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Gap state distribution profiles in amorphous silicon-nitrogen alloy films fabricated at various substrate temperatures
20
Journal of Non-Crystalline Solids 85 (1986) 20-28 North-Holland, Amsterdam
G A P S T A T E D I S T R I B U T I O N P R O F I L E S IN A M O R P H O U S S I L I C O N - N I T R O G E N ALLOY F I L M S F A B R I C A T E D AT V A R I O U S S U B S T R A T E T E M P E R A T U R E S J.F. W H I T E , K.C. KAO, H.C. C A R D and H. W A T A N A B E * Materials and Devices Research Laboratory, Department of Electrical Engineering, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 Received 8 October 1985 The gap state distribution profiles for amorphous silicon-nitrogen alloy films prepared by rf glow discharge in a SiH4-N 2 - H 2 gas mixture at various substrate deposition temperatures have been determined by the phase-shift analysis of the modulated photocurrent. The results indicate that the distribution of gap states is exponentially dependent on energy around the Fermi level and is not significantly influenced by the substrate deposition tehaperature.
1. Introduction Recently, a method based on the phase-shift of the modulated photocurrent, as a function of the modulation frequency of exciting light, has been developed for the determination of the energy distribution of localized gap states [1]. In contrast to conventional methods such as space-charge limited current (SCLC) [2,3], field-effect (FE) [4,5], and capacitance-voltage (CV) [6,7] methods, which utilize steady-state phenomena, this method is based upon a transient phenomenon. The method depends upon the relation between the density of gap states and the phase shift of the photocurrent with respect to the modulated exciting light, at a specific energy corresponding to the modulation frequency. This method has been used for the determination of the energy distribution of gap states in undoped a-Si : H films by Oheda et al. [8] and by Aktas and Skarlatos [9]. Unfortunately, the two sets of results on undoped a-Si : H films are not consistent with each other. However, the results of Oheda et al. [8] agree with those of Grunewall et al. [5], which, using the FE method, show a b u m p in the tail state distribution; while the results of Aktas and Skarlatos [9] agree with those of MacKenzie et al. [10], which, using an SCLC method, indicate an exponential distribution of gap states. The discrepancy between these two sets of results may be due to a legitimate difference in the nature of the gap states between these two stets of samples, under the influence of differing fabrication conditions. * Sendai National College of Technology, Miyagi 989-31, Japan. 0022-3093/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J.F. White et aL / Gap state distribution profiles
21
In this paper, we report new results on the gap state distribution profiles in nitrogen-incorporated amorphous silicon alloy films, as functions of substrate deposition temperature, measured using the phase-shift analysis of the modulated photocurrent.
2. Analytical and experimental techniques The analysis of the phase shift of the modulated photocurrent is based on the following assumptions: (i) the photocurrent is unipolar; (ii) the conduction is trap-limited, but proceeds via extended states; (iii) the energy of the optical excitation is greater than the energy band gap; (iv) the intensity of the optical excitation varies sinusoidally with time, giving rise to a carrier generation rate of g = go + gl exp(i~0t) with ~0 the modulation frequency; (v) the light intensity is sufficiently low to ensure monomolecular recombination; and (vi) the capture cross section of traps is independent of energy. The details of the analysis have been reported by Oheda [1]. The basic relation between the phase-shift ~j and the modulation frequency is tan 09 = B / A ,
(1)
where A ~ - -1 + Z k T In TR0
s= 2
"
vaM(E~_,)
(2)
COs -- 1
and
(3)
B = wi + ~ r k T v o M ( E j )
in which 1 _
TR0
1 +]E~°v,~M(E)~ TR
dE,
(4)
a El
E, = kT ln( Ucvo/,~j),
(5)
v is the electron thermal velocity, o is the capture cross-section of electron traps, Nc is the effective density of states in the conduction band, ~'R is the electron recombination time, M ( E ) is the density of gap states at an energy E below the conduction band edge, and Ej is the energy for which the thermal emission rate of a trapped electron coincides with the modulation frequency ~i" In the actual experiment the phase shift ,~j and the modulated photocurrent 1j are measured as functions of modulation frequency wj with j = 1, 2, 3 . . . . N over a range of temperatures. The suffix j increases as o~ increases. If Ej is not close to the band edge or o~j~'R0 is small enough to be
J.F. White et al. / Gap state distribution profiles
22
ignored, then the density of gap states, from eqs. (1)-(3), may be simply written as for j = 1, • . o V O M ( E , ) = (a/
(6)
kr) tan
and for j = 2, 3 . . . . N,
+kT
ln( S=2
\O3S
" ]~-RoOOM(E~ 1) tan ~/. 1/
(7) Also, the modulated photocurrent at a modulation frequency ~j is theoretically given by
lj = C / ( A 2 + B2) '/2,
(8)
where C is a constant which is chosen so that the theoretical magnitude of I;, is normalized to the value of 11 at ~1. When this theoretical value of (!j)~alc becomes arbitrarily close to observed value of (Ij)ob~, we can consider eqs. (6) and (7) to be appropriate for the determination of the density of gap states, based on the measured values of qSj related to %. The details of the a-SiN x alloy film fabrication processes have been described earlier [11,12]. For the samples used in the present investigation, the films were deposited on glass substrates with x = 0.2, corresponding to a N J S i H 4 mole fraction of 0.5 in the gas phase. The film deposition parameters are given in table 1. For the dark- and photo-current measurements a gap cell configuration with aluminum electrodes was adopted, with an electrode width of 2.0 m m and a separation between electrodes of 1.5 mm. Prior to measurements, the samples were heated to 125°C for about two hours, to drive off any absorbed moisture. The modulated photocurrent was measured at temperatures from 80°C to 120°C using a lock-in amplifier, with a reference signal provided by a fast pin diode. The excitation light was from a H e - N e laser, whose power was attenuated to a level between 0.1 and 1.0 /zW to maintain monomolecular recombination, and chopped mechanically to provide a range of modulation
Table 1 a-SiN0. 2 film deposition parameters Sample
Substrate temperature (°C)
Chamber pressure (Yorr)
rf power density ( W / c m 2)
Gas mixture ratio (N2/SiH4)
Thickness (# m)
E F G H J
150 200 250 300 400
2 2 2 2 2
0.1 0.1 0.1 0.1 0.1
0.5 0.5 0.5 0.5 0.5
1.01 2.24 1.57 0.73 0.89
J , F White et al. / Gap state distribution profiles
23
frequencies from 100 to 4000 Hz. Higher modulation frequencies than those used by other investigators [1,8,9] were used for this ivestigation, because it was necessary to ensure that energy levels were closer to the conduction band for valid analysis. The dark current was measured as a function of temperature using a Keithley 610C electrometer.
3. Results and discussion From the results of the temperature dependence of the dark current, the activation energy of all samples was found to be between 0.6 and 0.7 eV, which corresponds to the position of the Fermi level below the conduction band edge. This value of the activation energy is consistent with that reported elsewhere [11,12]. This energy then represents the lowest energy level that can be accurately analysed in the density of gap states calculations that follow. Fig. 1 shows typical results of the phase shift between the exciting light and the corresponding photocurrent as a function of the light modulation frequency, measured at three different temperatures for a typical sample of an a-SiN, 2 film deposited at a substrate temperature of 400°C.
%0
A B C
O0
,r ~o a.
20
o 10 2
I 103
I 10 4
MODULATION FREQUENCY (Hz)
Fig. 1. The phase shift as a function of modulation frequency of optical excitation, measured at temperatures of (A) 77°C, (B) 100°C, and (C) 112°C, for a-SiNo.2:H films deposited at a substrate temperature of 400°C.
-0.6
102
I
Ii
°
I
C
103
I
III •
al °
2
I I I I |
B
103
!
|
MODULATION FREQUENCY (Hz)
I'll
-
I
10 2
• OBSERVED
| II
I I
A
I I | I
!
&
103
I
|
Fig. 2. Normalized values of the calculated and the observed modulated photocurrent as functions of modulation frequency for (A) 77°C, (B) 100°C, and (C) 112°C, for a-SiN0.2: H films deposited at a substrate temperature of 400°C.
-I.0
g' -o.8
N
O
~- -0.4
z
-0.2
~o
• CA~U~T~
2.
4u.
J.F. White et al. / Gap state distribution profiles
25
The modulated photocurrent magnitude has been calculated as a function of modulation frequency for three different temperatures using eqs. (6) (8) and the measured phase shift. These calculated values, normalized with respect to the first value calculated at 100 Hz, and those measured directly (also normalized to the first value measured at 100 Hz) are plotted as functions of modulation frequency in fig. 2. It can be seen that the calculated values and the observed values agree reasonably well. This agreement implies the validity of the method employed for the determination of gap state distribution profiles. However, it should be mentioned that at temperatures outside the range of 80°C to 120°C, there is a discrepancy between the calculated and the observed values of the modulated photocurrent, indicating the influence of the gap state conductivity. The relative density of gap states, rRoOOM(E)as a function of modulation frequency calculated from eqs. (6) and (7), is shown in fig. 3. For this calculation the product Ncuo is assumed to be independent of temperature• Since the temperature dependence of the optical gap in the temperature range used is negligibly small, the temperature dependence of the density of gap states is due almost entirely to the temperature dependence of EJ [9]. According to eq. (5), Ej is proportional to T for a fixed 00j. Thus, the frequency scale for the spectra shown in fig. 3 can be converted to an energy scale• Using a value of 101~ for the attempt-to-escape frequency (Ncvo), we have calculated the relative density of gap states as a function of energy below the conduction band, and the results are shown in fig. 4. There are some overlapping regions of gap states due to different temperature-frequency combinations corre-
103
x~ £,_ ro
++
09 LU
F-
+ ++
i1 0 >F..-
+
10
+
+
10 2
+~
+ + +C ++ + + + ++++ +D + + + ++ + + + + + + + ~++ + +++
;;++÷ +
+
1
A
++++B
10 2
+
+
+
I
I
10 3
10 4
MODULATION FREQUENCY (Hz) Fig. 3. The relative density of gap states as a function of modulation frequency for (A) 77°C, (B) 92°C, (C) 100°C, and (D) 112°C, for a-SiN02:H films deposited at a substrate temperature of 400°C.
26
J.F. White et al. / Gap state distribution profiles lO3
4J c
-~ a:l 102
++
+ ++
(,o l.U
~5 10 >co
+ 4-
¢21 ]
I
0.45
I
0.50
I
0.55
0.60
I
0.65
ENERGY DEPTH FROMCONDUCTION BANDEDGE (eV)
Fig. 4. The relative density of gap states as a function of energy for a-SiN0.2 : H films deposited at a substrate temperature of 400°C. sponding to the same energy. Clearly, fig. 4 indicates that the density of gap states is exponentially distributed in the gap. A similar result for a m o r p h o u s silicon-nitrogen alloy films measured by a space-charges limited current technique has been reported b y F u r u k a w a et al. [2]. A least mean squares approximation, fitted on the data in fig. 4, gives a slope of - 8 . 5 with a correlation coefficient of - 0 . 9 9 5 . Following the same procedure, the gap state distribution profiles for all the samples listed in table 1 have been determined, and the results are shown in fig. 5. T h e y all exhibit an exponential distribution, at least over the energy range from 0.45 eV to 0.65 eV below the conduction b a n d edge. The slopes of the lines are all between - 8 . 5 and - 9 . 7 , and all have correlation coefficients between - 0 . 9 9 2 and - 0 . 9 9 7 . Assuming an exponential trap distribution of the form M(E)
= ~
exp
)~
,
(9)
where N t is a trap concentration parameter, E c is the conduction b a n d edge, k is the Boltzmann constant, and Tt is the characteristic temperature. We have calculated Tt from the data in fig. 5. The values of Tt for all the samples under investigation are between 440 K and 502 K, in reasonable agreement with those reported by other investigators [2]. O n the basis of the above results, the substrate temperature does not appear to affect either the gap state distribution profile or the characteristic temperature, at least in the energy region around the Fermi level• Since the parameters, TRO , O , P and N c are not known, it is not possible at this stage to obtain the
J.F. White et al. / Gap state distribution prqfiles
27
lO 3
c
lo 2 (y) ill
I--
F E
>-
/H kLl
~
\
]
0.45
G
|
I
I
I
0.50
0.55
0.60
0.65
ENERGY DEPTH FROM CONDUCTION BAND EDGE (eV)
Fig. 5. The relative density of gap states as a function of energy, for a-SiN0.2: H films deposited at substrate temperatures of (E) 150°C, (F) 200°C• (G) 250°C, (H) 300°C, and (J) 400°C. absolute value of M ( E ) by this method. However, the current voltage characteristics at low tempertures give a density of gap states of 4.6 × 10 is cm s eV ] at the Fermi level, and this value is independent of the substrate deposition temperature [13]. This implies that the changes in electronic and optical properties resulting from the change of the substrate deposition temperature [11,12] can be attributed to the change of the density of states with energy away from the Fermi level• It should be noted that the capture cross-section o is actually somewhat energy-dependent [14], and that the capture rate is dependent on the spatial location of the traps [15]. If these two factors are taken into accounL the calculated gap state distribution will be slightly modified.
4. Conclusions The gap state distributions for nitrogen-incorporated amorphous silicon films deposited at various substrate temperatures have been determined over an energy interval of 0.2 eV between 0.45 eV to 0.65 eV below the conduction band. The gap state density is exponentially distributed around the Fermi level and the shape of the distribution is independent of substrate deposition temperature. The present method, based on the phase shift analysis of the modulated photocurrent, gives reasonable results on gap state distribution profiles. However, it would seem that more work is necessary to justify the assumption that the energy dependence of the capture cross-section is not appreciably influencing the results.
28
J.F. White et al. / Gap state distribution profiles
T h e a u t h o r s w i s h to t h a n k the N a t u r a l S c i e n c e s a n d E n g i n e e r i n g R e s e a r c h C o u n c i l of C a n a d a for f i n a n c i a l s u p p o r t o f this research, a n d S.R. M e j i a , R . D . M c L e o d a n d J.J. S c h e l l e n b e r g for t e c h n i c a l assistance.
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
H. Oheda, J. Appl. Phys. 52 (1981) 6693. S. Furukawa, T. Kagawa and N. Matsumoto, Solid St. Commum. 44 (1982) 927. R.L. Weisfield, J. Appl. Phys. 54 (1983) 6401. M.J. Powell, Phil Mag. B43 (1981) 93. M. Grunewald, K. Weber, W. Fube and P. Thomas, J. de Phys. 42 (1981) C4-523. M. Hirose, T. Suzuki and G.H. Dober, Appl. Phys. Lett. 34 (1979) 234. J. Singh and M.H. Cohen, J. Appl. Phys. 51 (1980) 413. H. Oheda, S. Yamascki, T. Yoshida, A. Matsuda, H. Okushi and K. Tanaka, Japan. J. Appl. Phys. 21 (1982) L440. G. Aktas and Y. Skarlatos, J. Appl. Phys. 55 (1984) 3577. K. Mackenzie, P. keComber and W. Spear, Phil. Mag. B46 (1982) 377. H. Watanabe, K. Katoh and M. Yasui, Japan. J. Appl. Phys. 23 (1984) 1. T.V. Herak, R.D. McLeod, K.C. Kao, H.C. Card, H. Watanabe, K. Katoh, M. Yasui and Y. Shibata, J. Non-Cryst. Solids 69 (1984) 39. J.F. White, M.Sc. Thesis, University of Manitoba (1985). H. Okushi, Y. Tokumaru, S. Yamasaki, H. Oheda and K. Tanaka, Phys. Rev. B25 (1982) 4313. N.M. Johnson and W.B. Jackson, J. Non-Cryst. Solids 68 (1984) 147.
Journal of Non-Crystalline Solids 85 (1986) 20-28 North-Holland, Amsterdam
G A P S T A T E D I S T R I B U T I O N P R O F I L E S IN A M O R P H O U S S I L I C O N - N I T R O G E N ALLOY F I L M S F A B R I C A T E D AT V A R I O U S S U B S T R A T E T E M P E R A T U R E S J.F. W H I T E , K.C. KAO, H.C. C A R D and H. W A T A N A B E * Materials and Devices Research Laboratory, Department of Electrical Engineering, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 Received 8 October 1985 The gap state distribution profiles for amorphous silicon-nitrogen alloy films prepared by rf glow discharge in a SiH4-N 2 - H 2 gas mixture at various substrate deposition temperatures have been determined by the phase-shift analysis of the modulated photocurrent. The results indicate that the distribution of gap states is exponentially dependent on energy around the Fermi level and is not significantly influenced by the substrate deposition tehaperature.
1. Introduction Recently, a method based on the phase-shift of the modulated photocurrent, as a function of the modulation frequency of exciting light, has been developed for the determination of the energy distribution of localized gap states [1]. In contrast to conventional methods such as space-charge limited current (SCLC) [2,3], field-effect (FE) [4,5], and capacitance-voltage (CV) [6,7] methods, which utilize steady-state phenomena, this method is based upon a transient phenomenon. The method depends upon the relation between the density of gap states and the phase shift of the photocurrent with respect to the modulated exciting light, at a specific energy corresponding to the modulation frequency. This method has been used for the determination of the energy distribution of gap states in undoped a-Si : H films by Oheda et al. [8] and by Aktas and Skarlatos [9]. Unfortunately, the two sets of results on undoped a-Si : H films are not consistent with each other. However, the results of Oheda et al. [8] agree with those of Grunewall et al. [5], which, using the FE method, show a b u m p in the tail state distribution; while the results of Aktas and Skarlatos [9] agree with those of MacKenzie et al. [10], which, using an SCLC method, indicate an exponential distribution of gap states. The discrepancy between these two sets of results may be due to a legitimate difference in the nature of the gap states between these two stets of samples, under the influence of differing fabrication conditions. * Sendai National College of Technology, Miyagi 989-31, Japan. 0022-3093/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J.F. White et aL / Gap state distribution profiles
21
In this paper, we report new results on the gap state distribution profiles in nitrogen-incorporated amorphous silicon alloy films, as functions of substrate deposition temperature, measured using the phase-shift analysis of the modulated photocurrent.
2. Analytical and experimental techniques The analysis of the phase shift of the modulated photocurrent is based on the following assumptions: (i) the photocurrent is unipolar; (ii) the conduction is trap-limited, but proceeds via extended states; (iii) the energy of the optical excitation is greater than the energy band gap; (iv) the intensity of the optical excitation varies sinusoidally with time, giving rise to a carrier generation rate of g = go + gl exp(i~0t) with ~0 the modulation frequency; (v) the light intensity is sufficiently low to ensure monomolecular recombination; and (vi) the capture cross section of traps is independent of energy. The details of the analysis have been reported by Oheda [1]. The basic relation between the phase-shift ~j and the modulation frequency is tan 09 = B / A ,
(1)
where A ~ - -1 + Z k T In TR0
s= 2
"
vaM(E~_,)
(2)
COs -- 1
and
(3)
B = wi + ~ r k T v o M ( E j )
in which 1 _
TR0
1 +]E~°v,~M(E)~ TR
dE,
(4)
a El
E, = kT ln( Ucvo/,~j),
(5)
v is the electron thermal velocity, o is the capture cross-section of electron traps, Nc is the effective density of states in the conduction band, ~'R is the electron recombination time, M ( E ) is the density of gap states at an energy E below the conduction band edge, and Ej is the energy for which the thermal emission rate of a trapped electron coincides with the modulation frequency ~i" In the actual experiment the phase shift ,~j and the modulated photocurrent 1j are measured as functions of modulation frequency wj with j = 1, 2, 3 . . . . N over a range of temperatures. The suffix j increases as o~ increases. If Ej is not close to the band edge or o~j~'R0 is small enough to be
J.F. White et al. / Gap state distribution profiles
22
ignored, then the density of gap states, from eqs. (1)-(3), may be simply written as for j = 1, • . o V O M ( E , ) = (a/
(6)
kr) tan
and for j = 2, 3 . . . . N,
+kT
ln( S=2
\O3S
" ]~-RoOOM(E~ 1) tan ~/. 1/
(7) Also, the modulated photocurrent at a modulation frequency ~j is theoretically given by
lj = C / ( A 2 + B2) '/2,
(8)
where C is a constant which is chosen so that the theoretical magnitude of I;, is normalized to the value of 11 at ~1. When this theoretical value of (!j)~alc becomes arbitrarily close to observed value of (Ij)ob~, we can consider eqs. (6) and (7) to be appropriate for the determination of the density of gap states, based on the measured values of qSj related to %. The details of the a-SiN x alloy film fabrication processes have been described earlier [11,12]. For the samples used in the present investigation, the films were deposited on glass substrates with x = 0.2, corresponding to a N J S i H 4 mole fraction of 0.5 in the gas phase. The film deposition parameters are given in table 1. For the dark- and photo-current measurements a gap cell configuration with aluminum electrodes was adopted, with an electrode width of 2.0 m m and a separation between electrodes of 1.5 mm. Prior to measurements, the samples were heated to 125°C for about two hours, to drive off any absorbed moisture. The modulated photocurrent was measured at temperatures from 80°C to 120°C using a lock-in amplifier, with a reference signal provided by a fast pin diode. The excitation light was from a H e - N e laser, whose power was attenuated to a level between 0.1 and 1.0 /zW to maintain monomolecular recombination, and chopped mechanically to provide a range of modulation
Table 1 a-SiN0. 2 film deposition parameters Sample
Substrate temperature (°C)
Chamber pressure (Yorr)
rf power density ( W / c m 2)
Gas mixture ratio (N2/SiH4)
Thickness (# m)
E F G H J
150 200 250 300 400
2 2 2 2 2
0.1 0.1 0.1 0.1 0.1
0.5 0.5 0.5 0.5 0.5
1.01 2.24 1.57 0.73 0.89
J , F White et al. / Gap state distribution profiles
23
frequencies from 100 to 4000 Hz. Higher modulation frequencies than those used by other investigators [1,8,9] were used for this ivestigation, because it was necessary to ensure that energy levels were closer to the conduction band for valid analysis. The dark current was measured as a function of temperature using a Keithley 610C electrometer.
3. Results and discussion From the results of the temperature dependence of the dark current, the activation energy of all samples was found to be between 0.6 and 0.7 eV, which corresponds to the position of the Fermi level below the conduction band edge. This value of the activation energy is consistent with that reported elsewhere [11,12]. This energy then represents the lowest energy level that can be accurately analysed in the density of gap states calculations that follow. Fig. 1 shows typical results of the phase shift between the exciting light and the corresponding photocurrent as a function of the light modulation frequency, measured at three different temperatures for a typical sample of an a-SiN, 2 film deposited at a substrate temperature of 400°C.
%0
A B C
O0
,r ~o a.
20
o 10 2
I 103
I 10 4
MODULATION FREQUENCY (Hz)
Fig. 1. The phase shift as a function of modulation frequency of optical excitation, measured at temperatures of (A) 77°C, (B) 100°C, and (C) 112°C, for a-SiNo.2:H films deposited at a substrate temperature of 400°C.
-0.6
102
I
Ii
°
I
C
103
I
III •
al °
2
I I I I |
B
103
!
|
MODULATION FREQUENCY (Hz)
I'll
-
I
10 2
• OBSERVED
| II
I I
A
I I | I
!
&
103
I
|
Fig. 2. Normalized values of the calculated and the observed modulated photocurrent as functions of modulation frequency for (A) 77°C, (B) 100°C, and (C) 112°C, for a-SiN0.2: H films deposited at a substrate temperature of 400°C.
-I.0
g' -o.8
N
O
~- -0.4
z
-0.2
~o
• CA~U~T~
2.
4u.
J.F. White et al. / Gap state distribution profiles
25
The modulated photocurrent magnitude has been calculated as a function of modulation frequency for three different temperatures using eqs. (6) (8) and the measured phase shift. These calculated values, normalized with respect to the first value calculated at 100 Hz, and those measured directly (also normalized to the first value measured at 100 Hz) are plotted as functions of modulation frequency in fig. 2. It can be seen that the calculated values and the observed values agree reasonably well. This agreement implies the validity of the method employed for the determination of gap state distribution profiles. However, it should be mentioned that at temperatures outside the range of 80°C to 120°C, there is a discrepancy between the calculated and the observed values of the modulated photocurrent, indicating the influence of the gap state conductivity. The relative density of gap states, rRoOOM(E)as a function of modulation frequency calculated from eqs. (6) and (7), is shown in fig. 3. For this calculation the product Ncuo is assumed to be independent of temperature• Since the temperature dependence of the optical gap in the temperature range used is negligibly small, the temperature dependence of the density of gap states is due almost entirely to the temperature dependence of EJ [9]. According to eq. (5), Ej is proportional to T for a fixed 00j. Thus, the frequency scale for the spectra shown in fig. 3 can be converted to an energy scale• Using a value of 101~ for the attempt-to-escape frequency (Ncvo), we have calculated the relative density of gap states as a function of energy below the conduction band, and the results are shown in fig. 4. There are some overlapping regions of gap states due to different temperature-frequency combinations corre-
103
x~ £,_ ro
++
09 LU
F-
+ ++
i1 0 >F..-
+
10
+
+
10 2
+~
+ + +C ++ + + + ++++ +D + + + ++ + + + + + + + ~++ + +++
;;++÷ +
+
1
A
++++B
10 2
+
+
+
I
I
10 3
10 4
MODULATION FREQUENCY (Hz) Fig. 3. The relative density of gap states as a function of modulation frequency for (A) 77°C, (B) 92°C, (C) 100°C, and (D) 112°C, for a-SiN02:H films deposited at a substrate temperature of 400°C.
26
J.F. White et al. / Gap state distribution profiles lO3
4J c
-~ a:l 102
++
+ ++
(,o l.U
~5 10 >co
+ 4-
¢21 ]
I
0.45
I
0.50
I
0.55
0.60
I
0.65
ENERGY DEPTH FROMCONDUCTION BANDEDGE (eV)
Fig. 4. The relative density of gap states as a function of energy for a-SiN0.2 : H films deposited at a substrate temperature of 400°C. sponding to the same energy. Clearly, fig. 4 indicates that the density of gap states is exponentially distributed in the gap. A similar result for a m o r p h o u s silicon-nitrogen alloy films measured by a space-charges limited current technique has been reported b y F u r u k a w a et al. [2]. A least mean squares approximation, fitted on the data in fig. 4, gives a slope of - 8 . 5 with a correlation coefficient of - 0 . 9 9 5 . Following the same procedure, the gap state distribution profiles for all the samples listed in table 1 have been determined, and the results are shown in fig. 5. T h e y all exhibit an exponential distribution, at least over the energy range from 0.45 eV to 0.65 eV below the conduction b a n d edge. The slopes of the lines are all between - 8 . 5 and - 9 . 7 , and all have correlation coefficients between - 0 . 9 9 2 and - 0 . 9 9 7 . Assuming an exponential trap distribution of the form M(E)
= ~
exp
)~
,
(9)
where N t is a trap concentration parameter, E c is the conduction b a n d edge, k is the Boltzmann constant, and Tt is the characteristic temperature. We have calculated Tt from the data in fig. 5. The values of Tt for all the samples under investigation are between 440 K and 502 K, in reasonable agreement with those reported by other investigators [2]. O n the basis of the above results, the substrate temperature does not appear to affect either the gap state distribution profile or the characteristic temperature, at least in the energy region around the Fermi level• Since the parameters, TRO , O , P and N c are not known, it is not possible at this stage to obtain the
J.F. White et al. / Gap state distribution prqfiles
27
lO 3
c
lo 2 (y) ill
I--
F E
>-
/H kLl
~
\
]
0.45
G
|
I
I
I
0.50
0.55
0.60
0.65
ENERGY DEPTH FROM CONDUCTION BAND EDGE (eV)
Fig. 5. The relative density of gap states as a function of energy, for a-SiN0.2: H films deposited at substrate temperatures of (E) 150°C, (F) 200°C• (G) 250°C, (H) 300°C, and (J) 400°C. absolute value of M ( E ) by this method. However, the current voltage characteristics at low tempertures give a density of gap states of 4.6 × 10 is cm s eV ] at the Fermi level, and this value is independent of the substrate deposition temperature [13]. This implies that the changes in electronic and optical properties resulting from the change of the substrate deposition temperature [11,12] can be attributed to the change of the density of states with energy away from the Fermi level• It should be noted that the capture cross-section o is actually somewhat energy-dependent [14], and that the capture rate is dependent on the spatial location of the traps [15]. If these two factors are taken into accounL the calculated gap state distribution will be slightly modified.
4. Conclusions The gap state distributions for nitrogen-incorporated amorphous silicon films deposited at various substrate temperatures have been determined over an energy interval of 0.2 eV between 0.45 eV to 0.65 eV below the conduction band. The gap state density is exponentially distributed around the Fermi level and the shape of the distribution is independent of substrate deposition temperature. The present method, based on the phase shift analysis of the modulated photocurrent, gives reasonable results on gap state distribution profiles. However, it would seem that more work is necessary to justify the assumption that the energy dependence of the capture cross-section is not appreciably influencing the results.
28
J.F. White et al. / Gap state distribution profiles
T h e a u t h o r s w i s h to t h a n k the N a t u r a l S c i e n c e s a n d E n g i n e e r i n g R e s e a r c h C o u n c i l of C a n a d a for f i n a n c i a l s u p p o r t o f this research, a n d S.R. M e j i a , R . D . M c L e o d a n d J.J. S c h e l l e n b e r g for t e c h n i c a l assistance.
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
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