Electronic materials with a wide band gap: recent developments.

The development of semiconductor electronics is reviewed briefly, beginning with the development of germanium devices (band gap E g = 0.66 eV) after World War II. A tendency towards alternative materials with wider band gaps quickly became apparent, starting with silicon (E g = 1.12 eV). This improved the signal-to-noise ratio for classical electronic applications. Both semiconductors have a tetrahedral coordination, and by isoelectronic alternative replacement of Ge or Si with carbon or various anions and cations, other semiconductors with wider E g were obtained. These are transparent to visible light and belong to the group of wide band gap semiconductors. Nowadays, some nitrides, especially GaN and AlN, are the most important materials for optical emission in the ultraviolet and blue regions. Oxide crystals, such as ZnO and β-Ga2O3, offer similarly good electronic properties but still suffer from significant difficulties in obtaining stable and technologically adequate p-type conductivity.

Introduction

Semiconductors are crystalline or amorphous substances with a full v<span class="Chemical">alence band and an empty conduction band. These two bands are separated by the band gap energy E g. Electronic charge transport in such systems is possible by fulfilling the following conditions:

(i) Electrons must be emitted from the v<span class="Chemical">alence to the conduc<span class="Chemical">tion band, e.g. by therm<span class="Chemical">al emission. ‘Intrinsic conduction’ then results from the movement of these negative free electrons and the corresponding positive ‘defect electrons’ (or holes) in opposite directions, if an electric field is applied. The conduction rises with temperature T and becomes significant if the average thermal energy of the electrons k B T (∼25 meV at room temperature; k B is the Boltzmann constant, 1.3806488 × 10−23 m2 kg s−2 K−1) approaches E g/2. At sufficiently high T, this condition is fulfilled by every material.

(ii) Sm<span class="Chemical">all amounts of suitable impuri<span class="Chemical">ties can create addi<span class="Chemical">tional ‘dopant’ levels in the otherwise empty band gap. ‘Shallow acceptor’ levels are situated close to the bottom of the gap, typically a few tens of meV above the valence band. Consequently, at room temperature they are filled almost completely by thermal emission, leaving behind holes in the valence band (p-type conductivity). For ‘shallow donors’ close to the top of the gap the situation is opposite: these levels can emit electrons into the conduction band (n-type conductivity). Deep acceptors or deep donors, which are situated close to the middle of the energy gap, do not contribute significantly to the electric carrier concentration, and thus not to the electrical conductivity.

Insulators are materi<span class="Chemical">als with very lar<span class="Chemical">ge E g, typic<span class="Chemical">ally in excess of 3–5 eV. However, this limit is quite arbitrary and turns out to be subject to technological developments: substances such as aluminium nitride or even diamond are nowadays usually considered to be semiconductors. Semiconductors with E g considerably larger than the ‘normal’ semiconductors Si, Ge or GaAs (see Tables 1 ▶ and 3) are called wide band gap semiconductors, and are the topic of this article. In contrast, narrow band gap semiconductors have a small E g of a few hundreds of  meV.

Table 1

Semiconductor crystals with the diamond structure

	Diamond	Silicon	Germanium	Grey tin
a 0 (nm)	0.3567	0.5431	0.5658	0.6489
T range (°C)	≲1500	<1414	<938	<13
E g (eV)	5.48	1.12	0.66	0.08
λg (µm)	0.226	1.11	1.87	>15

A short look at history: germanium and silicon

Faraday reve<span class="Chemical">aled as early as the 1830s that so<span class="Chemical">me substances show an increase in their electric<span class="Chemical">al conductivity with T, which is in contrast with metals. However, it took more than a century before semiconducting Ge crystals were grown with the Czochralski method (Teal & Little, 1950 ▶; Teal et al., 1951 ▶; Uecker, 2014 ▶), which paved the way to the broad technological relevance of semiconductors. The growth of germanium bulk crystals with high crystalline perfection was a breakthrough and became the origin of today’s semiconductor-based electronic industry. Unfortunately, E g is comparatively narrow for germanium, leading to a particularly large intrinsic conduction which cannot be controlled by p–n junctions, and which is the origin of electronic noise.

Table 1 ▶ summarizes data from sever<span class="Chemical">al sources (Kasap & Capper, 2007 ▶; GTT Technologies, 2013 ▶; Glusker et <span class="Chemical">al., 1994 ▶) for the main group 4 ele<span class="Chemical">ments crystallizing in the diamond structure, like germanium. In the table, a 0 is the lattice constant; T range means the limit where disintegration of the diamond phase occurs, which for Si and Ge is by melting, for C is by transformation from metastable diamond to thermodynamically stable graphite, and for grey α-Sn is by transformation to tetragonal β-Sn, which is stable under ambient conditions. For every energy gap a value of λg = hc/E g can be calculated, which is the minimum optical wavelength for which the material is transparent. Compared with Ge, Si has a much broader E g, which reduces the intrinsic conduction and electronic noise of devices made from it. Indeed, silicon (mainly Czochralski-grown) is today the most important semiconductor material. Grey tin is not technologically relevant, but diamond receives increasing attention as a truly wide band gap semiconductor. Poly- and single-crystalline diamond are typically grown by chemical vapour deposition (CVD) processes, and devices such as diodes and transistors show excellent breakthrough stability up to as much as 20 MV cm−1. It is expected to outperform other wide band gap semiconductors such as 4H-SiC and GaN at 300°C by more than one order of magnitude (Hiraiwa & Kawarada, 2013 ▶; Shiomi & Kumazawa, 1996 ▶).

The diamond structure is characterized by sp 3 hybrid orbit<span class="Chemical">als which repel each other and are therefore directed from the centr<span class="Chemical">al atom to the corners of a regular tetrahedron. The tetrahedra are arranged in layers, and if the position of the first layer (perpendicular to the c axis) is designated A, subsequent layers are stacked in the somewhat shifted positions B and C, resulting in a cubic stacking A–B–C–A–B–C (see Fig. 1 ▶). In contrast, the orbitals in the stable modification of carbon, graphite, are sp 2 hybridized. Here, repulsion directs the orbitals in a planar fashion, 120° apart. The remaining non-hybridized delocalized electron is situated out of the carbon plane and is the origin of the almost metallic conductivity of graphite parallel to the basal (carbon atom) plane of its hexagonal structure. It is notable that carbon can form a wide variety of other allotropes (graphene, nanotubes, buckminster­fullerenes, lonsdaleite), some of which are the subject of intensive research, but they have not yet reached the level of particular technological relevance. In lonsdaleite, the carbon tetrahedra show hexagonal stacking, A–B–A–B. In the schematic of Fig. 1 ▶ this means that the uppermost layer is in the same position as the bottom layer.

Figure 1

The stacking of layers A–B–C (from bottom to top) in the diamond structure. One atom of each layer is hatched for a better demonstration of the stacking sequence.

The diamond-type ele<span class="Chemical">ments of main group 4 show par<span class="Chemical">ti<span class="Chemical">al (complete only in the case of Si–Ge) mutual solubility. Typically, the solubility is larger (possibly under non-equilibrium conditions) for epitaxial layers. Soref (2014 ▶) discussed the properties of alloys in the C–Si–Ge–Sn quaternary system and claimed that only alloys containing tin might offer direct band gaps. However, this publication disregarded the existence of the only intermediate compound in this system which is an important semiconductor, namely silicon carbide, and it will be discussed in §3. The homogeneity range of the three solid phases in the phase diagram (Fig. 2 ▶) is only a few parts per million.

Figure 2

The silicon–carbon phase diagram.

From the <span class="Chemical">cubic diamond structure and the hexagon<span class="Chemical">al <span class="Chemical">lonsdaleite structure, binary or ternary compound structures, respectively, can be derived if the C atoms are substituted in an ordered manner by other atoms in such a way that the average of four electrons per atomic site is maintained; for an overview, see e.g. Parthé (1964 ▶) and Delgado (1998 ▶). The structures of diamond and lonsdaleite, and derived tetrahedrally bound compounds, are called adamantane types. Fig. 3 ▶ shows the interdependency of such tetrahedral structures, with several sulfides as examples. It is obvious that the crystal symmetry drops with increasing chemical complexity. Only a few of these structure types, namely diamond, sphalerite and wurtzite, are found for wide-band gap semiconductors. Some others, such as kesterite and stannite, with narrow E g around 1.0–1.5 eV, are technologically relevant, e.g. as absorbers for thin-film solar cells (Redinger et al., 2011 ▶).

Figure 3

The derivation of tetrahedral multi-cation compounds from element structures.

Binary compounds derived from diamond and lonsdaleite

These AB compounds comprise <span class="Chemical">alternating AB 4 (or A 4 B, respectively) tetrahedra which are linked through their corners. Different stackings for the tetrahedron layers are observed, as for diamond and lonsdaleite. If diamond stacking is performed with the AB 4 tetrahedra, the atom sites are identical to those of diamond itself, with just the A and B atoms alternating. The structure remains cubic, but the symmetry is lowered to space group . This is the sphalerite (= zincblende) structure type. In a similar way, lonsdaleite stacking of AB 4 tetrahedra also results in conservation of the atomic positions with alternating atom types. The resulting wurtzite structure belongs to space group P63 mc. In an ideal wurtzite structure (stacking of ideal spheres), one has c/a = (8/3)1/2 = 1.633, but this is not always fulfilled and results then in distorted tetrahedral bonding.

Often the type of stacking is fixed for one specific AB compound, because devia<span class="Chemical">tions from the ide<span class="Chemical">al stacking increase the lattice energy of the crystal by the stacking-fault energy γ. Although γ is usually given in units of energy per area, scaling in energy per atom is preferred, as a certain number of bonds have to be broken to create the stacking fault. Gottschalk et al. (1978 ▶) showed that γ drops almost linearly if the ionicity of the A—B bonds rises, and for cubic A III B V compounds γ ranges from 53 ± 7 meV atom−1 for GaSb to 17 ± 3 meV atom−1 for InP. Low γ values are detrimental to crystal growth processes because even small thermal stresses can lead to stacking faults which impede the electronic properties of the material.

The <span class="Chemical">similarity of <span class="Chemical">carbon and <span class="Chemical">silicon is responsible for the low ionicity of SiC. In particular, a huge variety of stacking orders can be observed for this compound, called polytypes. It turns out that different SiC polytypes are energetically almost identical and all of them (especially α-SiC, see below) have very low stacking-fault energies (Hong et al., 2000 ▶). Consequently, they can easily coexist or be transformed into each other, or switching between polytypes can occur during growth (Rost et al., 2005 ▶). The polytypes are described by the Ramsdell notation, which is a number giving the period of the stacking followed by the letter H, C or R, indicating that the stacking symmetry is hexagonal, cubic or rhombohedral, respectively. In fact, SiC can belong to only one of the four space groups P3m1, R3m1, P63 mc or (Krishna & Pandey, 2001 ▶). Historically, cubic (zincblende, 3C) SiC is labelled β-SiC, whereas the other modifications are called α-SiC. Table 2 ▶ reports some relevant SiC polytypes between the pure hexagonal 2H and pure cubic 3C extremes. The second line reports the average thickness of a single layer, which does not differ much. All polytypes have rather large indirect band gaps, especially non-cubic α-SiC.

Table 2

Some polytypes of SiC (Bechstedt et al., 1997 ▶; Ching et al., 2006 ▶; Tairov & Tsvetkov, 1983 ▶)

	2H (= wurtzite)	4H	15R	6H	3C (= sphalerite)
a 0 (nm)	0.3076	0.30817	0.30817	0.30817	0.43579
c 0/n	2.524	2.5198	0.2520	0.2520	0.2517
E g (eV)	3.33	3.27	2.986	3.02	2.39

<span class="Chemical">SiC is <span class="Chemical">mechanic<span class="Chemical">ally hard, chemically inert, and can be integrated well into standard semiconductor production lines. The growth of single crystals is a challenge, as can be seen readily from the Si–C phase diagram in Fig. 2 ▶ which was calculated for a reduced pressure of p = 10 mbar (1 bar = 100 000 Pa). For significantly larger or even ambient p, the ‘liq’ phase field for Si-rich compositions extends to higher T, which then results in peritectic melting of SiC to an Si-rich melt and solid carbon (graphite). Only under reduced p << 1 bar is solid SiC in equilibrium with ‘gas’, enabling sublimation growth (physical vapour transport, PVT) which is the standard growth technique for SiC single crystals. Alternatively, at T ≤ 2300°C growth from melt solutions is an option (top-seeded solution growth, TSSG), and this was demonstrated and compared with PVT by Hofmann & Müller (1999 ▶). Often, a metal (Fe, Ni, Cr, Ti or Li) is added to the melt. Different polytypes (e.g. 4H) are now commercially available as wafers of 150 mm diameter, with n-type and p-type doping. The large band gap, good carrier mobility and stability of SiC allow the production of electronic and optoelectronic devices with superior properties and a high breakdown field that are able to work even under harsh conditions. It should be noted that SiC, under the name carborundum, is a mass product used e.g. as an abrasive and for specialized ceramics in car brakes. Here, as for electronics, its high thermal conductivity is beneficial as it allows the removal of waste heat.

<span class="Chemical">SiC is the only tetrahedr<span class="Chemical">ally bound semiconductor that can be derived from diamond or <span class="Chemical">lonsdaleite by replacing C alternately with C or Si, respectively. If the structure is derived from diamond, one obtains the cubic zincblende (sphalerite) structure; if it is derived from lonsdaleite, the hexagonal wurtzite structure is obtained. It is notable that the names of both structure types are derived from zinc sulfide (ZnS), which can be found as a natural mineral in both structure types. Other isoelectronic replacements, with identical structural features, can be obtained by replacing C (group 4 of the periodic system) alternately with elements from groups 3 and 5. Replacement with elements from main groups 2 and 6 results mainly in compounds with the sodium chloride structure, with a few exceptions such as the insulator BeO (Austerman et al., 1997 ▶) and the wide band gap semiconductor MgTe (Kuhn et al., 1971 ▶) belonging to the wurtzite type. However, many subgroup elements also form bivalent ions: the corresponding Me2+ chalcogenides often crystallize in the sphalerite or wurtzite structure and are semiconductors. Some of these A III B V or A II B VI semiconductors with technological relevance are shown in Table 3 ▶; even the A I B VII compound silver iodide crystallizes below ≲162°C in the wurtzite structure and has a wide band gap.

Table 3

Semiconductors with the sphalerite (S) or wurtzite (W) structure

	GaN	GaP	GaAs	AlN	ZnO	ZnSe	β-AgI
Type	W	S	S	W	W	S	W
a 0 (nm)	0.319	0.5451	0.5653	0.311	0.3253	0.5668	0.458
c 0 (nm)	0.519	–	–	0.498	0.5213	–	0.7494
E g (eV)	3.44	2.26	1.42	6.2	3.3	2.7	2.63
λg (µm)	0.36	0.59	0.87	0.20	0.38	0.46	0.47

Those compounds with higher ionicity tend to cryst<span class="Chemical">allize in the <span class="Chemical">wurtzite structure, and the higher ionicity goes along with a larger E g. For GaP, the optical transparency reaches the visible range and wafers are transparent to red light. AlP (wider E g = 2.45 eV) with the sphalerite structure only has relevance as a semiconductor in mixed crystals with other A III B V compounds. Pure AlP, in contrast with other group 3 phosphides and arsenides, tends to hydrolyze with moisture to form poisonous phosphine gas (PH3) and is used as a pesticide. Gallium and indium phosphides, arsenides and, partially, antimonides for semiconductor applications are typically grown as bulk single crystals from the melt, either by crystallization inside a crucible from the bottom to the top (Bridgman; vertical gradient freeze or VGF) or by pulling (Czochralski). Arsenides and more so phosphides tend to have a large arsenic or phosphorus vapour pressure (up to several tens of bar) at their melting points. Disintegration of these semiconductor compounds can be avoided by overpressure and ‘liquid encapsulation’ of the material with B2O3, which melts at 450°C, significantly lower than the semiconductor, and forms a liquid layer on top of the melt.

Among the group 3 <span class="Chemical">nitrides, BN has not yet reached its full poten<span class="Chemical">ti<span class="Chemical">al. Different modifications occur and for the wurtzite-type E g = 5.2 eV is reported, which makes the material almost an insulator. An excellent database on this interesting compound can be found on the World Wide Web (Ioffe Database, 2014 ▶; http://www.ioffe.ru/SVA/NSM/Semicond/BN/index.html). For the other group 3 elements, the affinity to nitrogen decreases in the order Al–Ga–In, which results in decomposition of the nitrides upon heating below their melting points. In fact, InN is so far only relevant as an admixture to (Al,Ga,In)N mixed crystals because the growth of single crystals is difficult. InN layers were obtained by hydride vapour-phase epitaxy (HVPE), a technique that will be explained below in the context of GaN (Sato & Sato, 1994 ▶), and InN nanowires were obtained from the gas phase in a vapour–liquid–solid (VLS) process (Tang et al., 2004 ▶). The stability of AlN is shown in the T–log[p] phase diagram in Fig. 4 ▶ where, below atmospheric pressure, AlN(s) is in equilibrium with the gas phase only (sublimation) and at intermediate pressure with the gas phase (containing N2 + Al) and the remaining molten Al, and only at high p does melting of AlN occur. The calculated triple point here is 2830°C and 17.4 bar. The accurate position of this triple point is still under discussion, and some other references claim high a p N beyond 100 bar (Ioffe Database; http://www.ioffe.ru/SVA/NSM/Semicond/AlN/thermal.html), but it should be acknowledged that it is almost impossible to measure exact values under such extreme conditions. Experimentally, AlN decomposition starts at a significantly lower T than the AlN(s) phase boundary in Fig. 4 ▶ if the material is heated in gases other than N2. The current author has obtained a 10% mass loss from a 33 mg AlN sample that was heated in a differential thermal analysis (DTA)/thermogravimetry (TG) apparatus in a helium atmosphere to 2040°C (unpublished results).

Figure 4

Temperature–pressure phase diagram for AlN, demonstrating the decomposition AlN  Al + 0.5N2 at insufficient pressure. Calculated using FactSage 6.4.

The extre<span class="Chemical">me condi<span class="Chemical">tions that are required to maintain a solid–liquid equilibrium for <span class="Chemical">AlN make sublimation growth more feasible, and indeed it is typically performed at T > 2040°C and p ≲ 1 bar (Hartmann et al., 2013 ▶). For GaN the establishment of suitable growth conditions is more difficult, because gallium (in contrast with aluminium) does not evaporate sufficiently for sublimation growth. In fact, Ga is the chemical element with the broadest range of liquid-phase stability under ambient pressure: 29.8 ≤ T (°C) ≤ 2203 (FactSage 6.4 Thermodynamic Databank; GTT Technologies, 2013 ▶). However, Karpiński et al. (1984 ▶) showed that, at high p and T, nitrogen does dissolve significantly in liquid gallium; a solubility of 1 mol% N2 was found at 1500°C and 16 kbar, which proved sufficient to establish melt solution growth of bulk GaN. Other technologies for the growth of bulk GaN rely on chemical transport of the gallium species: from a supercritical ammonia solution, 2 inch GaN crystals can now be grown (Dwilinski et al., 2010 ▶).

Hydride vapour-phase epitaxy (HVPE) is an epitaxy process for the depo<span class="Chemical">si<span class="Chemical">tion of semiconductor layers, including <span class="Chemical">GaN. For this process, metallic gallium reacts at ca 850°C with an HCl flow to form gaseous gallium(I) chlorideAfter passing the Ga source, the GaCl/HCl flow (with N2 as the carrier gas) reacts with ammonia and gallium nitride is depositedFig. 5 ▶ shows that, under these process conditions, GaCl gas is in equilibrium with solid GaN and the latter is formed if the HCl fugacity drops distant from the source. Equilibrium (ΔG = 0) for the GaN formation reaction given above is reached under ambient pressure at 918°C. Although HVPE is, in principle, a layer growth process, it is also suitable for the production of bulk material, with growth rates of around 100 µm h−1 and sample thicknesses of several millimetres possible. However, some drawbacks have to be taken into account: (i) as a side reaction between HCl and NH3, large quantities of solid NH4Cl are formed that can obstruct the system; (ii) HVPE-grown GaN is bowed, which interferes with the production of planar wafers (Lipski et al., 2012 ▶). Jacobs et al. (2010 ▶) showed that, in systems containing graphite, the halogen Cl can be replaced by the pseudo-halogen CN, and gaseous gallium(I) cyanide (GaCN) transports Ga. Crystalline GaN is then deposited either by the thermal decomposition of GaCN or by a reaction that is analogous to that of the common HVPE growth technique given above.

Figure 5

Predominance diagram for the Ga–N–H–Cl system for a prevailing NH3 fugacity of 1 bar. Calculated using FactSage 6.4.

Strite & Morkoç (1992 ▶), and more recently O’Leary et <span class="Chemical">al. (2006 ▶) with a deeper in<span class="Chemical">sight into electronic proper<span class="Chemical">ties, reviewed AlN, GaN, InN and their solid solutions, which cover a wide range of E g: 6.2 ≥ E g (eV) ≥ 0.68. Meanwhile, remarkable technological progress has been achieved, and now (Al,Ga,In)N-based devices are the basis for solid-state lighting applications. Because GaN and AlN substrates are still scarce and expensive, homoepitaxy plays no significant role and is still used mainly for basic research (Funato et al., 2012 ▶). Heteroepitaxy is performed on different surfaces of α-Al2O3 (sapphire), mainly (0001) but also and . Other useful substrates are several A III B V compounds such as GaAs, SiC polytypes and ZnO. LiAlO2 and LiGaO2 are interesting alternatives because their epitaxial misfit is much lower compared with e.g. sapphire, and large bulk single crystals for substrates up to 2 inch diameter are also available. After epitaxy, the substrates can easily be dissolved in dilute acids, which makes contacting of epitaxial layers from both sides feasible (Liu, 2004 ▶; Veličkov et al., 2008 ▶). Fascinating new possibilities are offered by the integration of GaN in silicon technologies, especially for high-electron-mobility transistors (HEMTs) (Hu et al., 2014 ▶). Even if the lattice mismatch for GaN(0001) on Si(111) is as large as 17%, satisfactory layers can be grown in such ‘GaN-on-Si’ systems by metal–organic chemical vapour deposition (MOCVD) using graded buffer layers (Drechsel et al., 2012 ▶).

Among the other substances in Table 3 ▶, <span class="Chemical">zinc oxide has by far the greatest prac<span class="Chemical">tic<span class="Chemical">al impact nowadays. It is a typical direct wide band gap semiconductor and its properties are reviewed in numerous articles (Look, 2007 ▶; Janotti & Van de Walle, 2009 ▶; Klimm et al., 2011 ▶). As for some other oxide semiconductors, the electronic properties of the ZnO surface are significantly different from the bulk, and can be manipulated by doping or adsorbance layers. The latter effect is used for gas-sensing applications, whereas ZnO ceramics with a small proportion of an additive such as Bi2O3 or other oxides have an extremely nonlinear resistance resulting from the grain/interlayer/grain boundaries. This nonlinearity is so large that ceramic ‘varistors’ are commercially produced with negligible resistance above and almost infinite resistance below a threshold voltage.

Like most other <span class="Chemical">oxide semiconductors, <span class="Chemical">ZnO is intrin<span class="Chemical">sically n-type. Numerous attempts to obtain stable p-type conductivity with a technologically adequate hole concentration and mobility have failed so far. This is a severe drawback compared with Al–Ga–In nitride and restricts or even prohibits the manufacture of many devices. If the n-type conductivity of ZnO is enhanced, for instance by doping with aluminium, then transparent electrodes, e.g. for solar cell applications or flat screen panels, can be produced which are much cheaper than ITO (indium tin oxide) electrodes (Kluth et al., 1999 ▶). Grundmann (2010 ▶) reports an electron concentration of around 1021 cm−3, a Hall mobility of 47.6 cm2 V−1 s−1 and a resulting specific resistivity of 8.5 × 10−5 Ω cm.

Other oxides

<span class="Chemical">ZnO is the only semi<span class="Chemical">conducting oxide materi<span class="Chemical">al presented in Table 3 ▶. As a result of the high electronegativity of oxygen (3.5) compared with the anions of classical semiconductors (S 2.5, P 2.1 and As 2.0), oxides tend to have a comparatively high ionicity and wide E g. Nitride semiconductors (electronegativity of N = 3.0) are in this respect intermediate between oxides and classical semiconductors.

Many <span class="Chemical">metal oxides are true isolators with a lar<span class="Chemical">ge band gap, such as α-<span class="Chemical">Al2O3 (corundum). The elements that follow aluminium in group 3 of the periodic system, and some other elements such as tin, lead, bismuth and titanium, have oxides with E g values that fall into the range of wide band gap semiconductors. The terms ‘transparent conducting oxide’ (TCO) or ‘transparent semiconducting oxide’ (TSO) are often used for such substances which combine optical transparency with electrical transport properties.

An increa<span class="Chemical">sing number of <span class="Chemical">TCO and TSO compounds have been studied during the last decade, and some of them can be found in Table 4 ▶. Ramesh & Schlom (2008 ▶) reviewed the status and prospects of ‘oxide electronics’, which have already yielded some remarkable results with technological relevance. The replacement of SiO2 in MOSFET gates by ‘high-κ’ materials, enabling a higher packing density of circuits, is an instructive example. Initially, experiments focused on well known substances such as BaTiO3, but failed because the gates degraded. Hubbard & Schlom (1996 ▶) and Schlom & Haeni (2002 ▶) performed a thermodynamic search for metal oxides that are stable in contact with silicon, which has a high oxygen affinity. About one decade after their discovery that hafnium oxide (HfO2) belongs to the few compounds which might replace SiO2, this high-κ material was introduced into the production of devices. However, thermodynamic equilibria have to be considered not only for the implementation of oxides into silicon electronics; redox equilibria also play a major role in the bulk or layer growth of oxides, more than is typically observed for other anions such as nitride or sulfide.

Table 4

Some wide band gap oxides

	α-Al2O3	β-Ga2O3	In2O3	SnO2	CuAlO2
Structure	Corundum	Monoclinic	Bixbyite	Rutile	Delafossite
Space group		C2/m		P42/mnm
a 0 (nm)	0.51284	1.2214	1.0117	0.47397	0.2857
b 0 (nm)	–	0.30371	–	–	0.2857
c 0 (nm)	–	0.57981	–	0.31877	1.6939
Angle (°)	α = 55.28	β = 103.83	–	–	–
E g (eV)	8.3	4.8	3.6	3.6	2.22

This dif<span class="Chemical">ference can be explained mainly by the vast number of dif<span class="Chemical">ferent <span class="Chemical">metal oxides that exist, in particular for the subgroup elements, with consequently smaller phase stability fields for each of them. Among the 4776 compounds of the FactPS thermodynamic database (FactSage 6.4; GTT Technologies, 2013 ▶) can be found e.g. for manganese, four oxides, two sulfides and two nitrides; for copper, two oxides, two sulfides and one nitride; and for titanium, 12 oxides, five sulfides and one nitride.

If <span class="Chemical">metal oxides with oxida<span class="Chemical">tion states m and m + 1 can transform via the redox equilibriumthen the Gibbs free energy chan<span class="Chemical">ge of this reaction is proportional to ΔG = RT ln[p O] if the fugacity of both oxides can be neglected. Plots of RT ln[p O] versus T are linear and separate predominance fields are observed for subsequent metal oxides (Cahn et al., 1991 ▶; Klimm et al., 2009 ▶). In a similar manner, the behaviour of one or more metals in dependence of several nonmetal fugacities can be calculated and yields predominance diagrams (T = constant) with straight phase boundaries. With this type of diagram, Fig. 5 ▶ explains the HVPE process for GaN, and Fig. 6 ▶ shows the equilibria between cadmium, oxygen and sulfur for two different temperatures.

Figure 6

Predominance diagram of the Cd–O–S system for two temperatures.

Heterostructures of <span class="Chemical">almost every compo<span class="Chemical">si<span class="Chemical">tion can be grown in modern epitaxial systems and, under sufficiently low T, nonequilibrium states can also be produced because they are metastable. However, one should be aware that, over time and especially if T increases e.g. in an active device, metastable structures might approach equilibrium. This is exactly what happened with BaTiO3 MOSFET gates before the introduction of HfO2! From Fig. 6 ▶ one reads that CdO and CdS are in equilibrium for a wide T range, and consequently heterostructures of the oxide and sulfide are possible. This agrees with experimental results (Li et al., 2009 ▶). On the other hand, for very high fugacities of O2 and S2, the sulfate CdSO4 is a stable intermediate phase between oxide and sulfide. Such an optional intermediate phase should not be forgotten for other heteroepitaxial systems such as nitride and oxide (Shimamura et al., 2005 ▶). The observation of NO bond signatures by photoelectron spectroscopy of oxidized InN surfaces (Eisenhardt et al., 2012 ▶) could hint at the formation of indium nitrate [In(NO3)3] or nitrite [In(NO2)3] as an intermediate phase between InN and In2O3.

Chemic<span class="Chemical">al stability con<span class="Chemical">sidera<span class="Chemical">tions also play a major role for the bulk growth of oxide crystals that can be used for substrates. At least ZnO, Ga2O3, In2O3 and SnO2 have in common that a high (in the case of SnO2 not even accessible) melting point exceeding 1800°C is combined with a comparatively high p O, which is necessary to avoid decomposition of the MeO oxide to metal (Me) and oxygen. Certainly for ZnO, a very broad range of methods have been published that allow one to circumvent the stability problem mentioned above, and these methods are more or less suitable for other wide band gap semiconducting oxides as well. These methods include:and were reviewed elsewhere (Klimm et al., 2011 ▶).

(i) growth from solu<span class="Chemical">tions, either <span class="Chemical">water- or <span class="Chemical">ammonia-based (often hydrothermal/ammonothermal conditions), or from molten salts (e.g. top-seeded solution growth, TSSG);

(ii) growth by phy<span class="Chemical">sic<span class="Chemical">al vapour transport (PVT, sublima<span class="Chemical">tion) or chemical vapour transport (CVT);

(iii) growth from the <span class="Chemical">melt, either from cold crucibles (‘skull <span class="Chemical">mel<span class="Chemical">ting’) or from hot iridium crucibles with a ‘reactive atmosphere’;

Bulk growth of the most important semiconductors, <span class="Chemical">silicon and <span class="Chemical">gallium arsenide, is exclusively performed from the melt, and ZnO (Schulz et al., 2006 ▶), β-Ga2O3 (Víllora et al., 2004 ▶; Aida et al., 2008 ▶; Galazka et al., 2010 ▶) and In2O3 (Galazka et al., 2013 ▶) can also be grown in this way. Tin(IV) oxide (SnO2) has not been melt-grown so far; the melting point of this substance is certainly much higher than 1630°C, as given in several references and databases (FactSage 6.4; GTT Technologies, 2013 ▶).

Klimm et <span class="Chemical">al. (2009 ▶) reported that the par<span class="Chemical">ti<span class="Chemical">al thermal dissociation of carbon dioxide gives the basis for melt crystal growth of oxides in a reactive atmosphere. Pure CO2, or (for a somewhat lower oxygen fugacity) CO2/CO mixtures, can give such a ‘self-adjusting atmosphere’, where p O(T) meets the stability field of the desired oxide for all T. For the semiconducting oxides mentioned so far, comparatively large p O(T) are required, and Fig. 7 ▶ explains why bulk crystal growth of SnO2 from the melt is so difficult: the required oxygen fugacity is so high that it cannot be produced by CO2 dissociation. As reported by Galazka et al. (2014 ▶), it is not the high melting point itself that is the problem, rather the oxide phase instability becomes an issue if the required oxygen fugacity approaches the p O(T) line of CO2, and growth is probably impossible this way if it is beyond the line.

Figure 7

The minimum oxygen fugacities of several transparent conducting oxides at their melting points T f, compared with the p O(T) that results from the thermolysis of carbon dioxide.

For β-<span class="Chemical">Ga2O3, lar<span class="Chemical">ge bulk crystals (EFG grown ribbons, and float zone and Czochralski boules) are available and epitaxial techniques (MOCVD, MBE) have been developed. Higashiwaki et al. (2012 ▶) reported the production of a metal–semiconductor field-effect transistor (MESFET) out of this material, and a high on/off drain current ratio of ∼10 000 was reached. The authors claimed that very high breakdown fields of around 8 MV cm−1 should be feasible with β-Ga2O3, which is almost as good as diamond (10–20 MV cm−1) and outperforms both the current high-power material 4H-SiC (2.5 MV cm−1) and also GaN (3.3 MV cm−1). Monoclinic β-Ga2O3 is the stable modification between the melting point and room temperature, enabling melt growth of bulk crystals. With epitaxial growth on sapphire (α-Al2O3) substrates and by alloying, α-(Al,Ga,In)2O3 layers can be grown which allow band-gap tuning from 3.8 to 8.8 eV (Fujita & Kaneko, 2014 ▶).

Nearly <span class="Chemical">all <span class="Chemical">oxide semiconductors are intrin<span class="Chemical">sically n-type, which is a result of the strong localization of holes (if formed by doping or nonstoichiometry) at the oxide ions and impedes the development of devices with p–n junctions. This is a general problem for all oxide semiconductors and cannot be overcome completely, but some circumstances such as tetrahedral coordination of oxide ions and some degree of covalency can improve p-type conductivity (Banerjee & Chattopadhyay, 2005 ▶). Kawazoe et al. (1997 ▶) demonstrated that delafossite-type CuAlO2 combines an encouraging p-type conductivity with transparency to visible light. The carrier density of 1.3 × 1017 cm−3 and the Hall mobility for holes of 10.4 cm2 V−1 s−1 were explained by a strong hybridization of the oxygen 2p orbitals with the 3d 10 electrons of the Cu+ closed shell, leading ultimately to a low hole effective mass. These ideas were the basis of an extended numerical study by Hautier et al. (2013 ▶). For 3052 binary and ternary oxides, density functional theory (DFT) computations were performed to identify substances with a low hole effective mass and a large band gap. Some substances which have so far been rarely studied could be promising here: K2Sn2O3, Ca4P2O, Tl4V2O7, PbTiO3, ZrOS, B6O and Sb4Cl2O5. It should be noted that the well known good hole mobility of Cu2O (which has, however, a small E g ≃ 2.1 eV) and CuAlO2 could be reproduced too.

<span class="Chemical">Copper exists in most compounds as <span class="Chemical">Cu2+, and the untypical low-valency Cu+ is directly responsible for the p-type conductivity of CuAlO2 and Cu2O. In a similar manner, SnO2 is the ‘normal’ tin oxide and n-conducting, whereas potassium stannate(II) (K2Sn2O3; Hautier et al., 2013 ▶), like tin(II) oxide (SnO), shows hole conductivity (Ogo et al., 2008 ▶). It is certainly possible to obtain small quantities of such low-valency oxides, either as epitaxial layers or in the bulk, just by crystallizing them together in an oxygen-poor atmosphere. This was demonstrated by Yoon et al. (2013 ▶) with millimetre-sized CuAlO2 crystals that could be grown from a Cu2O melt flux. Some time ago, Gadalla & White (1964 ▶) showed that, in air, CuAlO2 becomes unstable below 1030°C, undergoing partial oxidation to CuO. The stability diagram in Fig. 8 ▶ was calculated using FactSage 6.4. It demonstrates that the CuI compound CuAlO2 has a stability field between metallic copper for lower p O and CuO for higher p O. The calculation of such diagrams requires that thermodynamic data such as G(T) are available for the intermediate phase, here CuAlO2. But even if this is not the case, a coarse approximation can be reached if the relevant phase is simply neglected for the equilibrium calculation. An intermediate phase field, α-Al2O3 + Cu2O, then appears instead at almost the same place; just the upper and lower phase boundaries are shifted ca 5 kJ mol−1 inwards. This is because the formation energy for Al2O3 + Cu2O 2 CuAlO2 is not taken into account. The major contributions to the Gibbs free energy of the system result from the equilibria between the subsequent oxidation states of copper. Hence, it is almost sufficient to have G(T) data for all relevant element oxides available. One can expect that working in a suitable reactive atmosphere will pave the way to bulk crystal growth conditions where the delafossite phase can be kept thermodynamically stable.

Figure 8

Ellingham predominance diagram of the Cu–Al–O2 system with [Cu]:[Al] = 1:1.

Summary and conclusions

The successful story of technologic<span class="Chemical">al semiconductor applica<span class="Chemical">tions started in the early 1950s with the first p–n junc<span class="Chemical">tions, which were made inside Czochralski-grown germanium single crystals. For electronic applications, germanium is nowadays replaced almost completely by silicon. Optoelectronics, mainly based on A III B V compounds such as GaAs, opened a new field for semiconductors in the 1970s, but the arsenides and phosphides which could be grown in that time have a narrow band gap, enabling optical emission only from the infrared to the green spectroscopic range. This is sufficient e.g. for displays, indicators and optical data transmission, but not for general illumination, as the blue range is missing.

Beginning in the late 1980s, the successful growth of sever<span class="Chemical">al <span class="Chemical">nitrides, especi<span class="Chemical">ally the wide band gap semiconductors GaN and AlN on sapphire substrates, widened the accessible wavelength range into the ultraviolet region. White light can now be produced for solid-state lighting, with a positive impact on global energy consumption by replacing incandescent light bulbs with light-emitting diodes.

The substance p<span class="Chemical">aln>ette is extended by dif<span class="Chemical">ferent polytypes of <span class="Chemical">silicon carbide (SiC) and several oxides, such as ZnO, β-Ga2O3 and In2O3. These wide band gap semiconductors are used as substrates for layer deposition of the more classical semiconductors mentioned above, as well as for active devices. Unfortunately, the still unsatisfactory p-type conductivity of semiconducting oxides is an issue which significantly hinders the development of devices. Wide band gap semiconductors such as SiC, GaN and β-Ga2O3 have potential not only for optoelectronics, but also for high-power devices.

For so<span class="Chemical">me recently reported or<span class="Chemical">ganic–inor<span class="Chemical">ganic perovskite-type substances such as CH3NH3PbBr3 (Kojima et al., 2009 ▶) and CH3NH3SnI3 (Hao et al., 2014 ▶), band gap tuning is possible by substitution of the halide and/or metal ion. They have been used as absorbers in solar cell structures, enabling power conversion efficiencies greater than 15%. One can hope that further progress is possible here, but it seems too early to include this substance group into this review.