Advancing the performance of a wide variety of energy conversion devices─from photovoltaic and photoelectrochemical to thermoelectric and electroluminescent─requires the fundamental development of semiconductor materials. The present day is an exciting time in this respect. Indeed, innovations with inorganic (e.g., oxide (1,2) or chalcogenide (3,4)), organic (e.g., conjugated polymer (5,6) or small molecule (7,8)), and hybrid (e.g., lead halide perovskites (9,10) or layered perovskites (11)) semiconductors have been recently highlighted in ACS Energy Letters. Excitingly, researchers are using the ever-advancing tools of chemistry and materials science to engineer improved semiconductor properties and develop new inexpensive synthetic routes. One key semiconductor property is the charge carrier mobility, μ, which relates the average velocity at which a charge carrier drifts through a material in response to an applied electric field, and is typically specified in units of cm² V^–1 s^–1. The value of the charge carrier mobility for electrons in the conduction band μ_e (or μ_n) or holes in the valence band μ_h (or μ_p) is critical to the performance of the material. Specifically, the electrical conductivity is proportional to the product of mobility and carrier concentration, and thus in general, higher mobility leads to better device performance─all else equal. Accordingly, accurate estimates of μ are routinely needed. While there are many approaches, (12) the use of the space-charge-limited current (SCLC) method is one of the most common due to its apparent accessibility. A thin film or slab of the semiconductor is simply sandwiched between two symmetric selective ohmic contacts, as shown schematically in Figure 1 for a p-type semiconductor, and the electrical current is measured as a function of the applied voltage. In an ideal semiconductor over a particular range of applied voltage, V, the measured current density, J, becomes limited by the space-charge formed by the charge carriers and can be described by the Mott–Gurney equation as(1)where ε is the permittivity of the semiconductor material. In principle, one needs only to fit the J–V curve region where J ∝ V², to extract an estimation of μ (as long as an accurate estimation of ε is available). Moreover, since the sandwich device geometry is similar to what is used for many applications (e.g., photovoltaic devices, photoelectrodes, and light-emitting diodes), the application of the SCLC technique is straightforward. This has led to its widespread adoption in research on contemporary semiconductors (e.g., conjugated polymers, (13) amorphous oxides, (14) and lead halide perovskites (15)). Figure 1. Electron energy schematic for an idealized p-type semiconductor layer with thickness, L, sandwiched between two electrodes with ohmic contacts. The conduction band, CB, and a valence band, VB, are also shown. The application of a voltage, V, between the electrodes creates an electric field, in the semiconductor and drives the majority charge carriers (holes, h⁺) to drift through the semiconductors at an average velocity v_d. However, when I read papers reporting the μ of a semiconductor estimated by the SCLC technique, I am often not convinced that the results are accurate. This is in part because there are many assumptions that are implied in the derivation of the Mott–Gurney equation that can lead to incorrect mobility estimations. Some common pitfalls were recently described, (16) and can include the presence of asymmetric contacts (even if made from the same metal (17)), electronic trapping states, (18) or mobile ions (which are particularly important for the lead halide perovskites (19)). I would like to take this opportunity to encourage researchers to routinely employ a drift-diffusion model to account for asymmetric contacts (open source code is available (20)) and use the pulsed-voltage method (15) to mitigate the effects of mobile ions, when appropriate. In addition, I would like to point out a straightforward step that can be employed to improve estimations of μ that is not performed often enough in my view: make replicate devices and vary the semiconductor layer thickness. Indeed, often I see reports where only one J–V curve is shown to support a measurement of μ. However, examining eq 1, it can be noticed that J is proportional to L^–3. Any error in estimating the semiconductor layer thickness will be significantly amplified. Concretely, a 10% error in L will lead to a 28% error in the estimated mobility, and a 20% error in L means that μ can differ from the true value by more than 50% (considering the common definition for percentage difference as the absolute value of the difference between two values, divided by their average ×100). Reporting replicates of device results (with standard deviations) are needed to understand the magnitude of this possible source of error. Given the accepted standard in the photovoltaic community to report many device replicates, this is uncomplicated to implement for SCLC measurements and should be standard practice. Just ensuring the accuracy of thickness measurements is not sufficient in my view since some of the pitfalls of this technique (e.g., the presence of asymmetric or non-ohmic contacts and the effect of substrate roughness) will still lead to inaccurate μ estimates because the assumptions of the Mott–Gurney equation are not satisfied. Preparing devices with different semiconductor layer thicknesses and verifying that the estimated value of μ does not change with thickness will give more confidence that the material under test approximately satisfies the implied assumptions of Mott–Gurney (and if not, a more sophisticated model should be employed). Moreover, examining films with larger L can strengthen claims that the material under test has a low trap density since the minimum trap density detectable in an SCLC diode is proportional to L^–2. (16) As this short text cannot fully describe all of the nuances of SCLC device modeling (especially the filling and distribution of electron traps), I would encourage readers to study refs (15−19). The work of Le Corre et al. (16) is an especially good place to start (no matter what semiconductor material of interest). To sum up, the SCLC method of estimating μ can be very straightforwardly applied, but since there can be many possible deviations that complicate the accuracy of simply fitting the Mott–Gurney model to the resulting J–V data, a standard practice of including results from many devices with different semiconductor thicknesses to give insights into the standard deviation and thickness dependence of the estimated charge carrier mobility would help improve the quality of the conclusions obtained with this technique. While some researchers already apply this level of rigor to their SCLC measurements, I hope that this can become standard practice in the field. I look forward to reading about many new inventions of novel semiconductors for energy conversion research in ACS Energy Letters in the years to come. This article references 20 other publications. This article has not yet been cited by other publications. Figure 1. Electron energy schematic for an idealized p-type semiconductor layer with thickness, L, sandwiched between two electrodes with ohmic contacts. The conduction band, CB, and a valence band, VB, are also shown. The application of a voltage, V, between the electrodes creates an electric field, in the semiconductor and drives the majority charge carriers (holes, h⁺) to drift through the semiconductors at an average velocity v_d. This article references 20 other publications.

中文翻译：

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使用空间电荷限制电流测量时改进电荷载体迁移率估计

提高从光伏和光电化学到热电和电致发光的各种能量转换装置的性能，需要半导体材料的基础性发展。在这方面，今天是一个激动人心的时刻。实际上，无机（例如，氧化物 (1,2) 或硫属化物 (3,4)）、有机（例如，共轭聚合物 (5,6) 或小分子 (7,8)）和混合（例如，铅）的创新卤化物钙钛矿 (9,10) 或层状钙钛矿 (11)) 半导体最近在ACS 能源快报中得到重点关注. 令人兴奋的是，研究人员正在使用化学和材料科学的不断进步的工具来设计改进的半导体特性并开发新的廉价合成路线。一个关键的半导体特性是电荷载流子迁移率 μ，它与响应于施加电场的电荷载流子在材料中漂移的平均速度有关，通常以 cm ² V ^–1 s ^–1为单位指定。导带 μ _e（或 μ _n）中的电子或价带 μ _h（或 μ _{p ）中的空穴的电荷载流子迁移率值}) 对材料的性能至关重要。具体来说，电导率与迁移率和载流子浓度的乘积成正比，因此一般来说，更高的迁移率会导致更好的器件性能——其他条件相同。因此，通常需要准确估计 μ。虽然有很多方法，但 (12) 空间电荷限制电流 (SCLC) 方法的使用是最常见的方法之一，因为它具有明显的可访问性。半导体的薄膜或平板简单地夹在两个对称的选择性欧姆接触之间，如图 1 中 p 型半导体的示意图所示，电流测量为所施加电压的函数。在一个理想的半导体中，在特定的施加电压范围内，V，测量的电流密度，J，受到电荷载流子形成的空间电荷的限制，可以用 Mott-Gurney 方程描述为(1)，其中 ε 是半导体材料的介电常数。原则上，只需拟合J-V曲线区域，其中J ∝ V ², 提取 μ 的估计（只要 ε 的准确估计可用）。此外，由于夹层器件的几何形状类似于用于许多应用（例如，光伏器件、光电极和发光二极管）的器件，因此 SCLC 技术的应用很简单。这导致它在当代半导体（例如共轭聚合物、（13）非晶氧化物、（14）和卤化铅钙钛矿（15））的研究中得到广泛采用。图 1. 理想化 p 型半导体层的电子能量示意图，其厚度为L，夹在两个具有欧姆接触的电极之间。还显示了导带 CB 和价带 VB。在电极之间施加电压V会产生电场，在半导体中并驱动多数电荷载流子（空穴，h ⁺）以平均速度v _{d漂移通过半导体}. 然而，当我阅读报告用 SCLC 技术估计的半导体 μ 的论文时，我常常不相信结果是准确的。这部分是因为在 Mott-Gurney 方程的推导中隐含了许多假设，这些假设可能导致不正确的流动性估计。最近描述了一些常见的缺陷 (16)，可能包括不对称触点的存在（即使由相同的金属 (17) 制成）、电子俘获态 (18) 或移动离子（这对于卤化铅特别重要）钙钛矿（19））。我想借此机会鼓励研究人员定期使用漂移扩散模型来解释不对称接触（开源代码可用（20））并使用脉冲电压方法（15）来减轻移动离子的影响， 在适当的时候。此外，我想指出一个简单的步骤，可以用来改进我认为不经常执行的 μ 估计：制作复制设备并改变半导体层厚度。事实上，我经常看到只有一个显示J-V曲线以支持 μ 的测量。然而，检查 eq 1，可以注意到J与L ^–3成正比。估计半导体层厚度的任何错误都会被显着放大。具体来说，L中 10% 的误差将导致估计移动性的 28% 误差，L中 20% 的误差意味着 μ 可以与真实值相差 50% 以上（考虑百分比差异的常见定义为两个值之间差异的绝对值，除以它们的平均值 ×100）。需要报告设备结果的重复（带有标准偏差）以了解这种可能的错误来源的大小。鉴于光伏界公认的报告许多设备重复的标准，这对于 SCLC 测量来说实施起来并不复杂，应该是标准做法。在我看来，仅仅确保厚度测量的准确性是不够的，因为这种技术存在一些缺陷（例如，由于不满足 Mott-Gurney 方程的假设，不对称或非欧姆接触的存在以及基板粗糙度的影响）仍将导致 μ 估计不准确。准备具有不同半导体层厚度的器件并验证 μ 的估计值不随厚度变化，这将使被测材料大致满足 Mott-Gurney 的隐含假设更有信心（如果不满足，则应采用更复杂的模型）。此外，检查具有更大 应采用更复杂的模型）。此外，检查具有更大 应采用更复杂的模型）。此外，检查具有更大L可以加强关于被测材料具有低陷阱密度的说法，因为在 SCLC 二极管中可检测到的最小陷阱密度与L ^–2成正比。(16) 由于这篇短文无法完全描述 SCLC 器件建模的所有细微差别（尤其是电子陷阱的填充和分布），我鼓励读者研究参考文献 (15-19)。Le Corre 等人的工作。(16) 是一个特别好的起点（无论感兴趣的半导体材料是什么）。总而言之，估计 μ 的 SCLC 方法可以非常直接地应用，但是由于可能存在许多可能的偏差，这使得简单地将 Mott-Gurney 模型拟合到所得到的J-V的准确性变得复杂数据，包括来自具有不同半导体厚度的许多器件的结果的标准做法，以深入了解估计的电荷载流子迁移率的标准偏差和厚度依赖性，这将有助于提高使用该技术获得的结论的质量。虽然一些研究人员已经将这种严格程度应用于他们的 SCLC 测量，但我希望这可以成为该领域的标准做法。我期待在未来几年中阅读ACS 能源快报中有关用于能量转换研究的新型半导体的许多新发明。本文引用了其他 20 种出版物。这篇文章尚未被其他出版物引用。图 1. 理想化 p 型半导体层的电子能量示意图，厚度为L，夹在两个具有欧姆接触的电极之间。还显示了导带 CB 和价带 VB。在电极之间施加电压V会在半导体中产生电场，并驱动多数电荷载流子（空穴，h ⁺）以平均速度v _d漂移通过半导体。本文引用了其他 20 种出版物。