Interband optical absorption in amorphous silicon

234

Journal of Non-Crystalline Solids 103 (1988) 234-249 North-Holland, Amsterdam

INTERBAND OPTICAL ABSORPTION IN AMORPHOUS

SILICON

R.V. K R U Z E L E C K Y , C. U K A H , D. R A C A N S K Y and S. Z U K O T Y N S K I Dept. of Electrical Engineering, University of Toronto, Toronto, Ontario, Canada M5S 1,44

J.M. P E R Z Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1.4 7

Received 11 December 1987 The interband optical absorption characteristics of amorphous silicon films prepared by various techniques have been investigated. Above the main absorption edge, the absorption coefficient a can be fitted to the "Tauc" model (ahto) a/2 = C1/2(hta - EG). The experimental (ah~) 1/2 versus h~ plots are generally piecewise linear, with an increase in slope above an energy E u. Structure in the "Tauc" plotsis correlated with preparation conditions; the experimental results are consistent with a broadening of the density of states distribution at the band edges within a gap defined by E u. The incorporation of bonded hydrogen into the a-Si network results in compositional disorder and deeper potential fluctuations that widen E u. The bonded hydrogen increases both extrapolated energy gaps; the blue shift is proportional to the line density of hydrogen atoms over a wide range of bonded hydrogen concentrations. A unified model for the interband absorption edge in a-Si and a-Si : H is presented.

1. Introduction Interest in h y d r o g e n a t e d a m o r p h o u s silicon (aS i : H ) has been largely fostered by the suitability of a - S i : H for the fabrication of low-cost solar cells [1] and large area photodetectors for imaging [2] and xerography [3]. In this respect, a m o r p h o u s silicon exhibits a sharp " n o n d i r e c t " absorption edge that facilitates the fabrication of thin-film p h o t o a b s o r b i n g structures. Moreover, the optical gap of a-Si can be varied over a wide range from below 1.0 eV to above 2.0 eV b y alloying with the appropriate impurity such as G e [4], H [5] and C [6]. This provides considerable flexibility to optimize the spectral response of optoelectronic devices based on a-Si : H. Theoretical expressions for the interband absorption edge in a m o r p h o u s and crystalline silicon can be obtained by considering the imaginary part of the transverse dielectric constant [7]. U n d e r the assumptions of an energy-independent m o m e n t u m matrix element Pfi and zero temperature occ u p a n c y statistics, the corresponding expression for the absorption coefficient is given b y ah~=

2hVl( nc 1\

[PtilZJ(hw),

0022-3093/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

(1)

where V is the sample volume, n is the refractive index, J ( h t o ) is the joint density of states,

J( h,o) = f gc( E + h,0)gv(E) dE,

(2)

and the integral is over all pairs of states in the valence and conduction bands separated by an energy h~. Crystalline silicon (c-Si) is an indirect gap semiconductor with six ellipsoidal conduction b a n d valleys along the (100) directions in k-space and a corresponding gap of 1.1 eV at 300 K [8]. In intrinsic c-Si, interband transitions below the direct edge involve interactions with p h o n o n s to conserve m o m e n t u m , resulting in a temperature dependent edge of the f o r m [9]

ahw =

c(h

+ e (E,/kr)-

co) 2 1

+

c(h

- e.1 -

Eo) 2 '

e-(~./kr)

(3) where the first term corresponds to p h o n o n absorption and the second to p h o n o n emission. In

R. V. Kruzelecky et al. / lnterband optical absorption in amorphous silicon

a-Si, the lack of long-range order produces strong scattering such that k is not a well defined quantum number to describe the electron quantum state [10]. Experimentally it is found that a(hco) in a-Si: H follows [5,11] aho~ = Co( hto - EG) 2

(4)

above an extrapolated gap E C. This expression has also been obtained theoretically by Tauc [12] and Davis and Mott [13] under the assumptions of parabolic energy bands, an energy-independent momentum matrix element and a relaxation of momentum conservation. More recently, Cody et al. [14] have suggested that ( ~ / h t o ) = B o ( h t o E o ) 2, as obtained by assuming parabolic bands and an energy-independent dipole matrix element, fits the experimental a(h~0) data over a wider range in the magnitude of a. Jackson et al. [15] have used experimentally-determined density-ofstates distributions for the conduction band and valence band of a-Si: H to determine J(h~o), and hence to estimate the dipole and momentum matrix elements for interband transitions in a-Si: H. Their results indicate that the dipole matrix element is independent of photon energy below 3.4 eV. However, they found that the " T a u c " model provides the most accurate estimate of the band gap with respect to the actual mobility gap due to compensating errors in the assumptions of a constant momentum matrix element and square-root band edges. Despite the considerable effort that has been expended to develop a theoretical model of the optical absorption edge in a-Si, there is still considerable controversy regarding the interpretation of the experimentally determined optical gap. In the following paper, the interband absorption characteristics of a-Si and a-Si : H films prepared by various techniques are presented. Trends and regularities observed in the absorption characteristics are discussed, focusing on the effects of bonded hydrogen. A unified model of the interband absorption edge in amorphous silicon is presented that provides a physical basis for the interpretation of experimental optical absorption characteristics.

235

2. Film preparation Films for optical measurements were deposited onto glass slides; films for far infrared absorption measurements of S i - H vibrational modes were deposited onto resistive single-crystal Si wafers. The different preparation methods are discussed briefly in the following section. Control a-Si samples were prepared in an oilfree Varian ultra-high vacuum system model FC12E based on ionization pumps. These samples are designated (UEUXNN). High purity Monsanto silicon held in a vitreous carbon crucible was evaporated by RF inductive heating at total pressures below 10 _8 Torr. The substrates were attached to a copper holder held at a temperature Ts to which a DC bias VB was applied. The crucible was held at DC ground potential. Water-cooled cryopanels encircling the crucible were used to reduce outgassing. Hydrogen constituted 90% of the residual gas during the evaporations. A second set of evaporated samples, designated (EUOXNN), was prepared in a Balzers BA-10 vacuum system based on a diffusion pump using DOW Coming 705 oil at slightly higher background pressures of about 5 × 10-8 Torr. Reactive evaporation of a-Si : H facilitates more direct control of bonded hydrogen incorporation than is possible using glow discharge decomposition of silane. Two reactive evaporation techniques were investigated. The first, termed ionbeam reactive evaporation (IBRE), involved the evaporation of Si in the presence of "activated" hydrogen as provided by a DC saddle-field ion source similar in design to an Ion-Tech source (EUHXNN). Prior to the introduction of hydrogen, the total background pressure was about 5 × 10 -~ Torr with a hot, outgassed crucible. The defocused hydrogen ion beam was directed onto the growing film at an incidence angle of 30 °. The a-Si evaporations proceeded in a residual PH2 of about 5 × 10 6 Torr. The ion source was nominally operated at V~s = 4000 V, resulting in a beam current of about Its = 50/~A. A DC bias VB was applied to the substrate holder to control the concentration and energy of ions and electrons impinging on the substrate. A novel deposition technology, termed plasma-

236

R. V. Kruzelecky et a L / Interband optical absorption in amorphous silicon

enhanced reactive evaporation (PERE), was developed to combine the positive attributes of evaporation and glow discharge deposition. A detailed discussion of the PERE technique is presented in [16]. Briefly, silicon was evaporated in the presence of a DC glow discharge in hydrogen. "Activated" hydrogen ions and neutrals interacted with the Si vapour to form Sill n radicals. Film growth was influenced by both the presence of Sill, and "activated" hydrogen. Samples were prepared using one of two plasma chambers designed to obtain a H 2 discharge at low PH2 (about 10 to 50 mTorr) using DC power supplies [16]. In the ion-pumped design, hydrogen ions from a DC saddle-field ion source were used to sustain a discharge between a pair of parallel plate electrodes. The saddle-field plasma chamber consisted of a donut-shaped anode sandwiched between two parallel plate cathodes. In this configuration, electrons oscillated along the axis of the plasma chamber, increasing the effective path length for ionizing collisions. PERE samples are denoted by BUHXNN. The DC glow-discharge a - S i : H samples were deposited from Sill 4 ( G U H N N ) and S i H J P H 3 gas mixtures ( G N H N N ) in a pyrex chamber that was housed within a Balzers BA-10 vacuum system. The chamber contained a pair of parallel plate electrodes, 8.5 cm in diameter and about 3 cm apart. The grounded cathode was a stainless steel screen. The substrates were mounted on a heated holder positioned 0.8 cm above the cathode and maintained at ground potential. Gas flow was from anode to cathode. The substrate holder incorporated a rotary shutter mechanism that shielded the substrates during initial set up and stabilization of the discharge.

deposition, in situ masking did not produce a sharp step and the resulting film thicknesses were determined from infrared reflectance measurements of interference fringes. Zanzucchi et al. [5] have reported that the refractive index of glow discharge a-Si : H is within 20% of bulk c-Si values. A constant a-Si : H refractive index of 3.5 was assumed for the optical method. The experimental error in the determination of average film thickness was about + 10%. Optical reflectance and transmittance data were measured between 0.35 and 2.7 # m using a Perkin-Elmer 450 double beam spectrophotometer. Transmittances were measured at normal incidence; reflectances were measured at an incidence angle of 10 °. The experimental errors associated with the measured values of R and T were about +2%; the corresponding error in the absolute value of the photon energy was less than + 0.01 eV. The films used for optical measurements all exhibited smooth, relatively featureless surface topographies as observed by a Leitz metallurgical microscope. At long wavelengths where absorption was negligible, the sum of R and T was close to unity in all of the samples. These results indicate that material nonidealities did not play a significant role in the film optical properties. The following procedure was used to calculate the absorption coefficient a(hw) from measured R, T data. Consider an a-Si film of thickness d s and complex refractive index n I + j k l , where a = 4~rkl/~, that is supported on a substrate of complex refractive index r/2 + j k 2. Incident light of wavelength ~ undergoes multiple reflections at the air-film and film-substrate interfaces. Equations for the resulting reflection and transmission coefficients have been rigorously formulated by Heavens [17] and have been reformulated by Tomlin [18] into a simpler form:

3. Experimentalprocedure

A(nl,

The thickness of evaporated a-Si and a - S i : H films was determined from stylus displacement measurements across a step in the film obtained by masking a portion of the substrate during film deposition. In the case of DC glow discharge

= ( 4 n 2 A ) - ' ( F[B cosh(2a,) + 2D sinh(2al) ]

+G[C cos(2"r,) + -(1 + R)/T=0

2 E sin(2~fi)] }

(5)

R. V. Kruzelecky et al. / lnterband optical absorption in amorphous silicon

237

silane [23] for which hydrogen effusion measurements indicated that most of the incorporated hydrogen is indeed bonded.

and f2 (nx, kl) =(2n2A ) l{nl[Bsinh(2a,)+2Dcosh(2a,)] + k,[ C sin(2yl) - 2 E cos(2yl)] } -(1 -

R)/T=O,

4. Impurity content (6)

where A, B, C . . . . . G are polynomials in n a and k 1 (see [18]), a 1 = 2~rkadJX and 7x = 2~rnads/X. The refractive index nl(X ) and absorption index k l ( h ) of the a-Si films were calculated using a procedure similar to that outlined by Tomlin [18]. A range of reasonable values for n a between 2.0 and 5.5 was chosen, with an initial value of 2.0. For each value of n 1, the corresponding value of k 1 was determined by solving fl(nl0, kl0 ) = 0 and f2(nn, kll ) = 0. The calculations were repeated, incrementing n 1 by 0.01, until [ k l 0 - k n [ = 0 was satisfied to a specified degree of accuracy. For the optimum values of k m and k n, an average value k 1 = (kl0 + k n ) / 2 was chosen, k 1 could be determined to a better than _+5% precision over the spectral range of moderate to high optical absorption where interference fringes are not pronounced. Impurity incorporation into the resulting films was investigated using secondary ion mass spectroscopy (SIMS) [19], 15N hydrogen profiling [20] and FIR absorption measurements of Si-X vibrational modes [21,22]. Infrared transmission spectra of films deposited onto resistive c-Si wafers were measured using a Perkin-Elmer 621 spectrophotometers with an uncoated c-Si wafer placed in the reference beam. The number of S i - H bonds per unit volume, NsiH, was determined from the integrated absorption corresponding to the S i - H bond stretching vibrational modes near 2000 c m - 1 [211, Nsl H = (1.1 _+ 0.3 × 1 0 2 ° ) / a ( ~ ) dw c m - 3 .

%5

(7)

(.0

An average value for the constant of proportionality has been determined by calibrating the integrated absorption of the S i - H stretching modes with the total hydrogen content as determined by aSN profiling for several undoped a - S i : H films deposited by DC discharge decomposition of pure

Our experimental results indicate that, in the absence of significant activation mechanisms, hydrogen incorporation into UHV-evaporated a-Si depends logarithmically on the background PH2" The sticking coefficient for hydrogen approaches unity at PH~ below about 10 -s Torr, resulting in a residual bonded hydrogen content of about (0.3 +_ 0.2) at.%. lSN profiling indicates that the spatial distribution of hydrogen in the bulk of reactively evaporated and DC discharge-deposited a - S i : H films is uniform to within experimental error. FIR absorption spectra indicate that bonded hydrogen is largely incorporated into dihydride sites in reactively evaporated a - S i : H ( Ts < 250°C) and into monohydride sites in DC discharge-deposited aSi : H (50 ° C < Ts < 350 ° C). The incorporation of bonded hydrogen into reactively evaporated films depends on the relative impingement rate of hydrogen ions to Si; the bonded hydrogen content can be varied from about 1 to 10 at.% by adjusting the discharge (PERE) or ion source (IBRE) current and by applying a DC bias to the substrate holder. In addition, the high Pn2 during PERE depositions (about 50 mTorr) results in the trapping of several atomic per cent of molecular hydrogen into films deposited at lower Ts, as indicated by the difference between the corresponding values of hydrogen content as deduced from 15N profiling and FIR absorption spectra. The DC discharge-deposited films contain between 15 and 25 at.% bonded hydrogen, depending on the discharge conditions and the deposition temperature. SIMS profiling indicates that, apart from hydrogen, only C and O were incorporated into undoped films at levels above 1019 c m 3. The carbon content of UHV-evaporated a-Si films and reactively-evaporated a-Si : H films prepared using a carbon crucible is similar at about 2 at.%, while DC discharge-deposited films typically contain less than 0.1 at.% carbon. It is postulated that the

R. V:. Kruzelecky et al. / lnterband optical absorption in amorphous silicon

238

carbon in the evaporated films arises primarily from interactions between the silicon melt and the carbon crucible; Si-C phase data [24] indicate that a Si-C eutectic exists at 1404°C with a composition of about 99 at.% Si and 1 at.% C. SIMS profiling indicates a typical oxygen content in the bulk of about 0.2 at.% for the UHV-evaporated a-Si films, about 0.5 at.% for the IBRE samples and less than 0.1 at.% for the DC discharge-deposited films. The PERE samples had a larger oxygen content of about 1 to 2 at.% because of lack of cryopanels in the PERE deposition chamber.

5. Interband optical absorption The absorption coefficient a is plotted as a function of the photon energy in fig. 1 for several undoped a-Si and a-Si : H films prepared by various techniques. The absorption characteristic of 10 5 UEU005 (UHV a-S~)

E u

•

a-S~

•

E U H B l t (IBI~E)

('fS=256*C)

®

EUHBI2 {IBREI

•

BEUH10 (PERE)

Zk OUH37

(GD)

o

GUH3a

(GD)

D GUH39

(GD)

IJJ m

© II

LL I~l 10 4 o (,p :z o io

103

1.0

i

,!,

/'

18

2 2

ENERGY (eV)

Fig. 1. The interband optical absorption characteristics of several a-Si and a-Si:H films prepared by various techniques, and of crystalline silicon [25].

crystalline silicon [25] taken at 300 K is included for comparison. The IBRE films were prepared at Ts = 2 0 0 ° C using a DC saddle-field ion source operated at 4000 V, resulting in a beam current of 50 /~A; a DC substrate bias of 500 V (11) and - 5 0 0 V (q)) was applied during the evaporations, respectively. The PERE sample (A) was deposited at 2 2 0 ° C using a saddle-field plasma chamber operated at a discharge voltage VDC = 840 V and current density JDC = 45 # A cm -2. The glow discharge films were deposited at 250 ° C (zx), 300 °C (o) and 350 ° C (D), respectively, using a DC discharge in Sill 4 operated at VDC = 700 V and JDc ----24 #A cm -2. The reactively-evaporated a-Si : H films exhibit a sharp absorption edge that is comparable to that of glow discharge films. The blue shift in the absorption characteristics is correlated with an increasing amount of bonded hydrogen incorporated into the films. An exponential tail in the optical absorption characteristics of a - S i : H films has been observed [26]. In our thicker a-Si : H samples (about 1.5 /~m), ct was determined down to about 103 cm -1 using Tomlin's method. The corresponding variation of log(a) with h~0 exhibits curvature, indicating that an exponential tail, if any, occurs at lower values of a. Relative to a - S i : H films, the absorption characteristics UHV-evaporated a-Si films are considerably smeared at lower photon energies, reflecting the additional contribution of a high density of gap states to optical absorption. Fig. 2 shows the variation of a with hto and the corresponding fit to the " T a u c " model for a sequence of UHV-evaporated films deposited at 2 0 0 ° C and various Va. The (ethto) 1/2 v e r s u s hw characteristics are piecewise linear for hw > 1.5 eV. At lower h(o, the absorption characteristics of most samples exhibit a significant absorption tail that extends below the main absorption edge as defined by the " T a u c " gap. In samples for which a(hw) could be calculated over a wide range of magnitudes, an increase in the slope of the linear (cthw) 1/2 versus hw characteristics is observed above an energy referred to as E u of (1.77 + 0.03) eV. Values for E G and Co were obtained from the a = 0 axis intercept and the slope, respectively, of the linear sections of ( o t h ~ ) 1/2 v e r s u s ht0 plots above E u (EG2, Co2) and below Eu (EG1, Cm).

R. V. Kruzelecky et aL / Interband optical absorption in amorphous silicon

239

Table 1 Summary of optical absorption results for a-Si samples evaporated onto glass held at temperatures T, and bias VB. Optical data was fitted to (ah~) 1/2= C~/2 ( h ~ - EG) to estimate values for C o and EG(_+0.03 eV) above ( E o 2 , C02 ) and below ( E e l , C01 ) an energy E,, (_+ 0.03 eV). The bonded hydrogen content CsiH was determined from FIR absorption measurements Sample EUOB16 EUOB17 UEUB01 UEUB05 UEU005 UEU006 UEU007 UEUB02 EUOB18 UEUB06

I/B

Ts

(V)

( o C)

CsiH (at.%)

ds (/~ m)

EG] (eV)

Co] (cm. eV) - ]

E. (eV)

EG2 (eV)

C02 (cm. eV) -

1000 500 500 500 0 0 0 - 500 - 500 - 500

190 185 200 300 200 300 400 200 190 300

0.2 0.7 0.3 0.3 0.2

0.7 1.4 0.7 1.5 0.7 1.5 1.4 1.9 1.1 1.0

1.20 1.17 1.19 1.27 1.19 1.29 1.28 1.25 1.18 1.28

1.3 x 1.7 x 2.0 x 2.3 x 1.8 x 3.5 x 2.1 x 2.1 × 1.5 x 3.0 x

124 1.76 1.77

1.41 1.41 1.38

5.1 x 105 4.8 x l 0 s 4.4 x l 0 s

1.80

1.40

4.5 × l 0 s

1.72

1.36

3.5 x 10 s

The experimental results for several UHV-evaporated a-Si films are summarized in table 1. The typical experimental error is about + 0.025 eV for

DC SUBSTRATE

8~AS

~

105 l0 s 105 l0 s l0 s l0 s l0 s 105 105 105

E G and about + 10% for C 0. The energy gap EGt estimated from the "Tauc" region below E, increased slightly with Ts, with a corresponding increase in C0:; however, changing VB did not produce any systematic variation in the resulting optical absorption characteristics.

I

600

TS1200"C

O

rq

JA

/Y

: 77eV

LL;

>

/

~oo

/

100

,,',

i111 //ii /~, 14

200

// f,//b

H

I

18

0

100

/

2.0

(eV)

Fig. 2. Optical absorption coefficient versus photon energy for a sequence of UHV-evaporated a-Si films deposited at 200 o C with a D C bias VB applied to the substrate holder during the evaporations. The corresponding fit to the "Tauc" model is also shown.

/ o

,

,/

//

// ~5

/

//o / / /

///// / /t / / ~ //'/ / ~/

y . , J , ,

//// //4 /

i /

I 15

~Eu-20eV

// /

/

ENERGY

~/~

// /&

300

///

A/~2 / Ii 11~1 i1 A // / /J Z3. // / / / t/l/

///// // // 103 r 2

~

//

500

E

A

P

a] EUHBll (VB~-5OOV)

'

290

EUHB12 (VB=-500V)

~x EUHO02 (VB~OV)

-'. 300

E

,,/

l

EGI:ISleV EG2:160eV ,

,

20

.

.

.

.

25

ENERGY (eV) Fig. 3. Plots of (aE) 1/2 versus E for three IBRE a - S i : H films deposited at 200 o C and different D C substrate biases (Vts = 4000 V, I m = 46 #A).

R. V. Kruzelecky et a L / Interband optical absorption in amorphous silicon

240 i

900

ues of Co]. However, the magnitude of C 0 2 (about 5 X 105 (cm eV) -1) as determined from the slope of the "Tauc" region above E u is comparable to that observed for UHV-evaporated a-Si films. Moreover, the values of C01 and C02 that are observed for reactively-evaporated a - S i : H films are similar to those observed for DC discharge deposited a-Si : H films. As previously discussed, our evaporated a-Si and a - S i : H films contain about 2 at.% of C. Schmidt et al. [6] and Saito et al. [27] have examined the variation of E G with carbon content in discharge-deposited and reactively-sputtered aS i : C : H . In both cases, C was incorporated into the films from the gas phase via methane. Their results indicate that the incorporation of 2 at.% of C into a-Si increases E o by about 0.05 eV. This is within the scatter for Eo2(cH) values as reported by various groups in the literature (see for exam-

D BEUH09 O 8EUN10

800

7O0

60O m 500

U3 ~5

EU:220e

4O0

300 =215eV 200 O [ 167eV ,~

100

163eV

/Jj

r/ //

175eV ,1.77eV I

0 15

I

20

1 25

300

i

i

i

i

[

i

30

ENERGY (eV)

ix GUH3?(Ts:250"C!

Fig. 4. Plots of (aE) 1/2 versus E for two a-Si:H films deposited at 220 ° C using the PERE technique. BEUH09 was hydrogenated using an ion-pumped plasma chamber; BEUH10 was hydrogenated using a saddle-field plasma chamber.

o GUH38 (Ts=300"C) o GUH39(Ts=350"C1 EG2=I

Fig. 3 shows (ethos) 1/2 versus h~0 plots for a sequence of IBRE films deposited onto glass at 200 ° C and a substrate bias of 500 V (n), 0 V (zx) and - 5 0 0 V (o), respectively. Fig. 4 shows the fit to the "Tanc" model for two PERE a-Si : H films prepared at 2 0 0 ° C using an ion-pumped (BEUH09) and a saddle-filed plasma chamber (BEUH10), respectively. The corresponding fits to the "Tauc" model for several a - S i : H films deposited at various Ts by the DC glow discharge decomposition of pure Sill 4 are shown in fig. 5. As is observed for UHV-evaporated a-Si films, the (ahco) t/2 versus h,., plots are piecewise linear, with an increase in the slope at a demarcation energy E u. Values for E G and CO obtained from the linear sections above Eu(Eo2, C02 ), and below Eu(Eo], Coa) are listed in table 2. The presence of "activated" hydrogen during a-Si evaporations (IBRE, PERE) results in a sharper absorption characteristic below E~, as reflected by larger val-

I . - EG2:I ?SeV

200

~

/ N

+

EG2=180eV

/

(

g 100

/ EG1=1.67eV

/

J/

/

t

// / / / t z;

/

¢

/

'

EG1=l.70ev

t

EGl:173eV

'

/ II ~.6

/

I 1.5

/ 20

I

I 2,2

E N E R G Y (eV)

Fig. 5. Plots of ( f i r E ) 1 / 2 v e r s u s E for three a-Si:H films prepared by DC glow discharge decomposition of Sill 4 at progressively higher substrate temperatures.

R, V. Kruzelecky et al. / lnterband optical absorption in amorphous silicon

241

Table 2 Interband optical absorption constants of undoped a-Si:H. The bonded hydrogen content £si H was determined using combined results of 15N profiling and F I R absorption. Ion beam reactively-evaporated a - S i : H (IBRE) was prepared using " a c t i v a t e d " hydrogen provided by a saddle-field ion source operated at V m. The substrates were held at a DC bias VB; a corresponding current I u was measured. Plasma-enhanced reactively-evaporated a - S i : H (PERE) was prepared by evaporating in the presence of a glow discharge in H 2 operated at Vo¢ and loc, using either an ion-pumped (IP) or a saddle-field (SF) plasma chamber. Glow discharge films were prepared by the DC glow discharge decomposition of pure S i l l 4. Substrates for P ER E and G D films were mounted on the cathode. The respective cathode areas were about 113 cm 2 (PERE) and 57 cm z (GD) Sample

VDC ( VB) (V)

IBRE: EUHB12 - 500 EUH002 0 EUHBll + 500 PERE: BEUH52(SF) 650 BEUH19(IP) 900 BEUH53(SF) 680 BEUH10(SF) 840 BEUH09(IP) 900 DC Glow Discharge: GUH36 700 GUH37 700 GUH41 700 GUH49 710 GUH47 760 GUH48 810 GUH38 700 GUH39 700

It~c ( 1 B) (mA)

Vls (V)

T~ ( o C)

0.042 0.037 0.005

4000 4000 4000

200 200 200

5.4 0.8 5.4 5.0 0.8

0 3300 0 0 1600

220 260 200 220 220

1.2 1.2 1,2 1.1 1.1 1,1 1,2 1.2

-

200 250 250 250 250 250 300 350

CsiH (at.%)

dS (t~m)

EG1 (eV)

C01 (cm. eV)- 1

E~ (eV)

EG2 (eV)

C02 (cm. e V )- 1

4.7 0.8 0.9

0.3 0.7 0.4

1.51 1.41 -

3.5 x 105 4.1 x 105 -

1.97 2.00 1.94

1.60 1.55 1.57

5.2 x 105 7.0 x 105 5.3 x 105

2.8 3.3 3.6 7.5 8.0

1.0 0.7 1.0 0.3 0.3

1.38 1.51 1.60 1.63 1.67

1.4 x 1.5 × 2.6 x 3.5 × 4.6 x

105 l0 s 105 105 105

2.07 _ 2.15 2.20

1.72 _ 1.75 1.77

3.7 x 105 _ 5.6 x 105 6.5 x 105

1.9 2.1 1.3 1.5 1.8 1.4 2.1 2.0

1.73 1.72 1.71 1.71 1.74 1.70 1.67

3.2 × 3.1 x 3.2 x 2.9 x 3.4 x 3.1 x 3.0 x

105 10 s 105 105 105 105 105

2.03 2.03 2.00 2.00 2.03 1.97 1.97

1.77 1.80 1.80 1.76 1.78 1.80 1.75 1.74

5.3 x 5.2 x 5.5 x 5.0 x 4.8 × 5.6 x 4.6 x 5.4 x

18 19 15

105 105 10 s 105 105 105 105 105

Table 3 Summary of optical absorption results for PH3-doped a-Si : H films deposited onto glass held at temperatures T~ by plasma-enhanced reactive evaporation in a H 2 / P H 3 atmosphere and by DC glow discharge decomposition of S i H 4 / P H 3 gas mixture. The glow discharge was operated at a voltage Voc and a current density J o c . Optical absorption data was fitted to ( a h ~)1/2 = C~/2( h o: - E c ) to estimate values for C O and E G above (EG2, Co2 ) and below ( E o l , C01 ) an energy E u Sample

BENH01(IP) BENH02(IP) GNH43 GNH24 GNH22 GNH25 GNH01 GNH04 GNH09 GNH02 GNH06 GNH10 GNH03 GNH08 GNHll

Ts

VI)C JDc

PpH3/Px

Cia

ds

Eol

Col

Eu

EG2

(°C)

(V)

(,uA cm - 2 )

X = H 2 (Evap) X = Sill 4 (GD)

(at.%)

(#m)

(eV)

(cm.eV) - 1 )

(eV)

(eV)

C02 (cm. eV) -1

220 210 250 250 250 250 250 250 250 250 250 250 250 250 250

925 920 750 750 750 750 600 600 600 700 700 700 800 800 800

8 8 21 21 21 21 10 20 40 10 20 40 10 20 40

0.015 0.036 0.006 0.016 0.030 0.040 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005

1.4 2.0 18 17 15 19 19 19 21 22

0.7 0.2 0.9 2.3 2.1 2.8 0.3 0.7 1.3 0.5 0.9 1.3 0.5 1.7 1.3

1.37 1.43 1.73 1.70 1.66 1.62 1.63 1.62 1.71 1.70 1.68 1.72 1.76

1.8 x 1.0 x 3.4 x 2.8 x 2.3 x 2.0 x 0.9 x 1.5 x 2.2 x 1.8 x 1.1 x 1.9 x 2.3 x

105 105 105 105 105 l0 s

2.07 2.00 2.00 1.97 2.00 1.91

105 105

2.00 2.07 2.07 2.04 2.01 2.00 2.07

1.76 1.63 1.78 1.77 1.78 1.69 1.83 1.83 1.78 1.88 1.85 1.86 1.89 1.81 1.88

8.1 x 2.5 x 5.2 x 5.2 x 6.0 x 3.2 x 5.2 x 5.2 x 3.5 × 5.9 x 6.4 x 6.7 x 6.1 x 4.2 x 6.2 x

105 105 105 105 105

105 105 105 105 105 105 105 105 105 105 10 s 105 105 105 105

R. V. Kruzelecky et al. / Interband optical absorption in amorphous silicon

242

transitions are between localized states then the should decrease at lower temperatures due to the temperature dependence of the hopping mobility [29]. In this case, a blue shift in the photocurrent spectral response is expected as the ambient temperature is lowered. However, as shown in fig. 6, this was not observed, indicating that the photocurrent for hto > E G ] is dominated by carriers in extended states. This implies that electronic transitions in the " T a u c " region below E u involve extended states. The effect of doping on the interband optical absorption edge of a-Si : H was investigated using several sequences of PH3-doped films deposited onto glass by DC glow discharge decomposition of S i H 4 / P H 3 gas mixtures and by plasma-enhanced reactive evaporation in a H 2 / P H 3 atmosphere. Plots of (ahoy) ]/2 versus h~0 for several PERE samples deposited at Ts = 220 ° C using phosphine to hydrogen ratios of 0.000 (o), 0.015 (a) and corresponding IpH(h¢o)

BEUH09 O 440K, 305K O 260K 220K 0

175K

O 155K

c~

..'

v'

•

.:

/

• EG2 .. ". . . .

:, ~ " /

O...""

/"

.

: :

.L.. .3.." ..: ;..-~ ; ..'.' /:..:4....

... ':...)?' /

.:'..'.,-

/ ./.:" E U

......o ............. / ' " ./I/

:?-..~....................~ . : ?.., 0 10

I 15

~ 43 -"

I 20

25

30

ENERGY (eV)

Fig. 6. Spectral response of the photocurrent scaled to the dark current as measured at various temperatures for an undoped PERE film prepared using an ion-pumped plasma chamber. 800

pie [28]), making it difficult to ascertain -the •exact effect of C on E o in our samples. The spectral response of the photocurrent IpH, where IpH = / ( i l l u m i n a t e d ) - / ( d a r k ) , was measured for several a-Si : H samples between 1.2 and 2.5 eV using a Perkin Elmer E1 monochromator with a tungsten lamp as the light source. The measurements were performed using coplanar CrNi contacts with a 1 mm gap. Experimental data were corrected for the spectral response of the lamp. Fig. 6 shows the spectral response of the photocurrent scaled to the dark current of a typical reactively evaporated film. The corresponding positions of E~I, EG2 and E u at 300 K are indicated by arrows. To within experimental error, EG] corresponds to the rise in IpH due to interband transitions. Since 1pH is proportional to the carrier mobility /~, the temperature dependence of IpH(t~) reflects the temperature dependence of ~. If the electron

0

BEUH09 (PpN3/PH2=0 000)

A

BENH01 (PPH3/PH2:0 015)

O BENH02 (PF, H3/PH2 =0 035}

600

.

"T

E

400

200

EG~,I 43°v

" /~;/,,

EGI=I.,37ev

o

/

i 10

15

z {:~ # # / /

/EG1=167eV

'/

,

20

2.5

ENERGY (eV)

Fig. 7. Plots of_(aE) 1/2 versus E for three PH3-doped PERE films prepared using progressively higher ratios of PH 3 to H 2.

R.V. Kruzelecky et aL / Interband optical absorption in amorphous silicon 300

i

i

t

t

O C,NHI.3 (PPH31PSiH4:0006)

1

trast, the estimated values of E G 2 and C02 exhibit little dependence on doping and are similar to the values obtained for undoped films. The notable exceptions are samples BENH02 and GNH25 prepared using the highest PH 3 concentrations.

/

{3 GNH24(PPH3/PsiH4=0016) GNH22(PPH3/PsiHz=0 030) EG2:1"78eV~

~ /

200

EG2:177eV EG2=I78eV

100

/

EGl=lgSeV

16

/

t t / / ft t t z r J / EG1=lTOeV

/ / t / /t

EGI=I 73eV 1.8

I 2L0 ENERGY (eV)

I

243

212

Fig. 8. Plots of ( a E ) 1/2 versus E for three PH3-doped a-Si : H films prepared by DC glow discharge decomposition of

Sill 4 / P H 3 gas mixtures.

0.035 (0) are shown in fig. 7. The corresponding fit to the " T a u c " model for a sequence of DC discharge-deposited films prepared at 250 ° C using phosphine to silane ratios of 0.006 (o), 0.016 (rn) and 0.03 (zx) is shown in fig. 8. Other deposition parameters were kept fixed. As was observed for undoped samples, the (eth~) 1/2 versus h~ characteristics are piecewise linear, generally exhibiting a change in slope at an energy denoted by E~ of about (2.05 _ 0.05) eV. Values for E G and CO obtained from the linear sections below E~ (Ec], Co] ) and above Eu(EG2 , C02) are listed in table 3. Both Ec~ and Col exhibited a systematic dependence on doping; the estimated values of Ec] and C01 decrease with increasing doping concentrations. This reflects both the formation of an impurity-induced band below E c at higher doping levels and a broadening of the tail state distributions due to charge fluctuations resulting from a random distribution of ionized donors. In con-

6. Discussion A comparison of the optical absorption characteristics of a-Si and a - S i : H samples deposited by several different methods reveals several interesting trends and regularities. At higher a(ho~) a b o v e 10 3 c m - ] , the absorption characteristics give a good fit to the " T a u c " model (ahto) 1/2= C~/2(h~ - Ec). In samples for which a(hto) can be determined over an extended range of energies, the corresponding ( a h ~ ) 1/2 versus h~ plots are generally piecewise linear, with an increase in the slope above an energy referred to as E u. The film thickness defines the range of a which can be accurately determined. Thick films provide a values largely corresponding to electronic transitions involving the localized tail states at the band edges, while very thin films only provide a values corresponding to electronic transitions between deeper lying extended states in the valence and conduction bands. Because of the structure in the " T a u c " plots, one can determine E G values corresponding to the linear sections above, or below, E u, or some average of these values. Moreover, a for ho~ >> E u is dominated by electronic transitions between extended states deep in the valence and conduction bands where g ( E ) may deviate from a E 1/2 dependence. We find that consistent values for EG can be obtained using the Tauc model, values that are physically plausible with respect to other experimental data such as the spectral response of the photoconductivity, provided that the fitting to the " T a u c " model is done over the appropriate range of a values near Eu. C02, as determined from the " T a u c " region above Eu, is generally similar in magnitude (about 5.0 x 105 ( c m - e V ) - l ) ) for a-Si and a - S i : H samples despite differences in the respective values of Ec2. Moreover, C02 is not affected significantly by moderate doping with phosphorus. Since optical absorption above E u is dominated by interband

244

R. V. Kruzelecky et aL / Interband optical absorption in amorphous silicon

transitions between extended states, this suggests that the distribution of deeper lying states in the valence and conduction bands is not strongly perturbed by preparation conditions, and hence, by disorder. In contrast, a significant variation in C01 is observed as determined from the slope of the "Tauc" region below E u. For example, the presence of "activated" hydrogen during a-Si evaporations results in a steeper characteristic, while higher doping levels reduce the slope. The sensitivity of the optical absorption characteristics below E, to preparation conditions and doping suggests that optical absorption in the "Tauc" region below E, is primarily due to electronic transitions between localized tail states and extended states in the opposite band, and thus reflects the effect of the preparation conditions on the tail state distributions. We found that, for a given value of E~, there is a correlation between the experimental values of C01 and the corresponding gap Eol as shown in fig. 9 for a compilation of UHVevaporated films deposited at various substrate temperatures and substrate biases. As E~ decreases, for a fixed E~, a corresponding decrease in C01 is observed. The correlation between Eol and C0a is consistent with a broadening of the density of states distribution at the band edges within a gap defined by E u. In addition, higher energy transitions involving gap states can also contribute to optical absorption near the band edges, reducing the apparent slope of the interband absorption edge. Current theoretical derivations of the interband absorption edge in amorphous silicon (i.e. eq. (4)) assume a relaxation of k-conservation for electronic transitions in the amorphous phase. From Fourier transform theory, a spatially localized state can be represented as a superposition of many plane-wave states. As localization increases, the corresponding spectrum in momentum space broadens. Thus, a localized state is coupled to many extended k-states. This facilitates momentum conservation for transitions between localized and extended states. Above E~, photon-induced transitions are primarily between extended states. The extent to which order affects the interband absorption edge, and hence the apparent value of

'I

I

I

UHV a-Si E U : 1.80.0.05eV

+ +

3

,_o 'E

+ 2

0

1.15

+

+

+

I

I

I

1.20

1.25

1.30

EGI

(eV)

Fig. 9. Variation of the coefficient C m with the extrapolated gap EG1 as determined from the " T a u c " region below E u for a compilation of U H V a-Si films deposited at various substrate temperatures and DC substrate biases.

C02, can be deduced from the behaviour of a(h~o) in the transition from an amorphous to a microcrystalline structure. Janai et al. [30] have reported that the slope of the interband optical absorption edge in CVD Si decreases and approaches that of crystalline silicon as the average diameter of coherent regions in the films increases from a limiting value of about 20 .~ in a-Si. Indeed, it is found experimentally that high doping levels enhance the slope of the interband absorption edge in indirect crystalline semiconductors [31]. Scattering mechanisms such as impurity scattering [31] and electron-electron interactions [32] can also facilitate momentum conservation. In the amorphous phase, random fluctuations in the potential due to distortions from the average atomic configuration (i.e. variations in bond length and bond angle) result in strong scattering and a correspondingly short electron mean free path. Since thermal and topological disorder are additive, ho-

R. F. Kruzelecky et aL / Interband optical absorption in amorphous silicon

mogeneous a-Si can be regarded, to a first order approximation, as a high temperature equivalent of c-Si (i.e. T(effective) = T ( a m b i e n t ) + T(disorder)). This suggests that the sharp optical absorption edge in a-Si is the strong scattering limit of the indirect edge in c-Si as represented by (3); momentum conservation in a-Si is facilitated by scattering due to the "frozen-in" disorder (i.e. T(amorphous) >> T(ambient)). One of the attractive features of the Tauc model is that it provides a link to the indirect edge in crystalline silicon. The value of EG2 for a - S i : H extrapolated to 0 at.% hydrogen content of 1.23 eV, as previously reported by us [28], is close to the indirect gap in crystalline silicon, giving some credence to the above interpretation. Actual a-Si : H films contain microstructure that is dependent on the preparation conditions. Thus, C02 may reflect the extent to which momentum conservation is relaxed, averaged over all structural ensembles, in a given film. The following model is consistent with the observed structure in the interband optical absorption characteristics of a-Si and a - S i : H films and its dependence on preparation conditions. Let E0c and E0v represent idealized band edges of an unperturbed DOS. The idealized band edges are perturbed by random potential fluctuations arising from disorder. Demarcation energies Euv and E~c can be defined such that the depth of the screened local potential fluctuations at the respective band edges are restricted to a gap E~ = E~c Euv (see fig. 10). Conduction band states below Euc (valence band states above E~v ) are broadened into a band of tail states of width A E c = E~c - Elc (AE v --- Ely - Euv ). Deeper lying states are only weakly perturbed. The incorporation of bonded hydrogen widens E~ from about 1.8 eV in UHV a-Si to about 2.0 to 2.1 eV at higher hydrogen contents. In the quantum well model that has been proposed by Brodsky [33], S i - H sites are associated with correlated potential fluctuations in the valence and conduction bands that increase the effective gap near the vicinity of the S i - H bond. The increase in E~ upon hydrogenation reflects the additional compositional disorder and deeper potential fluctuations associated with the incorporation of bonded hydrogen. Moreover, the presence of other impurities such as oxygen

245

EUC E1C

E1V EUV

X

Fig. 10. Perturbation of the band edges due to potential fluctuations arising from quantitative and compositional disorder.

bonded to Si with high Si-X bonding energies may result in potential fluctuations that widen E u. This most likely accounts for the large values of Eu (about 2.2 eV) that are observed for several of the PERE films which contain an appreciable amount of bonded oxygen (about 1.5 at.%). To relate the experimental interband absorption characteristics to the model, the following first order approximations are made. A density of states proportional to E 1/2 is assumed in the valence and conduction bands. The distribution of states at the edge of the valence and conduction bands is broadened within a gap defined by E u, keeping the total number of states constant, resulting in tail state distributions of width A E c and AEv, respectively. The actual density of states distribution in the transition region between Euc (or Euv) and the onset of any exponential drop in the DOS is open to debate. Since A E c = 0.2 eV as suggested by transport measurements [34], determination of the taft state distribution is beyond the resolution limits of direct techniques such as inverse X-ray photoemission spectroscopy [15]. Mott [13] suggests that a linear distribution is appropriate. However, since the tail state DOS is only defined over a narrow range of energies, the exact form of the distribution is not critical. For simplicity, a parabolic DOS is assumed for the broadened tail state distribution as shown in the inset to fig. 11. Under the assumption of an energy independent matrix element, the absorption coefficient a(hto) is proportional to the integrated joint den-

R. V. Kruzelecky et a L / Interband optical absorption in amorphous silicon

246

a fixed EG2, the lower "extrapolated" gap is a measure of the DOS broadening due to disorder. A number of groups have examined the variation of E G with hydrogen content [35,36] in undoped amorphous silicon. When one considers the variation in E G over a wide range in hydrogen content including c H = 0, the experimental results suggest that E G is proportional to the cube root of the bonded hydrogen content as previously reported by us [28]. A least squares fit of our own data for Eo2(CH), and data for glow discharge, sputtered and reactively evaporated samples taken from the literature yields the following result [28]

~EE

C~LE

\-.,,

0.4

~EL

~

EUV EOVE1V

,/

ElC EOCEUC

E- 03

kt/

Z~ 0.2 2"

I) I)

r C 1~/3 EG2 : 1.08[ ~-~0J + 1.23 eV

I

0,1

'•./2.0eV EGI=1.71eV

0,0

I

1.5

I/ ~EG2=l,76e v

ii" '"//i " ~

[

i

• GUH49 1

20

i

i

i

2.5

ENERGY [eV) Fig. 11. Fit of the calculated spectral response of the joint density of states JT(E), as determined using g(E) shown in the inset, to the "Tauc" model.

sity of states (see eq. (2)). The total joint density of states J T ( h ~ ) is the sum of contributions from the different possible interband transitions. At higher photon energies, mainly LOC-EXT and EXT-EXT electronic transitions contribute to optical absorption. Assuming that aLL(h~) is negligible, fig. 11 shows the j~/2 versus h ~ characteristic as determined for the case AE c = 0.20 eV, A E v = 0.29 eV and E u = 2.0 eV. The experimental (ahw) 1/2 versus ho~ characteristic of an undoped film (GUH49) with similar values of EG1, EG2 and Eu is included in fig. 11. The calculated and experimental values of Col/Co2 agree to within experimental error (Co]/Co2(calculated) = 0.68, Co]/Co2(measured)= 0.64). In general, a kink is observed at h ~ = E,, with an increase in the slope for ha~ > E u, in agreement with experimental results. Since the curvature in JT(h~) is similar to that for the unperturbed bands for h~ > E~, EG2 = E0c - E0v. For hr0 < E~, EG1 ----rain( E~c - E l v , Elc - Euv }. Thus, for

(8)

with a standard deviation of 0.02 eV and a correlation coefficient of 0.96. The extrapolated value of EG(0 ) = 1.23 eV is close to the indirect energy gap of crystalline silicon (1.11 eV at 300 K [8]). The discrepancy between the two values may be due to differences in the topology of amorphous and crysialline films. In addition, correlation effects in amorphous silicon, arising from the presence of localized states, would tend to increase E G relative to c-S•. Photoelectron spectra by Roedern et al. [37] indicate that the formation of strong S i - H bonds shifts the corresponding Si bonding orbitals deep into the valence band, causing a recession of the valence band edge. The dependence of E G on the inverse of the average separation between the proton potentials suggests that the incorporation of bonded hydrogen also has a long-range effect in perturbing the Si binding energies. Indeed, Ushami et al. [38] have found that the incorporation of bonded hydrogen into a-S• increases the binding energy of the silicon core 2p levels slightly. Fig. 12 shows the variation of EG1 (o), EG2 (D) and E u (zx) with bonded hydrogen content for a compilation of PH3-doped films deposited at 250 ° C by DC glow discharge decomposition of S i H 4 / P H 3 gas mixtures using a fixed gas-phase doping ratio of PpH3/PsiH,= 0.005. The discharge current density Joc and voltage VDC were varied sequentially. The demarcation energy Eu, ranging from 2.00 eV to 2.10 eV, is not significantly affected by- the discharge parameters or moderate

R. V. Kruzelecky et aL / Interband optical absorption in amorphous silicon 24

I

I

I

I

I

I

I

I

the values of hydrogen content as determined using 15N profiling and FIR absorption spectra are generally in good agreement for the n-type samples [39], the notable exception being sample G N H l l deposited at the highest power. Since the optical gap of G N H l l is correlated with the total hydrogen content as given by 15N profiling, the discrepancy between the corresponding values of CsiH (about 18 at.%) and c H (about 22 at.%) most likely reflects the effect of the near-neighbor environment of the S i - H bonds on the FIR absorption strength, rather than a difference between the total and bonded hydrogen content. The variation of EG2 with c H for the PH3-doped a-Si : H films is in good agreement with the trend observed for undoped films as given by (8). The variation of EG1 with c n as given by (9) reflects the effect of phosphorus on the distribution of states within the gap defined by E u. The corresponding dependence observed for our undoped films is given by

EU

23

EG2 O

EGI

22

2~ z~ .

>tD CC LO Z W

.

.

.

.

.

.

.

.

tX

Zx . . . . . . . . . .

A

20

A

19

i

_+ ,7

1,6

I

15

I

I

I

I

I

I

I

20

I

25

[ C H ] '/3 Eo~ = 1.2 1 ~ + 1.06 eV

CH (ATOMIC PERCENT)

Fig. 12. Variation of the demarcation energy E~, and the extrapolated gap EG1 (EG2), as determined from the "Tauc" region below (above) E~, with hydrogen content for a compilation of PH3-doped a-Si:H films deposited at 250 ° C by DC glow discharge decomposition of a SiH4/PH 3 gas mixture using a fixed PH 3 to Sill 4 ratio of 0.005 and various discharge parameters J o c and V D C .

doping levels and is similar to that observed for undoped films. Despite the variations in morphology with VDC and JDC [39], the optical gaps EG1 and Ec2 of the resulting films are correlated with c H. A least squares fit yields the following results EG1 = 1 97[ CH ]1/3 + 0.56 eV " tl00J with a standard deviation of 0.01 eV, and r C 1~/3 EG2 = 0.98[ ~ ] + 1.28 eV

247

(9)

(10)

with a standard deviation of 0.02 eV. The optical data was fitted to c H as determined by 15N profiling rather than Csin due to the uncertainty in the value of the proportionality coefficient Cs (see eq. (7)) for the n-type samples. It should be noted that

(11)

with a standard deviation of 0.005 eV. A comparison of (9) and (11) indicates that the incorporation of phosphorus results in a considerable broadening of the tail state distributions as reflected by the small value of EG~(0 ) = 0.56 eV for the n-type films. A comparison of the variation of EG2 and EG1 with cn for both PH3-doped and intrinsic films indicates that EG2 -- EGI decreases at higher concentrations of bonded hydrogen. This reflects a narrowing of the tail state distributions at the band edges. The introduction of hydrogen into the a-Si network initially increases the depth of potential fluctuations due to the random distribution of proton potentials. This is reflected by the rapid increase in E u upon hydrogenation. As c H increases, overlap between the proton potentials reduces the depth of the potential fluctuations. The inductive effect of the proton potentials shifts the tail states deeper into the respective bands, accounting for the narrower tail state distributions. The concept of a mobility gap has played an important role for the interpretation of the optoe-

2'$8

R. V. Kruzelecky et al. / lnterband optical absorption in amorphous silicon

lectronic characteristics of amorphous semiconductors. In one dimension, potential fluctuations with a depth AV result in the localization of all allowed states within AV provided that AV is sufficiently deep such that bound states exist. However, the question of localization is more complex in two and three dimensions; channels can exist that bypass the potential barriers. Brodsky [33] suggests that higher hydrogen concentrations reduce the connectivity of Si states within the bonding-antibonding gap corresponding to Sill until islands of Si are formed ( E G = Esi), surrounded by a tissue of S i - H (EG=EsiH). Indeed, the value of Eu at higher hydrogen contents (15 to 20 at.%), about (2.05 + 0.05) eV, is consistent with the magnitude of the mobility gap estimated from combined transport and optical measurements for glow discharge a-Si: H films (about 2.0 to 2.1 eV [33,40]). At lower hydrogen contents, the mobility gap may be smaller than E~ due to the presence of percolation paths which bypass potential fluctuations associated with the proton potentials. According to our model, ( E u - E o a ) is a measure of the width of the wider band tail. An effective width for the respective tail state distributions can be obtained from the temperature dependence of the drift mobility. The experimental results, as reviewed by Spear [34], suggest that A E v is about 0.3-0.4 eV while AE c is about 0.13-0.20 eV for glow discharge a-Si : H films. For glow discharge films, ( E ~ - E G 1 ) = 0 . 3 eV, in agreement with the estimate of A E v that has been obtained from transport measurements.

7. Conclusions A new, unified model of the interband optical absorption edge in amorphous silicon films prepared by various techniques has been presented. The interband absorption characteristics of a-Si and a-Si : H films follow the " T a u c " model above the main absorption edge. Plots of (ahto) 1/2 versus hto are generally piecewise linear, exhibiting an increase in the slope above an energy denoted by Eu. As a result, E G must be estimated from the appropriate section to obtain consistent results.

Values for Co and EG were determined from the linear sections below and above E u. Absorption in the " T a u c " region below E u involves electron transitions between tail states and deeper lying extended states in the opposite band. The corresponding magnitude of C01 for U H V a-Si (about 1.0 × 105 to 3.0 × 105 (cm. eV) -1) is smaller than the values generally observed for undoped a-Si : H (about 3.5 × 105 (cm. eV)- 1), suggesting a broader distribution of tail states. For a given value of Eo, lower values of C01 are correlated with a smaller extrapolated gap EG1. This is consistent with a broadening of the tail state distributions within a gap defined by E u due to disorder and the resulting potential fluctuations. Physically, E u - E G 1 is a measure of the width of the tail state distribution in the wider tail. Hydrogenation increases E u from about (1.80 + 0.05) eV for U H V a-Si films to about (2.05 + 0.05) eV due to the resulting compositional disorder and deeper lying potential fluctuations associated with a random distribution of proton potentials. Absorption at energies above E u is dominated by transitions between extended states. The weak dependence of C02 on preparation conditions suggests that deeper-lying states in the bands are not strongly perturbed by the disorder. EG2 corresponds to the fictitious gap associated with the unperturbed bands. The incorporation of bonded hydrogen into a-Si increases both E61 and EG2; the blue shift is proportional to Csi _1/3 H or inversely proportional to the average separation between the proton potentials. The dependence of the optical gap on the average separation between proton potentials suggests that bonded hydrogen has a long-range effect on the Si-Si bonding energies. Moreover, EG2 -- EG1 decreases as CsiH increases (CsiH < 25 at.%), suggesting that higher hydrogen content narrows the width of the tail state distributions through the inductive effect of the proton potentials on the Si binding energies. A variation in the optical gap from 1.4 eV to 1.7 eV can be obtained for PERE samples, corresponding to a bonded hydrogen content between 1 and 10 at.%, by simply adjusting the discharge current a n d / o r substrate bias. This provides considerable flexibility to optimize the spectral response of resulting optoelectronic devices to the

R. V. Kruzelecky et al. / Interband optical absorption in amorphous silicon

illumination spectrum. Moreover, it should be possible to produce a graded-gap layer of a-Si : H with a variation exceeding 0.2 eV simply by ramping the discharge current. A graded gap would allow more efficient utilization of the solar spectrum for power conversion in a-Si : H solar cells.

References [1] D.E. Carlson and C.R. Wronski, Appl. Phys. Lett. 28 (1976) 671. [2] Y. Imamura, S. Ataka, Y. Takasaki, C. Kusano, T. Hirai and E. Maruyama, Appl. Phys. Lett. 35 (1979) 349. [3] N. Yamamoto, Y. Nakayama, K. Wakita, M. Nakano and T. Kawamura, Jpn J. Appl. Phys. Suppl. 20-1 (1981) 305. [4] W. Paul, D.K. Paul, B. von Roedern, J. Blake and S. Oguz, Phys. Rev. Lett. 46 (1981) 1016. [5] P.J. Zanzucchi, C.R. Wronski and D.E. Carlson, J. Appl. Phys. 48 (1977) 5227. [6] M.P. Schmidt, J. Bullot, M. Gauthier, P. Gordier, I. Solomon and H. Tran-Quoc, Phil. Mag. B51 (1985) 581. [7] M. Lax, Phys. Rev. 109 (1958) 1921; G.A.N. Connell, in: Amorphous Semiconductors, ed. M.H. Brodsky (SpringerVerlag, New York, 1985) p. 73. [8] J.l. Pankove, Optical Processes in Semiconductors (Dover, New York, 1975) p. 412. [9] For example, see ref. [8] p. 37. [10] N.F. Mott and E.A. Davis, Electronic Processes in NonCrystalline Materials, 2nd Ed. (Clarendon Press, Oxford, 1979) p. 287. [111 J.P. de Neufville, T.D. Moustakas, A.F. Ruppert and W.A. Lanford, Proc. 8th Int. Conf. on Amorphous and Liquid Semiconductors, eds., W. Paul and M. Kastner (Cambridge, MA, 1979) p. 481. [12] J. Tauc, in: Optical Properties of Solids, ed. F. Abeles (North-Holland, Amsterdam, 1972) p. 279. [13] E.A. Davis and N.F. Mott, Phil. Mag. 22 (1970) 903. [14] G.D. Cody, T. Tiedje, B. Abeles, B. Brooks and Y. Goldstein, Phys. Rev. Lett. 47 (1981) 1480. [15] W.B. Jackson, S.M. Kelso, C.C. Tsai, J.W. Allen and S.J. Oh, Phys. Rev. B31 (1985) 5187. [16] R.V. Kruzelecky, F. Gaspari, D. Racansky, C. Ukah, S. Zukotynski and J.M. Perz, to be published. [171 O.S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955).

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[18] S.G. Tomlin, J. Phys. D1 (1968) 1667. [19] See for example, C.W. Moges, R.E. Honig and C.A. Evans Jr, in: Secondary Ion Mass Spectrometry SIMS III, eds., A. Beninghoven et al. (Springer-Verlag, Berlin, 1982) p. 172. [20] W.A. Lanford, H.P. Trautvetter, J. Ziegler and J. Keller, Appl. Phys. Lett. 28 (1976) 566. [21] M.H. Brodsky, Manuel Cardona and J.J. Cuomo, Phys. Rev. B16 (1977) 3556. [22] J.C. Knights, C. Lucovsky and R.J. Nemanich, Phil. Mag. B37 (1978) 467. [23] R.V. Kruzelecky, DC Glow-Discharge-Deposited Amorphous Silicon Photovoltaics, M.A.Sc Thesis, University of Toronto, 1982; R.V. Kruzelecky, K.B. Ma and S. Zukotynski, Proc. National Conf. on Solar Energy, ed., B. Saulnier (Montreal, Canada, 1981) p. 96. [24] R.W. Olesinski and G.J. Abbaschian, Bull. Alloy Phase Diagrams 5 (1984) 486. [25] H.F. Wolf, Silicon Semiconductor Data (Pergamon Press, Oxford, 1969) p. 111. [26] G.D. Cody, B. Abeles, C.R. Wronski, B. Brooks and W.A. Lanford, Proc. 8th Int. Conf. on Amorphous and Liquid Semiconductors, eds., W. Paul and M. Kastner (Cambridge, MA, 1979) p. 463. [27] N. Saito, T. Yamada, T. Yamaguchi, I. Nakaaki and N. Tanaka, Phil. Mag. B52 (1985) 987. [28] R.V. Kruzelecky, D. Racansky, S. Zukotynski and J.M. Perz, J. Non-Cryst. Solids 99 (1988) 89. [29] N.F. Mott and E.A. Davis, see ref. [10] p. 215. [30] M. Janai, D.D. Allred, D.C. Booth and B.O. Seraphin, Solar Energy Mat. 1 (1979) 11. [31] J.I. Pankove and P. Aigrain, Phys. Rev. 126 (1962) 956. [32] C. Hass, Phys. Rev. 125 (1962) 1965. [33] M.H. Brodsky, Solid State Commun. 36 (1980) 55. [34] W.E. Spear, J. Non-Cryst. Solids 59-60 (1983) 1. [35] G.D. Cody, B. Abeles, C.R. Wronski, R.B. Stephens and B. Brooks, Solar Cells 2 (1980) 227. [36] W. Beyer, in: Tetrahedrally Bonded Amorphous Semiconductors, eds., D. Adler and H. Fritsche (1985) p. 129. [37] B. von Roedern, L. Ley and M. Cardona, Phys. Rev. Lett. 39 (1977) 1576. [38] K. Ushami, T. Shimada and Y. Katayama, Jpn J. Appl. Phys. 19 (1980) L389. [39] R.V. Kruzelecky, S. Zukotynski and J.M. Perz, J. NonCryst. Solids 103 (1988) 221 (preceding paper). [40] D.V. Lang, J.D. Cohen and J.P. Harbison, Phys. Rev. B25 (1982) 5285.