Hydrogen and the Light-Induced Bias Instability Mechanism in Amorphous Oxide Semiconductors

Hydrogen is known to be present as an impurity in amorphous oxide semiconductors at the 0.1% level. Using amorphous ZnO as a simplified model system, we show that the hydrogens pair up at oxygen vacancies in the amorphous network, where they form metal-H-metal bridge bonds. These bonds are shown to create filled defect gap states lying just above the valence band edge and they are shown to give a consistent mechanism to explain the negative bias illumination stress instability found in oxide semiconductors like In-Ga-Zn-O (IGZO).

Amorphous oxide semiconductors (AOS) such as In,Ga,Zn oxide (IGZO) are now widely used as thin film transistors (TFTs) in high resolution liquid crystal displays and as driver transistors of organic light emitting diode (OLED) displays, because of their higher electron mobility than hydrogenated amorphous silicon (a-Si:H) [1][2][3][4][5] . However, there remains the problem that the TFTs suffer from the negative bias light induced stress instability (NBIS), a shift of the gate threshold voltage during negative bias stress and illumination [6][7][8][9][10][11] . In NBIS, a slightly sub-bandgap light excites electrons from some filled defect states just above the valence band edge to the conduction band, where they produce a persistent photoconductivity (PPC) 7,11 . The defect states responsible are seen in hard X-ray photo-emission 12 , but their cause is still contentious.
There have been various models to account for this instability, involving oxygen vacancies 11,[13][14][15][16] , oxygen interstitials [17][18][19][20] , or hydrogen impurities 18,21,22 , but each of these models has its flaws. The instability has often been attributed to the oxygen vacancy as this is a common defect in oxides and the instability is worse in O-deficient films 15,16 . The O vacancy also has the 'negative-U' property 23,24 which is a mechanism that creates an energy barrier to carrier recombination and thus it explains the persistence of the photoconductivity 11 . However, the problem is that the vacancy states lie too high in energy in the band gap 24,25 compared their energy as seen by photoemission 12 .
The second model based on oxygen interstitials does produce states in the required energy range 17,18 , as seen in random network models 19 , and these can also have the negative-U like property 18 . However, the problem is that they are an oxygen excess defect while annealing the film in an oxygen excess is known to reduce the instability 15,16 . A related model to the O vacancy model links the instability with the presence of In 1+ valence sites whose In 6s lone pair states lie in the required energy range. However, this valence is not seen in the photoemission core level spectra 20 .
A final possibility is that it is due to hydrogen. It has been proposed that single hydrogen atoms could undergo a deep to shallow transition and become donor-like 21,22 . However, this defect does not correspond to an oxygen deficiency and there is little other evidence for this mechanism.
Thus, in this paper we propose a new mechanism in which the instability is associated with a complex of two hydrogen atoms at an oxygen vacancy, a V O /2H complex. This is an adaptation of the model of Du and Biswas 26 for hidden hydrogen in c-ZnO. We will show that this defect complex in the amorphous phase gives a consistent explanation of the bias stress instability and its persistent photo-conductivity. The complex gives rise to gap states lying just above the valence band maximum (VBM) as seen by photoemission, it clearly has an oxygen deficiency, it has the negative U property, and it has a low formation energy in the amorphous phase. In its neutral configuration, the hydrogens form 3-center bridging sites, whose vibrational signature has recently been seen experimentally in infra-red (IR) by Bang et al. 27 . It should be noted that a considerable hydrogen content of over 10 20 atoms cm −3 is seen in a-IGZO by thermal desorption spectroscopy or secondary ion mass spectrometry (SIMS) [28][29][30] , which is many orders of magnitude more than that seen in crystalline (c-) ZnO. This concentration is similar to the density of sub-gap defect states seen in the amorphous films by photoemission 12 , and much larger than the photo-excited carrier density created by NBIS 8 .
Hydrogen has a complicated role in oxide semiconductors. In c-ZnO or a-IGZO, interstitial hydrogen acts as a shallow donor 31,32 . In this case the hydrogen is bonded to an oxygen atom as a O-H bond. However, in the amorphous case, all the 10 20 cm −3 hydrogens cannot be acting as donors, most must be compensated in some way. One way would be if the hydrogens were compensated by interstitial O acceptors. However this would not have the necessary O deficiency. We show that the lowest energy of H pairs in a-ZnO is the V O /2H state which is self-compensated for E F above 2 eV. In this state, the hydrogens exist as anionic H − , forming bridge bonds to metal atoms.
To show this, we study the incorporation of H 2 and water into an a-ZnO network. We use a-ZnO as a simplifying model of the a-IGZO network 32 , as it has a higher symmetry crystalline phase, c-ZnO. We first create a random network of a-ZnO by density functional molecular dynamics using the CASTEP code 33,34 , and then substitute an H 2 molecule for an oxygen site and study its different charge states. We then introduce an H 2 O molecule into the defect-free network and study its behavior. Finally we consider the migration of the hydrogens from the dissociated water molecule to the oxygen vacancy. These results show that hydrogen or water can passivate the vacancy, but only at the expense of introducing states which lead to the possibility of the NBIS effect. Figure 1 shows the resulting 96 atom random network of ZnO. Most Zn and O atoms are 4-fold coordinated but some are 3-fold coordinated, reminiscent of the undercoordinated defects in a-GaAs 35,36 . Figure 1(b) shows the density of states (DOS) calculated using the screened exchange (sX) hybrid functional 34 . sX corrects the band gap error of simple density functional theory. We see that the band gap is 3.2 eV, slightly smaller than that of the crystal.

Results and Discussion
We first consider the case of inserting H 2 into c-ZnO. Figure 2(a,b) shows an H 2 molecule at an O vacancy in ZnO. Its simplest configuration is the V O 2+ (2H) state. Here, the four metal dangling bond orbitals pointing into the vacancy are empty. This leaves two electrons on the two hydrogen atoms. These form a neutral H 2 molecule trapped inside the vacancy. This molecule gives rise to a filled H-H bonding state lying at −6.5 eV below the ZnO valence band, whose wavefunction is shown in Fig. 2(b), and an empty anti-bonding state lying near + 5.5 eV in its conduction band, as is seen in the partial density of states plots of Fig. 2(a). We find that a H 2 molecule at a vacancy has essentially the same total energy as it has in free space 26 .
The second configuration of interest is the neutral V O°( 2H) state, as seen in Fig. 2(c,d). In this charge state, the complex has a completely different configuration of C 2v symmetry consisting of two 3-center Zn-H-Zn bridges. Each bridge uses two of the four Zn dangling bond orbitals at the vacancy. Each bridge creates three states; a filled 3-center bonding state lying at −5.5 eV whose wavefunction is shown in Fig. 2(d, upper panel), a filled 3-center state lying at +1.2 eV above the VBM, which is anti-bonding along the Zn-H bonds, whose wavefunction is shown in Fig. 2(d, lower panel), and finally an empty Zn-Zn antibonding state lying well into the conduction band at roughly 5 eV. The energies of the states agree with those found by Du and Biswas 26 . We also note that the PDOS of the neutral V O /2H complex in a-ZnO has a very similar energy spectrum to that in c-ZnO, comparing Fig. 2(c,e), showing that the bonding is similar in the two phases, although the gap state does lie slightly closer towards the valence band in a-ZnO.
A molecular orbital diagram showing the layout of these states is shown in Fig. 3. The ideal O vacancy has T d symmetry, and its vacancy orbitals form one A 1 and three T 2 states. When it acquires C 2v symmetry the T 2 states split into one of A 2 symmetry and a pair of B 2 symmetry. Meanwhile, the hydrogen orbitals form a symmetric and antisymmetric pair. The symmetric state interacts with the A 1 vacancy state and the antisymmetric one interacts with the A 2 vacancy state, each forming bonding and antibonding configurations. The four available electrons then fill the resulting two bonding states. The A 1 state lies at −5.5 eV and the A 2 state, being the key gap state, lies at +1.2 eV. The fact that both of these states are filled means that the H orbitals are overall 100% filled, giving the hydrogens an anionic H − configuration 24 . As the hydrogens have an H − configuration, the H − pair is essentially iso-electronic with the O 2− ion. Figure 4(a) shows the defect formation energies for the hydrogen interstitial donor and the V O /2H complex in c-ZnO. As noted by Du and Biswas 26 , the donor is the more stable configuration over the important range of Fermi energies (above midgap).
Although it is the same V O /2H defect complex as in c-ZnO, it has rather different properties in the amorphous phase a-ZnO because of changes in the free energies. This arises because a-ZnO has a lower mass density of 4.62 g/cm 3 compared to 5.  Figure 4(b) shows the calculated defect formation energies of the V O /2H complex in a-ZnO for each charge state. We see that the 0 and +2 states are the most stable over the critical range of Fermi energies, above midgap. The H + interstitial is less stable than the 2H/V O complex, over the range of Fermi energies, as seen in Fig. 4(b). Thus, the complex is a negative U defect. This is different to the situation in c-ZnO. This explains the compensation of hydrogen in a-ZnO, and is significantly different to c-ZnO.
The large positive defect formation energy of neutral V O /2H in c-ZnO means that the concentration of the V O /2H complex or 'hidden hydrogen' in c-ZnO is quite low, ~10 16 cm −3 . Its much lower formation energy of this defect in a-ZnO means that there is an orders of magnitude higher H concentration in the amorphous phase, even for a lower formation temperature. In addition, the formation energy of the V O /2H complex in the H-rich condition in a-ZnO is lower than that for the interstitial H donor configuration H i in Fig. 4(b), so that the compensated V O /2H complex configuration is dominant. Nomura et al. 28 noted that IGZO typically contains a large concentration of hydrogen due to the poor vacuum pumping in the typical sputtering systems used for oxide deposition. Bang et al. 27 identified the infra-red vibrational modes of the Zn-H-metal bridge groups in IGZO, and that they were more thermally stable than the vibrational modes of the O-H group. The greater stability of the Zn-H-metal bridge groups is because these defects are trapped at an O vacancy 37 . In contrast, the hydrogens at O-H bonds are interstitial, and migrate easily, as noted by Wardle et al. 38 .
Our calculations show that the states of metal-H bridge bonds are the typical cause of filled gap states at 1.0 eV above the valence band edge seen by X-ray photoemission 12 . Electrons in these states can be excited by photons of energy 2.5 eV into the conduction band and give the observed persistent photoconductivity 6,8,9 . These electrons can drift to the gate dielectric interface 7,9 , giving a charge that causes a negative threshold voltage shift. It should be noted that the V O 0 (2H)/V 0 2+ (2H) group also possesses a negative U, that is its 1+ state is less stable that the neutral or 2+ states. This energy barrier acts, as in the simple O vacancy 23,24 , as a recombination barrier, so maintaining the persistent photoconductivity. Overall, the details of the model have been calculated for the binary oxide a-ZnO, but a similar situation applies to other oxides like a-IGZO, ZnSnO x and In 2 O 3 etc, which all have similar band gaps. ZnO has a 4-fold covalent random network, while the other oxides have more ionic bonding associated with the In or Sn sites. Nevertheless the behaviour of H at an O vacancy is similar in each case, Fig. 5(a,b), in that it gives rise to Zn-H-Zn bridges with filled states in the lower band gap region, which can be photo-excited.
We finally consider the addition of a water molecule to the ZnO network. Figure 5(a,b) shows the water in crystalline and amorphous ZnO. The H 2 O species dissociates into H and OH groups which insert into a Zn-O bond. The OH group attaches itself to the metal dangling bond and the H attaches to the O dangling bond, resulting in two adjacent -OH groups. The OH groups remain close to each other, bound by a weak hydrogen bonding. In effect, each H is bonded strongly to one O site and weakly bonded to the second O site in an asymmetric bridge configuration resembling that the hydrogen sites in water.
An H 2 O group in ZnO consists of an excess of a H 2 and an O compared to the pure state. Figure 6(a) shows the (ZnO) n .1 H 2 O configuration plus two nearby neutral O vacancies. Figure 6(b,c) shows how two hydrogens from the H 2 O group could move to one of the vacancies and the O of the H 2 O could move to the other vacancy, via the transition state of Fig. 6(b). In the final state of Fig. 6(c), the O has filled one of the O vacancies, and thus passivated it. The two hydrogens have filled the other vacancy, and bonded to all the Zn dangling bonds. They have passivated it in the sense that they have removed the deep mid-gap state associated with a neutral O vacancy in ZnO. They have replaced its mid-gap state with states close to the VBM associated with the Zn-H-Zn bridges. The process has removed states in the upper half of the gap and mid-gap traps that affect the operation of the oxide as an n-type transistor. Thus the water molecule has passivated states affecting the transistor action, as seen experimentally 37,38 .
Finally it is interesting to compare the behavior of hydrogen in a-ZnO with that a-Si:H. Although hydrogen passivates the single Si dangling bond in a-Si:H 39 , it seems that hydrogen occurs mostly in pairs in Si or a-Si:H [40][41][42] . For example in crystalline Si, H will form the H 2 * defect, which is a low energy hydrogen configuration caused by inserting two hydrogens into a Si-Si bond 40 . This two hydrogen defect has an even lower energy in the a-Si:H network, and is also strongly involved in the network growth process of a-Si:H 42 . It is the main defect in the instability mechanisms of a-Si:H 43,44 . In the same way, the two-hydrogen defect is more stable in a-ZnO than in c-ZnO and this causes its leading role in the amorphous oxide semiconductors.

Summary
In summary, it is proposed that the sizable hydrogen content seen in amorphous oxide semiconductors exist as hydrogen atom pairs trapped at oxygen vacancies. These form metal-H-metal bridge bonds in oxide semiconductors and are the source of the negative bias illumination stress instability observed in these materials. Our calculations show that such bonds give rise to defect states in the lower gap region which are the cause of this instability.

Methods
The calculations are carried out using 96 atom supercells of amorphous ZnO. These are created by a molecular dynamics (MD) anneal at 2000K for 20 ps, followed by a quench to 300 K in 20 ps. The calculations are carried out using the CASTEP plane wave pseudopotential code 43,44 . It uses norm-conserving pseudopotentials with a cutoff energy of 760 eV. The energies are converged to 10 −5 eV per atom, and forces to under 0.01 eV/Å. Density functional theory (DFT) greatly under-estimates the band gap of ZnO which can lead to errors, particularly in the description of the donor states of hydrogen. For static calculations, these can be rectified by using hybrid functionals such as the screened exchange functional for the electronic exchange-correlation functional [44][45][46] . However, a less expensive method is desirable for the MD stage. For this, we use the GGA + U method. This includes an on-site potential U of 5 eV on the Zn 3d states to lower their binding energy 24,47 . However, this is not enough, and we also add a U potential of 5 eV on the O 2p states to further lower the energy of the valence band maximum 48 .
The transition states of intrinsic defects are calculated using the Lany and Zunger 49 scheme. The formation energy of each charge state is given by where q is the charge on the system, E q is the energy of charged system with a defect, E H is the energy of charged defect-free system. E V is the valence band maximum (VBM) and E F is the Fermi level with the respect to VBM. n α is the number of atoms of species α, μ α is the relative chemical potential of element α. We note that the first two terms are equal to the difference between the total energy of charged defect system and total energy of neutral defect-free system. The density of c-ZnO is 5.44 g/ cm 3 , the density of a-ZnO is 4.62 g/ cm 3 . The supercell of a-ZnO contains 96 atoms, and has a lattice constant of 11.3 Ǻ. The O vacancy is created by removing one O atom from the supercell, and taking it externally to form half an O 2 molecule. The network or supercell is then relaxed by GGA. For a-ZnO, several oxygen atom sites are sampled to obtain an average defect formation energy. We take the average of the 6 lowest formation energies from 20 sampled sites (high formation energy sites will have a low probability.) The water molecule is inserted into the bulk c-ZnO or a-ZnO network at a Zn-O bond. The structure is relaxed at constant volume.