A brief review of co-doping

Dopants and defects are important in semiconductor and magnetic devices. Strategies for controlling doping and defects have been the focus of semiconductor physics research during the past decades and remain critical even today. Co-doping is a promising strategy that can be used for effectively tuning the dopant populations, electronic properties, and magnetic properties. It can enhance the solubility of dopants and improve the stability of desired defects. During the past 20 years, significant experimental and theoretical efforts have been devoted to studying the characteristics of co-doping. In this article, we first review the historical development of co-doping. Then, we review a variety of research performed on co-doping, based on the compensating nature of co-dopants. Finally, we review the effects of contamination and surfactants that can explain the general mechanisms of co-doping.


Introduction
Doping is crucial for determining physical properties and applications of various materials, especially semiconductors. This notion has been confirmed by tremendously successful applications in semiconductor industry. Minor quantities of impurities determine the carrier concentrations and electrical conductivities of the materials. Fundamentally, a good dopant should achieve an ideal solubility in its host material and should exhibit a shallow defect level. However, there exist some fundamental doping bottlenecks, which strongly affect the device performance. In the case of wide band-gap materials, the problems are severe. For example, n-type doping was found to be difficult for high conduction-band minimum (CBM) energy; on the other hand, p-type doping was found to be difficult for low valence-band maximum (VBM) energy [1]. As a result, bipolar doping problems exist in many wide band-gap semiconductors, where either n-type or ptype dopants can be doped, but not both [2]. Therefore, a feasible solution is to simultaneously incorporate certain amounts of p-type and n-type dopants, for lowering their formation energy, which is also the fundamental principle of compensated co-doping.
Co-doping has been proposed for solving the problems of bipolar doping and compensation in semicon-ductors. In general, co-doping can be efficient for increasing the dopant solubility, increasing the activation rate by lowering the ionization energy of acceptors and donors, and increasing the carrier mobility [3]. Enhanced dopant incorporation is especially significant under nonequilibrium growth conditions owing to the introduction of new chemical species as co-dopants [2]. For example, without any co-dopants, the maximum hole concentration in Mg doped GaN is around 10 17 cm −3 [4]. However, such concentration can be raised for an order of magnitude when Mg and O are co-doped [5,6].
This paper is organized as follows. First, the history of co-doping is briefly reviewed. Next, we describe the methods of fully compensated co-doping, co-doping with partial compensation, co-doping without compensation, and unintentional co-doping. Then, we review surface effects and effects of defect complexes. Finally, we list our conclusions and provide an outlook.

Historical roadmap of co-doping
Although this paper focuses on co-doping, it is essential to first review the early history of doping. In 1930, Gudden noticed that conductivity of semiconductors was almost entirely due to the presence of minute quantities of impurities [7,8]. In 1931, Wilson was the first to apply the quantum mechanical formalism to semiconductors [9]. Later, the idea of p-type and n-type doping was put forward in a few pioneering works on rectifiers, based on copper oxide [10] and selenium (Se) [11,12]. The first model of a p-n junction was contributed by Davydov in 1938 [8, 13], who also explained the importance of minority carriers. As for a real experimental realization, in 1944, Woodyard was the first to develop a nonlinear circuit device using germanium (Ge) [14]. Woodyard also introduced the concept of "doping" [14]. Small controlled amounts of phosphorus (P), arsenic (As), or antimony (Sb) were incorporated into pure Ge to improve the electrical characteristics of circuit junctions [14]. In 1949, Shockley theoretically proposed a major innovation, namely, the "junction transistor" [15]. He posited that this novel device was superior to the point-contact type device [16]. However, manufacturing of junction transistors was plagued by a difficult problem: the device required a thin-spaced, sandwiched layer of two p-n junctions, joined back-to-back [16]. A solution was found in 1950, when Sparks and Teal, working at Bell Labs, fabricated a "grown junction transistor" using a technique known as "double doping" [17,18]. The first step in the proposed double doping process utilized molten n-type Ge; by adding a small amount of gallium (Ga), the molten Ge was transformed into p-type Ge. Then, moments later, a small pill of Sb was added to convert the p-type back to the n-type [16]. In this process, two types of dopants were introduced simultaneously. In a more general sense, a p-n junction can be considered as "co-doping" of p-type and n-type dopants into different regions of a semiconductor material.
The early history of co-doping can be traced back to the early 1950s. In 1952, Fuller studied the diffusion of donors and acceptors in Ge [19]. In 1953, he studied the diffusion and solubility of lithium (Li) in Ge-and siliconbased (Si-based) p-n junctions, and determined that Li acts as a strong donor [20]. Later, Reiss et al. studied the ionization effects of donors and acceptors on the electronic properties of semiconductors [21]. The solubility of Li in boron-doped (B-doped) Si was studied [22]. A mechanism for describing inter-defect interactions in Ge and Si was also proposed [23]. In 1956, Kröger and Vink proposed that the impurities with opposite effective charges tend to increase each other's concentration [24,25]. Later, the effects of ion pairing in Si [26] and the solubility of Li in Ge in the presence of Ga and zinc (Zn) [27] were studied too. It was found that co-doping can lead to increased conductivity owing to a number of factors [28]: (i) an enhanced equilibrium solubility, (ii) lower ionization energy, (iii) change in the carrier mobility. In 1960, Shockley and Moll reached a similar conclusion, stating that the solubility of a charged impurity in a semiconductor depends on the Fermi level [29].
Despite these fundamental works on co-doping, to the best of our knowledge, "co-dope" related words (such as "co-doping" and "co-doped") were introduced in 1963 [30] and were later used in other articles. The research at the time aimed to determine the mechanisms compensating for unintentional introduction of multiple dopants, and chemical mechanisms of growing and doping in materials such as alkaline earth halides (e.g., CaF 2 , BaF 2 , etc.) doped with rare earths or uranium (U), for potential use in optically pumped lasers [30,31]. In addition, optical energy transfer was investigated for chromium (Cr) and neodymium (Nd) doubly doped into Yt 3 Al 5 O 12 (YAG) [32] and other Cr-doped materials [33].
In the 1960s, a general descriptor of "co-doping" was mainly applied to describe the studies of absorption and luminescence properties. For example, these words were used to describe interactions between Eu 3+ and other rare earth elements in Y 2 O 3 [34], the effect of Pr 3+ fluorescence on LaF 3 owing to the presence of other rare earth co-dopants [35], the characteristics of Nd 3+ and Yb 3+ co-doped LaF 3 [36], and the characteristics of Nd 3+ and Ce 3+ co-doped LaCl 3 [37]. Rare earth-doped glass [38] was co-doped with UO 2+ 2 , Fe 2+ [41], for use in saturable-absorber giant-pulse lasers [42]. The optical spectra of CdF 2 single crystals co-doped with compounds such as YbF 3 and NaF were investigated as well in 1967 [43]. In 1969, the influence of an additional im-purity ion, Ce 3+ , on the fluorescence of Gd 3+ in SrF 2 was examined [44]. In addition, the protecting method of S and Mg co-doping into an electrode NiCl 2 was reported for applications to batteries [45]. Other co-doping effects related to absorption or fluorescence of Si [46], Sr-TiO 3 and TiO 2 [47,48], GaP [49,50], ZnSe [51,52], ZnS [53], and CdS [54] were also reported. In a different line of work, solution and diffusion of impurities in heavily doped semiconductors were addressed, as well as interactions among pairs of impurity ions. For example, an impurity interaction mechanism for P and Ga [55] and reactions of group III acceptors with O [56] in Si were investigated. Studies on vibrational modes of Li-O, Li-B in Si [57], Li-P [58] in Ge, were performed along with studies on cooperative diffusion in p-n-p structures [59]. The distribution and precipitation of gold (Au) in heavily phosphorus-doped (P-doped) Si [60][61][62] was revealed, and some experimental results of these studies [61] were consistent with the Reiss theory. In addition, ion pairing between Li and acceptors was discovered in GaSb [63] and GaAs [64].
In the 1970s, compared with the field of lasers, the word "co-dope" was not widely used in the field of traditional semiconductors. However, researches related to the effects of co-doping were widely reported. For example, the phenomena of Li-Li-O luminescence [75], Zn-O pairs [76] in GaP, defect pairs in ZnSe [77], CdS, and CdTe [78], were studied. The focus of the co-doping research at that time shifted toward wide-gap semiconductors. Researchers mainly focused on studying the effects of co-doping on optical properties and on studying the mechanisms of dopant pair interactions in these wide band-gap materials.
In the 1980s, in the application of a glass laser hosted by a silica (SiO 2 ) glass, co-doping was used to achieve ideal fluorescence properties for SiO 2 glasses [79][80][81] and SiO 2 optical fibers [82]. In addition, co-doping positively affected the crystal growth of GaAs single crystals [83]. Moreover, effects of co-doping were established for InP [84][85][86][87][88], and this method was applied for fabricating related devices [89]. In the 1990s, studies on contamination-related effects of defect complexes and diffusion, such as the studies of Fe, copper (Cu), or hydrogen (H) in Si [90][91][92][93][94] or wide band-gap materials [95,96], had attracted significant attention. More importantly, the tendency to overcome the doping bottle neck of wide band-gap materials [2,[97][98][99][100], such as ni-trides and oxides, using co-doping, has become increasingly prominent. In this article, we review several works performed in this direction. Thus far, doping of wide band-gap semiconductor materials, such as GaN, ZnO, and TiO 2 , remains a significant challenge.

Fully compensated co-doping
Fully compensated co-doping, or fully passivated codoping, refers to the formation of overall electrically neutral neighboring n-type and p-type defects. By using compensated dopants, the dopant solubility can be enhanced owing to the charge transfer between the donor and acceptor, and the Coulomb interaction between the charged defects [98]. Moreover, as discussed above, the Fermi energy is shifted towards VBM(CBM) with increasing the concentration of a p(n)-type dopant, so that the formation energy of n(p)-type defects is lowered proportionally. Self-compensation, i.e., formation of compensating intrinsic defects such as vacancies, antisites, and interstitials in an appropriate charge state, is thus driven thermodynamically. By applying fully compensated co-doping, the extent of compensation by undesirable intrinsic defects can be lowered, because the charge transfer between neighboring donors and acceptors largely restores the Fermi level. Although fully compensated co-doping is not effective in directly enhancing the dopant concentration, it is valuable in band structure engineering for effectively tuning the band edge and band-gap. Moreover, subsequent annealing of the defects of co-dopants, performed after co-doping, can effectively enhance the population of desired dopants. A significant body of research has been performed in this field. Due to the length limitation on this article, below we will focus on reviewing two interesting problems.

Band-gap engineering of TiO 2
TiO 2 has been actively considered as a photocatalyst for H 2 production by photo-electrochemical water splitting and other pollutant degradations. For a redox reaction to be energetically favorable, the CBM (VBM) must be higher (lower) than the redox potential of the corresponding reduction (oxidation) reaction [101]. For undoped TiO 2 , the valence band (VB) and conduction band (CB) consist of mainly O 2p states and titanium (Ti) 3d states, respectively, and are 1.6 eV lower and 0.3-0.4 eV higher than the corresponding redox potential for water splitting [101]. However, this 3.2 eV band-gap of undoped TiO 2 completely prevents absorption in the visible spectrum, resulting in a low catalytic efficiency under a visible light illumination [101][102][103]. A desirable material should have a band-gap narrower than 2.0 eV, with the band-edges matching the redox potentials [104]. Attempts have been made to improve efficiency by doping or co-doping with transition metal cations or anions for suitably narrowing the band-gap; however, the use of single dopant results in the presence of charged defects, which act as recombination centers and reduce the carrier lifetime, limiting the material's catalytic efficiency [101,105].
Different strategies for co-doping of TiO 2 have been proposed. By using first-principles calculations, Gai et al. proposed a transition metal-anion co-doping strategy using (V/Nb + N) and (Cr/Mo + C) [101]. Long et al. studied the passivated dopant pair (C + W/Re/Os) [106]. The co-doped band structure largely follows the mono-doped case, where nitrogen (N) and C anion substitution can lead to the defect band extending to ∼0.5 eV and 0.8-1.1 eV above the VBM, respectively [101,106]. The CBM position can be maintained for (Mo + C) dopant pairs [101], suitable for water splitting. For the case of (Nb + N) co-doping, Breault et al. demonstrated experimentally a 7-fold increase in the rate of photocatalytic decomposition [107]. For (Mo + C) codoped TiO 2 , Dong et al. [108] and Zhang et al. [102] observed photocurrents [102] and improved catalytic activity [102,108], in agreement with the elimination of recombination centers by co-doping elements. However, the band-gap was narrowed only to 3.0 eV [102], not as significant as the theoretical prediction [101]. The deviation was attributed to the low concentration of dopant and N 2 adsorption on the surface [102]. (W + C) codoped TiO 2 synthesized by Neville et al. [109] and by Xiao et al. [110], and (N + V) co-doped TiO 2 synthesized by Xu et al. [111], also exhibited similar red-shifts of the absorption edge. Improving the catalytic activity by (W + C) co-doping is inconclusive, and Xiao et al. demonstrated an increased photocatalytic activity with (W + C) co-doping compared to the undoped case [110], while the opposite was observed by Neville et al. [109]. The presence of elemental C and Ti-O-C bonding [102,108] suggests that doped C mostly remains in its elemental phase, with only a relatively minor amount incorporated into TiO 2 in the form of interstitial or anion substitutional defects. All of these detrimental defects may affect the reaction mechanism [108]. This also demonstrates the difficulty associated with doping of C into TiO 2 . Ma et al. showed that by utilizing the ease of incorporation of a transition-metal dopant, the formation energy of (2Nb/2Ta+C) can be significantly reduced, particularly in the O-rich limit [112].
Other than the transition metal-anion co-doping scheme discussed above, Long et al. [103,113,114] proposed co-doping of transition metal pairs with a complimentary valence for avoiding an isolated defect band, which exhibits inferior oxidative power and mo-bility [115]. Charge-compensated dopant pairs of (Mo + Zn/Cd), (Ta + Ga/In) [103] and (Mo/W + Mg/Ca) [114] were modeled by the formation of cation substitutional defects on the neighboring Ti sites. In the case of (Ta + Ga/In), fully compensated co-doping eliminates the intermediate defect band of Ti 3d that originates from local distortion [103]. In the case of (Mo + Zn/Cd/Mg/Ca), a defect band with mainly molybdenum (Mo) 4d component was reported to form, which is ∼0.4 eV below the CB [103,114]. The Zn 3d band is ∼0.1 eV above the VB [103]. Improved catalytic activity is expected owing to the increased density of states compared with the isolated defect band for transition, and owing to the elimination of recombination centers.
In summary, these studies suggest that fully compensated co-doping of TiO 2 can only partially improve the efficiency owing to the limited solubility of dopants, detrimental n-type dopants that significantly lower the CBM, detrimental gap states induced by the dopants, unwanted surface adsorption, and detrimental secondary phases of dopants formed in the crystal. Although it is possible to increase the VBM, the intrinsic challenge of co-doping associated with TiO 2 band engineering is that we should not significantly lower the CBM simultaneously. This limitation strongly constrains the choice of candidate co-doping pairs.

P-type doping of GaN
Co-doping of p-type GaN by Mg and H pairs is one of the most enchanting examples of fully compensated codoping. Mg-doped p-type GaN crystals grown by using high-temperature techniques inevitably form N vacancies (V N ), which are triple donors. Further increase in the partial pressure of an Mg precursor does not increase ptype conductivity, because charge compensation effects owing to the presence of N vacancies are energetically favorable [116]. However, because H is inevitably present in organometallic vapor phase epitaxy (OMVPE), this unintentionally co-doped H forms complexes of Mg and H defects with the formation energy lower than that of V N [116]. As shown in Fig. 1, this compensating technique yields ∼3 orders of magnitude enhancement in the concentration of Mg Ga [116]. The desired p-type conductivity can be activated by low-energy electron beam irradiation or thermal annealing [117]. A detailed explanation on the removal of compensating H will be provided in the section on unintentional co-doping below.
Fully compensated co-doping for enhancing the population of desired defects is one of the major advantages of co-doping, which has been widely applied in many semiconductor materials. Such techniques are often combined with post annealing techniques for removal of H from the defect complexes. Species with low diffusion barriers are often good candidates to serve as co-doping agents, because in general they can be easily removed. The full discussion on H-related defect complexes is far beyond the scope of this article. Here, we will focus on describing only the fundamental principles.

Partially compensated co-doping
Similar to fully compensated co-doping, partially compensated co-doping utilizes the charge compensation effect and Coulomb attraction between n-type and p-type dopants for enhancing the solubility of the dopants. However, different amounts of donors and acceptors are introduced into the system in the case of partially compensated co-doping (e.g., co-doping of a single donor with a double acceptor), making it possible to create partially occupied intermediate bands in the band-gap of the host system. Such scheme has been also referred to as non-compensated n-p co-doping [118][119][120][121]. Nevertheless, to distinguish this co-doping from non-compensated co-doping, in which the stabilization of co-doping pairs is not related to the formation of n-p pairs, it is perhaps better to refer to it as to partially compensated co-doping, emphasizing the nature of partial compensation in this co-doping scheme. Apart from the enhanced solubility, the presence of intermediate bands reduces the band-gap and enhances optical absorption. Therefore, partially compensated co-doping applies to the doping and band-gap engineering of large band-gap materials, as well as to the design of intermediate-band solar cell materials. This scheme is probably the most widely applied co-doping method among the existing co-doping techniques. Applications in different material systems are described in details in the following sections.

TiO 2
As discussed in the previous sections, TiO 2 is one of the most promising photo-catalyst materials, yet its efficiency is largely limited by its large intrinsic band-gap [100,[122][123][124]. In addition, dopant solubility in TiO 2 is usually low, particularly for p-type dopants, owing to the low VB and spontaneous formation of native defects [100]. While fully compensated co-doping could enhance dopant concentration and reduce the band-gap, the effect of the band-gap narrowing is not very significant, and the created occupied states inside the band-gap are usually localized and might become non-radioactive recombination centers. To overcome these difficulties, Zhu et al. proposed partially compensated co-doping of TiO 2 [118]. First-principles calculations showed that chromium-N (Cr-N) co-doping (a net p-type) enhanced the incorporation of N into O sites in anatase TiO 2 , both thermodynamically and kinetically [118]. Moreover, apart from a comparable band-gap reduction compared with compensated Cr-C or V-N co-doping, strong hybridization of partially compensated n-p pairs created extended intermediate bands that were broader than the localized impurity levels [118]. Experimental results also confirmed the band-gap reduction and enhancement of photo-activity by co-doping Cr and N into TiO 2 [118]. Besides the photo-catalyst application, formation of intermediate bands is also desirable for design of solar-cell materials [125], which will be described below.
Following this finding, additional theoretical and experimental works have been conducted to study the effect of Cr-N co-doping into TiO 2 . Kurtoglu et al. found that photo-activity of Cr-N co-doped TiO 2 under ultraviolet (UV) irradiation increased 10-fold compared with monodoped samples. In addition, their first-principles calculations further demonstrated that negatively charged defect centers of Cr − Ti -N − O may help to reduce the concentration of trivalent Ti and increase photo-activity [126]. On the other hand, Li et al. reported enhanced photodegradation of methyl orange under visible light for Crdoped or Cr-N co-doped TiO 2 , compared with undoped or N-doped cases; yet, reduced photo-activity under UV irradiation was observed in all doped samples [127]. Experiments by Chiodi et al. showed that Cr-N co-doping into nano-clustered TiO 2 thin films occurs on the substitutional sites and delocalized states are created inside the band-gap [128], consistent with earlier theoretical predictions [118]. In addition, experimental observations by Jaćimović et al. showed that the effect of Cr-N codoping largely depends on the growth condition, implying the critical role of structural defects in the doping process [129]. Wang et al. confirmed that co-doped Cr and N should both be substitutionally doped into TiO 2 , and the band-gap is narrowed to less than 2 eV, mainly owing to lifting of the VBM [130]. Cheney et al. iden-tified the nature of intermediate bands as Cr 3d 3 levels, and suggested that the observed delocalized N-derived 2p states near the CBM could provide the required carrier mobility for photo-catalyst or photovoltaic applications [131]. Lu et al. showed that a small amount of N in Crdoped TiO 2 reduces the concentration of Cr 6+ and suppresses electron-hole recombination [132]. Besides photocatalyst materials, Cr-N co-doped TiO 2 was also used as an anode for Li ion rechargeable batteries [133]. Enhanced electrical conductivity was measured following Cr-N co-doping, resulting in an improved performance compared with N mono-doped samples [133].
Other than Cr-N co-doping, some research has focused on the effects of other partially compensated co-doping pairs in TiO 2 . Khan et al. performed density functional theory (DFT) calculations and found that Mo-N codoping could reduce the band-gap to 1.5 eV, enhancing the absorption of visible light [134]. Experiments conducted by Zhang et al. confirmed the enhanced absorption of visible light, as well as an improved separation of electron-hole pairs [135]. Due to the lifting of the CB edge following the doping with Mo, the optimal concentration of Mo was found to be ∼1% [135,136].

Intermediate-band solar cell materials
To improve the quantum efficiency of a single junction, Luque and Martí proposed intermediate-band solar cell (IBSC) materials [125], in which a half-full impurity band is introduced into the semiconductor band-gap, as shown in Fig. 2. Owing to the additional optical transition from the VB to the CB via the intermediate band, lowerenergy photons in the solar spectrum can be utilized to generate a photocurrent [119,125]. As a consequence, the maximal efficiency of this device can reach 63.2%, much higher than the Shockley-Queissier limit for a single band-gap semiconductor [137]. The major challenge here is the controlled creation of intermediate bands inside the intrinsic band-gap of the candidate system [119]. Because partially filled delocalized states can be created inside the band-gap by partially compensated co-doping, and because the location of these intermediate bands can be tuned by choosing different co-doping pairs, partially compensated co-doping in large band-gap semiconductors becomes a promising strategy for designing IBSC materials [118]. A theoretical model, based on partially compensated co-doping of TiO 2 , predicted that the optimal efficiency can reach 52.7%, and can be even higher (56.7%) if current is allowed to be extracted from the intermediate bands [119].
Although partially compensated co-doping is a promising strategy for designing IBSC materials, the co-doping scheme unavoidably introduces many impurity atoms into the host system, increasing the probability of non-radioactive recombination of photo-generated electronhole pairs. To avoid introducing too many impurity atoms, a new strategy based on single-element partially compensated co-doping was proposed [120,121]. By performing first-principles calculations for CuAlSe 2 , Li et al. predicted that P can be substitution ally doped into adjacent aluminum (Al) sites and Se sites, thus behaving simultaneously as a double-donor and single acceptor [120]. The created half-full intermediate band significantly increases the optical absorption coefficient [120]. In addition, Han et al. predicted that doping group V elements (P, As, or Sb) into CuGaS 2 can create partially filled intermediate bands in the intrinsic band-gap, which is potentially promising for photovoltaic applications [121].

GaN
Group III-nitride semiconductors have attracted significant attention for applications in opto-electronic devices owing to their tunable and direct band-gap, and obtaining low-resistivity p-type GaN is one of the critical issues in the utilization of GaN-based opto-electronic devices [3,5,28,139,140]. Similar to TiO 2 , there is a natural doping limit for GaN, owing to its low-lying VB [100]. Attempts have been made to improve hole concentrations and conductivities of p-type GaN. In 2001, Katayama-Yoshida et al. proposed that formation of the acceptordonor-acceptor (ADA) complex by co-doping donors and acceptors in GaN would increase the p-type conductivity [3,139]. Although a single acceptor and single donor are used in this co-doping model, the unbalanced dopant numbers guarantees the partially compensated nature. The theoretical predictions made by these authors were consistent with the experimental observations of an enhanced hole concentration in Be-O co-doping [141], Mg- O co-doping [5,6], and Mg-Si co-doping [142]. The experimental observations and the ADA complex model have been reviewed in details by Korotkov et al. [28]. Later it has been also proposed that charge redistribution near the Mg Ga -Si Ga complex could enhance the piezoelectric field in GaN, thus splitting the tops of VBs [140]. Such splitting results in the upshift of the VBM and might lower the hole activation energy in GaN, leading to an increased hole concentration [140].
Because GaN is chemically stable even under harsh conditions, and band edges are located to enable water splitting under UV irradiation, this device is also considered to be a promising photo-catalyst [143,144]. To improve the absorption of visible light by this wide band-gap semiconductor, Pan et al. proposed partially compensated Cr-O co-doping in GaN [144]. Their first-principles calculations showed that incorporation of cations can be enhanced by co-doping with anions, owing to the reduced formation energy of the partially compensated complex, and the Fermi level can be shifted into the CB, leading to high carrier mobility in the Cr-O codoped GaN [144].

ZnO
Owing to its chemical stability and large band-gap (3.2 eV), ZnO is also a candidate photo-catalyst material [145]. Doping and band-gap engineering of wide bandgap ZnO encounter difficulties similar to those encountered for TiO 2 and GaN. Similar to the ADA complex model for GaN [3,139], the strategy of partially compensated co-doping of Ga, N, and P has been proposed in band-gap engineering of ZnO nanowires [145]. Firstprinciples calculations showed a redshift of the optical absorption spectrum for the co-doped case compared with N mono-doped ZnO, as well as lower defect formation energy, both of which indicate enhanced photoactivity in the partially compensated co-doping scheme [145].
Partially compensated co-doping has also been applied to realizing stable ferromagnetism (FM) in doped ZnO. By performing first-principles calculations, Pan et al. found not only enhanced thermodynamic and kinetic incorporation of dopants by using this co-doping strategy, but also stable long-range ferromagnetism owing to the extended states created by the co-doping pairs [144]. They identified Cr-N and V-N as possible co-doping pairs for achieving stable ferromagnetism in ZnO, and scandium-C (Sc-C) co-doped ZnO as a particularly interesting FM semiconductor with net p-type conductivity [144].

ZnS
The ADA complex model has also been applied to ZnS to achieve p-type conductivity in this large band-gap semi-conductor. For vapor-phase epitaxial ZnS, Kishimoto et al. found that (silver(Ag), indium(In), N) triple-doping can largely enhance the free hole concentration and carrier mobility [146]. The photo-luminance spectrum indicated the existence of donor-acceptor pairs, and weak temperature dependence of the hole concentration further hinted that impurity bands were possibly created [146]. Later, Yamamoto et al. conducted first-principles calculations and showed that this effect should be attributed to the formation of the N S -In Zn -N S complex, which transforms the localized impurity level of N into a delocalized state [147]. Therefore, the enhanced ptype conductivity can be explained by the ADA complex model [3,139].
Also, Muruganandham and Kusumoto found that codoping C and N into ZnS greatly enhances the visible light absorption compared with undoped ZnS [148]. This finding demonstrates the feasibility of non-metal doped sulfide semiconductors as photo-catalyst materials under visible light irradiation [148]. By performing firstprinciples calculations, Sun et al. showed that the partially compensated N S -C i -N S complex may be formed owing to its low formation energy, and the created impurity states in the middle of the band-gap of ZnS could improve the visible light photo-activity of ZnS [149]. This, too, demonstrates the power of partially compensated codoping in band-gap engineering of large band-gap semiconductors. Still, co-doping may lower the stability of the host material, which is a key issue in designing photocatalyst devices.

Non-compensated co-doping
Non-compensated co-doping refers to co-doping schemes that do not rely on the energy gain from donor-acceptor pairs to increase the incorporation of dopants. Thus, the mechanisms behind such co-doping schemes were often quite novel. In this section, a few types of materials with different properties will be discussed. First, we will review non-compensated co-doping of TiO 2 for photochemical reactions. In the previous sections, fully and partially compensated co-doping techniques were reviewed. Yet, a third technique was found to effectively increase the device efficiency in the visible light region. It was found that two acceptors, doped at neighboring O sites, can be effective [150,151]. Second, we will review co-doping of ZnO for improving its p-type conductivity and fabrication of diluted magnetic semiconductors (DMSs). Experimental and theoretical calculations showed that codoping of isovalent Mg Zn or Be Zn with N O acceptor can effectively reduce the transition level and improve the carrier concentration and conductivity [152,153]. Manganese (Mn) and N co-doping into ZnO was used for creating room-temperature FM [154,155]. Third, we will review p-doping of ZnS/Se, for improving its p-type conductivity, and co-doping of N and tellurium (Te) that was attempted with some success [156].

Double-hole doping of TiO 2
As was already argued in the previous sections, TiO 2 is one of the most promising materials for the aqueous photocatalytic reaction, yet its application has been hindered by its large band-gap of ∼3.2 eV [157]. Thus,many attempts have been undertaken to dope anion acceptors, such as C, sulfur (S), and N, into TiO 2 . Recently, it was found that N mono-doped [158], (C,S) [159] and (N,S/Se) [160] co-doped TiO 2 exhibit redshifts in their absorption spectra. A theoretical explanation of band-gap narrowing by (C,S) co-doping was first suggested by Wang et al. [151] and the concept was later generalized by Yin et al. [150]. By performing first-principles calculations, they found that two neighboring acceptors at O sites can couple strongly through non-bonding orbitals. The subsequent bonding pushed empty bands into the CBM as anti-bonding states. The coupling between the remaining states of the acceptors created substantial splitting of the filled states and raised some deep band-gap states, substantially reducing the band-gap [150,151]. Figure  3 schematically shows the co-doped structure and the coupling mechanism. There are ongoing attempts to codope cation dopant with the mentioned anions for increasing the efficiencies of photochemical reactions, such as Co-C-S [161] and Fe-N [162], yet, theoretical studies of these complex co-doping schemes are limited. Furthermore, owing to the complex nature of photochemical reactions, the dopant can affect the surface texture and the reaction pathway [150,157,161], all of which complicate theoretical studies.

Isovalent cation and N co-doping of ZnO
Novel methods were also suggested for co-doping wide band-gap semiconductors. Here, we will discuss ZnO as an example. ZnO is a wide band-gap semiconductor with the band gap of ∼3.3 eV. Its hole concentration is low when it is p-doped by N O . Owing to the low solubility of the dopant, compensation of intrinsic n-type defects and high transition levels were found [163]. Li et al. suggested that p-d coupling can be removed by Mg Zn or Be Zn substitution sites around the N atom, thus lowering the defect level [152]. Their first-principles calculations showed that the transition level of N O is 0.31 eV above the VBM, resulting in a low carrier concentration at room temperature. Calculations also showed that the deep level was contributed by the p-d coupling between the N and Zn atoms. Calculations showed that the N O -4Be Zn defect complex has the transition energy of 0.12 eV and defect binding energy of 1.9 eV [152]. There was some success with doping N into (Mg, Zn)O, notably by Zhang et al. [153]. They created a p-type sample with low resistivity (6.4 × 10 −2 Ω · cm), high mobility [11.7 cm 2 /(V · s)], and high carrier concentration (8.31 × 10 −2 cm −3 ), by using ultrasonic spray pyrolysis [153].
Another non-compensated co-doping scheme was created for ZnO in the pursuit of a DMS. Significant body of research focused on doping various transition metals, such as cobalt (Co) and Mn. Because they are chemically isovalent, these metals provide local magnetic moments, but lack charge carriers. It was found that Co and Mn require different polarities of charge carriers to achieve room-temperature FM: n-type for Co and p-type for Mn [164,165]. Co-doping of N and Mn into ZnO was also studied theoretically and experimentally [154,166]. Although the results show FM at room temperature, the exact mechanism for obtaining magnetic ordering remains elusive [155,167].

Enhanced p-type ZnS by N co-doping with isovalent dopant
The wide band-gaps of ZnS/Se make this material potentially useful as a blue light emitting diode (LED) and a laser diode [168]. Owing to the intrinsic difficulties associated with p-type doping, co-doping schemes can be appealing. Gaines et al. used N-doped Zn 1−x Mg x S y Se 1−y for the cladding layer of a blue-green injection laser [168]. However, this material has a low carrier concentration of 1 × 10 17 cm −3 [169], and p-ZnSe can only reach the carrier concentration of 1×10 18 cm −3 . To increase the p-type conductivity of ZnS and ZnSe, Jung et al. co-doped Te and N into ZnS and ZnSe by using the δ-doping technique and achieved the hole concentration of 10 20 cm −3 [156]. By inserting an N-doped ZnTe layer between undoped ZnS and ZnSe, they successfully increased the hole concentration of ZnSe to 7×10 18 cm −1 and achieved the hole mobility of 10 cm 2 /(V·s) at room temperature. However, for ZnS, an Ohmic contact between the doped and undoped layers could not be achieved [156]. Unfortunately, theoretical studies on the mechanism of this co-doping scheme are still largely lacking.
In this section, we review several methods of noncompensated co-doping. It should be noted that these co-doping schemes fall roughly into two categories. The first category involves co-doping multiple anion acceptors such that chemical bonds between these acceptors can be formed, leading to a filled defect state in the bandgap. The band-gap can be modified significantly without introducing carriers into the system. The second category involves co-doping of an isovalent cation dopant with anion acceptors. The doping pair yields different electronic and magnetic properties based on the p-d coupling (or the lack of one) in the cation and its bonding with the anion acceptor.

Unintentional co-doping and surfacerelated co-doping
Although the general discussion and organization of this article follows the logical order of different passivation mechanisms of co-doping, some very important experimental and theoretical works on unintentional co-doping and surface effects on co-doping should be emphasized and will serve as an extension of the general concept of co-doping. Unintentional co-doping usually happens when unexpected dopant that is present in the growth atmosphere is incorporated into semiconductors, and forms defect complexes with original dopants or intrinsic defects. Background contamination, such as H, C, or O, is often the source of such unexpected dopants [170][171][172]. In addition, defect complexes of intrinsic defects and dopants can sometimes be regarded as resulting from unintentional co-doping. In this sense, the surface as a special type of defect plays an important role in the incorporation of dopants and surfactant-enhanced doping or co-doping becomes especially interesting.

Hydrogen co-doping effects
Hydrogen is a common impurity in semiconductors [95,[173][174][175]. Hydrogen acting as a co-dopant is inevitably incorporated into well-doped semiconductor materials during growth, because many growth techniques include quite a few H atoms, especially OMVPE. One typical example is the famous account of unintentional H impurity co-doping with Mg in GaN, which has been mentioned in Section 2 of this article. Before 1992, it was difficult to achieve good p-type in GaN even after a major breakthrough contributed by Akasaki et al. [176]. Nakamura et al. found that the electric conductivity of Mg-doped GaN significantly increased after changing the annealing atmosphere from NH 3 to N 2 [177]. Thus, these researchers demonstrated that if Mg is present in the crystal, H atoms (dissociated from NH 3 during growth) form Mg-H complexes, thereby preventing from Mg to act as an acceptor [175,177]. Thermal annealing of the GaN: Mg sample in an H-free environment above approximately 400 • C allowed H to diffuse out of the crystal, thereby breaking up the Mg-H complexes [175,177]. A few years later, Neugebauer and van de Walle studied the effects of H and H complexes in GaN [95], by performing first-principles calculations. Their investigation demonstrated that the Mg-H complex has an H-N bond as its main feature, proposing possible mechanisms for H to diffuse out of the p-type regions [95]. Possibilities included diffusion into the substrate material, to the surface, or to extended defects that occur at high concentrations in epitaxial GaN, while the formation of H 2 was excluded because of its high formation energy [95].
In general, H displays a range of complex behaviors when introduced as an impurity in semiconductors. Interstitial H can bind to native defects or to other impurities, often passivating their p-or n-type conductivities [174]. It acts as a donor (H + ) in a p-type material and as an acceptor (H − ) in an n-type material, always counteracting the prevailing conductivity [174]. This depends on whether the transition level, ε(+/−), intersects the CB or is deep in the energy gap, and H 0 , is never thermodynamically stable [174,178]. Defect-related H effects in semiconductors have been investigated for materials such as Si, Ge, GaAs, and GaP, and this has been extensively reviewed elsewhere [170,174,[179][180][181]. Here, we describe only some recent progresses. For Si, new defect configurations of H/Si complexes [182] and H/N/O defect [183] complexes in Si have been theoretically discovered, yielding new insights into H-related dopant effects in Si. For compound semiconductors, the N-H and other H-induced defect complexes, interacting with intrinsic defects, were reported for GaNP, GaNAs, GaSb, and InN [184][185][186][187][188][189]. This indicates that H activates new defects [187] and tunes band-gaps [188] in such materials. Also in oxides, H-related defects were revealed to passivate C or N contamination by forming C-H or N-H complexes in Al 2 O 3 [190]. A theoretical study demonstrated that H exhibits amphoteric behavior by forming complexes with intrinsic and extrinsic defects in ZnO [191]. It can also passivate N-related acceptors in ZnO by forming neutral defect complexes [192,193]. In addition, H helps suppress sodium (Na) interstitials to enhance Nadoped p-type ZnO [194]. For TiO 2 in the rutile phase it was reported that H behaves as a deep donor in rutile and always forms an OH + complex, independent of the Fermi energy [195]. It can also form a stable H O -V O complex, still behaving as a deep donor [195]. Such behavior distinguishes H in TiO 2 from H in other semiconductors [195]. Besides, Pan et al. proposed that H acting as a codopant with N into anatase and brookite TiO 2 improves their photocatalytic performance [196], owing to the enhancement of absorption and reduction of recombination centers [196].
Effects of unintentionally doped H in DMSs were also investigated within the framework of DFT. The results suggest that interstitial H enhances the magnetic properties of ZnO:Co by the formation of a bridge bond for a spin-spin interaction among Co ions [197]. Besides, the role of H O is also important, as stable Co-H O -Co complexes would be formed. The formation of such complexes opens a channel for strong FM coupling by short-range exchange interaction with Co ions [198]. Also in (Mn, N)-co-doped ZnO, it may favor an -Mn-H-N-complex with the existence of H [199]. The strong hybridization between the H-impurity band and the 3d minority spin states of Mn at the Fermi level in the gap results in the FM coupling between the spins of Mn and N [199]. Hydrogen-dopant effects were also observed in some experiments [200][201][202] for DMS material systems. Except for semiconductors, the problem of H embrittlement for high-strength steels and Al alloys is also a crucial issue in modern materials physics [203]. By conducting firstprinciples calculations, it was revealed that vacancies in metals, such as Al, palladium (Pd), bcc-Fe, fcc-Fe, could trap from 5 to 12 H atoms [203][204][205][206], forming H-vacancy complexes. It was found that for H-rich conditions there is a dramatic increase in the vacancy concentration in the fcc-Fe [203]. These findings indicate the importance of vacancy-interstitial complexes in such systems.

Carbon co-doping effects
In addition, C is one of unintentional impurities that is especially found in the compounds that are grown by performing OMVPE. Decades ago, Theis et al. observed the substitutional C impurity in GaAs [207]. Carbon in OMVPE has been studied as both an unintentional and intentional dopant for a long time [171]. Carbon is an amphoteric dopant, which has been systematically investigated in AlN, GaN, InN, AlSb, and GaInNAs, to name a few [96,[208][209][210][211][212][213][214]. In GaN, for example, C-related defects are the likely origin of the yellow luminescence (YL) [212,214], which is frequently observed.
Recently, the effects of unintentionally doped C in ZnO by OMVPE growth have attracted significant attention [215][216][217][218][219], in studies that attempted to suppress the incorporation of C for achieving high-performance p-type N-doped ZnO. Experimentally, it was reported that C sp2 clusters, which are graphite-like along grain boundaries [220,221], were found in undoped [217,222] and N-doped ZnO [216,221,222]. This indicated that defect complexes of CH x , NH x , and NC x were likely to be present [193], with C concentration significantly increasing in N-doped samples [193,223,224]. This suggested that unintentionally doped C impurities prefer to form defect complexes with N [193,223,224]. Theoretically, O defect complexes were predicted to have low formation energies [193]. The formation energy of the (NC) 1+ O defect complex is lower than that of a single C interstitial [223]. This implies that C is one of the possible passivation factors of the N acceptor [225]. This effect was also observed in (Mn, N)-co-doped ZnO, with weakened spin polarization induced by unintentionally incorporated carbon [226]. On the other hand, Tan et al.

Other impurities
Much research has concentrated on the effects of unintentional oxygen doping into semiconductors [172,[228][229][230][231][232], especially GaN [229,231,232] and AlGaN [172,230]. Similar co-doping effects were demonstrated. For example, it was reported recently that unintentionally doped O in europium-doped (Eu-doped) GaN played an integral role in the location, stability, and local defect structure around the Eu ions [232]. The formation of these Eu-O complexes appears to be more beneficial to the crystal quality and stability than either defect is on its own [232]. Actually, during the growth of nitrides and oxides, unintentional As and B impurities were also observed [233][234][235].

Intrinsic defect complexes
Intrinsic defect complexes or complexes of intrinsic defects and dopants are often formed unexpectedly in ex-periments. First-principles calculations may help to understand the physical mechanisms underlying the formation of such complexes during growth. For instance, in ZnO, intrinsic defect complexes were present deep in the band-gap and were responsible for the observed luminescence peak in ZnO [236]. It was proposed that the often-observed green luminescence may result from the (V O + V Zn ) defect complex [236]. Further, it was proposed that the red/orange luminescence found in Zn-rich samples can arise from ZnO defects [236]. It was also proposed that YL may be caused by the (V O + V Zn ) defect complex [236]. Theoretical models of N O , V O , and Zn i were also proposed for ZnO, such as [237], which produce the appropriate electronic structures ready for enhanced visible absorption and H 2 generation from water [237]. Yet, chargecompensated intrinsic defect complexes were reported in Cu 2 ZnSnS 4 [238], which were calculated to have low formation energies and be able to passivate the deep donor levels. Such models may give rise to electrically benign characteristics of thin-film Cu 2 ZnSnS 4 solar cells [238].
In light of the aforementioned facts, we can conclude that: (i) background impurities are important factors determining the characteristic of semiconductors; they should be carefully controlled and considered, possibly exhibiting passivation effects; (ii) the investigations of intrinsic defects and defect complexes and their interactions with extrinsic dopants are crucial for achieving ideal material performance.

Surfactant-enhanced doping
In addition to the co-doping mechanisms in bulk crystals, surfactant-enhanced doping is a novel strategy, and can be considered as an extension of the general concept of co-doping. The only difference is that one of the co-doping elements is present on the surface.
Experimentally, it was found that Sb can enhance the incorporation of Zn into InGaP and GaP [248,253]. Howard et al. used Sb and bismuth (Bi) as surfactants to enhance the incorporation of Zn into InGaP during the OMVPE growth [253]. Hydrogen also plays a role in the doping process [253]. When Sb is incorporated into the growth process, both H and Zn concentrations increase [253]. The physical mechanism of surfactant-enhanced doping remained unclear at that time.
In  [254]. They concluded that Sb enhanced surface diffusion of Zn [254,255] and increased the Zn atom activation rate at a low growth temperature [254]. For InAs, Wagener et al. observed that the surfactant action of a small mole fraction of Sb increased the maximal p-type doping density twofold; this study was performed by using OMVPE and dimethyl cadmium as a p-type dopant source [256].
Zhang et al. theoretically modeled the dual surfactant effects from the perspective of electronic structures, for Sb and H. They pointed out that when P is replaced by the Sb surfactant, the high p-orbital energy of Sb provides a high level that could transfer electrons to the dopant level and lower the dopant formation energy. However, because Sb is isovalent to P, H is needed here to provide electrons to occupy the surfactant level that makes the electron transfer to the lower dopant level possible. They also pointed out that H is only needed when the higher level introduced by the surfactant is empty [251,255]. In addition, they explained the effect of Te on the p-type doping of ZnSe, and predicted that ZnO p-type doping can be enhanced by silver (Ag) through dual surfactants S and Te, together with H [251]. This hypothesis remains to be validated.
Surfactant-enhanced doping may also have some kinetic effects. Kahwaji et al. observed that lead (Pb) as a surfactant significantly affected the structural and magnetic properties of the sub-monolayer of Mn in Mn δ-doped layers in Si(001) growth, and also showed, from the theoretical point of view, that Pb changed the pathway for Mn to access the Si substitutional sites and enabled substitutional incorporation by lowering the formation energy of Si vacancies [257].
Surfactants also induced different strain sites around themselves in the growth front of epitaxial grown thin films. It is expected that an external strain that deforms the host lattice may reduce the dopant-induced strain, thus reducing the dopant formation energy [255,258]. Thus, a tensile strain may enhance the interstitial doping and a compressive strain may reduce the interstitial doping [255,259]. In addition, the size compensation effect can be a critical issue for choosing co-doping pairs. Ideal co-doping can be achieved only when both the size and electronic compensation are tuned and optimized. For example, group VII elements were proposed as effective co-dopants to help f electron metal elements doped in topological insulators owing to both the size and electronic compensation effects [260]. Another size-tuning example of surfactants is the study of Sb-enhanced In incorporation in InGaN. Antimony as a surfactant was found to largely enhance the incorporation of Ininto In-GaN [261], which is also owing to the surfactant-induced strain effect [262]. Merrell et al. found that an abrupt increase in the concentration of In was achieved by adding a small amount of Sb on InGaN surfaces during OMVPE growth [261]. Recently, Zhang et al. studied this phenomenon theoretically by conducting first-principles calculations, and found that under different surface reconstructions, the surface stress analysis indicates that Sb adatoms on H3 sites lead to tensile sites in the GaN bilayer, which can enhance the incorporation of In by lowering the formation energy of In Ga [262].

Summary and outlook
We reviewed co-doping methods for different compensating mechanisms, as well as contamination and surfactant effects. In general, co-doping may enhance the stability of defects, increase the solubility of impurities, and thus improve the conductivities of corresponding materials. However, many questions related to co-doping remain open. Co-doping may destabilize some crystals, form unwanted defects or defect complexes, introduce detrimental mid-gap bands, deactivate certain wanted defects or dopants. Therefore, there is often a compromise between the enhanced electronic properties and the drawbacks of the above-mentioned co-doping methods. One important application of co-doping is to improve the magnetic properties, which is especially important in DMS and topological insulators. Co-doping may be the method of choice for incorporating a large amount of magnetic dopants for forming a long-range magnetic order. Due to the limited length of the paper, we were not able to provide a detailed review of this problem. Yet, all these challenges and potential improvements in device physics based on co-doping methods call for more systematic and creative research efforts.
Acknowledgements This work was supported by the start-up funding, direct grant with the Project code of 4053134 at CUHK and ECS grant from HKRGC (Grant No. 24300814).

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