarizability between the initial and final states, an effect that always exists.

The absorption variation of the external electric field $\mathrm{\Delta }\alpha$ can be represented by the $\mathrm{\Delta }E$ term of the Maclaurin series, while the third and higher order terms can be ignored due to the small spectral changes.

$\mathrm{\Delta }\alpha (h\nu )=\left(\frac{d\alpha }{dE}\mathrm{\Delta }E\right)+\frac{1}{2}\left(\frac{d^2\alpha }{d^{2}E}\mathrm{\Delta }{E}^2\right)$----------(6)

The sole contribution of the first term comes from the second-order Strac effect $\frac{1}{2}\mathrm{\Delta }p{F}^2$, while the isotropic average of $(\mathrm{\Delta }mF{)}^2$ in the second term does not cancel out, but instead produces $\frac{1}{3}(\mathrm{\Delta }mF{)}^2$ in the randomly distributed matrix. The third contribution of $\mathrm{\Delta }\alpha (hv)$ comes from the transition of the oscillator to the previously forbidden state when the electric field is present, and this transition also has a quadratic relationship with F.

Adding up all contributions to $\mathrm{\Delta }\alpha (hv)$, we get:

$\mathrm{\Delta }\alpha =[a\alpha +b\frac{d\alpha }{dE}+C\frac{d^2\alpha }{d^{2}E}]F^2$----------(7)

For a composite electric field with AC component $E_{ac}\sin (\omega t)$ and DC component $E_{d}c$:

$E(t)=E_{ac}\sin (\omega t)+E_{d}c$----------(8)

Substituting formula (8) into (7) yields the modulation of $\mathrm{\Delta }\alpha$ at the fundamental frequencies $1\omega$ and $2\omega$:

$\mathrm{\Delta }\alpha \propto [\frac{1}{2}{E}_{ac}^2(1+\sin (2\omega t-\frac{\pi }{4}))+2E_{ac}(E_{dc}-E_{bi})\sin (\omega t)+(E_{dc}-E_{bi}{)}^2]$----------(9)

$E_{bi}=\frac{({\varphi }_{anode}-{\varphi }_{cathode})}{qd}$ represents the internal electric field generated by the equilibrium state of the two electrodes EF.

A phase-sensitive lock-in amplifier can measure the $2\omega$ component:

$\mathrm{\Delta }\alpha (2\omega )\propto \frac{1}{2}{E}_{ac}^2\sin (2\omega t-\frac{\pi }{4})$----------(10)

and $1\omega$ components:

$\mathrm{\Delta }\alpha (1\omega )\propto 2E_{ac}(E_{dc}-E_{bi})\sin (\omega t)$----------(11)

Since $\mathrm{\Delta }\alpha (1\omega )$ and $E_{dc}-E_{bi}$ are linearly related, the internal field $E_{dc}$ can be determined by measuring $E_{bi}$ required to eliminate the electroabsorption response at $1\omega$.