Calculated Hole Mobility Research Articles

Optical and Electronic Properties of p‐type Transparent Conductive Oxide Cs2Pb2O3: A Density Functional Theory Study

In this article, the properties of Cs2Pb2O3 have been investigated using the first‐principles method. It covers the relevant structural, stability, electronic properties, conductivity, and optical properties. The phonon spectra and elastic properties analysis show the stability of Cs2Pb2O3, band structure, density of states, charge density diagram, and bond populations are analyzed to show the electronic structure of the system more clearly. The calculated results indicate that considering spin‐orbit coupling (SOC) will reduce the band gap. The charge density diagram and bond populations indicate that the Cs–O bond is mainly ionic and the Pb–O bond is mainly covalent and partially ionic. The analysis of optical properties indicates good transparency, and the calculated hole mobility is 10.88 cm2 V−1 s−1, suggesting that it is a promising p‐type conductive oxide.

Promoting the carrier mobility of Nb2SiTe4 through cation coordination engineering

Ternary two-dimensional (2D) monoclinic Nb2SiTe4 has garnered significant attention for its potential applications in anisotropic photoelectronics. Yet, its intrinsic indirect bandgap nature and low hole mobility, attributed to the short Nb–Nb dimer configurations, hinder the efficient photogenerated carrier separation and transport. In this Letter, using density functional theory calculations, we demonstrate the interlayer intercalation of Si results in the formation of a metastable orthorhombic Nb2SiTe4 structure devoid of detrimental short Nb–Nb dimers. Notably, this Si intercalation leads to a remarkable reduction of hole effective masses of orthorhombic Nb2SiX4 (X = S, Se, and Te), a crucial factor for achieving high carrier mobility. Taking the orthorhombic Nb2SiTe4 monolayer as an example, the calculated hole mobility (>100 cm2 V−1 s−1) is comparable in magnitude to the respectable hole mobility observed in multiple layers of the monoclinic Nb2SiTe4. To simultaneously enhance electron and hole mobility, we establish a van der Waals junction between the monoclinic and orthorhombic Nb2SiTe4 structures, achieving high and comparable carrier mobilities. The Nb2SiTe4 junction exhibits a nearly direct bandgap of 0.35 eV, rendering it suitable for infrared light harvesting. Furthermore, carriers within the Nb2SiTe4 junction become spatially separated across different layers, resulting in an intrinsic built-in electric field, which is superior for efficient photo-generated charge separation and decreases the potential nonradiative carrier recombination. Our findings highlight the impact of cation coordination engineering on the electronic and optical properties of 2D Nb2SiTe4 and provide a feasible solution to achieve better carrier transport in low-dimensional photovoltaic functionalities.

Computational Approach for Molecular Design of Small Organic Molecules with High Hole Mobilities in Amorphous Phase Using Random Forest Technique and Computer Simulation Method

Abstract A molecular design system of small organic molecules was developed to realize high hole mobility in the amorphous phase by using the random forest (RF) technique and a computer simulation method. Since there was no accessible datasets of the hole mobilities in the amorphous phase, we have constructed a datasets of experimental hole mobilities for 321 organic molecules with calculated MO energies to utilize machine learning techniques for molecular design procedures. RF was applied to the machine learning technique using the constructed datasets. The optimized RF exhibited correlation coefficients of 0.885 and 0.764 for the training and testing datasets, respectively. The modified ChemTS to use optimized RF was adapted to design molecules with high hole mobilities. The successive conduction (SC) model that uses ab initio molecular orbital (MO) calculations and the Marcus theory was adapted to ensure the predicted mobilities. The generated molecules were verified to have high calculated hole mobility (the order of 10−2 cm2/Vs) owing to the highest transfer integral and lowest reorganization energy by the theoretical successive conduction (SC) model. The datasets and programs used in this work were publicly released on GitHub.

Janus dione derivatives: Novel high-mobility hole transport materials for perovskite solar cells

Developing efficient and stable hole-transporting materials (HTMs) is very important for improving the stability and increasing the power conversion efficiency of perovskite solar cells (PSCs). Herein, novel Janus dione based HTMs with X-shaped structure were investigated using quantum chemical calculations. The results showed that introducing appropriate groups on both sides of the core led to a suitable HOMO level, good optical properties, and satisfactory stability. Importantly, due to strong inter-molecular electronic coupling, the calculated hole mobility of JT6, is as high as 7.92 cm2 V−1 s−1, which is 50 times higher than that of Spiro-OMeTAD. Simulating the adsorption properties on perovskite material CH3NH3PbI3 has also shown that these high mobility HTMs are easy to adsorb on the surface of perovskite material and can achieve good charge transfer between surface layers. The present findings highlight the potential of Janus dione core based HTMs for efficient PSCs and provide a meaningful practice for the design of HTMs with controllable HOMO levels.

Electron and hole mobilities of GaN with bulk, quantum well, and HEMT structures

Electron and hole mobilities of GaN are calculated for three-dimensional (3D, bulk) and two-dimensional [2D, quantum well (QW), and HEMT] structures, including scattering processes of acoustic deformation potential, polar optical phonon, piezoelectric, ionized impurity, and so on. The calculated mobilities for 2D structures are strongly dependent on quantum well structures and impurity densities, although the temperature dependence of the mobilities behaves in a similar way to bulk values. In the present analysis, energy band structures of GaN are calculated by the empirical pseudopotential method including spin–orbit interaction, and then the electron effective mass of the conduction band and the hole effective masses of the valence bands are evaluated, which are used for the calculations of electron and hole mobilities. The calculated valence band structure of the heavy, light, and crystal field splitted valence bands reveal complicated dispersion due to the spin–orbit interaction. The obtained electron effective mass mc=0.145m is isotropic, and the heavy hole effective mass in the c∥ plane is mhh∥=1.20m, while in the c⊥ plane, the band edge effective mass is mhh0⊥=0.55m and the over all fitted heavy hole effective mass is mhh⊥=1.20m. The light hole effective masses are mlh∥=1.35m and mlh⊥=0.165m. Both of the electron and hole mobilities are limited by ionized impurity scattering at low temperatures and by polar optical phonon scattering at high temperatures. Calculated electron mobilities are 7100 cm2/Vs for bulk, 4600 cm2/Vs for high electron mobility transistor (HEMT), and 3600 cm2/Vs for QW at room temperature and calculated hole mobilities are 450 cm2/Vs for bulk, 450 cm2/Vs for HEMT, and 500 cm2/Vs for QW at room temperature. All the expressions for scattering rates and respective mobilities are derived for 3D and 2D (QW and HEMT) structures and enable readers to calculate electron and hole mobilities in different structures with parameters given in the table or modified ones.

Effects of thermal expansion and degeneracy on ambipolar carrier mobility of non-peripherally hexyl-substituted phthalocyanine

The origin of the negative temperature dependence of carrier mobility in a crystal phase of 1,4,8,11,15,18,22,25-octahexylphthalocyanine was studied by utilizing a charge transport simulation based on Marcus theory and density functional theory. In order to understand the unique negative temperature dependence of carrier mobility, the theoretical calculation was carried out by taking the thermal expansion of the lattice parameters into consideration. The calculated hole mobility exhibited the similar temperature dependence as the experimental results. In the electron mobility calculation, the negative temperature dependence could be simulated by considering the degeneracy of lowest unoccupied molecular orbitals as well as the thermal expansion.

Effect of π-linker extension on property of fluorene-based hole-transporting materials for perovskite solar cells

As π-linkers, conjugated bithiophene and trithiophene are respectively introduced into hole-transporting materials (HTMs) V86-2T and V86-3T to substitute thiophene core of V862. The influence of extended π-linkers on the electronic properties and spectral properties were investigated by employing the density functional theory (DFT). The results indicate that the obvious red-shifted, wide UV–Vis absorption range and high absorption strength are achieved. To further understand the effect of increasing thiophene rings of π-linker in HTMs on the hole transport properties in perovskite solar cells (PSCs), the hole mobility of HTMs was evaluated quantitatively by Marcus theory and Einstein relation. The calculated hole mobility of V86-2T is the largest relative to V862 and V86-3T due to the more efficient intermolecular π-π stacking. The V86-2T is likely to be a promising high performance HTMs because of its excellent hole mobility, solubility and hydrophobic property, which may significantly improve the photovoltaic performance of PSCs.

Machine-Learning Guided Quantum Chemical and Molecular Dynamics Calculations to Design Novel Hole-Conducting Organic Materials.

Materials exhibiting higher mobilities than conventional organic semiconducting materials such as fullerenes and fused thiophenes are in high demand for applications such as printed electronics, organic solar cells, and image sensors. In order to discover new molecules that might show improved charge mobility, combined density functional theory (DFT) and molecular dynamics (MD) calculations were performed, guided by predictions from machine learning (ML). A ML model was constructed based on 32 values of theoretically calculated hole mobilities for thiophene derivatives, benzodifuran derivatives, a carbazole derivative and a perylene diimide derivative with the maximum value of 10-1.96 cm2/(V s). Sequential learning, also known as active learning, was applied to select compounds on which to perform DFT/MD calculation of hole mobility to simultaneously improve the mobility surrogate model and identify high mobility compounds. By performing 60 cycles of sequential learning with 165 DFT/MD calculations, a molecule having a fused thioacene structure with its calculated hole mobility of 10-1.86 cm2/(V s) was identified. This values is higher than the maximum value of mobility in the initial training data set, showing that an extrapolative discovery could be made with the sequential learning.

A type-II GaSe/HfS2 van der Waals heterostructure as promising photocatalyst with high carrier mobility

In this paper, the electronic, optical, and photocatalytic properties of GaSe/HfS2 heterostructure are studied via first-principles calculations. The stability of the vertically stacked heterobilayers is validated by the binding energy, phonon spectrum, and ab initio molecular dynamics simulation. The results reveal that the most stable GaSe/HfS2 heterobilayer retains a type-II alignment with an indirect bandgap 1.40 eV. As well, the results also show strong optical absorption intensity in the studied heterostructure (1.8 × 105 cm−1). The calculated hole mobility is 1376 cm2 V−1 s−1, while electron mobility reaches 911 cm2 V−1 s−1 along the armchair and zigzag directions. By applying an external electric field, the bandgap and band offset of the designed heterostructure can be effectively modified. Remarkably, a stronger external electric field can create nearly free electron states in the vicinity of the bottom of the conduction band, which induces indirect-to-direct bandgap transition as well as a semiconductor-to-metal transition. In contrast, the electronic properties of GaSe/HfS2 heterostructure are predicted to be insensitive to biaxial strain. The current work reveals that GaSe/HfS2 heterostructure is a promising candidate as a novel photocatalytic material for hydrogen generation in the visible range.

Studies of band structures and electrical properties of uniaxially strained phosphorene by a simplified two-band k·p method

The band structures throughout the entire Brillouin zone of uniaxially strained phosphorene were calculated by diagonalizing a simplified two-band k·p Hamiltonian matrix. The simplified two-band k·p matrix was established as strain perturbation matrix employing the k·p approximation, while the parameters were obtained from the intrinsic band structures and electrical properties of monolayer phosphorus calculated by the first principle. The band structures and effective mass under uniaxially tensile strain along the armchair and zigzag directions were also calculated. It shows that the increasing of the effective mass with tensile strain is anisotropic, which is higher along the strain direction. The tensile strain along x direction is conducive to adjust the band gap, effectively reduce the effective mass of holes in zigzag direction to significantly enhance the carrier mobility, thus it can be used to modify the electrical properties of phosphorene. The calculated hole mobility in zigzag direction with 4% at 300 K was up to 26 900 cm2 V−1 s−1. Thus, strain engineering along armchair direction is an efficient method to improve the carrier mobility for phosphorene.

Self-catalyzed growth of GaSb nanowires for high performance ultraviolet-visible-near infrared photodetectors

A simple self-catalyzed chemical vapor deposition process was conducted to synthesize single-crystalline GaSb nanowires, where Ga droplets were utilized as the catalysts. The as-grown GaSb nanowires exhibited typical p-type semiconductor behavior with the calculated hole mobility of about 0.042 cm2 V−1 s−1 The photoresponse properties of the GaSb nanowires were studied by fabricating nanowire photodetectors on both rigid and flexible substrates. The results revealed that the photodetectors exhibited broad spectral response ranging from ultraviolet, visible, to near infrared region. For the device on rigid substrate, the corresponding responsivity and the detectivity were calculated to be 3.86×103A W−1 and 3.15×1013 Jones for 500 nm light, and 7.22×102A W−1 and 5.90×1012 Jones for 808 nm light, respectively, which were the highest value compared with those of other reported Ga1−xInxAsySb1−y structure nanowires. Besides, the flexible photodetectors not only maintained the comparable good photoresponse properties as the rigid one, but also possessed excellent mechanical flexibility and stability. This study could facilitate the understanding on the fundamental characteristics of self-catalyzed grown GaSb nanowires and the design of functional nano-optoelectronic devices based on Gasb nanowires.

Understanding the impact of polymorphism on the electronic structures and charge transport properties of contorted hexabenzocoronene

Organic semiconductors with polymorphism characteristics have been attracted increasing attention for their great importance on disclosing the structure-property relationship of organic solids. The impact of polymorphism on the electronic structures and charge transport properties of contorted hexabenzocoronene (c-HBC) is explored based on density functional theory (DFT) method combined with Marcus electron transfer theory. The geometry structures, reorganization energies, frontier molecular orbitals, ionization energies, electronic affinities, crystal packing motif, transfer integrals as well as charge carrier mobilities of three polymorphs are investigated to establish the relationship between the structure and property. The results show that the polymorphism has little influence on the optimized geometry structures, reorganization energies, and the distribution of the frontier molecular orbitals. The reorganization energies of hole and electron for the three polymorphs are small, which are 0.11 and 0.15 eV, respectively. However, the crystal packing arrangements and the transfer integrals of the three polymorphs are significantly different, leading to different charge carrier mobility. All the three polymorphs show high hole mobilities, indicating that they could be used as p-type semiconductors. Specially, for polymorph II, the calculated hole mobility is as high as 0.90 cm2V−1s−1. Meanwhile, the electron mobilities of polymorphs II and III are in the same order of magnitude with the hole mobilities, which are 0.47 and 0.17 cm2V−1s−1, respectively. Due to the high hole and electron mobilities of polymorph II, it may be used as a bipolar transport semiconductor.

Multiscale modeling of charge transfer in polymers with flexible backbones.

In order to evaluate the carrier transfer properties in polymers with flexible backbones, we have proposed a simplified multi-scale modeling approach combining molecular dynamics simulations, first-principles calculations and kinetic Monte Carlo simulations. Hole transfer in amorphous polyethylene (PE) is studied as a model system. It is shown that the characteristic length scale of hole localized states in PE is comparable to the Kuhn length of PE, which is the characteristic length scale in terms of the geometric structure. Because a PE oligomer whose length is equivalent to the Kuhn length (C12H26) has a similar electronic structure to amorphous PE, C12H26 is considered as an approximate model of amorphous PE. In line with experimental findings, computed hole mobility in the amorphous PE oligomer is several orders of magnitude smaller than that in crystalline PE. We show that this difference originates from strong hole localization and large site energy variation in amorphous PE due to the conformational disorder of PE oligomer chains. The agreement between experimental and calculated hole mobilities strongly supports the rationale of our modeling approach. The modeling approach proposed in this paper is considered capable of predicting carrier mobilities in polymers with flexible backbones with reasonable computational load.

Design of two novel hole transport materials via replacing the core of spiro-OMeTAD with tetrathiafulvalene and tetraazafulvalene for application in perovskite solar cells

Two novel hole transport materials (HTMs) were designed by way of replacing the core of 2,2′,7,7′-tetrakis-(N,N-di-4-methoxyphenylamino)-9,9′spirobifluorene (spiro-OMeTAD) with tetrathiafulvalene (TTF) and tetraazafulvalene (TAF). The frontier orbitals, stability and solubility, reorganization energy, and hole mobility of the new materials were investigated via density functional theory (DFT) calculations in combination with the Marcus hopping model. Time-dependent density functional theory (TD-DFT) was also used for evaluating the optical properties including the absorption and emission spectra. It was found that the HOMO level of the two proposed HTMs (−5.25 and −5.20 eV) is lower than that of spiro-OMeTAD (−5.17 eV). The results showed that the maximum absorption band of the new designed HTMs with the TTF and TAF cores is blue and red-shifted compared to spiro-OMeTAD. This may indicate that these materials have no competition with the perovskite in absorbing light. Additionally, the hole reorganization energy is less than the electron reorganization energy for our structures, revealing these materials can act as HTMs more efficiently than electron transport materials. The calculated hole mobility of TAF- and TTF- OMeTAD was obtained as 4.41 × 10−4 and 1.15 × 10−6 cm2 v−1 s−1, respectively. This result indicates that TAF-OMeTAD shows a great potential for use as an alternative HTM for expensive spiro-OMeTAD.

Charge transport in organic molecular semiconductors from first principles: The bandlike hole mobility in a naphthalene crystal

Predicting charge transport in organic molecular crystals is notoriously challenging. Carrier mobility calculations in organic semiconductors are dominated by quantum chemistry methods based on charge hopping, which are laborious and only moderately accurate. We compute from first principles the electron-phonon scattering and the phonon-limited hole mobility of naphthalene crystal in the framework of ab initio band theory. Our calculations combine GW electronic bandstructures, ab initio electron-phonon scattering, and the Boltzmann transport equation. The calculated hole mobility is in very good agreement with experiment between 100$-$300 K, and we can predict its temperature dependence with high accuracy. We show that scattering between inter-molecular phonons and holes regulates the mobility, though intra-molecular phonons possess the strongest coupling with holes. We revisit the common belief that only rigid molecular motions affect carrier dynamics in organic molecular crystals. Our work provides a quantitative and rigorous framework to compute charge transport in organic crystals, and is a first step toward reconciling band theory and carrier hopping computational methods.

DFT and TD–DFT calculations of the electronic structures and photophysical properties of newly designed pyrene-core arylamine derivatives as hole-transporting materials for perovskite solar cells

The electronic structures and photophysical properties of three newly designed pyrene (PY) core arylamine derivatives as hole-transporting materials (HTMs) have been studied by DFT and TD–DFT methods. The modifications made in the arylamine wings of the well-studied and successful HTM PYC compound result in three HTMs designated as HTM1, HTM2, and HTM3. Four of the (methoxyphenyl)amine rings in PYC were replaced by (methoxyphenyl) thiophene (HTM1), (methoxyphenyl) furan (HTM2) and (methoxyphenyl) pyrrole (HTM3). The calculated HOMO and LUMO levels of HTMs 1–3 show proper energy matching and hole-injecting layer, indicating that the hole transports of the HTMs 1–3 compounds are very comparable with that of PYC. The matching of HOMO levels of HTM1 and HTM2 and the LUMO level of HTM3 is even better than that of PYC compound. The FMO analysis elucidated that the PY core acts as an electron withdrawal and contributes mainly to LUMO levels and the arylamine wings act as an electron-donating group and contribute mainly to HOMO levels. HTMs 1–3 show large Stokes shifts based on their absorption and emission spectra. Additionally, the hole reorganization energy is less than that of electrons. Thus, their hole mobility is better than their electron mobility. Furthermore, the ionization potentials, electron affinities, and hardness values were also calculated and compared to evaluate the performance of the newly designed HTMs. The nonlinear optical properties for the newly designed HTMs 1–3 have been investigated as they are correlated with the photoelectric conversion performance. We have also predicted the hole and electron mobility of molecules, and the calculated hole mobility values are better than the electron mobility, so it can be concluded that these materials would be competent hole transfer materials.

Understanding the Impact of Thiophene/Furan Substitution on Intrinsic Charge-Carrier Mobility

One of the major challenges in rationalizing the intrinsic influences of molecular fine tuning on charge transport in organic semiconductors is due to changes in molecular packing. Thus, it is, to a limited extent, desirable to elaborate materials to exhibit similar packing arrangements that slightly differ in their molecular structures. A molecular system, consisting of a heterocyclic core flanked by phthalimide end-capping units, is promising to overcome this issue. Previous XRD measurements have revealed that, when the bithiophene (bi-T) core was replaced by bifuran (bi-F), the molecular packing was largely maintained, while the resulting difference in charge transport was substantial, substituting bi-T with bi-F results in more than 1 order of magnitude increase in hole mobility (i.e., 1.7 × 10–3 vs 2.6 × 10–2 cm2/(V s)) with a loss in electron mobility (i.e., 0.21 vs 0.0 cm2/(V s)). The calculated hole mobilities with the MPW1K/TZ2P methodology are found to be lower for bi-T, as the reorganization en...

Theoretical investigations on electronic and charge transport properties of novel organic semiconductors – Triisopropylsilylethynyl(TIPS)-functionalized anthradifuran and anthradithiophene derivatives

Triisopropylsilylethynyl(TIPS)-functionalized polyacenes, a new family of novel organic semiconductors, have attracted extensive interests due to their high solubility, good air stability, and high performance in organic field effect transistors (OFETs). In present study, the electronic and charge transport properties of a series of chalcogen-doped TIPS-pentacene (PENT) derivatives have been studied by density functional theory (DFT). Their electronic structures, ionization energies, electron affinities, reorganization energies, transfer integrals of possible hopping pathways, hole and electron mobilities, and anisotropic mobilities have be calculated to discuss the role of various factors affecting the charge transport properties of these novel organic semiconductors. Fluorination and chlorination effects on the electronic properties and reorganization energies of the studied molecules have also been studied. The calculated results show that the fluorination and chlorination are efficient strategies for tuning the molecular orbital level to decrease the charge injection barrier from metal electrode and improve their oxidative stabilities. Though the fluorination indeed lowers the lowest unoccupied molecular orbital (LUMO) levels of TIPS-PENT derivatives, it also leads to much larger reorganization energies and smaller electron transfer integrals. Thus, it may be not an effective way for TIPS-PENT derivatives to convert a p-type semiconductor to an n-type one. Our calculated hole mobilities for available experiment crystal structures are in good agreement with the experimental observation. The computed hole mobilities for TIPS-anthradithiophene (ADT) and TIPS-teracenothiophene (TT) are 0.622 and 1.186cm2V−1s−1, respectively, which are in good agreement with the corresponding experimental values of 0.6 and 1.25cm2V−1s−1, respectively. Their relative calculated electron mobilities are 0.607 and 0.637cm2V−1s−1, respectively. The results show that they have high balanced hole and electron mobilities and may be promising candidates for ambipolar organic semiconductors. The studies on anisotropic mobilities of the selected derivatives show that they exhibit remarkable anisotropic behaviors and the hole and electron transfers along the parallel hopping pathway make the dominant contribution on their charge carrier mobilities.

The Carrier Mobility Obtained by Admittance Spectroscopy Using an Equivalent Circuit

A single-carrier hole-only device of ITO/MoO3/NPB/Al was used to measure the hole mobility of NPB layer, where NPB is a hole transport material. The hole mobility of NPB at different electric fields was obtained from the hole transit time (τdc) which was extracted from the negative differential susceptance (ΔB) as a function of frequency. To eliminate the impact of the contact resistance on the mobility measurement, an equivalent circuit model has been introduced to calculate the capacitance and the conductance of the NPB layer. By fitting the Nyquist plot of the impedance spectroscopy using the equivalent circuit, the contact resistance can be extracted from the impedance measurements. It is found that the mobility at low electric field is lower than what was reported in literature after the consideration of the contact resistance. It is also found that the calculated hole mobility of the NPB layer follows the Poole-Frenkels rule.

Effect of Strained $k \cdot p$ Deformation Potentials on Hole Inversion-Layer Mobility

In the literature dedicated to strained p-type metal-oxide-semiconductor field-effect transistor inversion-layer mobility calculation via a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> · <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> valence-band structure, three key strain-related material parameters, namely, the Bir-Pikus deformation potentials <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">υ</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> , and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> , were widespread in magnitude. To improve such large discrepancies, in this paper, we conduct sophisticated calculations on 〈110〉/(001) and 〈110〉/(110) hole inversion-layer mobility for gigapascal-level uniaxial stresses along each of three crystallographic directions. The screening effect on surface roughness scattering is taken into account. We find that, to affect the calculated hole mobility enhancement, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">υ</sub> is weak, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> is moderate, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> is strong, particularly for the uniaxial compressive stress along the 〈110〉 direction. This provides experimental guidelines for an optimal determination of the primary factor, i.e., <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> , and the secondary factor, i.e., <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> , with the commonly used values for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">υ</sub> . The result remains valid for varying surface roughness parameters and models and is supported by recent first-principles and tight-binding calculations. Thus, the strained <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> · <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> valence-band structure with the optimized deformation potentials can ensure the accuracy of the calculated transport properties of 2-D hole gas under stress.