Hydrogen collision model of light-induced metastability in hydrogenated amorphous silicon

Solid State Communications.Vol. 105. No. 6. pp. 387-391. 1998 0 1998 Elsevier Science Ltd Printed in Great Britain. All tights twetved 0038-1098/98 $19.00+.00

PII: SOO38-1098(97)10142-9

HYDROGEN

COLLISION

MODEL OF LIGHT-INDUCED METASTABILITY AMORPHOUS SILICON

IN HYDROGENATED

Howard M. Branz National

Renewable

(Received

Energy Laboratory,

Golden, CO 80401, U.S.A.

13 May 1997; accepted 1 October 1997 by A.L. Efros)

A new model of light-induced metastability (Staebler-Wronski effect) in hydrogenated amorphous silicon is proposed. When two mobile H atoms generated by photo-induced carriers collide, they form a metastable, immobile complex containing two Si-H bonds. Excess metastable dangling bonds remain at the uncorrelated sites from which the colliding H were excited. The model accounts quantitatively for the kinetics of lightinduced defect creation, both near room temperature and at 4.2 K. Other experimental results, including light-induced and thermal annealing kinetics, are also explained. 0 1998 Elsevier Science Ltd

Light-induced metastability in hydrogenated amorphous silicon (a-Si:H) has been an important unsolved problem in amorphous semiconductor physics since its discovery by Staebler and Wronski (SW) in 1977 [l]. Briefly, exposure of device-quality a-Si:H to light or excess carriers increases the density of neutral threefoldcoordinated dangling-bond (DB) defects by one to two orders of magnitude. The excess defects reduce carrier lifetimes and sharply limit the application of a-Si:H as an inexpensive semiconductor material. The light-induced DBs are metastable; they can be thermally annealed in 2 h above about 150°C. Many microscopic models of the SW effect have been proposed, but no previous model accounts well and quantitatively for the enormous body of experimental data that has accumulated during 20 years of study. In this communication, I propose a new model of the Staebler-Wronski effect in undoped a-Si:H. When mobile H atoms generated by excess carriers collide, they form metastable, immobile complexes containing two Si-H bonds. The metastable defects of the SW effect are left behind on the sites from which the colliding H were excited. Hydrogen diffusion experiments reveal facts about H in a-Si:H that underpin the present model. The thermal H diffusion coefficient, DH, is activated with about 1.5 eV [2], the excitation energy of H atoms from Si-H bonds to a transport level [3]. Once excited from Si-H bonds, H are mobile, with diffusion constant, D,, many orders of magnitude greater than DH [3]. Excess carriers 387

introduced by light enhance the rate of H diffusion [4] through an increase of the excitation rate of H into transport [3]. At 25O”C, this excitation is roughly proportional to the carrier generation rate, G [4]. I assume, therefore, that the excitation rate of mobile H per unit volume is R, = kHNHG,

(1)

where kH is a proportionality constant (in cm3) that depends upon temperature and NH is the density of H atoms. The ansatz of equation (1) is discussed further, below. Each H excitation leaves behind an immobile DB. From the molecular dynamics calculations of Biswas et al. [5], we learn that the “bond-centered” H transport state is best viewed as a mobile complex of a Si-H bond and a DB. The Si-I-I/DB complex breaks one Si-Si bond after another as it transports rapidly through the amorphous network, but each broken bond reforms after the complex passes it. This Si-H/DB complex remains mobile until its mobile DB meets another DB and they annihilate to form a Si-Si bond. The transporting H is then immobilized as Si-H. Mobile H normally retraps to an immobile DB in this way, conserving the number of DBs. One immobile DB is created at the site of H excitation; another is annihilated at the site of H retrapping. Significantly, mobile H can also retrap by colliding with a second mobile Si-WDB. In this case, the two mobile dangling bonds annihilate and both mobile H are trapped to form an immobile, metastable complex of two

388

LIGHT-INDUCED METASTABILITY IN HYDROGENATED AMORPHOUS SILICON

Si-H bonds that I label M(Si-H)*. There are no DBs associated with M(Si-H)z. However, the number of metastable DBs in the material is increased by two in this process because immobile DBs are left behind at the sites from which the two colliding H were excited. If there were no barrier to H emission from M(Si-H)z, it would be energetically favorable for both H to diffuse away, leaving behind no DBs and eradicating two distant DBs. The excess DBs created by the illumination and collisions are therefore metastable and can be identified with the SW-effect dangling bonds. M(Si-H)2 differs from previously-proposed two-H complexes [6,7] because the two H sites need not be on the same Si-Si bond. The loss rates of mobile H by trapping to immobile dangling bonds (R,& and by collision between mobile H atoms (R,) are Rdb = kdbNmNdb

(24

and R, = 2k,N;.

(2b)

Here, Ndband N, are the densities of immobile dangling bonds and of mobile H, respectively, while kdb and k, are rate constants (in cm3 s-l) for the two trapping processes. I expect that kc = k& because the DB-DB annihilation processes are quite similar. There is a factor of two in equation (2b) because each collision removes two H from transport and leaves behind two metastable DBs. Equations (1) and (2) are combined to obtain coupled equations governing the evolution of N,(t) and N&t) during illumination dN,,,ldt = k,_,N,.,G- kdbN,,,Ndb- 2k,N,f,

(34

Equation (4) has a form identical to that of Stutzmann, Jackson and Tsai (SJT) [8], but with a different “Staebler-Wronski” coefficient, C,,. If k, = kdb, the low-excitation limit is N Q Ndb and the simplified form Of f2qUatiOU (4b) holds. @lCe Ndb(t) %- &jb(o), the solution of equation (4a) is N&(t)

=

(3C,,)

II3

z3

G

t

113

.

(5)

This form for Ndb(t) during defect creation is observed in numerous experiments [8,9]. Any T-dependence of C, depends on both kH(Z’)and kdb(T) through equation (4b). Annealing of the metastable DBs occurs when thermal excitation or illumination excites mobile H from M(Si-H)2. When the first mobile Si-IUDB is excited, it leaves behind a DB. The second Si-H is immediately mobile due to its proximity to this remaining DB. This is reminiscent of the negative-u hydrogen pair of Zafar and Schiff [7], but there is a different microscopic origin. Most of the mobile H retrap at immobile DBs, reducing Ndb. This annealing leads eventually to saturation of the created defect density. The light-induced annealing rate is an analog of equation (1) (dN&ldt), = - 2kuuN&,

(6)

where the constant, kHH, may be different from kH. A factor of two appears in equation (6) because excitation of either H from M(Si-H)2 anneals two light-induced DBs. The form of equation (6) was deduced phenomenologically by Wu et d. [lo]. When thermal annealing is negligible, one equates the creation and annealing rates of equations (4a) and (6) to obtain the saturated DB density, Nsa, =

and

Vol. 105, No. 6

(&u&d

113 l/3 G .

(7)

Combining equations (7) with equation (5), the saturation time is tsar= (6kHHG) - ’ . A weak dependence In this communication, I treat only the asymptotic of N,, upon G, consistent with equation (7), is observed solutions of equations (3). Computer numerical solutions [ 10, 111. The predicted dependence, C,, = N2a,, is also confirm these asymptotic solutions and will be presented observed 1121. elsewhere. Instead of the 1.4 to 1.5 eV required for thermal H At all times, N,,, 5 Ndb, because N,(O) < Ndb(O)and diffusion [2, 31 metastable DB annealing requires only the mobile H and DBs are created and annihilated in about 1.1 eV [8]. I postulate, therefore, that H emission pairs (except when two mobile H annihilate). After from M(Si-H)z requires less energy than does H N, equilibrates with N&b, dN,,,ldt ~50. In the low emission from isolated Si-H. I speculate that collision H-excitation limit, 2k,N,,, 4 kdbNdb and equation (3a) of two mobile Si-H/DB leaves the region of M(Si-H)r implies N,,, = kHNHG/kdbNdb. Substituting N,,, into strained by the addition of two H atoms. Release of equation (2b) yields the SW creation rate stored strain energy then reduces the H emission activation energy relative to emission from isolated (dN&dt)c = R, = &,,G2iN,$, (W Si-H bonds. In the dark, at temperatures at which H diffuses with readily, an equilibrium is established between H in 2k k2 N2 2khN; C,=----Z_*CH H (4b) isolated Si-H bonds and in M(Si-H)z. The activation kib kib energy of Ndb(T) is simply the difference between the

dN&/dt = kHNHG - kdbN,,,Ndb.

W)

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LIGHT-INDUCED METASTABILITY IN HYDROGENATED AMORPHOUS SILICON

activation energies of Du and of metastable DB annealing: 0.3 to 0.4 eV, as discussed above. Measurements of Ndb above 200°C and after rapid quenching from elevated T, give an activation energy of about 0.3 eV [13, 141 in good agreement with this prediction. In this model, as in the experiments, thermodynamic (“native”) DBs and light-induced DBs are indistinguishable. The density of M(Si-H)z complexes is NdJ2 whether the sample is light-soaked or well-annealed. DBs that cannot be annealed away correspond to the equilibrium density of M(Si-H)2. This model of thermal equilibrium defect formation is a specific realization of the “hydrogen glass” model of defect equilibration in a-Si:H [ 151. The analysis leading to equation (4a) deals entirely with the time after a steady-state mobile H population is established. At early times, however, N, rises much more rapidly than Ndb. The solution of equation (3a) when 2k,N, 4 kdbNdb and in the limit of near-constant Ndb is N,(t) = Ng[ 1 - exp ( - f/r,)],

with rr = (kdbNdb)- ‘. (8)

Here, Nz = kHNHGlkdbNdb, as described above equation (4) for the steady-state equilibrium of N, with Ndb.The rise time, r, is the trapping time for a mobile H from equation (2a) and represents a latency time for metastable DB production. Numerical solution of equations (3) does show N, peaking at t 2 7,. with a density near N&2. Ndb then begins to rise more rapidly due to mobile H collisions and soon follows the form of equation (5). In this steady-state regime, N, decays as llNdb a t- u3. It is tempting to identify this rise and fall of N, with infra-red (IR) absorption peaks that appear and disappear during the first hours of light-soaking certain samples [ 161. Darwich et al. [ 161 have attributed these peaks to mobile H. However, the low sensitivity of IR techniques should not permit direct observation of N,,, < Ndb. The decay time of N, and Ndb after the light is extinguished is also roughly r,, as given by equation (8). I next make rough estimates of the constants. The H emission rate is connected to H diffusion through R, = NHDHlh2, where X is the mean distance mobile H diffuses before retrapping [17]. With equation (l), kH = DHIGX2. Depending upon the assumptions made about the dominant D retrapping process, light-induced deuterium tracer diffusion measurements at 135°C yield 10m31cm3 < ku(135”C) < 4 X 10m2* cm3 [18]. Above 135”C, light-induced D diffusion is activated with 0.9 eV [4, 181 and kH should be similarly activated. No light-induced deuterium tracer diffusion is observed at 65°C [19]. This implies [18] that kH(65”C) < 4 X 10e2* cm3. I assume that

389

kH(65”C) = kH(600C) to obtain a lower bound from equation (4b). I first note that kH for hydrogen may

actually be greater than these upper bounds from D tracer diffusion. Recent experiments do show that

hot-electron emission of H from Si-H near an Si/Si02 interface is enhanced lo-50 times compared to D emission from Si-D [20]. Isomura et al. [21] measured C, (60°C) = 300 s cme3 for a high-quality sample at G = 3 X 10” cme3 s-‘. For the same illumination, N,,, = 2 X lOI cmm3 [21]. Substitution in equation (7) gives kHH(60”C) = 10m2’ cm3 slightly above the upper bound to kH(65”C) derived from D tracer diffusion measurements. Inspection of SW creation data [8] yields a conservative upper bound on the latency time for defect creation of r, < lo4 s. With Ndb < 1017cme3, equation (8) implies a lower bound of kdb(600C) > 10p2’ cm 3 s -‘. Substitution of C,(6O”C) and this bound to kdb(600C) into equation (4b) gives the desired lower bound and implies 4 X 10p2* cm3 > kH(65”C) > 8 X 1O-32 cm3. Substitution of C,(6O”C) and the upper bound to kH(65”C) into equation (4b) gives the desired upper bound to kdb(600C) and implies 2 X 10-l’ cm3 s- ‘> kdb(600C) > 10P21 cm 3 s -I. Diffusion-limited retrapping of free H means k&7’) = 47raD,(T) [ 141, where a is the Si-Si separation. Therefore, kdb(T) is activated with the energy of the barrier to mobile H diffusion. Very low temperatures suppress thermal diffusion of the mobile H, and might be expected to quench DB creation by H collision. However, Tzanetakis suggests that photocarriers might increase D, above its thermal value [22]. I use this concept, below, to derive the observed 4.2 K kinetics of N&t) m Cbtu3 with 6 = 0.44 2 0.05 [9]. First, I assume that at 4.2 K, some light-induced excitations create a Si-I-I/DB complex and also propel it far from the created DB. Thus the Si-H/DB complex and the created DB avoid a geminate annihilation that would reform the original Si-H bond. The emission rate of mobile H is again given by equation (1). The photo-excited Si-H/DBs are normally immobile at 4.2 K. However, when a Si-H/DB complex is excited by carrier trapping to the DB, the H becomes mobile until the energy imparted by the carrier dissipates. D, and kdb are therefore proportional to the electron (n) or the hole (p) density, which vary as G” with a low exponent [9]. The Si-H/DB is annihilated either by a DB (H retrapping) or by another Si-IUDB (SW effect). These trapping rates are Rdb 0: N,,,Ndbd and R, 0: N,$T, modified from equations (2) by carrier-trapping-driven diffusion of mobile H. In the limit, Ndb B N,,,, one obtains N,,, a G’ -‘INdb and (dNJdt), = R, 0: G2” -x’IN& by analogy with the

390

LIGHT-INDUCED METASTABILITY IN HYDROGENATED AMORPHOUS SILICON

arguments leading to equation (4b). Solving for N,+bin the limit N&t) % N&O) gives Nti&)

a G

2(1 -r)/3p3

(9)

I emphasize that I;quation (9) unambiguously predicts that N&?) a t creation kinetics apply at 4.2 K. Once the Si-H/DB is clear of the DB from which it was excited, the exact G-dependences of mobile H generation and diffusion do not influence the branching ratio between H retrapping at DBs (R& and by collision (R,). In contrast, the SJT model [8] is inconsistent with the 4.2 K t”3-creation kinetics, as Stradins and Fritzsche point out [9]. This is because n and p are nearly independent of DB density at 4.2 K. From equation (9) and the observed [9] value of 6 = 0.44 t 0.05, one obtains x = 0.33 + 0.08. Lowintensity light-induced electron spin resonance (ESR) measurements at 30 K give x = 0.2, for very low light intensity [23]. Either x or 6 may be slightly higher than the experiments [9, 231 would indicate, or some modification of this first-order treatment of the G-dependences is required. At 4.2 K, the M(Si-H)2 formed upon collision of two mobile Si-H/DB complexes has little chance to relax. Consequently, the thermal energy required to emit H into transport from the M(Si-H)* (i.e. DB annealing) is greatly reduced. Stradins and Fritzsche [9] find that nearly half of the DBs created at 4.2 K anneal out below 300 K, consistent with this suggestion. A contribution to this low T annealing may also be made by Si-H/DB complexes that were immobilized when the light was extinguished but became mobile again when the temperature is raised. All 4.2 K-created defects finally disappear with roughly the same anneal as 300 K-created defects, supporting a common microscopic origin of the metastability at different temperatures. The H-collision model provides a microscopic model of the long-suspected connection between H diffusion and the SW effect - long suspected [24] because the temperatures of metastable defect annealing and of macroscopic H diffusion are similar. Further, the H-collision creation mechanism leaves metastable DBs that are uncorrelated with each other or with H. It is therefore consistent with electron spin resonance (ESR) observations that the light-induced dangling bonds are indistinguishable from native DBs and are not near other DBs [24] or H atoms [25, 261. General disturbances caused by light-soaking a-Si:H are a byproduct of light induced H motion. During light-soaking, the Si-Si bonds are visited by a mobile H at a rate, D,N,,,la2 = DHNHla2. From extrapolations of DH at higher temperatures and generation rates, I estimate DH = 10m2*cm2 s-l at

Vol. 105, No. 6

l-sun (-10zl cmw3 s-‘) and 65°C. H therefore visits Si-Si bonds at a rate of more than lOI cme3 s-‘; nearly 1019crnv3 of them break and reform during each hour. Such a magnitude of disturbance accounts for small reversible shifts in core-electron X-ray photoemission spectra [27] and a variety of other reversible changes in the environment of a large fraction of the atoms in a-Si:H [28]. These effects are not directly related to the created DBs and may relax below the temperature for annealing the SW effect. Godet et al. [29] demonstrated a proportionality between N,,, and the 2000 cm-’ Si-H IR stretch mode intensity over various samples. However, ESR shows that there are no H atoms within 8 A of the light-induced DBs [25, 261. It is therefore unclear whether the SW-active H (NH) includes all of the 2000 cm-’ IR-active Si-H, or merely the “isolated” component [7] observed by nuclear magnetic resonance. Through equations (1) and (6), I postulate that the H emission rate from Si-H bonds is proportional to G. This simple form applies quite generally; at room temperature and at 4.2 K, when the photoconductivity varies as G’” and as G, and for H emission from M(Si-H)2 (lightinduced annealing). Though appealing in its simplicity, photochemistry is likely excluded because metastable DBs are produced by injected carriers at roughly the same rate as by photo-excited carriers [30]. The generality of R, m G suggests, therefore, that the rate of H emission is proportional to the energy emitted (as phonons) during relaxation of photoexcited or injected electrons and holes. The ansatz of equation (1) does not distinguish between direct np recombination and recombination through DBs as the source of H emission energy. In conclusion, the H-collision model of the StaeblerWronski effect represents the first quantitative microscopic model to unify the great majority of the experimental observations. The model predicts an early-time rise of N,, a latency time for metastable DB creation and a decay of Ndb due to mobile H retrapping after the incident light is extinguished. Acknowledgements-I thank P. Tzanetakis, M. Spanakis and H. Fritzsche for many helpful discussions. R. Biswas, J. Bullock and R. Crandall were also important influences. Tzanetakis and the Univ. of Crete Physics Dept. provided an excellent environment for physics during the work. The research was largely supported by the U.S. DOE under contract DE-AC36-83CH10093. The Fulbright Foundation and the Foundation of Research and Technology Hellas in Greece supplied additional financial support. REFERENCES 1. Staebler, D.L. and Wronski, C.R., Appl. Phys. Left., 31, 1977, 292.

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