Modeling of the effect of intentionally introduced traps on hole transport in single-crystal rubrene

Defects have been intentionally introduced in a rubrene single crystal by means of two different mechanisms: ultraviolet ozone (UVO) exposure and x-ray irradiation. A complete drift-diffusion model based on the mobility edge (ME) concept, which takes into account asymmetries and nonuniformities in the semiconductor, is used to estimate the energetic and spatial distribution of trap states. The trap distribution for pristine devices can be decomposed into two well defined regions: a shallow region ascribed to structural disorder and a deeper region ascribed to defects. UVO and x ray increase the hole trap concentration in the semiconductor with different energetic and spatial signatures. The former creates traps near the top surface in the 0.3–0.4 eV region, while the latter induces a wider distribution of traps extending from the band edge with a spatial distribution that peaks near the top and bottom interfaces. In addition to inducing hole trap states in the transport gap, both processes are shown to reduce the mobility with respect to a pristine crystal.

Figure 1

Temperature dependent $IV$ characteristics for pristine device #5 C1.

Figure 2

Temperature dependent $IV$ characteristics for crystal #5 device C1 before UVO and C2 after UVO.

Figure 3

Model parameters: (a) Energy dependence of the density of trap states, arbitrary or Gaussian shape; and (b) spatial dependence of the density of trap states, decaying exponentially from the contact(s) to the bulk.

Figure 4

Comparison of measurements (circles) and model fit (solid lines) for crystal #5 C1 at different temperatures and bias conditions.

Figure 5

Comparison of measurements (circles) and model fit (solid lines) for crystal #5 C2 at different temperatures and bias conditions after exposure of the rubrene crystal to UVO.

Figure 6

DOS for crystal #5 pristine (C1) and after UVO exposure (C2) at three different locations, from left to right: near the bottom contact, in the middle of the crystal, and near the top contact. The top right plot shows the difference between the estimated DOS for C2 and C1, i.e., the extra DOS induced by UVO exposure, which can be approximated by a Gaussian distribution with $\sigma =31$ meV.

Figure 7

Representation of the effect of UVO exposure on the DOS. (a) DOS for pristine sample is composed of a shallow tail of traps, related to disorder, and a deep region of traps due to chemical and/or impurity related defects. (b) After exposure to UVO, the concentration of traps around 0.35 eV increases; the tail of traps remains unchanged aside from a peak developing right at the ME. (c) After x-ray irradiation, the concentration of traps increases for the entire energy range, consistent with a broadening of the disorder-related tail of traps. Because of this, the dip separating the two trap concentrations around 0.2 eV disappears.

Figure 8

PDS of a rubrene single crystal before and after UVO exposure. No change in the absorption near the band edge is seen even after 150 s (5 times more than the dose used for the electrical measurements). The absorption in the subband-gap region is below the noise level of the setup and is not shown.

Figure 9

Spatial dependence of the mobility. A strong decrease of the mobility near the top surface, as shown in the figure, has a similar effect on the $IV$ characteristics as a peak in the concentration of traps near the ME. The equation used to describe ${\mu }_0^{\prime }\left(x\right)$ is shown, however any function with a strong spatial dependence will have a similar effect. Inset shows the trap distribution for the pristine and UVO exposed samples at selected points along the device. Note the absence of any peak near the ME.

Figure 10

Temperature dependent $IV$ characteristics for crystal #10, devices C1 and C3, before and after x-ray irradiation for 5000 and 10 000 s.

Figure 11

Comparison of measurements (circles) and model fit (solid lines) for crystal #10 C1 (pristine) at different temperatures and bias conditions.

Figure 12

Comparison of measurements (circles) and model fit (solid lines) for crystal #10 C3 after x-ray irradiation for 5000 s.

Figure 13

Comparison of measurements (circles) and model fit (solid lines) for crystal #10 C3 after x-ray irradiation for 10 000 s.

Figure 14

DOS for crystal #10 pristine (C1) and after x-ray irradiation for 5000 and 10 000 s (C3) at three different locations, from left to right: near the bottom contact, in the middle of the crystal, and near the top contact. Top right plot shows the degradation of the mobility with accumulated x-ray dose.