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Transport properties of hydrogenated amorphous silicon deposited by dc glow discharge decomposition
Journal of Non-Crystalline Solids 51 (1982) 129-142 North-Holland Publishing Company
129
TRANSPORT PROPERTIES OF HYDROGENATED AMORPHOUS S I L I C O N D E P O S I T E D BY dc G L O W D I S C H A R G E D E C O M P O S I T I O N Jin J A N G , C h o o n g H y u n C H O I a n d C h o o c h o n L E E Korea Advanced Institute of Science and Technology, PO Box 150, ChongyangnL Seoul, Korea
Received 4 January 1982 Revised manuscript received 26 May 1982
Conductivity and thermoelectric power measurements have been made as a function of temperature on a series of hydrogenated amorphous silicon samples. The samples were pepared by the dc glow discharge decomposition of silane and silane phosphine mixtures. The activation energy for conduction varied with the substrate temperature and discharge condition for undoped specimens. The difference in the activation energy for conduction as well as the dependence of photoconductivity and optical gap on the activation energy for conduction among undoped specimens can be explained by introducing centers acting as donors or by charge transfer between the island and hydrogen rich interfacial region. The kinks in the log o versus inverse temperature curves always appear at about 430 K for the undoped specimens prepared at 300°C, while they are absent for low substrate temperature specimens. The downward kinks with increasing temperature can be explained by a two-phase material model. A revised two-channel conduction path model including material heterogeneity is applied to interpret the conductivity and thermopower versus inverse temperature curves of doped a-Si : H films, and to determine the position of phosphorus donor levels. The levels are found to lie at about 0.47 eV below Ec, the mobility edge at the conduction band.
1. Introduction G l o w d i s c h a r g e d e p o s i t e d a m o r p h o u s silicon is an o u t s t a n d i n g m a t e r i a l d i s p l a y i n g high p h o t o c o n d u c t i v i t y a n d efficient low t e m p e r a t u r e p h o t o l u m i n e s cence. T h e d e n s i t y of states in the g a p for the m a t e r i a l is sufficiently low so that d o p i n g Of the m a t e r i a l i n t o p - t y p e or n - t y p e is possible. W h i l e it is certain t h a t the h y d r o g e n saturates the d a n g l i n g b o n d in h y d r o g e n a t e d a m o r p h o u s silicon (a-Si: H), the precise m a n n e r in which the h y d r o g e n modifies the structure o f this m a t e r i a l is n o t u n d e r s t o o d . T h e n a t u r e o f charge t r a n s p o r t in a - S i : H is also n o t c o m p l e t e l y u n d e r s t o o d . R e c e n t l y several w o r k e r s [1,2] have a t t e m p t e d to e x p l a i n the n a t u r e of the k i n k s at a b o u t 430 K a p p e a r i n g in the plots of log c o n d u c t i v i t y a n d t h e r m o p o w e r versus inverse t e m p e r a t u r e for u n d o p e d a - S i : H specimens. S p e a r et al. [ 1] suggested that the m o b i l i t y edge E c (or Ev) moves t o w a r d the gap center w i t h increasing t e m p e r a t u r e until the b o t t o m of the b a n d tail is reached. A n d e r s o n et al. [2] suggested that for a heterogeneous m i x t u r e of the two 0022-3093/82/0000-0000/$02.75
© 1982 N o r t h - H o l l a n d
130
J. Jang et al. / Transport properties of a-Si: H
phases, neither of which form a continuous channel between the electrodes, the conductivity would be governed by the phase of low conductance, resulting in downward kinks seen on the curves of the measured conductivity (o) and thermopower (S) versus inverse temperature. There are several different results and interpretations of the transport properties of doped a-Si: H films. The Dundee group [3] interprets their experimental results in terms of a two conduction path model. Beyer and Overhof [4] come to the conclusion that there exists a single type of conduction, probably in the conduction band. Drhler [5] argues that conduction proceeds by hopping only, even at high temperatures. Jan et al. [6] and Anderson et al, [7] interpret their results by a two-channel conduction path both at the extended and localized donor states found at - 0 . 4 5 eV below E c. In this paper we explain the differences in the activation energy for conduction between undoped specimens by introducing the S i - H - S i three center bonds (TCBs) in a-Si:H and material heterogeneity. We also present new data on the temperature dependence of the conductivity and thermoelectric power for specimens prepared by dc glow discharge decomposition of silane and silane phosphine mixtures, and discuss our results compared with the proposed models.
2. Experimental details The hydrogenated amorphous silicon films were produced in the capacitative glow discharge system. The dc or rf discharge was sustained between two disk electrodes of 6 cm in diameter, and the substrates (Corning 7059) were placed on the cathode or on the screen between the cathode and the anode. The deposition system is shown in fig. 1. The gas pressure during preparation was 0.8 Torr, the applied dc voltage to produce plasma was 730 V, the flow rate of the gas was ~ 5 sccm (standard cubic centimeters per minute), the base pressure of the reactor was less than 1 mTorr, and the power density during preparation was ~ 0.1 W / c m 2 throughout the experiments. The conductivity was measured in a four-probe geometry using four parallel evaporated strips of AI or Cr with 0.4 mm spacing. A 20 V dc power supply was used as a voltage source. The current and voltage were measured by a Keithley 616 Electrometer and a Keithley 610C Electrometer, respectively. There was no evidence of any nonlinearity in the I - V characteristics, nor was there any significant difference between two-probe and four-probe data on the same sample. Therefore, most of the data was measured by two-probe geometry. The measurements were carried out in a vacuum of ~ 10 -5 Torr. The samples to measure the thermopower were films of 1 cm × 1 cm, deposited on Coming 7059 glass, and mounted on a copper block which could be heated by main and auxiliary heaters to make gradual temperature difference between the planar, parallel electrodes. The thermal emf was measured across the two electrodes separated by 0.8 cm using a Keithley 642 Electrometer. The junction of the differential
J. Jang et aL / Transport properties of a-Si.'H (a)
~-GA', INLET
DC POW. S 4-1=. . . . . . L ~ . I i . . , ~ PIN(J {HEATER
O 1"
g L SUPPLY
I <--GAS INLET
I
(b) ANODE
131
S
I
N('~
I
HEATER
t D C POWER SUPPLY Fig. 1. (a) The schematic diagram of the dc plasma deposition system, where the substrate is held on the cathode. (b) The schematic diagram of the dc plasma deposition system, where the discharge is sustained between the anode and cathode, and the substrate is placed on the plate "S".
copper-constantan thermocouple, cemented in place just above the electrode on the substrate glass, was used to measure the temperature difference between two electrodes. The evaporated A1 or Ag metal was used as the electrode material, Ag gave a smaller offset voltage than Al. To reduce the distortion of the thermoelectric potential gradient, a 0.2 mm width electrode was used. At each measurement temperature a plot of emf AV versus AT (temperature difference between the two electrodes) was made to obtain the slope of the line which gives the thermopower S = - A V / A T . For the range of AT used (+--3°C) no curvature in the AV versus AT plot was observed, but the line rarely passed through the origin. The magnitude of this deviation from the origin (offset voltage) was temperature dependent and less than 0.15 inV. The measurements were carried out with decreasing temperature. However, there was no significant difference between results measured with increasing temperature and those measured with decreasing temperature after heating in vacuum. All data reported here were taken after the specimens had been heated to 250°C in vacuum for 30 rnin to avoid the formation of free surface adsorbates [9] and light induced changes [10]. In order to obtain data for the bulk [11], relatively thick samples ranging from 0.4 # m to 1.0 # m were used.
3. Results
The electrical conductivity of undoped a-Si: H films versus inverse temperature is plotted in fig. 2. The following characteristics can be seen: (1) The specimens prepared between 20°C and 200°C, and annealed at 300°C have larger activation energies than those prepared at 300°C. (2) The downward kink in the log a versus 1/T curve appears in the specimen prepared at 300°C while it does not appear in the specimens deposited at temperatures below 200°C. (3) The upward kink with increasing temperature appears in sample [] in
J. dang et a L / Transport properties of a-Si." H
132 iO-Z
[
[]
I T_ =9(3*('2. f D C ) ;aled.
10-3
DC) .~oled DC) -
1 0 -4
RF) ;aled
10-5 () ~ I 0 -~ >r-- 10 - r > I--¢j 10 -8 o 10-9
i o-IO
iO-II
2"0
40
:3"0 IO00/T
( K "~ )
Fig. 2. Conductivity in undoped a-Si : H films, deposited by the glow discharge method shown in fig. l(a) plotted against the inverse temperature. The solid lines describe the plot of data by eqs. (3) and (5) and the numbers along the line denote the activation energies. Ts, substrate temperature; DC, specimen deposited by dc glow discharge; RF, specimen deposited by rf glow discharge.
fig. 2 deposited at 20oc and annealed at 300°C, and the difference in activation energy between the high and low temperature region below 400 K is 0.4 eV. Fig. 3 shows the dependence of photoconductivity and optical gap on the activation energy for the conduction of undoped specimens deposited at 310°C. The samples were prepared for various substrate positions, keeping the other discharge conditions the same. The schematic diagram of the deposition system is shown in fig. l(b). The photoconductivity was measured with an incident photon flux of 1015 c m - 2 s - ! (hi,= 1.96 eV). The optical g a p (E~ pt) was deduced by using the experimental relation, ( a h u ) ! / 2 = B ( h p - - E~pt). As the activation energy for conduction increases, the optical gap and photoconductivity decrease. The conductivity versus inverse temperature curves are shown in fig. 4 for the n-type a-Si:H films doped with various phosphorus concentrations. The kinks appear at 380-430 K for both undoped and doped specimens. Down-
I
I
1.8
I0 -4 -
~
o
. O
~
A
~_ l0 -~
-
1.7 g
>_
v
t---
13_
Q O O 10-6 _ O -r
),
_ I. 6 4~ aO
UNDOPED o-Si:H I0 -7 0.6
I 0.7
I 0.8
I .5 0.9
E~t ( e V ) Fig. 3. The dependence of photoconductivity and optical gap on the activation energy for conduction for undoped a - S i : H films deposited at 310°C. The samples were prepared by varying substrate positions while keeping other deposition conditions the same. The deposition system is shown in fig. l(b). The photoconductivity was measured with a photon density of 1015 cm 2 s 1 (h~, = 1.96 eV). i0 °
I
l
I
pHi/Sill4 i0 -z -
~,~10 -4 _
)V-
z=°lO'e--o
"~'~
~
o
5XlO" _
X
I0 "5
IO-e-
UNDOPED I 0 -I°
I
I
20
3.0
~
I O 0 0 / T ( K "l
I
4'0 )
Fig. 4. Conductivity in p-doped a-Si : H films plotted against the inverse temperature for a series of specimens deposited by the dc glow discharge method shown in fig. l(a). The numbers along the lines denote the partial pressure of phosphine in silane. The upward solid lines denote the least square fitting of data to eq. (16).
PH3/SiH 4 (vppm)
0
1.0X 101
5.0× 101
1.0X 102
5.0× 102
1.0x 103
1.0× 104
Sample
1
2
3
4
5
6
7
H L H L H L H L H L H L H L
High temp. Low temp. 2.0 × 6.0 × 9.0× 1.7× 1.4X 5.4× 2.0× 1.5 × 7.0× 6.0× 2.0x 7.5 X 2.8× 1.0X
103 103 101 104 10 103 101 101 101 10 ° 102 10 ° 103 101
(eV) 0.62 0.82 0.50 0.69 0.42 0.64 0.43 0.31 0.39 0.27 0.36 0.25 0.46 0.26
oo
(fl - i cm - i )
Eo
0.17 0.10 0.28 0.11
0.36 0.52
0.54 0.75
(eV)
Es
0.19 0.15 0.18 0.15
0.06 0.12
0.08 0.07
(eV)
Eo -- E s
0.22
0.19
0.20
(eV)
AEo
0.55
0.46
0.47
0.47
(eV)
E c -- E D
0.18
0.21
AEs (eV)
Table 1 Data for the phosphorus doped n-type a-Si : H specimens used in the conductivity and thermoelectric power measurements. PH 3 / S i l l 4, gaseous impurity ratio used to prepare the specimens. High temp., high temperature region above ~ 4 3 0 K. Low temp., low temperature region below ~ 4 3 0 K. D, donor-related term. Eo, activation energy for conduction, o0, pre-exponential factor of conductivity. E~, activation energy for thermopower. A E o , difference in the activation energy for conduction between the high temperature and low temperature region. ED, the phosphorus donor level in energy band. AE~, difference in the activation energy for thermopower between the high and low temperature regions.
t~
J. Jang et a L / Transportproperties of a-Si: H I
-05
I
_
135
I
PH a /
Si H 4
_
10 -z
E -I.0 n" hl
°o ° ~ 0 O
:E
-1"5
Pr uJ T I--
~~
10 . 5
DOPED
o\
-2"0 I
I
3.0
20 I000
I
4"0 / T ( K "~ )
Fig. 5. Thermopower in p-doped a-Si : H .filmsplotted against the inverse temperature for a series of specimensdeposited by the dc glow discharge method shown in fig. l(a). The numbers along the lines denote the partial pressure of phosphine in silane. The upward solid lines denote the least square fitting of data to eq. (17).
ward kinks are observed in undoped and lightly doped specimens, while upward kinks are observed in heavily doped specimens (above 102 v p p m PH3) in the log o versus 1 / T plot. The plots of thermoelectric power versus inverse temperature are shown in fig. 5 for the representative specimens doped with a wide range of phosphine concentration. The behavior of temperature dependence is similar to that of conductivity, while the scatter in the data points about the solid lines is more apparent. Table 1 summarizes the relevant data for the seven specimens investigated. They are listed in order of increasing phosphorus content as indicated by the second column, which gives the phosphine to silane ratio in volume parts per million (vppm).
4. D i s c u s s i o n
It will be useful for the purpose of discussion to designate the specimens by A and B. Specimen A denotes the samples deposited at 300°C by dc glow discharge decomposition. Specimen B represents those deposited between 20°C
136
.I. Jang et al. / Transport properties of a-Si: H
and 200°C, and annealed at 300°C (250°C for ~ in fig. 2) for 30 min. The recombination form of specimen B was observed to be monomolecular: r = 0.95 in Oph = I r (Oph, photoconductivity; I, light intensity) for specimen ® in fig. 2, while it is bimolecular: r = 0.6, for specimen A. The density of states at the Fermi level for specimen A was observed to be 4.0 x 1017 eV - l cm -3, while it was 2.0 X 1018 eV - l cm -3 for specimen B (® in fig. 2) when the same insulated gate field effect geometry was used. * It is apparent, therefore, that the density of states around the Fermi level is larger for specimen B than specimen A. To begin with, the difference between the conductivity activation energies (Eo) of specimens A and B will be discussed. If the Fermi level exists near midgap in undoped a-Si: H, Eo will increase as the optical g a p (E~ pt) increases. But the behavior shown in fig. 3 is quite opposite to this; E~ pt decreases as Eo increases. Accordingly, the difference in Eo is not caused only by the difference in the band gap. Fig. 3 also shows that Eo is smaller for the specimens with higher photoconductivity than for those with lower photoconductivity. On the other hand, the undoped specimens with higher photoconductivity must have a smaller density of deep gap states, since deep gap states act as effective recombination centers. Accordingly, to interpret the experimental results shown in fig. 3, the existence of donor states should be assumed. If we assume the existence of the same distribution of donor state density in all the specimens shown in fig. 3, then, for the specimens with the lower density of deep gap states, the Fermi level will lie higher and consequently Eo will be smaller than for those showing high deep gap state density. The difference in Eo between specimen A and B shown in fig. 2 can also be explained by this assumption, because the optical gap of specimen A and B was observed to be nearly the same. In a-Si: H the ordinary silicon-silicon or silicon-hydrogen bonds such as Sill, Sill 2 and (Sill2) ~ cannot act as the donors. However, the S i - H - S i three center bonds (TCBs) can play the role of donors: the charge of the TCBs can be positive in thermal equilibrium. Fisch and Licciardello [12] suggested that the S i - H - S i TCBs are present in a-Si : H, and have negative correlation energy. However, the correlation energy of the TCBs is expected to be positive from the results of the tight binding calculations of Allan and Joannopoulos [13] and from the variation of the Fermi level with slight doping [14]. We suggest that 1016-10 t7 cm -3 of S i - H - S i TCBs are present in undoped a-Si:H to interpret the experimental results shown in figs. 2 and 3. Three electrons take part in a three center bond, and two electrons occupy the bonding states and one electron occupies the nonbonding state. The wavefunction of the bonding orbital (~bb) and the
* In o u r e x p e r i m e n t t h e r m a l l y g r o w n silicon d i o x i d e w a s u s e d as a n i n s u l a t o r .
J. Jang et al. / Transport properties of a-Si." H
137
nonbonding orbital (~k,b) can be described as [12]
¢,, =
1
= 1
+ ps,. + psi2), (ps,, -
(1) (2)
where pu is the hydrogen atomic wavefunction, PSi, and tOsi2 are the two silicon atomic wavefunctions in a TCB, A and A' denote the normalization factors, and a is a constant. The nonbonding states of the TCBs give rise to the states in the gap at E c - E - - 0 . 6 eV according to the calculations of Allan and Joannopoulos [13], while the bonding states give rise to the valence band states lying several electron volts below E v. The nonbonding states of the TCBs seem to be situated near the conduction band edge well above the midgap since the distance between Si and Si in a TCB is longer than the normal Si-Si distance [121. In thermal equilibrium the nonbonding states of the TCBs are not occupied because the Fermi levels of undoped specimens are near the midgap, and thus the nonbonding states act as donors. The band gap (mobility gap), Eg, of specimen A is assumed to be 1.9 eV since the largest value of the E~ is 0.95 eV as can be seen in fig. 2 and other works [15], and thus Eo (0.82 eV) of specimen A is smaller than Eg/2 by 0.13 eV. If we assume that N(E) is constant around E F, and that N F = 4 . 0 × 1017 eV - j cm -3 determined by the field effect technique is purely the bulk states, the state density of the TCBs will be 5.2 × 10 ]6 c m -3. Another interpretation is possible by introducing the structural inhomogeneity of a-Si:H. It has been suggested that the island structure may be characterized as a continuous random network of Si with dangling bonds saturated by hydrogen while the region between the islands is composed of a hydrogenrich, lower density material including the poly-silane structure [7]. One might think here of the hydrogen rich regions as the inter-grain surface layers between the islands. The transfer of electrons between interfacial layers and islands will cause a shift of the Fermi level in the islands. Since the density of gap states of the interfacial layer is considered to be higher than that of the island material and the size of an island ( ~ 100 ,~) is considered to be much smaller than the Debye length [16,17], the small change of Fermi level in the interfacial layer gives rise to the large variation of E F in the bulk. In order to explain the relation between Eo and Oph shown in fig. 3 by this model, the density of state minimum is assumed to be the result of the overlap of two tails extending from E c and E v into the gap. The conduction band tail is composed of acceptor-like states and they will carry negative charges below E F. On the other hand, the valence band tail states are donor-like and provide positively charged states above E F. If the E F of the bulk is moved toward E c by taking electrons from the interfacial layer, the positive charge density around the midgap will be reduced, resulting in the increase of the electron lifetime. Thus, the undoped a-Si : H films with smaller Eo show higher photoconductivity.
138
J. Jang et al. / Transport properties of a-Si : H
Downward kinks with increasing temperature in conductivity and thermopower versus inverse temperature curves are always observed for undoped specimens prepared at 300°C. The differences in conductivity activation energy between the high and low temperature region, above and below - 430 K, for the specimens showing downward kinks were observed to be 0.2 eV as shown in table 1. Spear et al. [1] suggest that the mobility edge moves in the band toward the midgap with increasing temperature. When it reaches the bottom of the band tail, the mobility edge can go no farther, giving rise to the kink in the plot of log a and S versus inverse temperature. However, there is an apparent difference between E~ and E s in the high temperature region as shown in table 1. It is also pointed out that the kink does not appear in specimen B, CVD a-Si [ 18], and evaporated a-Si [ 19]. These facts are difficult to interpret by this model. Another interpretation [2] has been introduced by Harvard group. That is three-dimensional structural model of islands surrounded and interconnected by the tissue material which has a wider band gap than the islands. It is suggested that conductivity and thermopower can be expressed as an activated form in both materials with different activation energies, and that the tissue has lower activation energy caused by hopping conduction between localized states. It is also suggested that neither material forms a continuous channel between the electrodes and the conduction takes place through a series connection of tissue and island material. For a series connection of elements, the measured conductivity will be dominated by the most resistive element, and thus downward kinks are expected. The value of ( E c - EF) 0 of the island material in specimen A is 0.82 eV and the temperature range in which the tissue conduction is dominant is not reached in specimen B because the conductivity of the island material in the specimen B is much lower than that of the island material in specimen A (see fig. 2). Thus specimen B does not show the downward kink, and the downward kink is observed only for specimen A as can be seen in fig. 2. If the transport of undoped and lightly doped specimens takes place at the conduction band mobility edge in the low temperature region and at the localized states of tissue material in the high temperature region, the conductivity and thermopower can be expressed in activated form: ° = O0H e x p ( - - e y / k r ) ,
7"> Zkink,
(3)
S = So.
T> Tki.k,
(4)
T < Ykink ,
(5)
T
(6)
lelT,
0~= O'OL e x p ( - g L / , k Y ) ,
Ek S=SoL
lelT,
where O0H and o0L are pre-exponential factors of conductivity in the high and
J. Jang et al. / Transport properties of a-Si." H
139
low temperature ranges, Eo and E s are activation energies for conduction and thermopower, respectively, subscripts H and L denote the high and low temperature region, respectively, SoL and Sou are constants obtained by extrapolating the linear lines of the thermopower to 1 / T = 0, e is the electronic charge, and Tkink denotes the temperature at which the kink occurs. If it is assumed that the conduction band has a constant density N,/~ is the mobility, and the Fermi level lies many k T below the conduction band edge, and depends on temperature as Ec - E F = (E¢ -- Ev) o + y r ,
(7)
o : eNkT# exp(-y/k) exp[- (E c - EF)o/kT ] ,
(8)
o o : e N k T # exp( - y / k
(9)
then
eo:
),
- EDo.
(lO)
The Harvard group has proposed that the conduction behavior of sputtered a-Si:H can be understood on the basis of a model of transport through two mixed phases with different structure, chemistry, electronic band states and transport parameter [7]. The island material is postulated to be a-Si:H with compensation of defect centers by hydrogen, so that the gap state density is low, resulting in the band edge conduction. The connective tissue is supposed to be rich in H and has a larger band gap and higher density of gap states, showing hopping conduction at the localized states. If the transport takes places at the localized states with energy E T by phonon assisted hopping, the conductivity can be described as o(T) = o0 exp(-EoH/kT)
(11)
with EoU= ( E T - ev)o + W T ,
where WT is the hopping energy between localized states of tissue and o0 is the pre-exponential factor in the formula of conductivity. We can obtain Eo and o0 from the experimental slope and intercept of the plot of log o versus 1 / T . Values of OOH,OOL,E~, E L, E~ and E L are determined by fitting eqs. (3)-(6) to experimental data shown in fig. 4 and given in table 1 (samples 1, 2 and 3). At higher doping concentrations the kinks in the log o and S versus 1 / T plot are upward with increasing temperature as shown in fig. 4. The transport data of these heavily doped specimens have been analyzed by the two-channel conduction path model [6,7]. We now consider how the introduction of phosphorus might affect two-phase structure and whether there is any connection between the downward kinks in the undoped films and the upward kinks of the doped films. However, there are a number of similarities in absorption, photoluminescence and photoconductivity between phosphorus doped samples and the specimens, prepared by sputtering in a high hydrogen partial pressure, which contain a large fraction of tissue material [20]. Therefore, the transport
140
J. Jang et aL / Transport properties of a-Si: H
of doped films in the high temperature region is also expected to take place at the localized states of tissue material. The E H of the specimens 1, 2, and 3, showing downward kinks, decreases as the E L decreases. The difference between E H and E L is ~0.2 eV for all specimens showing a downward kink. This means that the, Fermi level of the specimens moves toward E c both at the island and tissue by the same amounts. This is the evidence of tissue hopping in the high temperature region in slightly doped specimens (specimens 2 and 3). Accordingly, the two-channel conduction path model, in which the transport takes place both at extended and at localized donor states, should be changed. Since deposition conditions for moderate to heavily doped specimens showing upward kinks are the same as for the undoped and lightly doped specimens with downward kinks, it would be natural to assume that the conduction takes place through series connection of islands and tissues for doped samples as for undoped specimens. Therefore, the conductivity and thermopower can be written by the sum of the localized state hopping in the tissue and the donor state hopping in the island in the high temperature region, and the sum of the band edge conduction and the donor state hopping in the low temperature region. Thus, o=o1+o
3,
(12)
= Oo. exp(--EoU/kT) + OoD e x p ( - E ~ / k T ) , T>
Tkink ,
s= So. T>
lelr!I°'+ o
s0o
ief
o'
(13)
Tkink ,
O ~ O2 -~- (I3,
=o0, exp(- GL/k r ) + Ooo exp(- G ° / k r ),
(14)
T < Tkink,
S
.
SOL lelT .
.
.
o + So,
i
f"
7,
T < Tkink. where the first term (ol) and the second term (%) in eq. (12) denote the contribution to conductivity by the hopping in tissue material and the hopping in donor states respectively, the first term in eq. (14) denotes the conduction in the band edge, EoDis (E D --EF) 0 + W o , ED denotes the phosphorus donor level, WD the average hopping energy between donor states, and the subscript D the donor related term. For moderate to heavily doped films represented by samples 4, 5, 6 and 7, in table 1, it can be seen that over the whole temperature range of the measurements, the overall conductivity and thermopower can be fitted, within experimental error, to the sum of two terms each. In these doped samples, the
J. Jang et al. / Transport properties of a-Si: H
141
first term (o 1) is dominant in the high temperature region (because o0n > gOD), while the second term (o 3) is dominant in the low temperature region because of E L > E y . Thus neglecting the second term in eq. (12) and the first term in eq. (14), we obtain the following conductivity formula valid over the whole temperature range of measurement: O = O 1 "[-03,
o = OOHe x p ( - - E ~ / k T ) + O0D e x p ( - E o ° / k T ) ,
(16)
by the same argument,
s=
S0.-lel----y
o
lel z
o
The solid lines of the samples showing upward kinks in figs. 4 and 5 denote the fitting of eqs. (16) and (17) to the experimental data. Values of O0H versus Eo" and O0L versus E L satisfy the experimental relation o0 = o00 exp(AEo) with A = 1.7 × 10 (eV) - l and O0o= 8.5 × 10 -z f~-i cm-1. The differences between the activation energies for conduction in the high and low temperature ranges, AEo = E L EoH, are ~ 0.2 eV in the samples 1, 2 and 3, shown in table 1. This value of AEo corresponds to that of AE s, the difference of the activation energy for thermopower between the high and low temperature region, shown in table 1. The difference between Eo and Es lies between 0.06 and 0.19 eV, which is interpreted as the mobility activation energy: hopping energy between localized states in hopping conduction. The hopping energy between localized donor states, WD = 0.15 eV, is shown for the samples 6 and 7 in table 1. The transport in these films takes place at localized donor states in the low temperature region, and at localized states of tissue in the high temperature region. The series connection of the donor state hopping in the island and the hopping at localized states in the tissue gives rise to the upward kinks in the plot of log o and S versus 1/T, while that of the band edge conduction in the island and the hopping in the tissue gives rise to the downward kinks for undoped and slightly doped films. Since the Fermi levels of island and tissue move together by the same amounts toward E c as a result of phosphorus doping and the tissue hopping is the dominant transport mechanism in the high temperature region, the Fermi level of these doped films is expected to be related to E H as ( E c - Ev) o = Eon + A E o, i.e., the AEo for the specimens showing downward kinks is ~ 0.2 eV, the same value of AEo is expected for the samples 4, 5, 6 and 7, because the transport mechanism at the high temperature region is the same as that for the samples 1, 2 and 3. Then, the position of phosphorus donor level is determined by -
-
(e0--ED)0=EY+AEo-ey+
W D.
(18)
The column second from the last in table 1 lists the values of (E~ -- E o ) o obtained from our data. In view of the oversimplicity of the two discrete level conduction model, there is a small scatter in the value listed, but all the measurements indicate that the E D lies around 0.47 eV below E c. The devia-
142
J. Jang et al. / Transport properties of a-Si: H
tion of ( E ¢ - ED) 0 for specimen 7 in table 1 from the other values m a y be related to the decrease in A E o . It a p p e a r s that the k i n k ( A E o ) m a y be changed in highly d o p e d specimens (over 10 4 vppm). T h e c o n d i t i o n showing d o w n w a r d kinks with increasing t e m p e r a t u r e should be investigated to clarify this point.
5. Summary T h e difference in the activation energy for c o n d u c t i o n as well as p h o t o c o n ductivity a n d optical gap versus activation energy for c o n d u c t i o n curves of a series of u n d o p e d specimens can be i n t e r p r e t e d either b y i n t r o d u c i n g centers acting as d o n o r s or charge transfer between the island a n d h y d r o g e n rich interfacial region. The d o n o r states are suggested to be S i - H - S i three center b o n d s in this work, a n d 1016-1017 c m 3 of the TCBs are necessary to explain the e x p e r i m e n t a l data. The d o w n w a r d kinks with increasing t e m p e r a t u r e a p p e a r i n g in the plot of log c o n d u c t i v i t y a n d t h e r m o p o w e r of u n d o p e d a n d lightly d o p e d a - S i : H films versus inverse t e m p e r a t u r e can be i n t e r p r e t e d b y a t w o - p h a s e m a t e r i a l model. A revised two-channel c o n d u c t i o n p a t h m o d e l i n c l u d i n g the m a t e r i a l heterogeneity is a p p l i e d to i n t e r p r e t the log c o n d u c t i v i t y a n d t h e r m o p o w e r versus inverse t e m p e r a t u r e curves of d o p e d a - S i : H films, a n d to d e t e r m i n e the p o s i t i o n of p h o s p h o r u s d o n o r levels. T h e levels are f o u n d to lie at a b o u t 0.47 eV b e l o w E c. T h e a u t h o r s are grateful to professor W. Paul for sending us some articles p r i o r to p u b l i c a t i o n .
References [1] W.E. Spear, D. Allan, P. LeComber and A. Gaith, Phil. Mag. B41 (1980) 419. [2] D.A. Anderson and W. Paul, Proc, 15th Int. Conf. Physics of Semiconductors, Kyoto, 1980, J. Phys. Soc. Japan. 49 (1980) 1197. [3] D.I. Jones, P.G: LeComber and W.E. Spear, Phil. Mag. B36 (1977) 541. [4] W. Beyer and H. Overhof, Sol. St, Commun. 31 (1979) 1. [5] G.H. Drhler, Phys. Rev. 19 (1979) 2083. [6] Z.S. Jan, R.H. Bube and J.C. Knights, J. Electron. Mater. 8 (1979) 47. [7] D.A. Anderson and W. Paul, to be published in Phil. Mag. [8] P.Z. Zanzuchi, C.R. Wronski and D.E. Carlson, J. Appl. Phys. 48 (1977) 5227. [9] M. Tanielian, H. Fritzsche, C.C. Tsai and E. Symbalisty, Appl. Phys. Lett. 33 (1978) 353. [10] D.L. Staebler and C.R. Wronski, J. Appl. Phys. 51 (1980) 3262. [11] D.G. Arts and M.H. Brodsky, Phil. Mag. B41 (1980) 273. [12] R. Fisch and C.C. Licciardello, Phys. Rev. Lett. 41 (1978) 889. [13] D.C. Allan and .I.D. Joanfiopoulos, Phys. Rev. Lett. 44 (1980) 43. [14] W.E. Spear and P.G. LeComber, Phil. Mag. B33 (1976) 935. [15] M.H. Bronsky, Fundamental Physics of Amorphous Semiconductors, ed., F. Yonezawa (Springer-Verlag, 1981), p. 56. [16] W. Paul, Solar Energy Materials 5 (1981) 229. [17] I. Solomon, T. Dietl and D. Kaplan, J. Phys. 39 (1978) 1241. [18] M. Hirose, M. Taniguchi and Y, Osaka, Proc. 7th. Int. Conf. on Amorphous and Liquid Semiconductors, ed., W.E. Spear (CICL, Univ. of. Edinburgh, 1977) p. 352, [ 19] W. Beyer, Sol. St. Commun. 29 (1979) 291. [20] D.A. Anderson, G. Moddel and W. Paul, J. Non-Crystalline Solids 35-36 (1980) 345.
129
TRANSPORT PROPERTIES OF HYDROGENATED AMORPHOUS S I L I C O N D E P O S I T E D BY dc G L O W D I S C H A R G E D E C O M P O S I T I O N Jin J A N G , C h o o n g H y u n C H O I a n d C h o o c h o n L E E Korea Advanced Institute of Science and Technology, PO Box 150, ChongyangnL Seoul, Korea
Received 4 January 1982 Revised manuscript received 26 May 1982
Conductivity and thermoelectric power measurements have been made as a function of temperature on a series of hydrogenated amorphous silicon samples. The samples were pepared by the dc glow discharge decomposition of silane and silane phosphine mixtures. The activation energy for conduction varied with the substrate temperature and discharge condition for undoped specimens. The difference in the activation energy for conduction as well as the dependence of photoconductivity and optical gap on the activation energy for conduction among undoped specimens can be explained by introducing centers acting as donors or by charge transfer between the island and hydrogen rich interfacial region. The kinks in the log o versus inverse temperature curves always appear at about 430 K for the undoped specimens prepared at 300°C, while they are absent for low substrate temperature specimens. The downward kinks with increasing temperature can be explained by a two-phase material model. A revised two-channel conduction path model including material heterogeneity is applied to interpret the conductivity and thermopower versus inverse temperature curves of doped a-Si : H films, and to determine the position of phosphorus donor levels. The levels are found to lie at about 0.47 eV below Ec, the mobility edge at the conduction band.
1. Introduction G l o w d i s c h a r g e d e p o s i t e d a m o r p h o u s silicon is an o u t s t a n d i n g m a t e r i a l d i s p l a y i n g high p h o t o c o n d u c t i v i t y a n d efficient low t e m p e r a t u r e p h o t o l u m i n e s cence. T h e d e n s i t y of states in the g a p for the m a t e r i a l is sufficiently low so that d o p i n g Of the m a t e r i a l i n t o p - t y p e or n - t y p e is possible. W h i l e it is certain t h a t the h y d r o g e n saturates the d a n g l i n g b o n d in h y d r o g e n a t e d a m o r p h o u s silicon (a-Si: H), the precise m a n n e r in which the h y d r o g e n modifies the structure o f this m a t e r i a l is n o t u n d e r s t o o d . T h e n a t u r e o f charge t r a n s p o r t in a - S i : H is also n o t c o m p l e t e l y u n d e r s t o o d . R e c e n t l y several w o r k e r s [1,2] have a t t e m p t e d to e x p l a i n the n a t u r e of the k i n k s at a b o u t 430 K a p p e a r i n g in the plots of log c o n d u c t i v i t y a n d t h e r m o p o w e r versus inverse t e m p e r a t u r e for u n d o p e d a - S i : H specimens. S p e a r et al. [ 1] suggested that the m o b i l i t y edge E c (or Ev) moves t o w a r d the gap center w i t h increasing t e m p e r a t u r e until the b o t t o m of the b a n d tail is reached. A n d e r s o n et al. [2] suggested that for a heterogeneous m i x t u r e of the two 0022-3093/82/0000-0000/$02.75
© 1982 N o r t h - H o l l a n d
130
J. Jang et al. / Transport properties of a-Si: H
phases, neither of which form a continuous channel between the electrodes, the conductivity would be governed by the phase of low conductance, resulting in downward kinks seen on the curves of the measured conductivity (o) and thermopower (S) versus inverse temperature. There are several different results and interpretations of the transport properties of doped a-Si: H films. The Dundee group [3] interprets their experimental results in terms of a two conduction path model. Beyer and Overhof [4] come to the conclusion that there exists a single type of conduction, probably in the conduction band. Drhler [5] argues that conduction proceeds by hopping only, even at high temperatures. Jan et al. [6] and Anderson et al, [7] interpret their results by a two-channel conduction path both at the extended and localized donor states found at - 0 . 4 5 eV below E c. In this paper we explain the differences in the activation energy for conduction between undoped specimens by introducing the S i - H - S i three center bonds (TCBs) in a-Si:H and material heterogeneity. We also present new data on the temperature dependence of the conductivity and thermoelectric power for specimens prepared by dc glow discharge decomposition of silane and silane phosphine mixtures, and discuss our results compared with the proposed models.
2. Experimental details The hydrogenated amorphous silicon films were produced in the capacitative glow discharge system. The dc or rf discharge was sustained between two disk electrodes of 6 cm in diameter, and the substrates (Corning 7059) were placed on the cathode or on the screen between the cathode and the anode. The deposition system is shown in fig. 1. The gas pressure during preparation was 0.8 Torr, the applied dc voltage to produce plasma was 730 V, the flow rate of the gas was ~ 5 sccm (standard cubic centimeters per minute), the base pressure of the reactor was less than 1 mTorr, and the power density during preparation was ~ 0.1 W / c m 2 throughout the experiments. The conductivity was measured in a four-probe geometry using four parallel evaporated strips of AI or Cr with 0.4 mm spacing. A 20 V dc power supply was used as a voltage source. The current and voltage were measured by a Keithley 616 Electrometer and a Keithley 610C Electrometer, respectively. There was no evidence of any nonlinearity in the I - V characteristics, nor was there any significant difference between two-probe and four-probe data on the same sample. Therefore, most of the data was measured by two-probe geometry. The measurements were carried out in a vacuum of ~ 10 -5 Torr. The samples to measure the thermopower were films of 1 cm × 1 cm, deposited on Coming 7059 glass, and mounted on a copper block which could be heated by main and auxiliary heaters to make gradual temperature difference between the planar, parallel electrodes. The thermal emf was measured across the two electrodes separated by 0.8 cm using a Keithley 642 Electrometer. The junction of the differential
J. Jang et aL / Transport properties of a-Si.'H (a)
~-GA', INLET
DC POW. S 4-1=. . . . . . L ~ . I i . . , ~ PIN(J {HEATER
O 1"
g L SUPPLY
I <--GAS INLET
I
(b) ANODE
131
S
I
N('~
I
HEATER
t D C POWER SUPPLY Fig. 1. (a) The schematic diagram of the dc plasma deposition system, where the substrate is held on the cathode. (b) The schematic diagram of the dc plasma deposition system, where the discharge is sustained between the anode and cathode, and the substrate is placed on the plate "S".
copper-constantan thermocouple, cemented in place just above the electrode on the substrate glass, was used to measure the temperature difference between two electrodes. The evaporated A1 or Ag metal was used as the electrode material, Ag gave a smaller offset voltage than Al. To reduce the distortion of the thermoelectric potential gradient, a 0.2 mm width electrode was used. At each measurement temperature a plot of emf AV versus AT (temperature difference between the two electrodes) was made to obtain the slope of the line which gives the thermopower S = - A V / A T . For the range of AT used (+--3°C) no curvature in the AV versus AT plot was observed, but the line rarely passed through the origin. The magnitude of this deviation from the origin (offset voltage) was temperature dependent and less than 0.15 inV. The measurements were carried out with decreasing temperature. However, there was no significant difference between results measured with increasing temperature and those measured with decreasing temperature after heating in vacuum. All data reported here were taken after the specimens had been heated to 250°C in vacuum for 30 rnin to avoid the formation of free surface adsorbates [9] and light induced changes [10]. In order to obtain data for the bulk [11], relatively thick samples ranging from 0.4 # m to 1.0 # m were used.
3. Results
The electrical conductivity of undoped a-Si: H films versus inverse temperature is plotted in fig. 2. The following characteristics can be seen: (1) The specimens prepared between 20°C and 200°C, and annealed at 300°C have larger activation energies than those prepared at 300°C. (2) The downward kink in the log a versus 1/T curve appears in the specimen prepared at 300°C while it does not appear in the specimens deposited at temperatures below 200°C. (3) The upward kink with increasing temperature appears in sample [] in
J. dang et a L / Transport properties of a-Si." H
132 iO-Z
[
[]
I T_ =9(3*('2. f D C ) ;aled.
10-3
DC) .~oled DC) -
1 0 -4
RF) ;aled
10-5 () ~ I 0 -~ >r-- 10 - r > I--¢j 10 -8 o 10-9
i o-IO
iO-II
2"0
40
:3"0 IO00/T
( K "~ )
Fig. 2. Conductivity in undoped a-Si : H films, deposited by the glow discharge method shown in fig. l(a) plotted against the inverse temperature. The solid lines describe the plot of data by eqs. (3) and (5) and the numbers along the line denote the activation energies. Ts, substrate temperature; DC, specimen deposited by dc glow discharge; RF, specimen deposited by rf glow discharge.
fig. 2 deposited at 20oc and annealed at 300°C, and the difference in activation energy between the high and low temperature region below 400 K is 0.4 eV. Fig. 3 shows the dependence of photoconductivity and optical gap on the activation energy for the conduction of undoped specimens deposited at 310°C. The samples were prepared for various substrate positions, keeping the other discharge conditions the same. The schematic diagram of the deposition system is shown in fig. l(b). The photoconductivity was measured with an incident photon flux of 1015 c m - 2 s - ! (hi,= 1.96 eV). The optical g a p (E~ pt) was deduced by using the experimental relation, ( a h u ) ! / 2 = B ( h p - - E~pt). As the activation energy for conduction increases, the optical gap and photoconductivity decrease. The conductivity versus inverse temperature curves are shown in fig. 4 for the n-type a-Si:H films doped with various phosphorus concentrations. The kinks appear at 380-430 K for both undoped and doped specimens. Down-
I
I
1.8
I0 -4 -
~
o
. O
~
A
~_ l0 -~
-
1.7 g
>_
v
t---
13_
Q O O 10-6 _ O -r
),
_ I. 6 4~ aO
UNDOPED o-Si:H I0 -7 0.6
I 0.7
I 0.8
I .5 0.9
E~t ( e V ) Fig. 3. The dependence of photoconductivity and optical gap on the activation energy for conduction for undoped a - S i : H films deposited at 310°C. The samples were prepared by varying substrate positions while keeping other deposition conditions the same. The deposition system is shown in fig. l(b). The photoconductivity was measured with a photon density of 1015 cm 2 s 1 (h~, = 1.96 eV). i0 °
I
l
I
pHi/Sill4 i0 -z -
~,~10 -4 _
)V-
z=°lO'e--o
"~'~
~
o
5XlO" _
X
I0 "5
IO-e-
UNDOPED I 0 -I°
I
I
20
3.0
~
I O 0 0 / T ( K "l
I
4'0 )
Fig. 4. Conductivity in p-doped a-Si : H films plotted against the inverse temperature for a series of specimens deposited by the dc glow discharge method shown in fig. l(a). The numbers along the lines denote the partial pressure of phosphine in silane. The upward solid lines denote the least square fitting of data to eq. (16).
PH3/SiH 4 (vppm)
0
1.0X 101
5.0× 101
1.0X 102
5.0× 102
1.0x 103
1.0× 104
Sample
1
2
3
4
5
6
7
H L H L H L H L H L H L H L
High temp. Low temp. 2.0 × 6.0 × 9.0× 1.7× 1.4X 5.4× 2.0× 1.5 × 7.0× 6.0× 2.0x 7.5 X 2.8× 1.0X
103 103 101 104 10 103 101 101 101 10 ° 102 10 ° 103 101
(eV) 0.62 0.82 0.50 0.69 0.42 0.64 0.43 0.31 0.39 0.27 0.36 0.25 0.46 0.26
oo
(fl - i cm - i )
Eo
0.17 0.10 0.28 0.11
0.36 0.52
0.54 0.75
(eV)
Es
0.19 0.15 0.18 0.15
0.06 0.12
0.08 0.07
(eV)
Eo -- E s
0.22
0.19
0.20
(eV)
AEo
0.55
0.46
0.47
0.47
(eV)
E c -- E D
0.18
0.21
AEs (eV)
Table 1 Data for the phosphorus doped n-type a-Si : H specimens used in the conductivity and thermoelectric power measurements. PH 3 / S i l l 4, gaseous impurity ratio used to prepare the specimens. High temp., high temperature region above ~ 4 3 0 K. Low temp., low temperature region below ~ 4 3 0 K. D, donor-related term. Eo, activation energy for conduction, o0, pre-exponential factor of conductivity. E~, activation energy for thermopower. A E o , difference in the activation energy for conduction between the high temperature and low temperature region. ED, the phosphorus donor level in energy band. AE~, difference in the activation energy for thermopower between the high and low temperature regions.
t~
J. Jang et a L / Transportproperties of a-Si: H I
-05
I
_
135
I
PH a /
Si H 4
_
10 -z
E -I.0 n" hl
°o ° ~ 0 O
:E
-1"5
Pr uJ T I--
~~
10 . 5
DOPED
o\
-2"0 I
I
3.0
20 I000
I
4"0 / T ( K "~ )
Fig. 5. Thermopower in p-doped a-Si : H .filmsplotted against the inverse temperature for a series of specimensdeposited by the dc glow discharge method shown in fig. l(a). The numbers along the lines denote the partial pressure of phosphine in silane. The upward solid lines denote the least square fitting of data to eq. (17).
ward kinks are observed in undoped and lightly doped specimens, while upward kinks are observed in heavily doped specimens (above 102 v p p m PH3) in the log o versus 1 / T plot. The plots of thermoelectric power versus inverse temperature are shown in fig. 5 for the representative specimens doped with a wide range of phosphine concentration. The behavior of temperature dependence is similar to that of conductivity, while the scatter in the data points about the solid lines is more apparent. Table 1 summarizes the relevant data for the seven specimens investigated. They are listed in order of increasing phosphorus content as indicated by the second column, which gives the phosphine to silane ratio in volume parts per million (vppm).
4. D i s c u s s i o n
It will be useful for the purpose of discussion to designate the specimens by A and B. Specimen A denotes the samples deposited at 300°C by dc glow discharge decomposition. Specimen B represents those deposited between 20°C
136
.I. Jang et al. / Transport properties of a-Si: H
and 200°C, and annealed at 300°C (250°C for ~ in fig. 2) for 30 min. The recombination form of specimen B was observed to be monomolecular: r = 0.95 in Oph = I r (Oph, photoconductivity; I, light intensity) for specimen ® in fig. 2, while it is bimolecular: r = 0.6, for specimen A. The density of states at the Fermi level for specimen A was observed to be 4.0 x 1017 eV - l cm -3, while it was 2.0 X 1018 eV - l cm -3 for specimen B (® in fig. 2) when the same insulated gate field effect geometry was used. * It is apparent, therefore, that the density of states around the Fermi level is larger for specimen B than specimen A. To begin with, the difference between the conductivity activation energies (Eo) of specimens A and B will be discussed. If the Fermi level exists near midgap in undoped a-Si: H, Eo will increase as the optical g a p (E~ pt) increases. But the behavior shown in fig. 3 is quite opposite to this; E~ pt decreases as Eo increases. Accordingly, the difference in Eo is not caused only by the difference in the band gap. Fig. 3 also shows that Eo is smaller for the specimens with higher photoconductivity than for those with lower photoconductivity. On the other hand, the undoped specimens with higher photoconductivity must have a smaller density of deep gap states, since deep gap states act as effective recombination centers. Accordingly, to interpret the experimental results shown in fig. 3, the existence of donor states should be assumed. If we assume the existence of the same distribution of donor state density in all the specimens shown in fig. 3, then, for the specimens with the lower density of deep gap states, the Fermi level will lie higher and consequently Eo will be smaller than for those showing high deep gap state density. The difference in Eo between specimen A and B shown in fig. 2 can also be explained by this assumption, because the optical gap of specimen A and B was observed to be nearly the same. In a-Si: H the ordinary silicon-silicon or silicon-hydrogen bonds such as Sill, Sill 2 and (Sill2) ~ cannot act as the donors. However, the S i - H - S i three center bonds (TCBs) can play the role of donors: the charge of the TCBs can be positive in thermal equilibrium. Fisch and Licciardello [12] suggested that the S i - H - S i TCBs are present in a-Si : H, and have negative correlation energy. However, the correlation energy of the TCBs is expected to be positive from the results of the tight binding calculations of Allan and Joannopoulos [13] and from the variation of the Fermi level with slight doping [14]. We suggest that 1016-10 t7 cm -3 of S i - H - S i TCBs are present in undoped a-Si:H to interpret the experimental results shown in figs. 2 and 3. Three electrons take part in a three center bond, and two electrons occupy the bonding states and one electron occupies the nonbonding state. The wavefunction of the bonding orbital (~bb) and the
* In o u r e x p e r i m e n t t h e r m a l l y g r o w n silicon d i o x i d e w a s u s e d as a n i n s u l a t o r .
J. Jang et al. / Transport properties of a-Si." H
137
nonbonding orbital (~k,b) can be described as [12]
¢,, =
1
= 1
+ ps,. + psi2), (ps,, -
(1) (2)
where pu is the hydrogen atomic wavefunction, PSi, and tOsi2 are the two silicon atomic wavefunctions in a TCB, A and A' denote the normalization factors, and a is a constant. The nonbonding states of the TCBs give rise to the states in the gap at E c - E - - 0 . 6 eV according to the calculations of Allan and Joannopoulos [13], while the bonding states give rise to the valence band states lying several electron volts below E v. The nonbonding states of the TCBs seem to be situated near the conduction band edge well above the midgap since the distance between Si and Si in a TCB is longer than the normal Si-Si distance [121. In thermal equilibrium the nonbonding states of the TCBs are not occupied because the Fermi levels of undoped specimens are near the midgap, and thus the nonbonding states act as donors. The band gap (mobility gap), Eg, of specimen A is assumed to be 1.9 eV since the largest value of the E~ is 0.95 eV as can be seen in fig. 2 and other works [15], and thus Eo (0.82 eV) of specimen A is smaller than Eg/2 by 0.13 eV. If we assume that N(E) is constant around E F, and that N F = 4 . 0 × 1017 eV - j cm -3 determined by the field effect technique is purely the bulk states, the state density of the TCBs will be 5.2 × 10 ]6 c m -3. Another interpretation is possible by introducing the structural inhomogeneity of a-Si:H. It has been suggested that the island structure may be characterized as a continuous random network of Si with dangling bonds saturated by hydrogen while the region between the islands is composed of a hydrogenrich, lower density material including the poly-silane structure [7]. One might think here of the hydrogen rich regions as the inter-grain surface layers between the islands. The transfer of electrons between interfacial layers and islands will cause a shift of the Fermi level in the islands. Since the density of gap states of the interfacial layer is considered to be higher than that of the island material and the size of an island ( ~ 100 ,~) is considered to be much smaller than the Debye length [16,17], the small change of Fermi level in the interfacial layer gives rise to the large variation of E F in the bulk. In order to explain the relation between Eo and Oph shown in fig. 3 by this model, the density of state minimum is assumed to be the result of the overlap of two tails extending from E c and E v into the gap. The conduction band tail is composed of acceptor-like states and they will carry negative charges below E F. On the other hand, the valence band tail states are donor-like and provide positively charged states above E F. If the E F of the bulk is moved toward E c by taking electrons from the interfacial layer, the positive charge density around the midgap will be reduced, resulting in the increase of the electron lifetime. Thus, the undoped a-Si : H films with smaller Eo show higher photoconductivity.
138
J. Jang et al. / Transport properties of a-Si : H
Downward kinks with increasing temperature in conductivity and thermopower versus inverse temperature curves are always observed for undoped specimens prepared at 300°C. The differences in conductivity activation energy between the high and low temperature region, above and below - 430 K, for the specimens showing downward kinks were observed to be 0.2 eV as shown in table 1. Spear et al. [1] suggest that the mobility edge moves in the band toward the midgap with increasing temperature. When it reaches the bottom of the band tail, the mobility edge can go no farther, giving rise to the kink in the plot of log a and S versus inverse temperature. However, there is an apparent difference between E~ and E s in the high temperature region as shown in table 1. It is also pointed out that the kink does not appear in specimen B, CVD a-Si [ 18], and evaporated a-Si [ 19]. These facts are difficult to interpret by this model. Another interpretation [2] has been introduced by Harvard group. That is three-dimensional structural model of islands surrounded and interconnected by the tissue material which has a wider band gap than the islands. It is suggested that conductivity and thermopower can be expressed as an activated form in both materials with different activation energies, and that the tissue has lower activation energy caused by hopping conduction between localized states. It is also suggested that neither material forms a continuous channel between the electrodes and the conduction takes place through a series connection of tissue and island material. For a series connection of elements, the measured conductivity will be dominated by the most resistive element, and thus downward kinks are expected. The value of ( E c - EF) 0 of the island material in specimen A is 0.82 eV and the temperature range in which the tissue conduction is dominant is not reached in specimen B because the conductivity of the island material in the specimen B is much lower than that of the island material in specimen A (see fig. 2). Thus specimen B does not show the downward kink, and the downward kink is observed only for specimen A as can be seen in fig. 2. If the transport of undoped and lightly doped specimens takes place at the conduction band mobility edge in the low temperature region and at the localized states of tissue material in the high temperature region, the conductivity and thermopower can be expressed in activated form: ° = O0H e x p ( - - e y / k r ) ,
7"> Zkink,
(3)
S = So.
T> Tki.k,
(4)
T < Ykink ,
(5)
T
(6)
lelT,
0~= O'OL e x p ( - g L / , k Y ) ,
Ek S=SoL
lelT,
where O0H and o0L are pre-exponential factors of conductivity in the high and
J. Jang et al. / Transport properties of a-Si." H
139
low temperature ranges, Eo and E s are activation energies for conduction and thermopower, respectively, subscripts H and L denote the high and low temperature region, respectively, SoL and Sou are constants obtained by extrapolating the linear lines of the thermopower to 1 / T = 0, e is the electronic charge, and Tkink denotes the temperature at which the kink occurs. If it is assumed that the conduction band has a constant density N,/~ is the mobility, and the Fermi level lies many k T below the conduction band edge, and depends on temperature as Ec - E F = (E¢ -- Ev) o + y r ,
(7)
o : eNkT# exp(-y/k) exp[- (E c - EF)o/kT ] ,
(8)
o o : e N k T # exp( - y / k
(9)
then
eo:
),
- EDo.
(lO)
The Harvard group has proposed that the conduction behavior of sputtered a-Si:H can be understood on the basis of a model of transport through two mixed phases with different structure, chemistry, electronic band states and transport parameter [7]. The island material is postulated to be a-Si:H with compensation of defect centers by hydrogen, so that the gap state density is low, resulting in the band edge conduction. The connective tissue is supposed to be rich in H and has a larger band gap and higher density of gap states, showing hopping conduction at the localized states. If the transport takes places at the localized states with energy E T by phonon assisted hopping, the conductivity can be described as o(T) = o0 exp(-EoH/kT)
(11)
with EoU= ( E T - ev)o + W T ,
where WT is the hopping energy between localized states of tissue and o0 is the pre-exponential factor in the formula of conductivity. We can obtain Eo and o0 from the experimental slope and intercept of the plot of log o versus 1 / T . Values of OOH,OOL,E~, E L, E~ and E L are determined by fitting eqs. (3)-(6) to experimental data shown in fig. 4 and given in table 1 (samples 1, 2 and 3). At higher doping concentrations the kinks in the log o and S versus 1 / T plot are upward with increasing temperature as shown in fig. 4. The transport data of these heavily doped specimens have been analyzed by the two-channel conduction path model [6,7]. We now consider how the introduction of phosphorus might affect two-phase structure and whether there is any connection between the downward kinks in the undoped films and the upward kinks of the doped films. However, there are a number of similarities in absorption, photoluminescence and photoconductivity between phosphorus doped samples and the specimens, prepared by sputtering in a high hydrogen partial pressure, which contain a large fraction of tissue material [20]. Therefore, the transport
140
J. Jang et aL / Transport properties of a-Si: H
of doped films in the high temperature region is also expected to take place at the localized states of tissue material. The E H of the specimens 1, 2, and 3, showing downward kinks, decreases as the E L decreases. The difference between E H and E L is ~0.2 eV for all specimens showing a downward kink. This means that the, Fermi level of the specimens moves toward E c both at the island and tissue by the same amounts. This is the evidence of tissue hopping in the high temperature region in slightly doped specimens (specimens 2 and 3). Accordingly, the two-channel conduction path model, in which the transport takes place both at extended and at localized donor states, should be changed. Since deposition conditions for moderate to heavily doped specimens showing upward kinks are the same as for the undoped and lightly doped specimens with downward kinks, it would be natural to assume that the conduction takes place through series connection of islands and tissues for doped samples as for undoped specimens. Therefore, the conductivity and thermopower can be written by the sum of the localized state hopping in the tissue and the donor state hopping in the island in the high temperature region, and the sum of the band edge conduction and the donor state hopping in the low temperature region. Thus, o=o1+o
3,
(12)
= Oo. exp(--EoU/kT) + OoD e x p ( - E ~ / k T ) , T>
Tkink ,
s= So. T>
lelr!I°'+ o
s0o
ief
o'
(13)
Tkink ,
O ~ O2 -~- (I3,
=o0, exp(- GL/k r ) + Ooo exp(- G ° / k r ),
(14)
T < Tkink,
S
.
SOL lelT .
.
.
o + So,
i
f"
7,
T < Tkink. where the first term (ol) and the second term (%) in eq. (12) denote the contribution to conductivity by the hopping in tissue material and the hopping in donor states respectively, the first term in eq. (14) denotes the conduction in the band edge, EoDis (E D --EF) 0 + W o , ED denotes the phosphorus donor level, WD the average hopping energy between donor states, and the subscript D the donor related term. For moderate to heavily doped films represented by samples 4, 5, 6 and 7, in table 1, it can be seen that over the whole temperature range of the measurements, the overall conductivity and thermopower can be fitted, within experimental error, to the sum of two terms each. In these doped samples, the
J. Jang et al. / Transport properties of a-Si: H
141
first term (o 1) is dominant in the high temperature region (because o0n > gOD), while the second term (o 3) is dominant in the low temperature region because of E L > E y . Thus neglecting the second term in eq. (12) and the first term in eq. (14), we obtain the following conductivity formula valid over the whole temperature range of measurement: O = O 1 "[-03,
o = OOHe x p ( - - E ~ / k T ) + O0D e x p ( - E o ° / k T ) ,
(16)
by the same argument,
s=
S0.-lel----y
o
lel z
o
The solid lines of the samples showing upward kinks in figs. 4 and 5 denote the fitting of eqs. (16) and (17) to the experimental data. Values of O0H versus Eo" and O0L versus E L satisfy the experimental relation o0 = o00 exp(AEo) with A = 1.7 × 10 (eV) - l and O0o= 8.5 × 10 -z f~-i cm-1. The differences between the activation energies for conduction in the high and low temperature ranges, AEo = E L EoH, are ~ 0.2 eV in the samples 1, 2 and 3, shown in table 1. This value of AEo corresponds to that of AE s, the difference of the activation energy for thermopower between the high and low temperature region, shown in table 1. The difference between Eo and Es lies between 0.06 and 0.19 eV, which is interpreted as the mobility activation energy: hopping energy between localized states in hopping conduction. The hopping energy between localized donor states, WD = 0.15 eV, is shown for the samples 6 and 7 in table 1. The transport in these films takes place at localized donor states in the low temperature region, and at localized states of tissue in the high temperature region. The series connection of the donor state hopping in the island and the hopping at localized states in the tissue gives rise to the upward kinks in the plot of log o and S versus 1/T, while that of the band edge conduction in the island and the hopping in the tissue gives rise to the downward kinks for undoped and slightly doped films. Since the Fermi levels of island and tissue move together by the same amounts toward E c as a result of phosphorus doping and the tissue hopping is the dominant transport mechanism in the high temperature region, the Fermi level of these doped films is expected to be related to E H as ( E c - Ev) o = Eon + A E o, i.e., the AEo for the specimens showing downward kinks is ~ 0.2 eV, the same value of AEo is expected for the samples 4, 5, 6 and 7, because the transport mechanism at the high temperature region is the same as that for the samples 1, 2 and 3. Then, the position of phosphorus donor level is determined by -
-
(e0--ED)0=EY+AEo-ey+
W D.
(18)
The column second from the last in table 1 lists the values of (E~ -- E o ) o obtained from our data. In view of the oversimplicity of the two discrete level conduction model, there is a small scatter in the value listed, but all the measurements indicate that the E D lies around 0.47 eV below E c. The devia-
142
J. Jang et al. / Transport properties of a-Si: H
tion of ( E ¢ - ED) 0 for specimen 7 in table 1 from the other values m a y be related to the decrease in A E o . It a p p e a r s that the k i n k ( A E o ) m a y be changed in highly d o p e d specimens (over 10 4 vppm). T h e c o n d i t i o n showing d o w n w a r d kinks with increasing t e m p e r a t u r e should be investigated to clarify this point.
5. Summary T h e difference in the activation energy for c o n d u c t i o n as well as p h o t o c o n ductivity a n d optical gap versus activation energy for c o n d u c t i o n curves of a series of u n d o p e d specimens can be i n t e r p r e t e d either b y i n t r o d u c i n g centers acting as d o n o r s or charge transfer between the island a n d h y d r o g e n rich interfacial region. The d o n o r states are suggested to be S i - H - S i three center b o n d s in this work, a n d 1016-1017 c m 3 of the TCBs are necessary to explain the e x p e r i m e n t a l data. The d o w n w a r d kinks with increasing t e m p e r a t u r e a p p e a r i n g in the plot of log c o n d u c t i v i t y a n d t h e r m o p o w e r of u n d o p e d a n d lightly d o p e d a - S i : H films versus inverse t e m p e r a t u r e can be i n t e r p r e t e d b y a t w o - p h a s e m a t e r i a l model. A revised two-channel c o n d u c t i o n p a t h m o d e l i n c l u d i n g the m a t e r i a l heterogeneity is a p p l i e d to i n t e r p r e t the log c o n d u c t i v i t y a n d t h e r m o p o w e r versus inverse t e m p e r a t u r e curves of d o p e d a - S i : H films, a n d to d e t e r m i n e the p o s i t i o n of p h o s p h o r u s d o n o r levels. T h e levels are f o u n d to lie at a b o u t 0.47 eV b e l o w E c. T h e a u t h o r s are grateful to professor W. Paul for sending us some articles p r i o r to p u b l i c a t i o n .
References [1] W.E. Spear, D. Allan, P. LeComber and A. Gaith, Phil. Mag. B41 (1980) 419. [2] D.A. Anderson and W. Paul, Proc, 15th Int. Conf. Physics of Semiconductors, Kyoto, 1980, J. Phys. Soc. Japan. 49 (1980) 1197. [3] D.I. Jones, P.G: LeComber and W.E. Spear, Phil. Mag. B36 (1977) 541. [4] W. Beyer and H. Overhof, Sol. St, Commun. 31 (1979) 1. [5] G.H. Drhler, Phys. Rev. 19 (1979) 2083. [6] Z.S. Jan, R.H. Bube and J.C. Knights, J. Electron. Mater. 8 (1979) 47. [7] D.A. Anderson and W. Paul, to be published in Phil. Mag. [8] P.Z. Zanzuchi, C.R. Wronski and D.E. Carlson, J. Appl. Phys. 48 (1977) 5227. [9] M. Tanielian, H. Fritzsche, C.C. Tsai and E. Symbalisty, Appl. Phys. Lett. 33 (1978) 353. [10] D.L. Staebler and C.R. Wronski, J. Appl. Phys. 51 (1980) 3262. [11] D.G. Arts and M.H. Brodsky, Phil. Mag. B41 (1980) 273. [12] R. Fisch and C.C. Licciardello, Phys. Rev. Lett. 41 (1978) 889. [13] D.C. Allan and .I.D. Joanfiopoulos, Phys. Rev. Lett. 44 (1980) 43. [14] W.E. Spear and P.G. LeComber, Phil. Mag. B33 (1976) 935. [15] M.H. Bronsky, Fundamental Physics of Amorphous Semiconductors, ed., F. Yonezawa (Springer-Verlag, 1981), p. 56. [16] W. Paul, Solar Energy Materials 5 (1981) 229. [17] I. Solomon, T. Dietl and D. Kaplan, J. Phys. 39 (1978) 1241. [18] M. Hirose, M. Taniguchi and Y, Osaka, Proc. 7th. Int. Conf. on Amorphous and Liquid Semiconductors, ed., W.E. Spear (CICL, Univ. of. Edinburgh, 1977) p. 352, [ 19] W. Beyer, Sol. St. Commun. 29 (1979) 291. [20] D.A. Anderson, G. Moddel and W. Paul, J. Non-Crystalline Solids 35-36 (1980) 345.