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Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Design Principles of p‑Type Transparent Conductive Materials Ruyue Cao,†,‡ Hui-Xiong Deng,*,‡,† and Jun-Wei Luo*,†,‡,§ †
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State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China ‡ Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China § Beijing Academy of Quantum Information Sciences, Beijing 100193, China ABSTRACT: Transparent conductive materials (TCMs) has always been playing a significant role in electronic and photovoltaic area, due to its prominent optical and electronic properties. To render those transparent materials highly conductive, efficient n- and p- type doping is critically needed to obtain high concentration of free electron and hole carriers. Despite extensive research over the past five decades, highquality p-type doping of wide-band-gap transparent materials remains a challenge. Here, we summarize four proposed design principles to enhance the p-type conductivity of these wide band gap materials, including (i) reducing the formation energy of the acceptors to enhance the dopant concentration; (ii) lowering the ionization energy and, hence, increasing the ionization of the acceptors to increase the concentration of the free holes; (iii) increasing the VBM of the host material to approaching the pinned Fermi level; and (iv) suppressing the compensating donors to shifting the pinning Fermi level toward the VBM. For each mechanism, we discuss in detail its underlying physics and provided some examples to illustrate the design principles. From this review, one could learn the doping principles and have a strategic mind when designing other p-type materials. KEYWORDS: transparent conductive materials, p-type doping, formation energy, ionization energy, donor compensation
1. INTRODUCTION Technological application of semiconductors depends critically on their capability of doping to produce enough free carriers (electrons and/or holes) at working temperature. Wide-bandgap (WBG) semiconductors, such as ZnO,1,2 SiC,3 GaN,4,5 and AlN,6,7 are extensively studied because of their promising applications in many short-wavelength optoelectronic devices and high-power electronic devices. Those WBG semiconductors with high conductivity (>1 × 104 Ω−1 cm−1) and large band gap (>3 eV) have long been considered as intriguing materials functioning as transparent conductive materials (TCMs) in flat panel display,8,9 photovoltaic solar cells,10,11 light-emitting diodes (LED),12−14 etc., because light can pass through them with low absorption. To realize their full potential, it is highly desirable for TCMs to achieve high conductivity in both n- and p-type with free-carrier concentrations exceeding 1 × 1019 cm−3, to fabricate highquality homogeneous p−n junctions.15 Unfortunately, those WBG semiconductors suffer doping limit issues either in ntype or p-type because of the doping asymmetry.16,17 In general, we can dope most WBG semiconductors n-type but have difficulty obtaining high-performance p-type doping with high hole conductivity. The challenge in p-type doping of TCMs has significantly hindered the application of transparent electronic devices. Consequently, p-type doping in TCMs has gained a great attention over past five decades. For instance, it © XXXX American Chemical Society
is hoped that ZnO, with a large band gap of 3.37 eV at room temperature, can be used in UV-blue optoelectronic devices, transparent thin-film transistors, gas sensors, etc.18,19 Although it is easy to dope ZnO n-type, the difficulty in p-type doping remarkably limits its applications.20−23 Generally, substituting oxygen with nitrogen is the most widely adopted approach in the fabrication of p-type transparent conductive oxides (TCOs). Unfortunately, according to recent more reliable report from Look et al.,24 the maximum achievable hole concentration in ZnO is only 9 × 1016 cm−3 with a poor hole mobility of 2 cm2/(V s) for a sample grown on an Li-diffused semi-insulating ZnO substrate using molecular beam epitaxy (MBE) approach. Apparently, this low p-type doping is far from enough for applications, and an effective method is still lacking for ZnO to dramatically increase its p-type conductivity. It is also true that many other TCMs suffer from low p-type conductivity, which seriously restrains their further development and utilizations. To make TCMs with better performance, a number of strategies25−29 have been proposed to overcome the p-type doping limit based on detailed studies on individual cases. Special Issue: Materials Discovery and Design Received: January 20, 2019 Accepted: April 2, 2019
A
DOI: 10.1021/acsami.9b01255 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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which the formation energy Ef (α,q) of the dopant α in charge state q is equal to the formation energy Ef(α,q′) in charge stateq′. Here, Ef (α,q) can be obtained from the total energy calculations and is defined as17
However, individual examples often distract attentions from observing the doping rules and concluding the p-type doping design principles. Thus, to make the p-type doping more efficient for TCMs, we review the origin of the p-type doping limit in TCMs and present a state-of-the-art comprehensive view on p-type doping design principles with concrete examples, which helps general readers and give a tutorial for beginners to understand how these design principles come from in physics. In section 2, we introduce in detail the underlying physics on doping mechanism and the method on how to calculate the defect formation energy and ionization level; section 3 shows the doping limit rule to further explain the doping asymmetry, and then in section 4 we propose four p-type doping design principles and provide some examples to illustrate each approach.
E f (α , q) = ΔE(α , q) +
(1)
The number of electrons occupied the conduction-band levels is given by the total number of states N(E) multiplied by the occupancy F(E), integrated over the conduction band n=
∫E
εα(q/q′) =
∞
N (E)F(E)dE
(2)
C
p ≈ N A−
F
energy level, which can be determined from the charge neutrality condition and is usually measured from the valence band edge EV. k is the Boltzmann’s constant and T is the temperature at thermal equilibrium. The ionized concentration for donors depending strongly on the impurity energy level and the lattice temperature is given by ND 1 + gDexp[(E F − E D)/kT ] NA 1 + gA exp[(EA − E F)/kT ]
(6)
(7)
That is, the ionized holes contributed from acceptors are going to the host valence band, after acceptor impurities diffuse or are injected into the host crystal. Likewise, for only donor impurities doped to the crystal, the charge neutral condition requires n ≈ ND+
(8)
indicating that ionized electrons contributed from donors are going to the host conduction band. First-principles calculations based on density functional theory (DFT)31,32 have become a cornerstone of research in studying doping and defects in materials by providing insight into fundamental physics. In a specific calculation, the most common way to study defects is to use the supercell approach with the application of the periodic boundary condition, due to its well description of the host band structure without any perturbation of surface states.33,34 The defect or defect complexes are put in a supercell and surrounded by host atoms, thus are separated from its periodic images when cell size is sufficiently large. We only need to concentrate on one single defect at a time and neglect their interaction with each other. Additionally, the periodic boundary condition leads the defect state to be the difference of the band structures between the supercells of the perfect host crystal and of the host crystal containing the defect. Generally speaking, isolated defects possess discrete energy levels. However, in the first-principles calculations, we have to adopt a finite supercell, which renders defect interactions with its periodic images in adjacent supercells and discrete defect levels developing into dispersive
(3)
and for acceptors is given by N A− =
E(α , q) − E(α , q′) − εVBM(host) q′ − q
Considering the case where only acceptor impurities are added to the crystal, the charge neutrality condition becomes
The occupancy is represented by the Fermi−Dirac distribution 1 function F(E) = 1 + exp[(E − E ) / kT ] , where EF is the Fermi
ND+ =
(5)
where ΔE(α,q) = E(α,q) − E(host) + ∑ niE(i) + qεVBM(host). E(α,q) is the total energy of the supercell containing the defect α in charge state q; E(host) is the total energy of the supercell but containing the perfect host crystal; E(i) is the energy of elemental solid or gas; μi is the chemical potentials of these elemental species i referenced to E(i), with the number ni of atoms removed (positive sign) from or added (negative sign) to the perfect host crystal to produce the defect α. Note that chemical potentials represent the energy reservoirs of atoms that are involved in forming a defect, relying on the temperature and pressure of experimental conditions. EF is the Fermi energy level measured from the host valence band edge εVBM(host). For charged defects, the electrons or holes are added to a virtual state (a plane-wave-like jellium state in the supercell) with an average energy equal to EF. Take Zn vacancy in ZnO as an example, the formation energy of VZn with one negative charge can be expressed as Ef(VZn, − 1) = E(VZn, − 1) − E(ZnO) + E(Zn) + μZn − EF − εVBM(ZnO). Therefore, for a dopant α, the transition level with respect to VBM can be calculated as
2. DOPING PHYSICS AND COMPUTATIONAL METHOD When dopants are introduced to the semiconductor crystals, the charge neutrality condition requires the total negative charges (electrons n plus ionized acceptors N−A ) must equal the total positive charges (holes p plus ionized donors N+D):30 n + N A− = p + ND+
∑ niμi + qEF
(4)
where NA and ND are concentrations of acceptor and donor dopants, respectively, and gD and gA are the ground-state degeneracy of the donor and acceptor impurity levels, respectively. For a donor with the impurity energy level ED, its ionization energy is the impurity energy level EC − ED measured from the host conduction band edge EC, and the ionization energy for acceptors is EA − EV. The ionization energy, also known as the transition level, determines how difficult for a donor/acceptor to ionize as donating or accepting electrons to or from the host crystal, giving rise to free electrons or holes. A lower ionization energy (small EC − ED for donors or small EA − EV for acceptors) of dopants produces more carriers in the host material, causing higher conductivity in contrast to impurities with a larger ionization energy. Note that, the transition level for a dopant α is usually denoted by εα(q/q′) and defined as the Fermi-level position at B
DOI: 10.1021/acsami.9b01255 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces bands.35 To minimize the discrepancy arising from the dispersion of defect bands in the defect calculation using a finite supercell, we usually apply a special k-points method,36 which provides the average energy values of dispersion defect bands at some chosen k points, to obtain the result approximately equal to that of isolated one in an ideally infinite supercell. It is worth to note that the Γ point is usually excluded because the interaction among defects from different supercells is strongest at Γ. However, the exclusion of the Γ point gives rise to a poor description on the symmetry of defect states and the host VBM and conduction band minimum (CBM) states, which are usually located at Γ, are sensitive to the k-point sampling. To solve this problem, we employ a hybrid approach to take both advantages of special kpoints and the Γ point.37 First, the transition level of an acceptor defect α referenced to VBM is given by
causing an upper bound limit in the p-type doping. Such aspect is substantially determined by the intrinsic nature of semiconductors42,43 and thus becomes the biggest challenge to overcome the p-type doping, especially for WBG semiconductors. eq 5 tells that the formation energy of defects linearly depends on the position of the Fermi level EF, which is in the range from VBM to CBM of the host material. If we dope a material in p-type, we increase the concentration of acceptor dopants and thus ionized acceptors to raise the free hole concentration, resulting in the shift in the Fermi level EF toward VBM. However, accompanying the shift of the Fermi level EF toward VBM, a reduction in the formation energy of donors is usually occurred (as shown in Figure 1), giving rise
ε(0/q) = E1 + U Γ = εDΓ(0) − εVBM (host)
+
E(α , q) − (E(α , 0) − qεDk (0)) −q
Γ E1 = εDΓ(0) − εVBM (host)
U=
E(α , q) − (E(α , 0) − qεDk (0)) −q
(9) Figure 1. Formation energies of neutral and charged defects in dependence of the Fermi level. A+ and A− represent the donor and acceptor, respectively. The p-type pinning position ε(p) pin is the Fermi energy at which the formation energy of dopant A becomes zero. Adapted with permission from ref 37. Copyright 2011 John Wiley and Sons.
(10)
(11)
where q is negative for an acceptor; εΓD(0) and εΓVBM(host) are energy levels of the neutral defect and host VBM at the Γ point, respectively; εkD(0) is the defect level at special k-points (weight-averaged). E1 means the energy cost to take an electron from the host VBM to the neutral defect level. Note that this approach involves two systems, and thus two different reference energies. We utilize the core level approach38 to carry out the alignment of these two reference energies, following the same procedure as used in the X-ray photoemission spectroscopy (XPS). The relaxation energy U is induced by the change of charge density in different charge state at the special k-points, including Coulomb interaction and the atomic relaxation contribution, which is the extra energy cost of moving (-q) electrons to the defect.
to the birth of the free electrons and in turn causing a partial compensation of increased free holes. As we continuously increase the acceptor concentration and shift the Fermi level, the formation energy of the donor defect will approach finally zero. Subsequently, the donor defects will form spontaneously and produce free electrons to compensate completely the increased free holes from rising in acceptor concentration. The Fermi level EF could not be further shifted toward the VBM because any increase in the holes as further increasing the concentration of acceptors will be completely compensated by electrons induced by spontaneously formed donors, thus EF is pinned at this situation. This pinning position of EF is referred as ε(p) pin . Conversely, n-type doping can also cause Fermi level pinning at ε(n) pin around CBM. Consequently, EF is limit in a range setting by these two values16,44−46
3. DOPING LIMIT RULE According to eq 7, in heavily doped p-type semiconductors, the concentration of holes is approximately equal to the ionized acceptors, which depends on the dopant solubility NA and the ionization energy EA, as illustrated by eq 4. To obtain a large hole density having p-type conductivity, acceptors must be doped in high concentration or possess low ionization energy in the host crystal. In the host crystal, the concentration of acceptors is limited by the solubility of acceptor dopants, which depends mainly on the growth condition of the dopants, such as anion-rich or cation-rich (or anything in between) in equilibrium condition or even using a nonequilibrium growth technique, due to the regulation in the chemical potentials of host and dopant elements. The ionization energy mainly associates with the dopant properties, like the atomic orbitalfilling of the dopant atom. Therefore, these two factors can usually be modified by controlling the growth conditions or choosing appropriate dopants. Besides small solubility and large ionization energy of acceptor dopants, the emerging of compensating n-type donors39−41 is another crucial aspect
(p) (n) εpin ≤ E F ≤ εpin
(12)
Every semiconductor material has its own such two Fermi pinning points ε(n/p) pin , which often line up for the same class of semiconductors as shown in Figure 2.37 From Figure 2 we are ready to understand why some semiconductors can be easily doped heavily in n-type but experience more difficulty in p-type and some semiconductors are the opposite. Take ZnO as an example, ε(n) pin locates in conduction band but ε(p) pin is much higher than VBM, for which EF can be close to CBM but cannot approach VBM, and thus ZnO can be heavily doped in n-type but not in p-type. On the other hand, ZnTe with much higher VBM possesses a ε(n) pin lower than the CBM but ε(p) pin in the valence band, and therefore, ZnTe can be easily doped in p-type but not in ntype. Whereas, both n- and p-type are easily doped for CuInSe2 but n-type doping is difficult for CuInTe2, CuAlSe2, or CuGaSe2. In another word, materials with high CBM are C
DOI: 10.1021/acsami.9b01255 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
Figure 3. Reduction of the formation energy for acceptors to enhance p-type doping. A0 and A− means the charge neutral and negative acceptors, respectively. ε(0/−1) is the transition point from A0 to A−. The red line with a lower formation energy is the advantageous orientation.
chemical potentials of both the host elements and the dopants. For instance, Figure 4 shows the calculated formation energies
Figure 2. Band alignment and Fermi pinning energy ε(n/p) of II−VI pin and I−III−VI2 semiconductors. Adapted with permission from ref 37. Copyright 2011 John Wiley and Sons.
difficult to be doped in n-type, and likewise, materials with low VBM are difficult to be doped in p-type. This is called the doping limit rule.
4. DESIGN PRINCIPLES TO ENHANCE P-TYPE DOPING Guided by the doping limit rule, there appears some common routes to improve the quality of p-type doping: increase the dopant concentration, lower the ionization energy, and suppress the donor compensation. Therefore, we generalized four basic design principles for designing p-type doping TCMs as follows. Note that although it is difficult to achieve free hole concentrations above 1 × 1017 cm−3 in ZnO, we still mainly take ZnO as a typical example to demonstrate the four design principles for p-type doping because they have been implemented in such a single material. 4.1. Design Principle 1: Reduce the Formation Energy of Acceptors to Increase Its Concentration. In thermodynamic equilibrium, the solubility concentration of a defect in crystals depends on its formation energy Ef as follows:35 c = Nsiteexp( −E f /kT )
Figure 4. Calculated formation energies of charge-neutral intrinsic defects Zn vacancy (VZn), O vacancy (VO), Zn interstitial (Zni), O interstitial (Oi) and Zn antiposition (ZnO), and N substitution (NO) in ZnO. Adapted with permission from ref 17. Copyright 2008 John Wiley and Sons.
of the native defects and the acceptor NO in N-doping ZnO as a function of the O chemical potential. It can be seen that NO achieves a much lower formation energy under the O-poor condition, due to the larger μN than that under O-rich. Note that this O-poor or O-rich condition can be controlled by the oxygen radicals flux that arrive at the substrate surface or the ratio of Zn- and O-containing precursors during growth. The left region of the dashed line implies the condition where the secondary phase Zn3N2 will precipitate, which is detrimental to the N solubility. Thus, the O chemical potential should not come into this region to avoid the formation of Zn3N2.17 It has been proposed that the epitaxial growth method can be applied to suppress the secondary phase precipitation and improve the solubility. For example, the previous calculations indicated that N has a low thermodynamic solubility (
