Molecular Weight Tuning of Organic Semiconductors for Curved Organic–Inorganic Hybrid X‐Ray Detectors

Abstract Curved X‐ray detectors have the potential to revolutionize diverse sectors due to benefits such as reduced image distortion and vignetting compared to their planar counterparts. While the use of inorganic semiconductors for curved detectors are restricted by their brittle nature, organic–inorganic hybrid semiconductors which incorporated bismuth oxide nanoparticles in an organic bulk heterojunction consisting of poly(3‐hexylthiophene‐2,5‐diyl) (P3HT) and [6,6]‐phenyl C71 butyric acid methyl ester (PC70BM) are considered to be more promising in this regard. However, the influence of the P3HT molecular weight on the mechanical stability of curved, thick X‐ray detectors remains less well understood. Herein, high P3HT molecular weights (>40 kDa) are identified to allow increased intermolecular bonding and chain entanglements, resulting in X‐ray detectors that can be curved to a radius as low as 1.3 mm with low deviation in X‐ray response under 100 repeated bending cycles while maintaining an industry‐standard dark current of <1 pA mm−2 and a sensitivity of ≈ 0.17 μC Gy−1 cm−2. This study identifies a crucial missing link in the development of curved detectors, namely the importance of the molecular weight of the polymer semiconductors used.

Note S1. Fowler-Nordheim tunnelling model. This mechanism involves charge tunnelling through a potential barrier which generally reduces upon application of an electric field (in the range of 10 5 -10 6 V m -1 or higher).
Assuming that the potential barrier is triangular, and the electric field is uniform, the tunnelling current density ( ) is given as [41] : where is the electric field and is given by √ ⁄ and represents barrier height, is the effective mass of the charge carrier, is the electron charge, and is the Planck's constant. In order to confirm whether the charge conduction is governed by the Fowler-Nordheim model, dark diode and X-ray photocurrent response characteristics were plotted as ( ) vs ( Figure S11 and S12). For the Fowler-Nordheim characteristics to be prevalent, the gradient of the ( ) vs plots should be negative. Since all the detectors display a positive gradient, this indicates that Fowler-Nordheim is a less dominant charge conduction mechanism for these detectors in reverse bias.

Note S2. Space charge-limited current model
The SCLC model is existent when electric fields higher than 10 5 -10 6 V m -1 are applied.
Initially the concentration of the background carriers is higher than the injected carriers, hence the charge conduction follows an Ohmic behaviour where the gradient of the ( ) ( ) is equal to 1. This situation is explained as given below [42] : (2) where is the current, is the applied bias, is the electron charge, is the dominant carrier density, is the charge carrier mobility, and is the active layer thickness. Upon increasing applied bias, concentration of injected carriers become higher than the background carriers.
This results in the traps present within the system being filled. If the deep traps are present, the current density-voltage relationship follows the form of where . After reaching a specific applied bias, all the traps present within system become filled, therefore resulting in the trap free SCLC regime which is described as [42] : where is the current density, is the applied bias, is the charge carrier mobility, is the relative permittivity and is the permittivity in free space or vacuum, and is the active layer thickness. During the trap free SCLC regime, the gradient of the ( ) ( ) is equal to 2.

Note S3. Poole-Frenkel model.
This mechanism is only applicable at electric fields higher than 10 5 -10 6 V m -1 and involves extraction of charge trapped in a potential well upon application of a sufficient electric field and is explained using the equation given below [41] : where is the current density, is the electric field, is the potential energy of the traps, is the absolute temperature, is the electron charge, is the Boltzmann constant, and is given as the √ ⁄ . The represents relative permittivity and is permittivity in free space or vacuum. In order to confirm whether extraction of such charge trapped in a potential well assists charge conduction in this NP-BHJ system, dark diode and X-ray photocurrent response characteristics were plotted as ( ) vs ( Figure S14 and S15). One of the main features which indicates that Poole-Frenkel mechanism is responsible for charge conduction within a material system is a linear behaviour between ( ) vs with a positive gradient. However, under both dark diode and X-ray irradiation conditions, all the detectors indicate a negative gradient which indicate that Poole-Frenkel mechanism is less dominant under those situations.

Note S4. Schottky model
The Schottky model is explained using the equation given below [41] : where is the current density, is the electric field, is the Schottky barrier height, is the modified Richardson constant, is the absolute temperature, is the electron charge, is the Boltzmann constant, and is given as the √ ⁄ . Here, is relative permittivity and is permittivity in free space or vacuum.