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Characterisation of a-Si:H by complex impedance measurements
Journal of Non-Crystalline Solids 64 (1984) 21-28 North-Holland, Amsterdam
21
CHARACTERISATION OF a-Si: H BY C O M P L E X IMPEDANCE MEASUREMENTS P.Y. T I M B R E L L *, B. R A N C H O U X and H. H A M D I Groupe des Transitions de Phases, CNRS, B.P. 166, 38042 Grenoble Cbdex, France Received 6 June 1983
The electrical impedance of rf sputtered amorphous hydrogenated silicon has been measured in the sandwich configuration over the frequency range 5 Hz-500 kHz and temperature range 380-436 K. Complex impedance plots took the form of single half circles indicating that a-Si : H can be modelled as a parallel RC circuit. The centers of the half circles fall along a line angled at a~r/2 rad from the real axis and the parameter a is shown to qualitatively measure the microscopic homogeneity of the a-Si : H samples. New evidence is presented for the formation of an interface space charge layer (thickness 0.06 #m) that occurred after the injection of carriers upon the application of a high electric field (105 V/cm).
1. Introduction
The linear response of a solid to an applied sinusoidal electric field V sin(~0t), inducing a current I sin(~0t- ~), can be represented by plotting its impedance Z(to) in the complex plane as a function of frequency. The complex impedance Z(to) is defined as a vector of norm 1I/1 and argument ~, the phase difference between the voltage and current, with real and imaginary parts given by Z cos ~, and Z sin g, respectively. Complex impedance measurements differ from ac conductivity o(~0) measurements in that one takes into account the phase difference between the current and applied voltage. The negative of the imaginary part of the impedance, -Z"(~0), versus its real part, Z'(~0), is plotted from 5 Hz to 500 kHz. This technique, used in electrochemistry to study ionic conduction in glasses for example [1], was applied to study and characterise samples of rf sputtered amorphous hydrogenated silicon. The experimental impedance curves obtained for a-Si : H were analysed by the equivalent circuit method whereby one models the linear response of the sample in terms of an equivalent electrical circuit of resistances and capacitances, which are then given a physical interpretation. The use of electrical models is based on the observation that the impedance of simple electrical circuits take the form of half circles or straight lines in the complex plane. In * Present address: PCS Group, Cavendish Laboratory, Madingley Road, Cambridge, C B 3 0 H E , England. 0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
22
P.Y. Timbrell et al. / Characterisation of a-Si: H
Pd
a-Si:H ~ '0 .~I~m
~Agpd l--n+
a-Si:H~r
f
3.35rnm--,-II-.-I-..-12mm-,-I l----IB.4rnm =-I
Fig. 1. a - S i : H sample and contact geometry. The sample thickness, d, is 8 . 4 × 1 0 contact surface area, S, is 8.84x 10 -6 m 2.
7 m and Pd
the case of a-Si : H the RC parallel circuit is of relevance and the expression of the impedance
Z(o~) = R / ( 1 +j~0r)
where ~"= RC
(1)
describes a half circle of radius R / 2 centered on the real axis at Z ' = R/2. At q, = 45 °, 0~r = 1 and hence the value of the capacitance is given by C = 1/~oR where ¢0 is the angular frequency at this point. A more complicated electrical model of two RC parallel circuits in series yields two successive half circles in the complex plane, provided their RC time constants differ sufficiently (factor of 100), each circle being representative of its corresponding RC circuit. This model is needed because complex impedance measurements not only allow one to study the conductivity in the bulk of the sample but also investigate the interface between the electrical contacts and the a-Si : H.
2. Experimental The a-Si : H samples were deposited by rf diode sputtering of a polycrystalline Si target in a reactive 80% argon/20% hydrogen mixture. The base pressure was 10 -6 Torr and the deposition rate governed by the dc bias of the substrate holder. The a-Si : H films were deposited at rates of 20 A / m i n and 125 A / m i n onto substrates of degenerate n + silicon and were 0.84 /~m in thickness. Evaporated Pd contacts, onto which wires were connected with Ag lacquer, were placed so that the impedance measurements were made through the bulk of the a-Si: H sample (fig. 1). A good ohmic contact was obtained through the use of the Pd contacts and a linear i(V) characteristic obtained for voltages of both polarities up to 500 mV [2]. The samples were first characterised by dc conductivity measurements as a function of temperature to permit a later comparison with the complex
P. }( Tirnbrell et a L /
23
Characterisation o f a- Si : H
impedance measurements. A log o versus T -~ plot of the dc conductivity showed that the samples exhibited a well defined activation energy of E a = 0.75 eV with a pre-exponential factor of about 4 x 10-1°I2-~ cm ~ above room temperature. An Alcaltel T2531 impedance bridge was used to measure the complex impedance over the frequency range 5 H z - 5 0 0 kHz. The bridge maintained a constant selectable current through the sample, 0.01 mA being a typical value. An alumina sample holder assured good thermal stability and the temperature was measured with a NiCr/NiA1 thermocoupie imbedded close to the sample. The temperature could be varied from 380 K to 436 K with a Buchi T0-50 regulator to an accuracy of 0.5 K.
3. Results and discussion
3.1. Complex impedance measurements (fig. 2) The complex impedance, measured at five different temperatures (380 K, 393 K, 406 K, 419 K, 436 K), of a - S i : H deposited at a rate of 20 , ~ / m i n is
_ Z I' / /
(lO%'~)
J
f
/
/ /
// _
kHZ
lkHz
o
"~"
Z' 1104Q)
Fig. 2. Complex impedance curves at T = 380 K, 393 K, 406 K, 419 K, 436 K for a-Si : H deposited at 20 ,A/min. The curves are circular arcs whose centers, represented by open circles, fall along a line angled a~r/2 rad from the real axis. Frequencies are given in kHz. Experimental points are omitted from the 436 K and 419 K curves for clarity. The 380 K curve falls short of the circular arc commenced at high frequencies (dotted curve) and is explained in §3.3. The black triangles represent dc resistance measurements at the given temperatures.
24
P . Y . Timbrell et al. / Characterisation o f a - Si: H
Table 1 Equivalent circuit values of the parallel R C circuit that models the a-Si : H impedance curves of fig. 2. T+0.5 K
R+1%
C+5%
393 406 419 436
15.0 k$2 8.1 kl2 4.0 k/2 1.67 k12
1.66 1.67 1.81 1.58
K K K K
nF nF nF nF
plotted in fig. 2. The isothermal curves take the form of single half circles revealing that a-Si : H is well modelled by a simple R C parallel circuit over this temperature and frequency range. The 380 K impedance curve is not circular and will be discussed in § 3.3. The values of the complex impedance at 100 kHz have a large imaginary component, whereas at 5 Hz they are real and coincide with the measured dc resistance represented by the black triangles. The equivalent circuit values of R and C for the experimental impedance curves are given in table 1. The calculated capacitance remains constant with temperature suggesting it is a measure of the static dielectric constant, %(0), of the a-Si : H sample found to be (18 + 5)% which is reasonable given the value for crystalline Si is 11.6 [3]. The measured resistance follows a R = R 0 e x p ( E J k T ) law, with E a = 0.75 eV, and is representative of dc conduction processes in the extended states above the mobility edge. The experimental impedance curves are not rigorously modelled by a simple R C parallel circuit. The experimental points are seen to fall along circular arcs whose centers, represented by open circles in fig. 2, fall below the real axis along a line passing through the origin. This line is angled a~r/2 rad below the real axis and a = 0.034 + 0.01 for the a-Si : H sample deposited at a rate of 20 A / m i n . The expression for the impedance of the experimental points is given by
Z(~o)= R / ( 1
"
'-'~ ,
(2)
where the ohmic resistance R is the real axis intercept, r -1 the angular frequency at the apex of the arc and a~r/2 the angle mentioned previously [4]. This equation reduces to the expression of the impedance of a pure R C parallel circuit with r = R C when a = 0. Thus with the aid of complex impedance plots it is possible to characterise an a-Si : H sample by the three parameters R, r and a. The physical significance of a is debatable though it is thought to be a measure of the dispersion of the local conductivity o ( r ) within the sample and hence its microscopic homogeneity [5]. The complex impedance curves obtained for a-Si : H deposited at a rate of 125 A / m i n are identical to the circular arcs shown for the 20 A / m i n sample (fig. 2) except that the value of a is higher at 0.067 __. 0.01. This result is consistent with the notion that ~x is a measure of the sample's microscopic homogeneity as a sample deposited at a higher rate is assumed to have less time to relax into a more ordered structure.
25
P.Y. Timbrell et al. / Characterisation of a- Si: H
3.2. The ac conductivity (fig. 3) The ac conductivity, o(~0, T), is given by considering the norm of the complex impedance o(~, T)=
llZ(,~, T ) l l - ] d / S ,
(3)
where d is the sample thickness (8.4 × 10 -7 m) and S the sample surface area (8.84 × 10-6m2). One does not expect the contribution to the ac conductivity from carriers in the extended states to differ from the dc conductivity o(0) over the examined range of frequencies ( < 500 kHz) [6]. A log[o(~0) - o(0)] versus log ~o plot (fig. 3) was done in order to see if the ac hopping conductivity from carriers in the localised states obeyed the empirical law o(00) =Ao0 s,
(4)
where A is weakly dependent on temperature and s - 0 . 8 [7]. It can be seen from fig. 3 that such a law is obeyed though the experimental value of s is somewhat higher at 1.4.
-3 ~436K
393KF O 1
-5-
3
ID
_9. ° -6-
-73
I
4
I
5 togw
I
6
7
(s-~1
Fig. 3. L o ~ o ( o ~ ) - o ( 0 ) ] versus log(00) curves at T = 393 K, 406 K, 419 K, 436 K for a-Si:H deposited at 20 , ~ / m i n .
26
P.Y. T i m b r e l l et al. / Characterisation o f a - S i : H
One would expect o(w, T ) - o ( 0 , T ) to show an exponential activation energy and increase in magnitude with temperature should the ac hopping conductivity primarily take place in the Anderson localised states at the conduction band edge. The results obtained, indicating the ac hopping conductivity actually decreases with temperature by a factor of 2 for a 40 K change, suggest that most of the ac hopping conduction takes place between defect states at the Fermi level. This decrease with temperature could be explained by a depopulation of carriers at the Fermi level as they are excited to the conduction band where they contribute to the dc conductivity o(0).
3.3. Contact phenomena (fig. 4) Phenomena associated with the metal/semiconductor interface of the P d / a S i : H contact (fig. 1) fall into two categories. Firstly carrier injection was observed when the applied sinusoidal bridge potential exceeded 50 mV and secondly the formation of an interface space charge region occurred after the sample had been exposed to a high electric field (105 V/cm). The way in which these effects were observed by complex impedance measurements is described. The 380 K impedance curve in fig. 2 does not describe a circular arc. At 10 kHz it begins to flatten and fall short of the circle, represented by the dotted curve, commenced at higher frequencies. This behaviour can be interpreted as carrier injection from the electrical contacts. The Alcaltel impedance bridge maintains a constant current (0.01 mA) through the sample so that the applied potential increases with the sample's impedance. At 10 kHz the amplitude of the in phase component of the applied potential, given b y / [ R e Z(~0)] where I is the 0.01 mA bridge current and Re Z(~0) the real part of the complex impedance, for the 380 K curve is 50 mV. Above 50 mV the Pd contact may begin to inject carriers into the bulk giving rise to an added injection current, on top of the bridge current, explaining the fall in measured impedance. This was verified by repeating the measurements at a fixed temperature of 406 K with different bridge currents (0.01 mA, 0.04 mA, 0.1 mA, 0.4 mA). The 0.01 mA impedance curve was identical to the previous 406 K curve of fig. 2 and described a circular arc, while the higher current curves all began to flatten w h e n / [ R e Z(~o)] exceeded 50 mV. After an a-Si : H sample, deposited at a rate of 20 ,~/min, had been exposed to an applied 5 Hz potential of 105V/cm at 436 K the impedance curves took the form of two successive half circles (fig. 4). The equivalent circuit values for the two R C parallel circuits in series that model the impedance curve are given in table 2. The analysis of these curves by the equivalent circuit method shows the first circle at high frequencies, modelled by R1 and C1, to be similar to those found in the first set of measurements (fig. 2) and thus representative of the bulk. One possible explanation for the appearance of the second circle, modelled by R 2 and C2, is that the Pd contact has injected electrons into the bulk, where they have become trapped by defect or surface states, and lead to the formation of a space charge layer. This interpretation agrees with earlier
27
P. Y. Timbrell et aL / Characterisation o f a - Si : H
-Z"]
t*05K
kH~
"
~
~
"
"
"
.
.
0
0.5
1
(i04~) Fig. 4. Complex impedancecurves at T = 406 K, 436 K for a-Si : H depositedat 20 ,~/min with the interface spacecharge layer appearingas the second circle at low frequencies. Frequenciesare given in kHz.
Table 2 Equivalent circuit values of the two parallel R C circuits in series (fig. 5) that model the impedance curves (fig. 4) of a-Si : H with a space charge layer. T+0.5 K
Rl+l%
C1+5%
R2+1%
C2+5%
405 K 436 K
4.4 k~2 1.0 k~2
1.83 nF 1.62 nF
7.8 kI2 1.8 kI2
20.4 nF 23.6 nF
do
6
d=do+6 R'I =
1 ..qb e x p ( E o / k T ) O(T) S = g,
CI =ErEo S
R2= R e x p ( V / k T ) C2= ErE S__ o6
Fig. 5. Equivalent circuit model of a-Si : H with the space charge layer represented by R2 and C2 and the bulk by R1 and C1.
28
P.Y. Tirnbrell et al. / Characterisation of a - Si : H
thickness dependent conductivity measurements [8] but the present method gives a more direct measurement and estimate of the space charge layer thickness. The layer can be crudely modelled as a leaky polarised parallel plate capacitor [9] and the corresponding model for a - S i : H is given in fig. 5. The space charge layer is represented by R 2 and C2 and bulk by R1 and C1. In this model the thickness of the space charge layer, 8, is given by d / ( 1 + C 2 / C 1 ) where d is the total sample thickness of 0.84 g m and C1 and C2 the capacitances deduced from the impedance plots. The calculated value of 8, for the a-Si : H sample deposited at 20 A / m i n , is 0.06 gm.
4. Conclusions The complex impedance curves obtained for a-Si : H are half circles tilted at an angle a ~ r / 2 rad from the real axis. a is a new parameter by which to characterize a-Si : H samples and m a y be a measure of their bulk inhomogeneity. The ac h o p p i n g conduction, measured below 500 kHz, appears to take place primarily between defect states at the Fermi level. The complex impedance technique allows one to elucidate the electrical contact problem and detect the presence of interface space charge layers in a sandwich configuration a-Si : H. The authors thank Professors A. Deneuville and J.L. Souquet for fruitful discussions and H. Matraire for his invaluable technical assistance.
References [1] [2] [3] [4] [5] [6]
D. Ravaine, J. Non-Crystalline Solids 49 (1982) 507. J.C. Bruyere and A. Deneuville, J. de Phys. Lett. 41 (1980) 27. H.W. Icenogle, B.C. Platt and W.L. Wolfe, Appl. Opt. 15 (1976) 10. D. Ravaine and J.L. Souquet, C.R. Acad. Sci. Paris C277 (1973) 489. D. Ravaine, These d'Etat, Universite de Grenoble (1976). N.F. Mott and E.A. Davis, Electronic Processes in Non-Crystalline Materials, 2nd ed. (Clarendon, Oxford, 1979). [7] M. Pollack and T.H. Geballe, Phys. Rev. 122 (1961) 1742. [8] D.G. Ast, M.H. Brodsky, J. Non-Crystalline Solids 35/36 (1980) 611. [9] B.R. Gossick, Potential Barriers in Semiconductors (Academic Press, New York, 1964).
21
CHARACTERISATION OF a-Si: H BY C O M P L E X IMPEDANCE MEASUREMENTS P.Y. T I M B R E L L *, B. R A N C H O U X and H. H A M D I Groupe des Transitions de Phases, CNRS, B.P. 166, 38042 Grenoble Cbdex, France Received 6 June 1983
The electrical impedance of rf sputtered amorphous hydrogenated silicon has been measured in the sandwich configuration over the frequency range 5 Hz-500 kHz and temperature range 380-436 K. Complex impedance plots took the form of single half circles indicating that a-Si : H can be modelled as a parallel RC circuit. The centers of the half circles fall along a line angled at a~r/2 rad from the real axis and the parameter a is shown to qualitatively measure the microscopic homogeneity of the a-Si : H samples. New evidence is presented for the formation of an interface space charge layer (thickness 0.06 #m) that occurred after the injection of carriers upon the application of a high electric field (105 V/cm).
1. Introduction
The linear response of a solid to an applied sinusoidal electric field V sin(~0t), inducing a current I sin(~0t- ~), can be represented by plotting its impedance Z(to) in the complex plane as a function of frequency. The complex impedance Z(to) is defined as a vector of norm 1I/1 and argument ~, the phase difference between the voltage and current, with real and imaginary parts given by Z cos ~, and Z sin g, respectively. Complex impedance measurements differ from ac conductivity o(~0) measurements in that one takes into account the phase difference between the current and applied voltage. The negative of the imaginary part of the impedance, -Z"(~0), versus its real part, Z'(~0), is plotted from 5 Hz to 500 kHz. This technique, used in electrochemistry to study ionic conduction in glasses for example [1], was applied to study and characterise samples of rf sputtered amorphous hydrogenated silicon. The experimental impedance curves obtained for a-Si : H were analysed by the equivalent circuit method whereby one models the linear response of the sample in terms of an equivalent electrical circuit of resistances and capacitances, which are then given a physical interpretation. The use of electrical models is based on the observation that the impedance of simple electrical circuits take the form of half circles or straight lines in the complex plane. In * Present address: PCS Group, Cavendish Laboratory, Madingley Road, Cambridge, C B 3 0 H E , England. 0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
22
P.Y. Timbrell et al. / Characterisation of a-Si: H
Pd
a-Si:H ~ '0 .~I~m
~Agpd l--n+
a-Si:H~r
f
3.35rnm--,-II-.-I-..-12mm-,-I l----IB.4rnm =-I
Fig. 1. a - S i : H sample and contact geometry. The sample thickness, d, is 8 . 4 × 1 0 contact surface area, S, is 8.84x 10 -6 m 2.
7 m and Pd
the case of a-Si : H the RC parallel circuit is of relevance and the expression of the impedance
Z(o~) = R / ( 1 +j~0r)
where ~"= RC
(1)
describes a half circle of radius R / 2 centered on the real axis at Z ' = R/2. At q, = 45 °, 0~r = 1 and hence the value of the capacitance is given by C = 1/~oR where ¢0 is the angular frequency at this point. A more complicated electrical model of two RC parallel circuits in series yields two successive half circles in the complex plane, provided their RC time constants differ sufficiently (factor of 100), each circle being representative of its corresponding RC circuit. This model is needed because complex impedance measurements not only allow one to study the conductivity in the bulk of the sample but also investigate the interface between the electrical contacts and the a-Si : H.
2. Experimental The a-Si : H samples were deposited by rf diode sputtering of a polycrystalline Si target in a reactive 80% argon/20% hydrogen mixture. The base pressure was 10 -6 Torr and the deposition rate governed by the dc bias of the substrate holder. The a-Si : H films were deposited at rates of 20 A / m i n and 125 A / m i n onto substrates of degenerate n + silicon and were 0.84 /~m in thickness. Evaporated Pd contacts, onto which wires were connected with Ag lacquer, were placed so that the impedance measurements were made through the bulk of the a-Si: H sample (fig. 1). A good ohmic contact was obtained through the use of the Pd contacts and a linear i(V) characteristic obtained for voltages of both polarities up to 500 mV [2]. The samples were first characterised by dc conductivity measurements as a function of temperature to permit a later comparison with the complex
P. }( Tirnbrell et a L /
23
Characterisation o f a- Si : H
impedance measurements. A log o versus T -~ plot of the dc conductivity showed that the samples exhibited a well defined activation energy of E a = 0.75 eV with a pre-exponential factor of about 4 x 10-1°I2-~ cm ~ above room temperature. An Alcaltel T2531 impedance bridge was used to measure the complex impedance over the frequency range 5 H z - 5 0 0 kHz. The bridge maintained a constant selectable current through the sample, 0.01 mA being a typical value. An alumina sample holder assured good thermal stability and the temperature was measured with a NiCr/NiA1 thermocoupie imbedded close to the sample. The temperature could be varied from 380 K to 436 K with a Buchi T0-50 regulator to an accuracy of 0.5 K.
3. Results and discussion
3.1. Complex impedance measurements (fig. 2) The complex impedance, measured at five different temperatures (380 K, 393 K, 406 K, 419 K, 436 K), of a - S i : H deposited at a rate of 20 , ~ / m i n is
_ Z I' / /
(lO%'~)
J
f
/
/ /
// _
kHZ
lkHz
o
"~"
Z' 1104Q)
Fig. 2. Complex impedance curves at T = 380 K, 393 K, 406 K, 419 K, 436 K for a-Si : H deposited at 20 ,A/min. The curves are circular arcs whose centers, represented by open circles, fall along a line angled a~r/2 rad from the real axis. Frequencies are given in kHz. Experimental points are omitted from the 436 K and 419 K curves for clarity. The 380 K curve falls short of the circular arc commenced at high frequencies (dotted curve) and is explained in §3.3. The black triangles represent dc resistance measurements at the given temperatures.
24
P . Y . Timbrell et al. / Characterisation o f a - Si: H
Table 1 Equivalent circuit values of the parallel R C circuit that models the a-Si : H impedance curves of fig. 2. T+0.5 K
R+1%
C+5%
393 406 419 436
15.0 k$2 8.1 kl2 4.0 k/2 1.67 k12
1.66 1.67 1.81 1.58
K K K K
nF nF nF nF
plotted in fig. 2. The isothermal curves take the form of single half circles revealing that a-Si : H is well modelled by a simple R C parallel circuit over this temperature and frequency range. The 380 K impedance curve is not circular and will be discussed in § 3.3. The values of the complex impedance at 100 kHz have a large imaginary component, whereas at 5 Hz they are real and coincide with the measured dc resistance represented by the black triangles. The equivalent circuit values of R and C for the experimental impedance curves are given in table 1. The calculated capacitance remains constant with temperature suggesting it is a measure of the static dielectric constant, %(0), of the a-Si : H sample found to be (18 + 5)% which is reasonable given the value for crystalline Si is 11.6 [3]. The measured resistance follows a R = R 0 e x p ( E J k T ) law, with E a = 0.75 eV, and is representative of dc conduction processes in the extended states above the mobility edge. The experimental impedance curves are not rigorously modelled by a simple R C parallel circuit. The experimental points are seen to fall along circular arcs whose centers, represented by open circles in fig. 2, fall below the real axis along a line passing through the origin. This line is angled a~r/2 rad below the real axis and a = 0.034 + 0.01 for the a-Si : H sample deposited at a rate of 20 A / m i n . The expression for the impedance of the experimental points is given by
Z(~o)= R / ( 1
"
'-'~ ,
(2)
where the ohmic resistance R is the real axis intercept, r -1 the angular frequency at the apex of the arc and a~r/2 the angle mentioned previously [4]. This equation reduces to the expression of the impedance of a pure R C parallel circuit with r = R C when a = 0. Thus with the aid of complex impedance plots it is possible to characterise an a-Si : H sample by the three parameters R, r and a. The physical significance of a is debatable though it is thought to be a measure of the dispersion of the local conductivity o ( r ) within the sample and hence its microscopic homogeneity [5]. The complex impedance curves obtained for a-Si : H deposited at a rate of 125 A / m i n are identical to the circular arcs shown for the 20 A / m i n sample (fig. 2) except that the value of a is higher at 0.067 __. 0.01. This result is consistent with the notion that ~x is a measure of the sample's microscopic homogeneity as a sample deposited at a higher rate is assumed to have less time to relax into a more ordered structure.
25
P.Y. Timbrell et al. / Characterisation of a- Si: H
3.2. The ac conductivity (fig. 3) The ac conductivity, o(~0, T), is given by considering the norm of the complex impedance o(~, T)=
llZ(,~, T ) l l - ] d / S ,
(3)
where d is the sample thickness (8.4 × 10 -7 m) and S the sample surface area (8.84 × 10-6m2). One does not expect the contribution to the ac conductivity from carriers in the extended states to differ from the dc conductivity o(0) over the examined range of frequencies ( < 500 kHz) [6]. A log[o(~0) - o(0)] versus log ~o plot (fig. 3) was done in order to see if the ac hopping conductivity from carriers in the localised states obeyed the empirical law o(00) =Ao0 s,
(4)
where A is weakly dependent on temperature and s - 0 . 8 [7]. It can be seen from fig. 3 that such a law is obeyed though the experimental value of s is somewhat higher at 1.4.
-3 ~436K
393KF O 1
-5-
3
ID
_9. ° -6-
-73
I
4
I
5 togw
I
6
7
(s-~1
Fig. 3. L o ~ o ( o ~ ) - o ( 0 ) ] versus log(00) curves at T = 393 K, 406 K, 419 K, 436 K for a-Si:H deposited at 20 , ~ / m i n .
26
P.Y. T i m b r e l l et al. / Characterisation o f a - S i : H
One would expect o(w, T ) - o ( 0 , T ) to show an exponential activation energy and increase in magnitude with temperature should the ac hopping conductivity primarily take place in the Anderson localised states at the conduction band edge. The results obtained, indicating the ac hopping conductivity actually decreases with temperature by a factor of 2 for a 40 K change, suggest that most of the ac hopping conduction takes place between defect states at the Fermi level. This decrease with temperature could be explained by a depopulation of carriers at the Fermi level as they are excited to the conduction band where they contribute to the dc conductivity o(0).
3.3. Contact phenomena (fig. 4) Phenomena associated with the metal/semiconductor interface of the P d / a S i : H contact (fig. 1) fall into two categories. Firstly carrier injection was observed when the applied sinusoidal bridge potential exceeded 50 mV and secondly the formation of an interface space charge region occurred after the sample had been exposed to a high electric field (105 V/cm). The way in which these effects were observed by complex impedance measurements is described. The 380 K impedance curve in fig. 2 does not describe a circular arc. At 10 kHz it begins to flatten and fall short of the circle, represented by the dotted curve, commenced at higher frequencies. This behaviour can be interpreted as carrier injection from the electrical contacts. The Alcaltel impedance bridge maintains a constant current (0.01 mA) through the sample so that the applied potential increases with the sample's impedance. At 10 kHz the amplitude of the in phase component of the applied potential, given b y / [ R e Z(~0)] where I is the 0.01 mA bridge current and Re Z(~0) the real part of the complex impedance, for the 380 K curve is 50 mV. Above 50 mV the Pd contact may begin to inject carriers into the bulk giving rise to an added injection current, on top of the bridge current, explaining the fall in measured impedance. This was verified by repeating the measurements at a fixed temperature of 406 K with different bridge currents (0.01 mA, 0.04 mA, 0.1 mA, 0.4 mA). The 0.01 mA impedance curve was identical to the previous 406 K curve of fig. 2 and described a circular arc, while the higher current curves all began to flatten w h e n / [ R e Z(~o)] exceeded 50 mV. After an a-Si : H sample, deposited at a rate of 20 ,~/min, had been exposed to an applied 5 Hz potential of 105V/cm at 436 K the impedance curves took the form of two successive half circles (fig. 4). The equivalent circuit values for the two R C parallel circuits in series that model the impedance curve are given in table 2. The analysis of these curves by the equivalent circuit method shows the first circle at high frequencies, modelled by R1 and C1, to be similar to those found in the first set of measurements (fig. 2) and thus representative of the bulk. One possible explanation for the appearance of the second circle, modelled by R 2 and C2, is that the Pd contact has injected electrons into the bulk, where they have become trapped by defect or surface states, and lead to the formation of a space charge layer. This interpretation agrees with earlier
27
P. Y. Timbrell et aL / Characterisation o f a - Si : H
-Z"]
t*05K
kH~
"
~
~
"
"
"
.
.
0
0.5
1
(i04~) Fig. 4. Complex impedancecurves at T = 406 K, 436 K for a-Si : H depositedat 20 ,~/min with the interface spacecharge layer appearingas the second circle at low frequencies. Frequenciesare given in kHz.
Table 2 Equivalent circuit values of the two parallel R C circuits in series (fig. 5) that model the impedance curves (fig. 4) of a-Si : H with a space charge layer. T+0.5 K
Rl+l%
C1+5%
R2+1%
C2+5%
405 K 436 K
4.4 k~2 1.0 k~2
1.83 nF 1.62 nF
7.8 kI2 1.8 kI2
20.4 nF 23.6 nF
do
6
d=do+6 R'I =
1 ..qb e x p ( E o / k T ) O(T) S = g,
CI =ErEo S
R2= R e x p ( V / k T ) C2= ErE S__ o6
Fig. 5. Equivalent circuit model of a-Si : H with the space charge layer represented by R2 and C2 and the bulk by R1 and C1.
28
P.Y. Tirnbrell et al. / Characterisation of a - Si : H
thickness dependent conductivity measurements [8] but the present method gives a more direct measurement and estimate of the space charge layer thickness. The layer can be crudely modelled as a leaky polarised parallel plate capacitor [9] and the corresponding model for a - S i : H is given in fig. 5. The space charge layer is represented by R 2 and C2 and bulk by R1 and C1. In this model the thickness of the space charge layer, 8, is given by d / ( 1 + C 2 / C 1 ) where d is the total sample thickness of 0.84 g m and C1 and C2 the capacitances deduced from the impedance plots. The calculated value of 8, for the a-Si : H sample deposited at 20 A / m i n , is 0.06 gm.
4. Conclusions The complex impedance curves obtained for a-Si : H are half circles tilted at an angle a ~ r / 2 rad from the real axis. a is a new parameter by which to characterize a-Si : H samples and m a y be a measure of their bulk inhomogeneity. The ac h o p p i n g conduction, measured below 500 kHz, appears to take place primarily between defect states at the Fermi level. The complex impedance technique allows one to elucidate the electrical contact problem and detect the presence of interface space charge layers in a sandwich configuration a-Si : H. The authors thank Professors A. Deneuville and J.L. Souquet for fruitful discussions and H. Matraire for his invaluable technical assistance.
References [1] [2] [3] [4] [5] [6]
D. Ravaine, J. Non-Crystalline Solids 49 (1982) 507. J.C. Bruyere and A. Deneuville, J. de Phys. Lett. 41 (1980) 27. H.W. Icenogle, B.C. Platt and W.L. Wolfe, Appl. Opt. 15 (1976) 10. D. Ravaine and J.L. Souquet, C.R. Acad. Sci. Paris C277 (1973) 489. D. Ravaine, These d'Etat, Universite de Grenoble (1976). N.F. Mott and E.A. Davis, Electronic Processes in Non-Crystalline Materials, 2nd ed. (Clarendon, Oxford, 1979). [7] M. Pollack and T.H. Geballe, Phys. Rev. 122 (1961) 1742. [8] D.G. Ast, M.H. Brodsky, J. Non-Crystalline Solids 35/36 (1980) 611. [9] B.R. Gossick, Potential Barriers in Semiconductors (Academic Press, New York, 1964).