Ultrabroadband Density of States of Amorphous In-Ga-Zn-O

The sub-gap density of states of amorphous indium gallium zinc oxide ($a$-IGZO) is obtained using the ultrabroadband photoconduction (UBPC) response of thin-film transistors (TFTs). Density functional theory simulations classify the origin of the measured sub-gap density of states peaks as a series of donor-like oxygen vacancy states and acceptor-like metal vacancy states. Donor peaks are found both near the conduction band and deep in the sub-gap, with peak densities of $10^{17}-10^{18}$ cm$^{-3}$eV$^{-1}$. Two deep acceptor-like metal vacancy peaks with peak densities in the range of $10^{18}$ cm$^{-3}$eV$^{-1}$ and lie adjacent to the valance band Urbach tail region at 2.0 to 2.5 eV below the conduction band edge. By applying detailed charge balance, we show increasing the density of metal vacancy deep-acceptors strongly shifts the $a$-IGZO TFT threshold voltage to more positive values. Photoionization (h$\nu$>2.0 eV) of metal vacancy acceptors is one cause of transfer curve hysteresis in $a$-IGZO TFTs owing to longer recombination lifetimes as they get captured into acceptor-like vacancies.

TFTs.Unfortunately, the disordered nature of amorphous oxide thin films such as a-IGZO makes the this an unsolved problem.In addition, measuring sub-gap trap density in amorphous thin film materials like IGZO presents many inherent challenges.Not only is the sub-gap state concentration small (< 10 18 cm -3 ), but the TFT threshold voltage tends to drift, making sensitive transport and photoconductive measurements challenging.
Substantial work has been reported on the characterization of defect states in a-IGZO from first principles, [15][16][17][18] and experiments utilizing both photoexcitation [19][20][21] and electrical 22,23 methods.Most notably, lamp-based optical illumination methods of a-IGZO TFTs, such as photoexcitation charge collection spectroscopy (PECCS), 24 have been successful in identifying the density of defect states in the sub-gap.TFT behavior under illumination has also been shown to depend strongly on photon energy (hν), especially when photoexciting "deep states" near the valence band, [25][26][27][28] which suggests the existence of multiple species of sub-gap states.However, the near-bandgap photoexcited TFT behavior has been attributed to defects related to both excess oxygen, [29][30][31] and contradictorily, the lack of oxygen. 32Thus, ambiguity still remains in the exact structural origin of sub-gap states.
In this work, metal vacancy defects are considered as an alternative explanation for TFT behavior due to near-bandgap photoexcitation.To clarify this point, the density of states (DoS) of a-IGZO is quantified from the TFT photoconduction (PC) response measured from 0.3 to 3.5 eV with continuously tunable lasers.The respective energy distributions of oxygen and metal vacancy defects are found from ab-initio a-IGZO simulations and are used to identify the measured sub-gap states.A direct comparison between the photoexcited behavior of oxygen versus metal vacancies in a-IGZO TFTs supports this assignment.Importantly, acceptor-like metal vacancies are shown to have a large impact on TFT threshold voltage by considering charge balance in a-IGZO, even though they are energetically positioned more than 2 eV below the conduction band minimum.

RESULTS:
Figure 1a plots a representative a-IGZO DoS profile as determined by our ultrabroadband photoconduction technique (UBPC; see Experiment and Analysis for a detailed discussion of the UBPC method).The DoS profile in Fig. 1a derives from the a-IGZO TFT photoconduction (PC) response, shown in Fig. 1b (color map), which is collected for laser excitation energies ranging from hν = 0.3 to 3.5 eV.The resulting PC spectrum is proportional to the total sub-gap trap density, NTot (cm -3 ) plotted in Fig. 1a (gray squares).The sub-gap DoS (g(E-Ec)) in Fig. 1a (black circles) is obtained by numerical differentiation with respect to energy of NTot , i.e., g(E-Ec) = dNTot / dE (cm -3 eV -1 ), where energy is given in reference to the conduction band minimum Eight sub-gap peaks are identified in Fig. 1a and are fitted with Gaussian distributions.
Six of these peaks are ascribed to oxygen vacancies (gold shading), VO, while the two other peaks are attributed to metal vacancies (red shading), VM.A detailed discussion on defect peak identification will follow later using DFT (see First-Principles DoS Analysis), charge balance considerations, and electron capture lifetimes measurements.VO are donors, i.e., neutral when filled with an electron, and positively charged (ionized) when not filled with an electron, whereas VM are acceptors, i.e., negatively charged (ionized) when filled with an electron and neutral when not filled with an electron.The peak energy (ET), density (DT), and width (w, full 1/e width) of Gaussian sub-gap state distributions as well as valence band tail parameters, obtained from the DoS in Fig. 1a are summarized in Table 1.The sum of these distributions constitutes the black line in Fig. 1a. 5][36][37][38] where SD N is the total density of shallow VO donors, ( )  TFT transfer curve in the supplemental section).The threshold voltage, VT, is estimated using the discrete donor trap model 39 once EF is known, given by, where q is the electron charge, CI is the insulator capacitance density (~ 11.5 nF cm -2 , for 300 nm of SiO2 gate dielectric), and 0 DA N is the density of neutral metal vacancy deep acceptor states.
As VM deep acceptor density increases from 17 10 to 18 10 cm -3 in Fig. 1c  conditions, the hv = 2.5 eV curve deviates greatly.In particular, the turn-on of the hv = 1.4 eV illuminated curve is well behaved, showing almost no hysteresis.By contrast, the hv = 2.5 eV curve is highly non-ideal, exhibiting a large amount of clockwise hysteresis and a much higher VT shift, with the maximum current decreased, and the minimum current increased.The hysteresis voltage, VH, is given as the separation of forward and reverse sweeps at ID = 10 -10 .
Figure 2b illustrates another photoinduced trend, in which the PC response of an a-IGZO TFT is monitored during and after laser excitation (see inset of Fig. 2b).After hν = 1.4 eV photoexcitation (Fig. 2b, gold curve) the fall time is noticeably shorter than the fall time associated with hν = 2.5 eV photoexcitation (Fig. 2b, red curve).To quantify this, the average PC decay fall time (τ) is given as the 1/e lifetime of the longest monoexponential component (dashed line fits), which is attributed to electron recombination with vacancy defect sites.
Hysteresis and PC-lifetime trends as a function of photon energy are displayed in the upper two panels of Fig. 2c.Comparison of Fig. 2ci and ii shows a clear onset exists when hν > ~ 2 eV, above which the hysteresis voltage and the PC fall time both abruptly increase.We ascribe this onset to the initiation of metal vacancy photoexcitation.The key point here is that recombination of photoexcited electrons is found to be more sluggish when electrons are photoexcited from metal vacancy states than from oxygen vacancy states.Why is this?
We believe that this photoexcited electron recombination trend is associated with the acceptor-or donor-like nature of the metal or oxygen vacancy, respectively.This follows from the fact that the electron capture time, τc, is given by τc ≈ 1/(σn vth n), where σn is the electron capture cross section, vth is the electron thermal velocity (~ 10 7 cm s -1 ), and n is the free electron concentration.Electron capture by a donor-like defect (e.g., an oxygen vacancy in a-IGZO) is a coulombically-attractive process, i.e., an empty donor is positively charged such that a recombining electron experiences coulombic attraction prior to capture, thus enhancing the probability of its capture.In contrast, electron capture by an acceptor-like defect is an electrostatically neutral process, i.e., an empty acceptor is neutral such that there is no coulombic enhancement to electron capture.The capture cross section for neutral capture is given as σn ~ 10 -15 cm 2 and for coulombically-attractive capture is σn ~ 10 -12 cm 2 , 40 implying that electron capture to donor states is intrinsically more rapid than electron capture to acceptor states.
Reexamining Fig. 2b and Fig 2cii, it becomes clear why the PC decay time is maximal near hν ~ 2.5 eV, since this corresponds to the only area of the spectrum where there are a majority of metal vacancy defect states, which agrees well with predictions based on capture cross section.
Using the simple expression for the electron capture time, τc and the electron concentration, n, we now assess the plausibility of the measured a-IGZO defect electron capture time scales.When an a-IGZO TFT is turned on, the accumulation layer electron concentration can easily reach a value of ~ 10 18 cm -3 (or larger), such that electron recombination is extraordinarily rapid, e.g., τc ~ 10 -10 s (acceptor) or ~ 10 -13 s (donor).However, far away from the accumulation layer where the semiconductor is in depletion, the electron concentration can be 10 8 cm -3 (or smaller), such that electron recombination is much slower, e.g., τc ~ 1 s (acceptor) or ~ 10 -3 s (donor).Thus, since n spans many orders of magnitude across an a-IGZO TFT structure, an extremely wide range of electron capture times is accessed in a photoexcitation experiment.
As a consequence, we argue that the measured photoexcitation fall times of τ ~ 400 µs and ~ 700 µs for donor-like and acceptor-like trap states, respectively, are reasonable since each measured time constant constitutes a spatial average of all possible recombination times.
The photoconduction transient fall times involve a time scale much different than that of ID -VG transfer curve hysteresis, i.e., ~ 10 -4 -10 -3 s, and ~10 s, respectively.Thus, even though each phenomenon is attributed to metal vacancy photoexcitation, the dynamics of these processes will differ significantly since the PC decay curves are measured when the TFT is in accumulation (VG >> VT), while the hysteresis measurements will require the TFT gate voltage to be held at a strong negative bias for part of the ID -VG scan, severely limiting the number free carriers in the device while simultaneously exciting trap states.
Finally, Fig. 2ciii plots the DoS of four high-quality a-IGZO TFTs fabricated with different processing conditions.While the DoS curves exhibit some variability (less than one order of magnitude), the overall similarity of curves in Fig. 2ciii, suggests the DoS profile presented here are characteristic of most high-quality a-IGZO TFTs.Comparison of Fig. 2c.iii to its upper panels might lead the reader to think that the abrupt increase in VT and τ could be associated with the onset of the Urbach tail states.However, note that Fig. 2c.iii is plotted on a log scale, and the Urbach tail increases exponentially to the valence band edge, whereas VT and τ (plotted on a linear scale) only increase until around ~2.6 eV, making their association with Urbach tail states unlikely.Therefore, taken with the above arguments for electron recombination to donor-vs.acceptor-like states, the red shaded area in Fig. 2c.iii most likely contains the extent of metal vacancies in the DoS of a-IGZO, which are responsible for the strong TFT dependencies on photoexcitation when hv > 2.0 eV.

EXPERIMENTAL TECHNIQUE AND ANALYSIS:
The UBPC experimental setup, shown in Figure 3a, chiefly consists of multiple tunable laser sources coupled into a modified scanning photocurrent microscope 41 (SPCM).Coupling is realized using all-reflective optics, enabling diffraction-limited excitation of a-IGZO TFTs using lasers that continuously span a photon energy range of hv = 0.
where d is the thickness of the a-IGZO layer, Cox is the capacitance of the oxide layer, and q is the fundamental electron charge; the partial derivative, /  incident on the TFT active area that produces a meaningful increase in PC magnitude 42 and is used to find the absolute DoS.
max ph N is found by measuring the incident power at which the PC saturates with photoexcitation energy, hv ~ 3.0 eV.Equation 1.3 is a consequence of treating the PC signal as the result of the photofield effect, 43 which causes a shift in the TFT threshold voltage, ∆VT, when illuminated. 24The approximation ( ) The density of states is recovered by differentiating NTot with respect to energy after suppressing small oscillations associated with thin-film interference using a local numerical regression filter (Loess filter).Figure 3b shows the raw data, while the filtered data was shown as the gray dots in Fig. 1a.Thus, we establish that the photon normalized PC spectral response is directly proportional to the total trap density, and the DoS is found by taking the derivative of the trap density.
The bandgap, Eg, is determined to be ~ 3.12 eV by constructing a Tauc plot 44 from the measured UBPC data (Figure 3b, inset).This is justified since the EQE spectrum is shown to be proportional to the joint density of states given by 45 where C is a constant proportional to the coupling of initial and final states (assumed to be independent of photon energy for sub-gap states), fD is the Fermi-Dirac distribution, EQF is the quasi-Fermi level due to gate bias, and g(ε) is the DoS in Fig. 1a.Note that EQF is < ~100 meV from the conduction band since all EQE measurements are taken with the device in the "ON" state, i.e., VG >> VT.The resulting output of Eq. 1.4, shown in Figure 3b as the red line, agrees remarkably with the raw UBPC data (black dots) after amplitude scaling.This result shows that the UBPC EQE spectrum approximates well the joint density of states stepwise functional form.
As a final integrity-check of our UBPC approach, in Fig. 3c EQE spectra are taken at temperatures increasing from 125 to 380 K.The blue and red dashed lines highlight the changing Urbach tail disorder, characterized by the Urbach energy, EU, which increases from 94 to 128 meV for this temperature range.Similar trends are observed in other oxide semiconductors. 30,31  room temperature EU value for a-IGZO is found to be 111 meV.The inset in Fig. 3c shows the Urbach energy extracted from the EQE spectra taken at different temperatures.The dashed line in the inset of Fig. 3c represents the temperature-dependent Urbach energy, EU (T), calculated from 47 ( ) where E0 is the temperature-independent structural disorder due to the lack of long-range order, E1 parameterizes the temperature-driven disorder due to phonons, and θE is the Einstein temperature.We found that E0 ~ 80 meV, E1 ~ 31 meV and θE ~ 185 K.The average energy of phonons in the lattice is then given as kBθE = 15 meV.This value is notably smaller than that of Si and Ge 48 , and could lead to enhancement of electron-phonon scattering processes in a-IGZO at room temperature, compared to Si and Ge, since the phonon energy for a-IGZO is less than kBT (at room temperature).

FIRST-PRINICPLE DoS ANALYSIS:
The energetic distribution of vacancy defects in a-IGZO was constructed from individual DFT+U simulations for 160 oxygen vacancies, and 60 metal vacancies.(See Supplemental Information for DFT+U simulation parameters.)A vacancy defect is created by removing either an oxygen or a metal atom from a simulated a-IGZO cell to form either VO or VM, respectively.
Two stoichiometric a-IGZO cells, each consisting of 140 atoms, were used as test structures for the vacancy DoS analyses.For each simulation, one atom was removed, and the atomic structure was relaxed to minimize energy in the lattice.To compare the relative vacancy defect energies in reference to the conduction and valence bands, the energy axes of each simulation were scaled to approximate the experimental a-IGZO bandgap.
Figure 4ai shows the DoS for a pristine a-IGZO cell (i.e.no vacancies).The Fermi-level is positioned to the right of the last filled state near the VB.In general, after an oxygen vacancy is created (prior to structural relaxation), a deep state forms in the sub-gap.However, after the structural relaxation, either a "deep state" forms in the sub-gap due to the inward relaxation of the coordinating metals (e.g., Fig. 4aii, gold shading); or a "shallow state" is formed in the conduction band due to the outward relaxation of the coordinating metals (e.g., Fig. 4aii).The formation of a deep state indicates that a trap for electrons is created in the sub-gap, whereas the formation of a shallow state indicates that electrons are donated to the CB.By contrast, the creation of a metal vacancy tends to increase VB tail state disorder while the Fermi-level shifts further away from the CB, leaving unfilled states in the sub-gap (e.g.Fig. 4aiv, shaded red).The fact that oxygen vacancies shift EF to the right of states, meaning they are filled, is a direct indication that oxygen vacancies are donor states.Conversely, metal vacancies shift EF to the left of states, leaving them empty, which is a direct indication that metal vacancies are acceptor states.
Figure 4bi shows the composite DoS, which is the summation of all DoS obtained from vacancy defect simulations (black line).This is overlaid with the experimental DoS (orange line) for comparison.There is good agreement between the defect distributions suggested by the composite DoS and experiment, as both indicate defect states span, virtually, the entire sub-gap.
It is necessary to compare the sum of all DoS from vacancy defect simulations (as opposed to an individual vacancy defect simulation) with the experimental DoS, since the experiment represents a stochastic spatial average of all defects contained within the laser excitation area.
220 vacancy defects are sufficient to provide a representative sample of metal-oxygen (M -O) coordination environments (see Supplemental Information).This is important since TFT behavior depends on the stochastic defect population, and so consideration of all defect states is required.
A clear indication of the energetic distribution of oxygen versus metal vacancies is shown in Fig. 4bi.The gold shaded area is the sum of the last filled states for all deep VO (e.g., Fig. 4aii), and the red shaded area is the sum of the unfilled states for each VM (e.g., Fig. 4aiv).Thus, according to DFT + U simulations, VM acceptor states are found from VBM to ~ −2 eV, and VO donor states are found from −2.5 eV to −0.5 eV.These sub-gap VO donor states constitute the 53% of oxygen vacancy simulations that led to the formation of "deep states," while the remaining 47% led to "shallow" states forming in the CB.

CONCLUSIONS:
In summary, the ultrabroadand DoS of a-IGZO is measured spanning the sub-gap states

Figure 1 .
Figure 1.(a) The total integrated sub-gap trap density (NTot, gray squares) of a-IGZO, as measured by ultrabroadband photoconduction (UBPC).The density of states (DoS, black circles) is the first derivative of the gray curve.Sub-gap DoS peaks originate from oxygen vacancies (gold peaks) and metal vacancies (red peaks).The green (blue) line is the conduction (valence) band and band tail states.(b) The a-IGZO TFT photoconduction response (PC, color bar) is proportional to NTot, overlaid with TFT reflectance map (grayscale).(c) Using the UBPC-derived DoS, we invoke charge balance to extrapolate both the TFT VT and EF dependence on to the metal vacancy deep acceptor concentration (NDA).The red line corresponds to the total integrated concentration of metal vacancy states measured for the a-IGZO TFT shown above..
dotted line in Fig.1c, and confirmed by experimental

3 )
, VT increases monotonically from ~ -5 V to ~ 10 V. VT is negative (depletion mode) when DA included in Fig. 1c.If DA SD N N < , EF is positioned very close to the conduction band minimum so that n becomes the balancing negative charge term in Eq. 1.1, resulting in the depletion-mode TFT behavior due to the formation of an accumulation layer.For this limiting range of DA N , EF remains almost constant in Fig. 1c.However, this trend in EF changes abruptly when DA SD N N ≈ , as EF drops precipitously to ~ 1.2 eV below the CBM.This abrupt change in EF (and concomitant increase in the slope of VT) is a consequence of the very small (~1×10 16 cm -3 ) densities of both the O-1 and O-2 sub-gap states.As DA N is increases, both these states are easily emptied (and ionized) as EF pushes towards the valence band in order to maintain charge balance.A second less abrupt drop in EF occurs as the higher density Ois ionized, until it encounters the much higher densities of the Opeaks, which tend to clamp the EF near ~ 2 eV below the conduction band minimum.A final step terminates at ~ 2.5 eV when EF encounters Otrend reveals that strong enhancement-mode TFT behavior, i.e., VT ~ 10 V, is associated with the existence of empty VO, VM, and valence band tail states in the subgap, as a result of charge balance.Our second example shows how metal vacancy deep acceptors impact a-IGZO TFT performance under illumination by tuning photoexcitation energies in order to preferentially excite either VO or VM type vacancies.Figure 2a shows a comparison of a drain current-gate voltage (ID -VG) transfer curve for an a-IGZO TFT illuminated with hν =1.4 eV (Fig. 2a, gold curve) or at 2.5 eV (Fig. 2a, red curve).While the transfer curve at 1.4 eV is almost identical to the curve measured under dark

Figure 2 .
Figure 2. (a) Two TFT ID -VG transfer curves differ starkly with the photon energy of illumination.(b) Transient PC decay curves for the same two photon energies.Dashed lines are exponential fits to the longest decay component (fall time, τ).Dotted line gives the instrument response.(c) i. Hysteresis voltage, VH, versus photon energy.ii.Photoconduction decay fall time, τ, versus photon energy.iii.DoS plots from four TFTs fabricated using different processing conditions.Regions dominated by VM (VO) are shaded red (gold).
photons, Nph, incident on the a-IGZO layer at is the slope of the TFT (dark) transfer curve, evaluated at the gate voltage used during PC spectral measurements; max ph N is the maximum number of photons
used to extract the shift in VT due to laser excitation by monitoring drain current, where ∆ID is the magnitude of the PC signal, i.e., ∆ID = ILight -IDark.∆ID is extracted by the lock-in amplifier while modulating laser illumination of the TFT with a mechanical chopper at fchop ≈ 100 Hz.Lock-in amplification has the essential benefit of isolating the PC contribution from charges that recombine quickly after photoexcitation (e.g., within ~ 10 ms), as well as excluding any slow VT drift associated with positive bias (or illumination) stress.In this way UBPC is similar to a photon-normalized PECCS spectrum, where the background drift of the threshold voltage is removed via lock-in amplification, and ∆ID is monitored in place of ∆VT in order to calculate NTot.

Figure 4 .
Figure 4. (a) DFT+U DoS simulations for a-IGZO.i. Pristine a-IGZO cell (structure on right) shows EF is located near the valence band.ii.An oxygen vacancy (VO) creates a deep donor state (shaded gold) and EF shifts toward CB.iii.A (different) VO creates a shallow donor state and EF shifts into the conduction band.iv.A metal vacancy (VM) creates a deep acceptor state (shaded red) and EF shifts away from CB.(b) i.The composite DoS is the sum of DFT+U vacancy simulations, with overlay of experimental data.Contribution of VM states is shaded red, and VO are shaded gold.ii.-iv.Coordination-specific composite DoS show the sum of last filled states due VO deep donors with majority In, Ga or Zn as nearest neighbors (light shading), and the sum of unfilled VM acceptor states due to In, Ga, Zn, removal (hashed shading) The distribution of deep sub-gap states arising due to different M -O coordination environments is shown in Figure4bii-iv.VO deep donor sites with a majority of In atoms as nearest neighbors (Fig.4bii, light green shading) tend to form defect states closest to the CBM.Deep VO sites having majority Ga atoms as nearest neighbors are shifted slightly further from away from the CB (Fig.4biii, light blue shading).Deep VO sites with a majority of Zn atoms as nearest neighbors tend to form the deepest states on average (Fig.4biv, light gray shading).VM acceptor states with In or Ga vacancies are found nearest the valence band (Fig.4bii, hashed green shading or Fig.4biii, hashed blue shading), and those created by removing Zn atoms are found furthest from the VB (Fig.4biv, hashed gray shading).Therefore, DFT simulations can not only provide an expectation of where to find defect states in DoS of amorphous oxides, but also atomic structural insights regarding the coordination environment of the defects that give rise to these states (VO versus VM).

(0. 3 - 3 .
5 eV) using our ultrabroadband photoconduction (UBPC) technique.Eight sub-gap peaks are correlated to the local coordination environments of vacancy defects using density functional theory, and transient PC measurements.UBPC measurements give a Tauc-gap (~ 3.15 eV) and VB Urbach energy (110-120 meV, at room temperature) across multiple a-IGZO TFTs.Six donor-like oxygen vacancy peaks dominate the majority of the sub-gap extending to ~ 2.5 eV below the conduction band edge.Two acceptor-like metal vacancy peaks are also detected at about 2.1 eV and 2.6 eV below the conduction band edge.TFT characteristics such as threshold voltage and photoinduced hysteresis are shown to be directly related to the density of metal vacancy states.The impact of the metal vacancy concentration on TFT threshold voltage is a consequence of detailed charge balance in a-IGZO, given their acceptor-like nature.In addition, electron recombination is found to be slower when electrons are photoexcited from metal vacancy states than from oxygen vacancy states.This trend is ascribed to the acceptor-or donorlike nature of the metal or oxygen vacancy, respectively, due to neutral or coulombically attractive capture.By identifying the energy distributions and, moreover, the electronic structural configurations of vacancy defects through density functional theory, this work reveals the unanticipated impact metal vacancy deep acceptors play in tuning the electronic properties of a-IGZO TFTs.

Table 1 :
a-IGZO DoS figures of merit.