DOI:
10.1039/D5LF00104H
(Perspective)
RSC Appl. Interfaces, 2025, Advance Article
Modeling heterojunctions: a computational chemistry perspective
Received
14th April 2025
, Accepted 3rd June 2025
First published on 10th June 2025
Abstract
The design of heterojunction photocatalysts with enhanced photocatalytic performance is a key challenge. Computational chemistry is a valid strategy to access, with atomistic details, the nature of heterojunction-based materials. In this review, we revise and recall a series of important modeling aspects to account for in the modeling of heterojunctions, such as structural models (including lattice mismatch), band offsets, and interface polarization. Lattice mismatch is essential to be considered to avoid spurious effects. Band offsets determine the relative positioning of the band edges, which in turn indicates the way photogenerated charge carriers prefer to move. The charge polarization has an effect on efficient charge separation which instructs the unidirectional charge migration through the preferential migration path of photogenerated charge carriers. In general, we describe general concepts for designing heterojunction photocatalysts. Drawbacks and potential prospects are discussed to help the field in creating more effective photocatalysts.
 Mesfin Eshete | Mesfin Eshete is a research fellow at the Department of Materials Science, University of Milano Bicocca. He received his Ph.D. from the University of Science and Technology of China in 2020. His main research interests are structural and electronic properties of novel materials, electron dynamics at the surface and interface, and design of novel heterojunctions in energy conversion for application of photocatalysis, catalysis, perovskites and single-atom catalysis. |
 Giovanni Di Liberto | Giovanni Di Liberto received the PhD in Chemistry in 2019. He is a tenure-track assistant professor at the Department of Materials Science, University of Milano Bicocca, Italy. His research is devoted to the simulations of nanomaterials for catalysis. He was a visiting scientist at the University of Barcelona in 2019. He has obtained awards from the physical chemistry, theoretical and computational chemistry and catalysis divisions of the Italian Chemical Society over the past few years. |
1. Introduction
The need for overcoming or at least taming the need for fossil fuels has attracted a lot of attention.1–3 A possible way to contribute to solving this problem is the use of solar light to make reactions with photocatalysts.4–7 Investigating highly efficient and environmentally benign photocatalytic materials to convert water into hydrogen is promising for the creation of renewable energy and environmental cleanup.8–10 In order to accomplish this, current research has focused on thoroughly examining semiconductor photocatalysts with low cost, appropriate band gaps, and high durability to enhance the efficiency of solar-to-hydrogen energy conversion.11–13
Semiconductor photocatalysis is a promising and environmentally favorable technology.14–17 During excitation by UV or visible light, electrons are promoted from the valence band maximum (VBM) to the conduction band minimum (CBM), leaving holes in the valence band. The two photo-generated charge carriers can in principle promote reactions of interest. Several different oxides are used, such as TiO2,4,18 ZnO,19,20 Cu2O,21,22 and others.23,24 However, these materials often suffer from performance limitations due to two drawbacks: high band gap and fast charge carrier recombination. The fabrication of heterojunctions has been suggested to tame the limitations of single-phase semiconductors.25–28 In heterojunctions, it is possible to improve the separation of charge carriers by engineering the alignment of the band edges. Also, one component of the system can act as a sensitizer improving the absorption of visible light.14,29–31
Increased rates of charge migration and separation, and the use of a broad spectrum of solar light, lead to the improved photocatalytic efficiency of these devices. Key examples in this regard are TiO2/TiO2 and TiO2/BiVO4 junctions.32,33
Over the past ten years, numerous photocatalysts have been created and applied to a variety of reactions, including water splitting, wastewater treatment, and CO2 reduction.9,11,26,34 To deeply analyze the charge dynamics and mechanism of a heterojunction, one needs to focus on the materials synthesis and characterization techniques and also theoretical modeling.12,13,23 Recently, many techniques have been employed to boost the performance of photocatalytic materials, including doping, nanostructuring, semiconductor heterojunction formation, co-catalyst use, or a mix of these methods.9,12,31,35 For example, the formation of a metal–semiconductor Schottky junction can help the electron–hole separation, while the plasmonic effect of noble metals has been used to increase the light absorption of wide-band gap semiconductors.23,36,37 In general, design of heterojunction photocatalysts must consider: (1) appropriate band edge positioning of the VB and CB, (2) efficient charge separation of photoexcited electron–hole pairs upon light illumination and (3) chemical stability.15,34,38–40
In principle, heterojunctions can be classified as p–n junctions (type-I, type-II and type-III), Fig. 2, Z-scheme (including S-scheme), Fig. 3, and ternary heterojunctions, Fig. 4. In this context, the ability to create and design interfaces between various semiconductors allow a wide range of systems to be investigated. In such investigation, consideration of lattice mismatch with the two or more interface structures, the charge transfer mechanism, interface polarization, the nature of chemical bonds, the band gap and band edge positions are important aspects. Density functional theory (DFT)-based electronic structure computations are crucial in this setting.
The number of applications of heterojunctions is very vast, ranging from energy to environmental remediation. The potential of these systems has stimulated increasing interest, which can be clearly shown by scrutinizing the number of publications related to the field, Fig. 1a. Nowadays, thousands of publications are reported every year, related to CO2 reduction, water splitting, hydrogen generation and photodegradation of pollutants, Fig. 1b.
 |
| Fig. 1 (a) Bar graph presentation from Scopus on the number of publications from 2015 to 2024, using keywords “heterojunction + oxidation” and “heterojunction + reduction”. (b) Pie chart on the adopted keywords. | |
Quantum chemical calculations allow us to provide atomistic insight into the nature of heterojunction materials. The state-of-the-art approach is based on density functional theory (DFT). This tutorial review focuses on the designs with quantum chemical approaches for different semiconductor heterojunctions. In addition, a detailed emphasis is given to structural and electronic properties at the interface including the band edge position, band edge offsets, built-in electric field and charge polarization at the interface.
2. Different types of heterojunctions
2.1. Semiconductor–semiconductor (S–S) heterojunctions
Heterostructures are typically classified according to the relative alignment of the band edges. One can then refer to type I, type II, and type III heterostructures, Fig. 2. In the type-I junction, the valence band maximum (VBM) and conduction band minimum (CBM) of one component are within the band gap of the second unit composing the system, Fig. 2a. Photogenerated charge carriers will migrate (thermodynamically) toward the first phase. In a type-II junction, the band edges of one component are higher in energy than the second, Fig. 2b. If the VBM of one component is higher in energy than the CBM of the second unit, then a type-III junction is formed, Fig. 2c. In this type, photoinduced charges lose their energy while traveling long distance to reach their neighbor CB/VB. In type I (straddling band gap), high energy electrons and holes transfer to the same semiconductor, preventing photocatalytic activity.41,42 The type-II system is the ideal one for charge carrier separation, as photogenerated holes and electrons will be promoted to spatially separate in the different phases. In addition, the efficiency can also be enhanced by forming ternary heterojunction catalysts by integrating type II heterostructures with noble metals.43,44 Table 1 lists a series of possible type-II heterojunctions and their applications.
 |
| Fig. 2 Schematic diagrams of type I (panel a), II (panel b) and III (panel c) junctions. | |
Table 1 A summary of available experimental examples of heterojunctions
Model |
Type |
Application |
References |
CdS/Cu2O |
Type II |
H2 generation |
45 |
α-Fe2O3/ZnO |
Type II |
H2 production |
46 |
TiO2/BiOBr |
Type II |
Degradation of rhodamine B (RhB) and methyl orange (MO) |
47 |
BaTiO3/CuO |
Type I |
MO degradation |
48 |
ZnO/NiO |
Type II |
Degradation of RhB |
49, 50 |
SnO2/NiO |
Type II |
Degradation of RhB |
51 |
CuCo2O4/TiO2 |
Type II |
H2 evolution |
52 |
MoS2/WSe2 |
Type II |
H2 production |
53, 54 |
TiO2/Cu2O |
Type II |
H2 generation |
55–58 |
Cu3SnS4/BiVO4 |
Type II |
Degradation of methyl blue (MB) |
59 |
MoS2/ TiO2 |
Type II |
H2 generation, degradation of MB and acetone |
60 |
CdS/CuS |
Type II |
H2 production |
61 |
BiFeO3/ZnO |
Type II |
Photodegradation of 2,4-dichlorophenol and RhB |
62 |
ZnO/TiO2 |
Type II |
H2 production |
63 |
BiOBr/BiVO4 |
Type II |
Degradation of MB |
64 |
α-Fe2O3/CuPc |
Type II |
Photoreduction of CO2 |
65 |
SnO2/Bi2O3 |
Type II |
Degradation of RhB |
66 |
Ag3PO4/AgBr |
Type II |
Degradation of MB |
67 |
CdS/LaFeO3 |
Type II |
Degradation of MB, RhB, and MO |
68 |
CoP3/Ni2P |
Type II |
H2 production |
69 |
ZnO/CuO |
Type II |
Photodegradation of phenol |
70, 71 |
CuO/TiO2 |
Type II |
Degradation of MB |
72 |
TiO2/CeO2 |
Type II |
Oxidative degradation of crystal violet (CV) |
73 |
TiO2/CuS |
Type II |
H2 generation |
74 |
Fe2O3/Co3O4 |
Type II |
Overall water splitting |
75 |
WO3/MoS2 |
Type II |
Degradation of Congo red (CR) |
76 |
SnO2/CuO |
Type II |
Decomposition of MB |
77 |
ZnO/SnS |
Type II |
Degradation of MO and RhB |
78 |
The photocatalytic performance of S–S heterojunctions is limited by some drawbacks, even though better charge separation and enhanced photocatalysis are achieved. In particular, the charge carrier migration is accompanied by a partial loss of energy of the absorbed photons, which lowers the photocatalytic activity.
2.2. Z-scheme heterojunctions
Even though better charge separation is achieved in p–n heterojunctions, most of them fall to straddling band gaps (type I) (Fig. 2a). In such cases, both photogenerated electrons and holes migrate to the narrow band gap semiconductor, which leads to a high rate of recombination. On the other hand, type-II and type-III (Fig. 2b and c) junctions guarantee efficient charge separation onto distinct semiconductors.
In recent years, more complex systems have been proposed. Relevant examples are the so-called Z-scheme junctions. The Z-scheme combines two distinct photocatalysts with the help of a suitable shuttle redox couple, such as Fe3+/Fe2+ and IO3/I−. Compared to conventional one-step water splitting systems, visible light can be used more efficiently.79–82
Z-scheme heterostructures are depicted in Fig. 3a, where the three elements composing the system are reported, the two photocatalysts and redox couple in aqueous solution. When a photocatalyst (PS II) is photoexcited, the excited electrons migrate from the lower CB to the redox couple, which in turn transfers the electrons to the other semiconductor (PS I) and the electrons recombine with the holes formed at the VBM of PS I. As a result, holes will concentrate at the photocatalyst with a lower VBM, whereas electrons will accumulate on the photocatalyst with a higher CBM. This strategy allows increasing the redox power of the charge carriers.38,40,83 An alternative solution is to replace the redox couple with a metal.34,79,84,85 A list of Z-scheme heterojunctions reported in the literature is in Table 2.
 |
| Fig. 3 a) Schematic representation of the Z-scheme. b) Schematic representation of the S-scheme. | |
Table 2 A summary of available experimental examples of Z-scheme heterojunctions
Model |
Type |
Application |
References |
Fe2O3/ZnSe |
Z-scheme |
CO2 to CO photoconversion |
86 |
BiVO4/Cu2O |
Z-scheme |
CO2 reduction |
87, 88 |
CsPbBr3/BiOC |
Z-scheme |
CO2 reduction |
89 |
ZnIn2S4/BiPO4 |
Z-scheme |
Cr(VI) removal |
90 |
BiOBr/Bi2WO6 |
Z-scheme |
Degradation of tetracycline (TC) |
91 |
ZnIn2S4/TiO2 |
Z-scheme |
Overall water splitting |
92 |
TiO2/NiO |
Z-scheme |
H2 evolution |
93 |
Ag2O/Fe–TiO2 |
Z-scheme |
CO2 conversion into methane |
94 |
NiSe2/Co-CdS |
Z-scheme |
H2 evolution |
95 |
ZnO/Ag/Ag2WO4 |
Z-scheme |
Photoelectrochemical water oxidation |
96 |
Bi2WO6/Au/CdS |
Z-scheme |
CO2 reduction |
97 |
TiO2/Au/g-C3N4 |
Z-scheme |
CO2 reduction |
98 |
g-C3N4/Au/ZnO |
Z-scheme |
CO2 reduction |
36 |
g-C3N4/Au/SnS |
Z-scheme |
CO2 reduction |
99 |
Ag3PO4/Ag/GdCrO3 |
Z-scheme |
CO2 reduction |
100 |
BiVO4(010)/Au/Cu2O |
Z-scheme |
CO2 reduction |
101 |
WO3/Ag/GdCrO3 |
Z-scheme |
Photothermocatalytic toluene degradation and CO2 reduction |
102 |
TiO2/Cu/CaTiO3 |
Z-scheme |
H2 evolution |
103 |
g-C3N4/WO3/Ag |
Z-scheme |
Degradation of oxytetracycline hydrochloride |
104 |
BiOBr/Ag3PO4/Rgo |
Z-scheme |
Degradation of TC |
105 |
SnS2/RGO/g-C3N4 |
Z-scheme |
Degradation of organic dye |
106 |
SnS2/LaNiO3 |
Z-scheme |
Degradation of TC |
107 |
The efficiency of Z-schemes is highly dependent on the locations to the band positions of the VB of semiconductor 1 and the CB of semiconductor 2 relative to the redox potential of the AD species. This limits the combinations of semiconductors that can produce effective photocatalytic heterojunctions. Another possible approach is S-scheme heterojunctions, without a shuttle redox mediator as discussed here after.
2.3. S-scheme heterojunctions
A very special case of Z-scheme systems are the S-scheme junctions, Fig. 3b. In an S-scheme heterojunction, a critical role is played by the interface polarization. Indeed, if an interface dipole is generated with an appropriate orientation, it is possible to promote the spatial separation of charge carriers opposite to what happens to classical type-II systems. As a result, high energy electrons and holes separate in different semiconductors.39,40,108,109 Table 3 summarizes a few S-scheme heterojunctions applied in the literature.
Table 3 A summary of available experimental examples of S-scheme heterojunctions
Model |
Type |
Application |
References |
ZnCdS/ZnS |
S-scheme |
H2 evolution |
110 |
CdS/Mo2C |
S-scheme |
H2 evolution |
111 |
α-Fe2O3/CeO2 |
S-scheme |
H2 evolution |
112 |
α-Fe2O3/TiO2 |
S-scheme |
H2 evolution |
113 |
ZnIn2S4/NiTiO3 |
S-scheme |
H2 evolution |
114, 115 |
TiO2/ZnIn2S4 |
S-scheme |
H2 evolution |
116–118 |
ZnIn2S4/ZnWO4 |
S-scheme |
H2 evolution |
119 |
WO3/BiOBr |
S-scheme |
Degradation of TC and enrofloxacin (ENR) |
120 |
BiOI/TiO2 |
S-scheme |
Degradation of RhB |
121 |
Bi3TaO7/ZnIn2S4 |
S-scheme |
H2 evolution |
122 |
Co9S8/In2O3 |
S-scheme |
H2 evolution |
123 |
Co9S8/Bi2S3 |
S-scheme |
H2 evolution |
124 |
CdS/BiOIO3 |
S-scheme |
CO2 reduction |
125 |
Co3Se4/TiO2 |
S-scheme |
H2 evolution |
126 |
BiVO4/CeO2 |
S-scheme |
CO2 reduction |
127 |
TiO2/CdS |
S-scheme |
Overall water splitting |
128 |
ZnIn2S4/CdIn2S4 |
S-scheme |
CO2 reduction |
129 |
Cs2AgBiBr6/Bi2WO6 |
S-scheme |
CO2 reduction |
130 |
CsPbBr3/AgBr |
S-scheme |
CO2 reduction |
131 |
In4SnS8/Cs3Bi2Br9 |
S-scheme |
Photoreduction CO2 and CO selectivity |
132 |
ZnO/WO3 |
S-scheme |
H2O2 production |
133 |
WO3/ZnIn2S4 |
S-scheme |
H2 production |
134 |
MoS2/BiVO4 |
S-scheme |
Degradation of RhB |
135 |
BiVO4/Ag3VO4 |
S-scheme |
Degradation of MB |
136 |
Bi2S3/CeVO4 |
S-scheme |
Degradation for naphthalene (NAP) |
137 |
Cu2-xS/TiO2 |
S-scheme |
CH4 production |
138 |
MoS2/2D PbTiO3 |
S-scheme |
Degradation of MB |
139 |
MoS2/Ag3PO4 |
S-scheme |
Removal of RhB and ofloxacin (OFL) |
140 |
Bi2WO6/Bi2O3 |
S-scheme |
H2 production |
141 |
BiVO4/CsPbBr3 |
S-scheme |
CO2-to-CO conversion |
142 |
NiS2/MoSe2 |
S-scheme |
H2 evolution |
143 |
LaNiO3/TiO2 |
S-scheme |
Degradation of MO |
144 |
CeO2/ZnIn2S4 |
S-scheme |
H2 production |
145 |
In2S3/Bi2O2CO3 |
S-scheme |
Degradation of RhB and TC |
146 |
Cu3SnS4/L-BiOBr |
S-scheme |
Ciprofloxacin degradation |
147 |
TiO2/FePS3 |
S-scheme |
H2 production |
148 |
BiOBr/Bi2WO6 |
S-scheme |
CO2 reduction |
149 |
ZnIn2S4/WO3 |
S-scheme |
H2 production |
150 |
FeS2/ZnIn2S4 |
S-scheme |
H2 production |
151 |
AgBr/BiOBr |
S-scheme |
CO2 reduction and H2 production |
152 |
FeS2/S-ZnSnO3 |
S-scheme |
H2 evolution |
153 |
Bi2O2S/NiFe2O4 |
S-scheme |
Degradation of TC |
154 |
Bi2MoO6/BiOI |
S-scheme |
CO2 reduction |
155 |
BiFeO3/Bi2Fe4O9 |
S-scheme |
O-chlorophenol degradation |
156 |
CuWO4−x/Bi12O17Cl2 |
S-scheme |
Degradation of TC |
157 |
Cu2O/ BiOI |
S-scheme |
CO2 reduction |
158 |
In2O3/ZnO |
S-scheme |
CO2 reduction |
159 |
Ta3N5/BiOCl |
S-scheme |
Degradation of TC and Cr(VI) |
160 |
WO3/TiO2 |
S-scheme |
H2 production |
161 |
NiCo2S4/ZnIn2S4 |
S-scheme |
H2 production |
162 |
Co9S8/ZnSe |
S-scheme |
H2 production |
163 |
SnO2/SnS2 |
S-scheme |
Overall water splitting |
164 |
WO3/CuBi2O4 |
S-scheme |
CO2 reduction |
165 |
BaTiO3/TiO2 |
S-scheme |
Norfloxacin degradation |
166 |
WS2/BiYWO6 |
S-scheme |
Degradation of RhB |
167 |
Bi12O17Cl2/α-Bi2O3 |
S-scheme |
Degradation of TC |
168 |
BiOCl/MoS2 |
S-scheme |
Degradation of TC |
169 |
Ag3CuS2/VO2 |
S-scheme |
MB photodegradation and Cr(VI) photocatalytic reduction |
170 |
ZnS/CoMoO4 |
S-scheme |
H2 production |
171 |
CuCo2O4/CeO2 |
S-scheme |
CO2 reduction |
172 |
SnFe2O4/ZnFe2O4 |
S-scheme |
Degradation of TC |
173 |
Bi2Sn2O7/Bi2MoO6 |
S-scheme |
Degradation of TC |
174 |
2.4. Ternary heterojunctions
The discussion was limited to two-phase systems. Nowadays, it is possible to invoke more involved catalytic systems made by three (or more) components. In ternary heterojunction photocatalysts, three semiconductors can be combined to create direct Z-schemes. These photocatalysts are commonly referred to as “ternary Z-schemes” or “dual Z-schemes”. These systems promote spatial separation of electron–hole pairs, which favors reduction and oxidation reactions. In addition, it is possible to increase the absorption of visible light.35,38,175,176 A schematic representation of the alignment of the band edges of ternary heterojunctions is reported in Fig. 4. Typically, ternary heterojunctions are categorized as cascade-type (Fig. 4a), arrow-up (Fig. 4b) and arrow-down (Fig. 4c) Z-scheme systems.35
 |
| Fig. 4 Systematic representation of ternary heterojunctions. (a) Cascade type ternary heterojunction. (b) Arrow-down type ternary heterojunction. (c) Arrow-up type heterojunction. | |
In the case of the cascade Z-scheme, the excited electrons will concentrate toward the system with the highest CBM. At the same time, holes will follow an opposite path, concentrating to the system with the lowest VBM, Fig. 4a. In an arrow-down system, the holes in PS I and PS III's VBs join with the electrons in PS II's CB, as depicted Fig. 4b. In this ternary Z-scheme, the excited electrons from PS II combine with the holes in both PS III and PS I, thus favoring the oxidation on semiconductor PS II and reduction on PS III and PS I. The other type is an arrow-up Z-scheme ternary heterojunction. In this heterojunction, the excited electrons from the CB of PS I and PS III migrate and combine with the holes at the VB of PS II. Consequently, oxidation can take place on PS III and PS I while reduction on PS II, as depicted in Fig. 4c. A summary of typical ternary heterojunctions is reported in Table 4.
Table 4 A summary of available experimental examples of ternary heterojunctions
Model |
Type |
Application |
References |
TiO2/Ti3C2/g-C3N4 |
Cascade |
H2 production |
177 |
Cu2O/ZnO/Ag3PO4 |
Arrow-up |
Degradation of MO |
178 |
ZnS/ZnO/g-C3N4 |
Cascade |
H2 production |
179 |
Bi2S3/MoS2/TiO2 |
Cascade |
Degradation of MB and CO2 reduction |
180, 181 |
ZnO/CuO/CeO2 |
Arrow-down |
Degradation of CV and MO |
182 |
g-C3N4/ZnO/CeO2 |
Cascade |
Degradation of MB |
183 |
WO3/g-C3N4/WS2 |
Arrow-up |
Degradation of RhB and MO |
184 |
Bi2O3/CeO2/ZnO |
Arrow-up |
Degradation of RhB |
185 |
ZnO/NiWO4/Ag2CrO4 |
Arrow-down |
Degradation of MB, MO, and fuchsine |
186 |
ZnO/Bi2MoO6/AgBr |
Arrow-up |
Degradation of RhB |
187 |
ZnO/CoWO4/Ag3VO4 |
Arrow-down |
Degradation of RhB |
188 |
O–g-C3N4/Zn2SnO4N/ZnO |
Cascade |
Degradation of organic dyes and NO removal |
189 |
ZnO/ZnS/g-C3N4 |
Cascade |
H2 production |
190 |
ZnFe2O4/ZnO/CdS |
Cascade |
CO2 reduction |
191 |
CNT/NCDs/Ni2P |
Cascade |
H2 production |
192 |
MoP4/Ni3S2/MoO3 |
Arrow-up |
Overall water splitting |
193 |
g-C3N/Bi2WO6/AgI |
Arrow-up |
Removal of tetracycline |
194 |
g-C3N4/Bi4Ti3O12/Bi4O5I2 |
Arrow-up |
H2 production and ofloxacin (OFL) removal |
195 |
BiOCl/BiVO4/N-GQD |
Arrow-up |
Photodegradation of bisphenol A |
196 |
Ag3PO4/Co3(PO4)2/g-C3N4 |
Arrow-up |
Degradation of TC |
197 |
WSe2/In2S3/ZnIn2S4 |
Arrow-up |
Degradation of MB |
198 |
TiO2−x/BiOI/AgBr |
Arrow-up |
Degradation of RhB |
199 |
BiOBr/ZnO/BiOI |
Arrow-up |
Degradation of RhB |
200 |
Cu2O/S-TiO2/CuO |
Arrow-down |
CO2 conversion |
201 |
TiO2/ZnO/SnO2 |
Cascade |
Degradation of 2,4-dichlorophenol (2,4-DCP) and bisphenol A (BPA) |
202 |
CdS/1 T-MoS2/TiO2 |
Arrow-down |
H2 production |
203 |
TiO2/CdS/MoS2 |
Arrow-up |
H2 production |
204 |
Cu2O/WO3/CeO2 |
Cascade |
CO2 reduction |
205 |
ZnIn2S4/Ni12P5/g-C3N4 |
Cascade |
CO2 and H2O2 production |
206 |
g-C3N4/CuFe2O4/ZnIn2S4 |
Cascade |
CO2 reduction |
207 |
Bi2S3/β-Bi2O3/ZnIn2S4 |
Arrow-down |
H2 production and degradation of TC |
208 |
Ag2CO3/Bi4O5I2/g-C3N4 |
Arrow-down |
Degradation of TC |
209 |
MoS2/Bi2S3/BiVO4 |
Arrow-up |
Degradation of fluoroquinolones |
210 |
In2S3/Nb2O5/Nb2C |
Arrow-up |
H2 production |
211 |
2.5. 2D/2D heterojunctions
It has been shown that ultrathin 2D materials have special physical, chemical, and electronic properties. These properties include high carrier mobility, large specific surface area and unique optical band gaps.212–215
Two-dimensional (2D) heterojunctions have benefits for catalysis because of their large surface area, ultrathin thickness and short charge migration distance across the interface. In general, 2D interfaces maximize quantum efficiency, broadening the range of light absorption for improved photocatalytic activity compared to three-dimensional interfaces. Consequently, the creation and application of 2D/2D heterojunctions has quickly emerged as one of the most popular areas of study.216–222
It is possible to generate 2D/2D heterostructures using various contact interfaces oriented laterally or vertically as depicted in Fig. 5. By stacking two or more monolayers of various materials in a vertical direction, 2D/2D heterostructures with a face-to-face interface contact can be created, Fig. 5a and b. Alternatively, both paralleled and patterned connections, like the heterostructures in Fig. 5c and d, can be created in a lateral direction.223–226 A special case in the family of 2D-based heterojunctions is carbon nitride. Carbon nitride is one of the most promising metal-free photocatalysts for efficient utilization of sunlight. A comprehensive summary of typical g-C3N4 heterojunctions is shown in Table 5.
 |
| Fig. 5 Methodical representation of 2D/2D heterostructures with various contacts, face-to-face (a and b), lateral and parallel (c and d). Reproduced with permission.223 Copyright 1999–2025 John Wiley & Sons. | |
Table 5 A summary of available experimental examples of g-C3N4 heterojunctions
Model |
Type |
Application |
References |
g-C3N4/WO3 |
Type II |
CO2 reduction, Cr(VI) reduction and MB degradation |
227, 228 |
BiVO4/g-C3N4 |
Z-scheme |
Overall water splitting |
229, 230 |
g-C3N4/BiFeO3 |
Direct Z-scheme |
Overall water splitting |
231 |
g-C3N4/Bi2WO6 |
Z-scheme |
Ciprofloxacin photodegradation |
232 |
α-Fe2O3/g-C3N4 |
Direct Z-scheme |
Overall water splitting |
233 |
g-C3N4/TiO2 |
Type II |
Overall water splitting, degradation of diclofenac |
234–236 |
AgCl/g-C3N4 |
S-scheme |
H2 production |
237 |
MnCo2S4/g-C3N4 |
S-scheme |
H2 production |
238 |
BiOIO3/g-C3N4 |
Z-scheme |
Degradation of NO |
239 |
W18O49/g-C3N4 |
Direct Z-scheme/S-scheme |
Overall water splitting |
240–242 |
Bi4NbO8Cl/g-C3N4 |
Direct Z-scheme |
H2 evolution |
243 |
Cu2O/g-C3N4 |
Type II |
H2 production |
244 |
K4Nb6O17/g-C3N4 |
Z-scheme |
Organic pollutant removal and H2 production |
245 |
Bi2S3/g-C3N4 |
Z-scheme |
Photoreduction of CO2 to CO |
246 |
Ag3PO4/ g-C3N4 |
S-scheme |
O2 production and conversion of Cr(VI) to Cr(III) |
247 |
g-C3N4/Bi8(CrO4)O11 |
S-scheme |
Degradation of norfloxacin and BPA |
248 |
CoFe2O4/ g-C3N4 |
S-scheme |
Degradation of TC, amoxicillin, ciprofloxacin, and sulfamethoxazole |
249 |
Bi4V2O11/g-C3N4 |
S-scheme |
Photocatalytic antibiotic degradation |
250 |
Fe-g-C3N4/Bi2WO6 |
Z-scheme |
Degradation of TC |
251 |
MnCo2O4/g-C3N4 |
Type II |
H2 production |
252 |
WS2/g-C3N4 |
Type I |
H2 production |
253 |
CuInS2/g-C3N4 |
Direct Z-scheme |
H2 evolution |
254 |
Cu3P/g-C3N4 |
Type II |
H2 evolution |
255 |
LaCoO3/g-C3N4 |
Z-scheme |
Phenol degradation |
256 |
MnIn2S4/g-C3N4 |
Direct Z-scheme |
H2 evolution |
257 |
ZnSe/g-C3N4 |
Type II |
H2 evolution |
258 |
g-C3N4/SnS |
Type II |
Reduction of aqueous Cr(VI) |
259 |
g-C3N4/Ag3PO4 |
Z-scheme |
Degradation of TC and dye |
260 |
g-C3N4/BiOBr |
Type II |
Oxidation of NO and reduction of CO2 |
261 |
Fe2O3/g-C3N4 |
Direct Z-scheme |
H2 evolution |
262 |
O-g-C3N4/B-RGO |
Type II |
H2 evolution |
263 |
g-C3N4/Nb2O5 |
Type II |
Degradation of RhB and phenol |
264 |
g-C3N4/C-doped BN |
Direct Z-scheme |
H2 evolution |
265 |
g-C3N4/MnO2 |
Z-scheme |
Dye degradation and phenol removal, overall water splitting |
266, 267 |
CdS/g-C3N4 |
Z-scheme |
H2 production |
268 |
CoO/g-C3N4 |
Type II |
Evolution of H2 and O2 |
269 |
O–C3N4/SnS2 |
S-scheme |
H2 evolution |
270 |
ZnO/g-C3N4 |
S-scheme |
Degradation of MB |
271 |
NiSe2/g-C3N4 |
Type II |
CO2 reduction |
272, 273 |
TiO2/g-C3N4 |
Z-scheme |
Degradation of RhB |
274 |
CoNi2S4/g-C3N4 |
Type II |
Evolution of H2 and O2 |
275 |
TiO2/g-C3N4 |
Type II |
Degradation of MB, decomposition of fluorescein |
276, 277 |
BiOBr/g-C3N4 |
S-scheme |
Degradation of RhB |
278, 279 |
g-C3N4/Bi12O17Cl2 |
S-scheme |
CO2 reduction |
280 |
Cu2O/g-C3N4 |
S-scheme |
Oxidation TC, reduction of Cr(VI) and H2 evolution |
281 |
CoWO4/g-C3N4 |
S-scheme |
H2 production |
282 |
Co3O4/ g-C3N4 |
S-scheme |
Degradation of TC |
283 |
NiCo2O4/g-C3N4 |
S-scheme |
H2 production |
284 |
Bi3NbO7/g-C3N4 |
S-scheme |
CO2 reduction |
285 |
g-C3N4/Bi2MoO6 |
S-scheme |
Degradation of phenol and H2 evolution |
286 |
g-C3N4/CoTiO3 |
S-scheme |
H2 production |
287 |
Ni5P4/g-C3N4 |
S-scheme |
H2 production and carbamazepine degradation |
288 |
g-C3N4/Nb2O5 |
S-scheme |
CO2 reduction |
289 |
g-C3N4/MoO3−x |
S-scheme |
H2 evolution |
290 |
WO3/g-C3N4 |
S-scheme |
H2 evolution |
291 |
CdS/g-C3N4 |
S-scheme |
Overall water splitting |
292 |
ZnO/g-C3N4 |
S-scheme |
H2O2 production |
293 |
g-C3N4/TiO2 |
S-scheme |
Degradation of MB and RhB |
294 |
3. How to model an interface
3.1. Importance of structural engineering
The design of suitable interface models is a crucial step in the construction of heterojunctions. When modeling an interface, one needs to accommodate two different material surfaces in the same simulation cell. This introduces an unavoidable lattice mismatch, i.e. the lattice parameters of the interface do not correspond exactly to those of the independent units. Ideally, a well-designed interface should have the smallest possible lattice mismatch. Importantly, the electronic structure of the heterostructure is affected by the strain at the interface that resulted from the lattice mismatch.23,26,295 A good practice always consists of a checking post-process, i.e. after geometry optimization of the interface model that the lattice mismatch of the independent units does not alter their electronic structure, such as the band gap and band edge positioning. Typically, it is considered acceptable if the lattice mismatch induces changes in band edges and the band gap within 0.1 eV. Typically, it is possible to achieve a small lattice mismatch by invoking a rotational angle between the two composing units. For instance, the interface between two stable BiOIO3 surfaces, (010) and (100), can be obtained with a relatively small lattice mismatch, lower than 2% for both a and b lattice parameters with good cation–anion matching achieved by rotating the two surfaces by 90 degrees. The impact of lattice mismatch is very small, about 0.1 eV.296,297
The introduction of lattice mismatch comes from the need for designing an a priori suitable working simulation cell for the heterostructure. A better-grounded approach consists of avoiding the need for introducing lattice mismatch. This is possible by invoking unconstrained energy mapping of material interfaces. Among the possible strategies, Fig. 6 reports the case of the “rotating nanodisk” approach. In this framework, disk-shaped nanoparticles of separated units are generated, and they are interfaced by sampling three different degrees of freedom: the in-plane displacement, s = (sx,sy), and the rotational angle, α. In this way, it is possible to sample the energy landscape of heterostructures, and if the size of the disks is sufficiently large, typically a radius of 2.5 nm is a good trade-off; the effect of lattice mismatch is not sizeable. It must be mentioned that free-fitted potential energy surfaces or force fields are needed to sample the energy landscape, and therefore the resulting structures must be used as starting points for more elaborated geometry optimizations with quantum chemical approaches.298
 |
| Fig. 6 Systematic approach to exploring disk interface models for the TiO2 anatase (101)/(001) interface. (a) Two disks are cut from the TiO2 (101) and (001) reference slabs. (b) The two disks are orientated with their (101) and (001) surfaces facing each other after being translated by s. (c) Rotation of the (001) disk relative to the (101) disk at angle α. (d) An illustration of a typical anatase disk. Reproduced with permission.298 Copyright 2022. | |
Another important and more subtle aspect in the modeling of interfaces is the surface termination. When combining two materials and creating an interface, the nature of the interaction strongly depends on the surfaces considered. In some cases, the effect determines the type of alignment of the band edges. The key example is the BiVO4/TiO2 heterojunction. Compelling experimental evidence was reported suggesting that the photocatalytic performances of TiO2/BiVO4 heterojunctions vary upon the exposure of the facet, Fig. 7. More specifically, the TiO2(101)/BiVO4(110) interface outperforms the TiO2(101)/BiVO4(010) one.299 Quantum chemical calculations showed that the BiVO4 band edges are higher than those of TiO2 in the TiO2(101)/BiVO4(110) interface leading to a type II alignment. If BiVO4(010) is considered, then the system is predicted to have a type-I alignment.
 |
| Fig. 7 (a) and (b) Schematic representation for the band alignment of TiO2 (101) and BiVO4 (010) with two different hybrid functionals. (c) and (d) Schematic representation for the band alignment of TiO2 (101) and BiVO4 (110). Reproduced with permission.299 Copyright 2020, IOP Publishing Ltd. | |
Similar theoretical studies have been reported for Si/anatase TiO2,300 GaN/black phosphorus,301 and ZnO/BeCdO heterojunctions.302 The matching of the interface is so important, such that in some cases, the way the two units are terminated determines the properties of the interface. For instance, quantum chemical calculations showed that the BiOIO3(010)/(100) surface junction cannot be made by the direct interaction of the two most stable terminations of the two surfaces.296 This would lead to a band alignment not compatible with experimental evidence, Fig. 8. In this case, the formation of the interface leads to the formation of new chemical bonds, promoting a metastable termination of one surface. This allows reconciling the electronic structure of the material with its photoactivity.
 |
| Fig. 8 Systematic representation of band alignment for BiOIO3 interfaces with different surface terminations: (a–c) model I, model II and model III interfaces. Labeling of atoms: orange: Bi; red: O; purple: I. The two nanostructures that make up the mixed systems are distinguished by their light blue and orange areas. The experimental CBM is indicated by the horizontal dashed line. Reproduced with permission.296 Copyright 1999–2025 John Wiley & Sons. | |
Crucially, strain engineering is also employed to adjust and enhance a range of material characteristics in order to control the electrical characteristics and promote charge separation across the heterojunction.303–305 For instance, the calculations of Yang et al. showed a negligible effect (less than 0.1 eV in total energy) of a 5% compressive strain of the MoS2/ZnO heterojunction. The finding also shows that with increasing tensile biaxial strain, the spectrum's absorption edge gradually moves to the infrared region, while compressive biaxial strain causes the spectrum to blue-shift.306 In another study, Quan Li et al. constructed bilayer and trilayer heterojunctions of WS2/C2N, WS2/C2N/WS2, and C2N/WS2/C2N in which biaxial strain can affect the band gap.307
On the other hand, the buffer layer mechanism is also an important strategy to improve photocatalytic activity in heterojunctions.308,309 Recently, Nguyen Dinh Lam et al. proposed a p-Si/p-CuO buffer layer/n-ZnO heterojunction, where the addition of a 250 nm thick CuO buffer layer is beneficial for the activity. In addition, the pseudo-order rate constant (k) was improved by up to 12% in comparison with the p-Si/n-ZnO composite film.310 Similar studies focused on CZTSSe/Zn(O,S),311 ZnO/ZnS/g-C3N4,190 and ZnO/CuO/g-C3N4.312
4. Electronic properties
In the construction of an interface, first-principles investigation plays an important role in determining electronic properties such as charge separation, band offsets and interface polarization.
4.1. Band edges and band offsets
In the modeling of an interface, the evaluation of the band offsets is essential. This allows determining the nature of the band edge alignment. The most popular method relies on the electrostatic potential line-up approach, which calculates the plane-averaged electrostatic potential (V) of the heterostructure and separated components. The conduction band minimum (CBM) and valence band maximum (VBM) of the composing units are then aligned using the macroscopic average or stationary points of V as a common reference.308,313,314 An alternative approach uses as a reference core energy levels of specific atoms.315,316
More specifically, the VBM and CBM of the bulk composing units (VBM1, CBM1) and (VBM2, CBM2), are aligned using a common reference, which can be taken as the macroscopic average of V, the band offsets are defined as:
|
VBO = (VBM1 − 1) − (VBM2 − 2) − ( Het1 − Het2)
| (1) |
|
CBO = (CBM1 − 1) − (CBM2 − 2) − ( Het1 − Het2)
| (2) |
where
1 and
2 are the macroscopic averages of the separated components, and
Het1 and
Het2 are the same for the composite model. Importantly, the electrostatic potential may display oscillations introducing some uncertainty, and its convergence should be checked, especially in the case of insufficiently thick models.
A very similar approach has been proposed by Conesa, and is based on the use of the stationary points of the electrostatic potential.317 This method allows also overcoming the problem of the potential convergence. In this case, one does not need to evaluate the macroscopic average of the electrostatic potential since the stationary points, as the maxima, are directly taken as a reference.317
The band offsets can be calculated also by defining other common references, such as the energy of the core levels, e.g. the 1s orbitals, E1s.315,318 Core level energies are usually adopted as a reference in XPS measurements.315,318–324 In this case,
1 and
2 are replaced with E1,1S and E2,1S, and
Het1 and
Het2 with EHet1,1S and EHet2,1S. The band offsets become:
|
VBO = (VBM1 − E1,1S) − (VBM2 − E2,1S) − (EHet1,1S − EHet2,1S)
| (3) |
|
CBO = (CBM1 − E1,1S) − (CBM2 − E2,1S) − (EHet1,1S − EHet2,1S)
| (4) |
By using core levels, it is possible to avoid the calculations of a plane-average electrostatic potential. This allows the methodology to be applied to both thick surfaces and ultrathin films. The energy of the core levels must be carefully considered because it is dependent on the chemical environment, and it may be necessary to properly compute the shifts in order to account for the relaxation of charged cells.
325–327 This contribution, which introduces an inevitable uncertainty, is typically overlooked. Illas and co-workers have thoroughly examined the precision of core level binding energies using PAW-based computations, in which the atomic cores are maintained frozen.
325
Fig. 9 reports the case of the SrTiO3(001)/TiO2(001) interface, where the calculated valence band offset (VBO) changes from 0.28 to 0.37 eV and the conduction band offset (CBO) from 0.03 to 0.14 eV compared to the isolated slab (depicted in Fig. 9a and b).
 |
| Fig. 9 Band offsets for the SrTiO3/TiO2 scheme where TiO2(001) is in contact with a SrO layer of SrTiO3(001). (a) Individual slabs. (b) The result obtained from the heterojunction model. Reproduced with permission.319 Copyright 2020 AIP Publishing LLC. | |
In another combined experimental and theoretical heterojunction investigation on WO3(001)/BiVO4(010), the heterojunction forms a stable interface with favorable band alignment and smooth charge transfer due to small lattice mismatch at the interface, which allows us to attain high efficiency. Similar work has been applied to ZnCoMOF/g-C3N4,328 N-ZnO-g-C3N4,329 and g-C3N4/ZnIn2S4.330
4.2. Interface polarization
In the construction of S-scheme heterojunctions, interface polarization at the junction plays an important role in efficient charge separation. Engineering a semiconductor heterojunction in consideration of an internal electric field allows clearly identifying the route for charge transfer for efficient charge separation to minimize the recombination.331–335
The fundamental principle of heterojunction modeling between semiconductors is based on two different semiconductors which are directly in contact. As an example, shown in Fig. 10a, a positive charge is left behind by each electron from the n-type semiconductor that diffuses into the p-type semiconductor; a negative charge is left behind by a hole that migrates from the p-type semiconductor to the n-type semiconductor. Diffusion of electrons and holes persists until the system reaches equilibrium. Consequently, a charged area known as the “internal electric field” develops near the p–n contact. As depicted in Fig. 10b, upon sunlight illumination, the photoinduced electrons migrate from a higher CB to a lower CB and holes transfer from a low VB to a high VB which is facilitated by formation of an internal electric field (IEF) which further keeps the e–h pairs well separated.23,25
 |
| Fig. 10 (a) Diagram showing a p–n junction between two semiconductors. (b) Electron–hole separation with an effect of the IEF in a type II p–n junction photocatalyst upon light illumination. | |
To make an example, Wang et al. reported a study on an S-scheme BiOBr(002)/NiO(200) heterojunction for CO2 photoreduction. NiO nanosheets with hierarchical porous structures result in enhanced light absorption due to their surface area increment. In addition, efficient charge separation is expected with the effect of electric field creation at the interface.
From the first-principles optimization, NiO possesses a band edge higher in energy and can be conceived as a reductive photocatalyst, while BiOBr with a lower band edge can be conceived as an oxidative photocatalyst. Workfunction computation and in situ irradiation X-ray photoelectron spectroscopy results show that the photoexcited electrons migrated from BiOBr to NiO through the S-scheme system, which results in strong redox ability and charge separation. When NiO and BiOBr come into contact, their electrons will move to BiOBr, Fig. 11a and b. At the interface, depletion thus leaves the interface polarized. As a result, a strong IEF that points from NiO to BiOBr is created.
 |
| Fig. 11 a) The band structure of BiOBr and NiO. b) Formation of an IEF between BiOBr and NiO. c) Electron transfer system of the BiOBr/NiO junction under visible light illumination. Reproduced with permission.336 Copyright 1999–2025 John Wiley & Sons. | |
Upon illumination of light, low energy photoexcited electrons in the CB of BiOBr will combine with low energy holes in the VB of NiO while preserving high energy holes and electrons of BiOBr and NiO, respectively, Fig. 11c. On the other hand, the CO2 photoreduction process takes place on the surface of NiO.336 Similar work can be found in GeC/SGaSnP335,337 and others.338 Additional studies on the effects of the IEF and interface polarization can be referenced from BiOCl/TiO2,339 C2N/α-In2Se3,340 CH3NH3PbI3/TiO2,341,342 CdS/WS2,343 BP/Bi2WO6,344 HCa2Nb3O10/g-C3N4,345 and MoO3–Bi4TaO8Cl.346
5. Conclusion and outlook
In this perspective, we presented a tutorial summary on the modeling of heterojunction materials with quantum chemical approaches. We first recalled the main archetypes of heterojunction-based materials by reporting a series of experimental studies. Then, we revised a series of fundamental ingredients to model heterojunctions. First, we discussed the crucial role of the interface model, focusing on the minimization of the lattice mismatch, the role of the surfaces in contact and their termination to the nature of the system including strain engineering and buffer layer creation. Once the importance of the structural model was analysed, we discussed how to determine the band offsets, which in turn determine the type of band edge alignment, the primary actors for improving the separation of charge carriers upon photoexcitation. Finally, we discussed the interface polarization, as the formation (and its direction) of an interface dipole can determine the nature of the heterojunction system.
Importantly, hybrid functionals are important to accurately determine the band gap and band edge positions for the individual semiconductors and also the heterojunction. Moreover, the lattice mismatch at the interface, which causes strain in the system, should be carefully taken into account while modeling a heterojunction. Electronic properties, such as band edges and offsets, and charge migration are all directly impacted by the lattice mismatch at the interface. In principle, one should work with the lowest possible lattice mismatch, ideally close to zero. If not possible, it is important to check for the spurious effects induced by the working strain.
Once the heterojunction model is obtained, other aspects like the direction of charge polarization must be considered. It is worth mentioning that the presence of buffer layers in certain systems can be utilized to change the band alignment's nature and charge polarization. In addition, considering strain engineering is important to manage the electrical characteristics and encourage charge space separation across the heterojunction. We finally highlight that the information extracted from heterojunction models is obtained from “nearly” ideal systems. A possible strategy to scale-up the computational models is to invoke multi-scale approaches to reduce the gap between the complexity of experiments and the theoretical models. We hope that this review could help in modeling novel heterojunction materials and existing ones for which atomistic explanation is still missing.
Data availability
The data reported in this manuscript can be found in the mentioned references. No new data were produced in this work.
Conflicts of interest
The authors declare no conflicts of interest.
Acknowledgements
We thank the COST Action 18234 supported by COST (European Cooperation in Science and Technology).
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