High-resolution charge carrier mobility mapping of heterogeneous organic semiconductors

The performance of organic electronic devices is sensitive to the structuring of the active layer across multiple length scales. The transport of charge is highly dependent on molecular order, orientation, and packing motif.^1–3 Boundaries between crystalline segments act as resistive barriers, with the resistance depending on the relative orientation of adjacent grains, and for polymer systems, the presence of tie molecules.^4–6 Moreover, spatial variations in film formation and film wetting can lead to performance variations or electrical discontinuities.

Multi-component systems introduce additional complexity. Processing conditions and the compatibility of the components can affect miscibility, phase separation, and co-crystallization.^7–10 This is particularly important for organic photovoltaic (OPV) active layers where domain size and connectivity play critical roles in charge photogeneration and transport.^7,8 Blending of n- and p-type organic semiconductors has been employed to promote ambipolar transistor characteristics, which are central for developing organic logic elements and light-emitting transistors.^11,12 The addition of insulating polymers to organic semiconductors has also been investigated as a means of lowering manufacturing costs without significant detriment to charge transport.^13,14

The overall electrical performance of organic electronic active layers thus depends on the collective contributions of many structural heterogeneities, often manifested at the nano- and micro-scales. Device-scale electrical characterization, however, provides little insight into the local electrical processes that govern active layer performance. To further understand the effects of structural heterogeneity on charge transport, it is therefore critical to develop tools for investigating local electrical properties.

Conductive atomic force microscopy (C-AFM) is uniquely suited to non-invasively probe the nano- and micro-scale electrical properties of organic materials.¹⁵ C-AFM typically uses a metal-coated atomic force microscope (AFM) probe, with an apex radius of under 25 nm, as a movable electrical contact. In the standard imaging mode, the probe is scanned across the sample with a constant applied force and a fixed voltage between the probe and sample, while recording current. The C-AFM probe can also be held at user-specified sample locations to record local current-voltage characteristics. Analysis of these curves provides insight into local charge transport mechanisms and quantitative performance metrics such as charge carrier mobility.¹⁵ 

The space charge limited current (SCLC) model is widely used to quantify charge carrier mobility in organic semiconductors.^16–18 The trap-free field-independent Mott-Gurney law is

where J is the current density, ε is the relative dielectric constant of the active layer, ε₀ is the permittivity of free space, μ is the charge carrier mobility, V is the applied voltage, and L is the thickness of the active layer. For certain materials, a field-dependent term is also included to account for electric field effects.^16,18 The SCLC model assumes single charge carrier transport of either holes or electrons. In practice, hole-only or (electron-only) transport has been achieved through the use of high (or low) work function electrical contacts to block the injection of unwanted electrons (or holes).¹⁸ 

A similar approach can be applied to measure local out-of-plane charge carrier mobility in organic semiconductor films by using a C-AFM probe as a top electrode in a vertical configuration.^19–21 The small contact area between the probe and sample surface allows for high spatial resolution while eliminating pinhole effects that can hinder large-area measurements in a sandwich geometry. Ginger et al. demonstrated, however, that it is necessary to use a modified SCLC model that takes the C-AFM probe-sample geometry into account;²⁰ otherwise, anomalously high mobility values are obtained relative to those from large-area measurements.

Guided by finite element simulations, Ginger's model introduces a factor of (L/d)^1.6, changing the typical J ∝ L⁻³ dependence of current density with film thickness for the planar electrode geometry to J ∝ L^−1.4 for the C-AFM probe-sample geometry;²⁰ d is the diameter of the probe-sample contact. In the field-independent form, Ginger's SCLC relation can be written as

The empirical parameter δ accounts for any remaining minor offset between C-AFM data and large-area measurements.

Using this framework, Ginger et al. measured the out-of-plane hole mobility of conjugated polymer films as a function of film thickness, with consistency between nanoscale and device-scale SCLC measurements.²⁰ This approach has subsequently been used to quantify out-of-plane mobility in small-molecule organic semiconductors and donor-acceptor blends.^1,21 By applying similar analysis to current-voltage data recorded at several hundred sample positions, Wilson et al. obtained two-dimensional hole mobility maps of a poly(3-hexylthiophene-2,5-diyl) (P3HT) film.²² 

In this letter, we use C-AFM to quantify and map local out-of-plane charge carrier mobility with a high spatial resolution (below 10 nm) and high pixel count (as many as 16 000 current-voltage curves for a single map). To establish the efficacy of this approach for sensing local variations in electrical properties, we consider two types of heterogeneous systems: (1) a small molecule organic semiconductor film with a heterogeneous crystal structure and (2) a high-performance organic photovoltaic (OPV) active layer with a heterogeneous composition.

Building on the approach developed by Ginger for extracting out-of-plane charge carrier mobility from C-AFM current-voltage characteristics, we employ Eq. (2) but with a term added to account for the built-in potential, V_bi

The built-in potential results from a difference in work function between the contact electrodes.^16,23 In the above relation, we use δ = 1. Based on analysis of Ginger's data, we observe that δ (derived from the offset between C-AFM and macroscopic data) can vary over a wide range, between at least 1.1 and 8.0 (see supplementary material). The use of a non-unity value for δ presumes that macroscopic single carrier diodes provide accurate reference data, despite being prone to effects from metal atom penetration during top electrode deposition, film thickness variations, and current leakage. Wilson et al. argue that δ can be eliminated by using the Johnson-Kendall-Roberts (JKR) contact model for an improved estimate of the tip-sample contact diameter.²² We have determined, however, that a consequence of the (L/d)^1.6 term in Eqs. (2) and (3) is that the resulting charge carrier mobility is only weakly dependent on the contact diameter (μ ∝ d^−0.4; see supplementary material). As summarized in Table I, while the choice of the JKR or Derjaguin-Muller-Toporov (DMT)²⁴ contact mechanics model has a significant effect on the estimated probe-sample contact radius, it has a minor impact on the resulting charge carrier mobility, suggesting that the simpler DMT model is adequate.

The procedure for charge carrier mobility mapping is shown in Fig. 1. First, a metal-coated AFM probe is approached to the sample surface until the desired applied force is achieved. Since this work focuses on hole mobility, a high work function Pt-coated AFM probe was used. Next, while maintaining a constant applied force, the probe-sample voltage is swept and the local current through the film is recorded. To preclude unwanted photocurrent generation due to stray light, the AFM uses a 1300 nm infrared laser for cantilever deflection detection, a wavelength that is outside the absorption range for the materials under study. The probe is then retracted from the sample surface and is moved to the next sample location. This process is repeated at an array of sample positions to produce a series of current-voltage curves [Fig. 1(b)]. Next, the curves are plotted in terms of √J versus V and linear regression is performed in the SCLC region to extract the charge carrier mobility from the slope and the built-in potential from the y-intercept.¹⁶ We employ the topographic height at each sample location together with the average film thickness to determine the local film thickness to use in Eq. (3). To verify the voltage range over which SCLC occurs, the data are replotted in terms of log J versus log (V-V_bi). According to Eq. (3), a slope of 2 indicates SCLC behavior. Finally, a color value is assigned at each sample position to generate a map, as illustrated in Fig. 1(d). An advantage of this approach to mobility mapping is that the probe is retracted between pixels, thus limiting lateral forces that may damage delicate samples during contact mode scanning.

To establish the capabilities of C-AFM mobility mapping for detecting local electrical differences in films with heterogeneous crystal structures, we prepared 5,11-Bis(triethylsilylethynyl)anthradithiophene (TES-ADT) films bearing regions with two distinct film structures. As-spun TES-ADT displays limited molecular order with nanocrystals under 50 nm in size, leading to a modest in-plane field effect hole mobility of 0.002 cm²/V s.^25,26 A change in polymorph and further crystallization can be induced through solvent vapor annealing (SVA), resulting in the evolution of millimeter-scale spherulites and an in-plane field effect hole mobility of 0.1 cm²/V s.²⁵ The pre-SVA semicrystalline film has a monoclinic crystal structure while the post-SVA spherulites have a triclinic crystal structure with both polymorphs exhibiting an edge-on molecular orientation with respect to the substrate.

As shown in Fig. 2(a), by stopping the SVA process midway through spherulite growth, we generated TES-ADT films with crystalline and semicrystalline areas. The crystalline region exhibits crystal grain boundaries running radially from the spherulite center, while the semicrystalline region has a homogeneous appearance. Interestingly, topographic images of the boundary region, measured by AFM, show little difference between the crystalline and semicrystalline regions [Fig. 2(b)]. The C-AFM current map [Fig. 2(c)], however, exhibits sharp contrast between the two regions, reflecting the important impact of molecular packing on charge transport. The current in the semicrystalline region shows a granular film structure, with individual grains about 100–200 nm in size, representative of individual crystallites or small groups thereof. On the other hand, the crystalline area exhibits a higher and more uniform current level than the semicrystalline region.

The mobility map shown in Fig. 2(d), constructed from 5852 current-voltage curves, displays similar qualitative features to the current map, i.e., high contrast between the semicrystalline and crystalline regions and a granular structure in the semicrystalline region. Using the DMT probe contact model, the average out-of-plane hole mobility for the semicrystalline region is 2.71 × 10⁻⁴ cm²/V s, while the average out-of-plane hole mobility for the crystalline region is nearly one order of magnitude higher, 1.65 × 10⁻³ cm²/V s. Both values are lower than those measured in transistors, which is to be expected since SCLC mobilities are generally lower than field-effect mobilities that are measured in a higher carrier density regime; moreover, the edge-on molecular stacking in the TES-ADT films favors in-plane charge transport,²⁶ while the mobility mapping performed here probes out-of-plane transport. The hole mobility histogram [Fig. 2(e)] shows clear groupings of mobility values associated with crystalline and semicrystalline regions, with a broader distribution of values for the semicrystalline region due to its heterogeneous, granular structure. Interestingly, while high quality SCLC fits were obtained throughout the sample (average R-squared = 0.9984), the poorest fits, indicating small deviations from ideal SCLC behavior, were obtained at the boundary between crystalline and semicrystalline regions (see supplementary material).

To investigate the effects of a heterogeneous film composition on charge carrier mobility, we prepared an OPV active layer consisting of an electron donating component, p-DTS(FBTTh₂)₂, and an electron accepting component, PC₇₁BM [see Fig. 3(a) for chemical structures]. This type of photovoltaic blend has been shown to produce a power conversion efficiency as high as 8.9%.²⁷ OPV blends rely on a nanostructured active layer to promote charge separation at donor-acceptor interfaces. The interplay between miscibility, phase separation, and crystallization of the donor and acceptor components, however, leads to a complex film structure with poorly understood implications for charge transport.

Figure 3(b) shows a high-resolution hole mobility map of a p-DTS(FBTTh₂)₂:PC₇₁BM active layer, assembled from 16 002 current-voltage curves acquired in a nitrogen environment. The quality of the SCLC fit is characterized by an average R-squared of 0.9992. Interestingly, the hole mobility varies by less than a factor a three [see histogram in Fig. 3(c)], suggesting that the presence of the electron transporting component, PC₇₁BM, does not drastically hinder local out-of-plane hole mobility. Device-scale studies of organic semiconductor blends have shown similar results. For example, adding p-SIDT(FBTTh₂)₂ to PC₇₁BM at a 50:50 weight ratio only reduced the SCLC hole mobility from 1 × 10⁻³ cm²/V s to 4 × 10⁻⁴ cm²/V s.²⁸ It should be noted that, rather than traveling directly across the active layer, charge percolates through nanostructured OPV active layers via tortuous pathways. Thus, even though the nanoscale PC₇₁BM domains do not participate in hole transport, these areas can be circumvented to enable reasonably efficient hole transport. Figure 3(b) shows that C-AFM mobility mapping can detect small changes in mobility due to local variations in charge percolation.

Closer examination of the mobility map reveals a nanometer-scale domain structure in the p-DTS(FBTTh₂)₂:PC₇₁BM active layer. As shown in Fig. 3(d), features smaller than 10 nm can be discerned with the shown gap between two high mobility regions being 9 nm across. For the p-DTS(FBTTh₂)₂:PC₇₁BM mobility data, rather than using the DMT model, this 9 nm minimum feature size was used to estimate the probe-sample contact diameter.

As shown in Fig. 3(e), it is also possible to map the built-in potential, V_bi, by fitting the current-voltage curves to Eq. (3). V_bi plays an important role in organic electronic devices with asymmetric electrodes, impacting the turn-on voltage of organic light emitting diodes and setting an upper limit for open-circuit voltage in organic solar cells.^23,29 In the simplest case, V_bi is given directly by the work function difference between the contact electrodes. In practice, however, effects from charge accumulation, interface dipoles, or Fermi level pinning can lead to deviations from the ideal situation.^23,29,30 The average built-in potential of 0.76 V reasonably matches the expected value of 0.7 V based on the work function difference between the PEDOT:PSS/ITO substrate and the Pt AFM probe. As seen in the histogram in Fig. 3(f), local V_bi values range from as low as 0.4 V to as high as 1.1 V. Such non-uniformities will impact local charge injection and extraction in bipolar devices, affecting overall performance.²⁹ 

In summary, we have demonstrated high-resolution out-of-plane charge carrier mobility mapping of heterogeneous organic semiconductor films, providing insight into the effects of local crystal structure and composition on charge transport. First, we determined that the estimated probe-sample contact diameter has a limited impact on the measured charge carrier mobility. Hole mobility mapping of TES-ADT films showed strong contrast between semicrystalline and crystalline areas with the former exhibiting a granular structure and a modest hole mobility while the latter exhibited a uniform mobility that is nearly an order of magnitude higher. The hole mobility in an OPV active layer, p-DTS(FBTTh₂)₂:PC₇₁BM, exhibited a nanometer-scale domain structure with resolved features under 10 nm in size. Minor variations in the spatial dependence of the hole mobility indicate that the presence of the electron acceptor did not significantly interrupt local hole percolation in the blend. Built-in potential mapping showed substantial spatial variations which can impact local charge injection and collection. These results establish the potential of using C-AFM mobility mapping to quantitatively investigate nanoscale structure-function links in organic electronic systems and elucidate the nanoscale origins of device-scale performance.

See supplementary material for further experimental details and discussion of contact mechanics.

We gratefully acknowledge support from the National Science Foundation (CAREER Award No. DMR-1555028). Preliminary experiments were supported by the Binghamton University Smart Energy Transdisciplinary Area of Excellence. The authors acknowledge assistance from Jeremy Mehta with preparing photovoltaic active layer blends.