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Charge transient and optical absorption measurements of characteristic gap states in phosphorus doped a-Si:H
Journal of Non-Crystalline Solids 68 (1984) 147-152 North-Holland, Amsterdam
147
CHARGE TRANSIENT AND OPTICAL ABSORPTION MEASUREMENTS OF CHARACTERISTIC GAP STATES IN PHOSPHORUS DOPED a - S i : H * N. M. JOHNSON and WARREN B. JACKSON Xerox Pale Alto Research Center, Palo Alto, CA 94304 Recent electron capture experiments claim that the emission prefactor Yn decreases exponentially with trap energy and that the characteristic peak in the gap-state distribution of a-Si:H is ~0.5 eV below the conduction band, rather than at ~0.8 eV as found in other studies. Arguments are presented demonstrating that an exponential dependence of 7n on energy can result from an overly-simplified analysis of the trap filling process in a capacitance transient measurement. Furthermore, it is shown that within experimental uncertainty electrical and optical measurements yield the same peak densities over a range of phosphorus doping concentrations. 1. INTRODUCTION The energy of the characteristic peak in the gap-state distribution of a-Si:H has become controversial with reports t -3 from electron capture data that the prefactor 7n of the thermal emission coefficient decreases exponentially with energy in the band gap and has a magnitude in the range of 109 sec- 1. These results place the peak at approximately 0.5 eV below the conduction - band mobility edge. This paper presents a brief summary of arguments showing that the exponential dependence of 7n on energy is due to an overly- simplified analysis of the dynamics of trap filling in an amorphous semiconductor which specifically ignores the spatial and temporal dependences of the capture rate. Spatially-varying capture rates are known to affect the pulse-width measurement of capture cross-sections for discrete levels in crystalline semiconductors 4. When this effect is considered, the results of the capture-rate measurements in Ref. 1 are found to be in good agreement with other studies5,6. Furthermore, both electrical and optical measurements of the subgap defect profiles yield consistent estimates of the magnitude and location in energy of the peak in the gap-state distribution. Consequently, only a single defect, rather than a two-defect model 7, is needed to account for the measured gap-state distribution.
* This article was inadvertently omitted from Vol. 66, nos. 1,2 containing the Proceedings of the International Topical Conference on Transport and Defects in Amorphous Semiconductors, Bloomfield Hills, Michigan, U.S.A., March 1984.
0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
148
Charge transient and optical absorption measurements (a) Metal* ~ - ~
Semiconductor
~ T ~ P
FIGURE 1 Energy - band diagrams for a Schottky- barrier diode with deep levels in the semiconductor band gap: (a) zero applied bias at the onset of trap filling and (b) reverse bias VR in steady state.
~g"(x,
~ x
Xot3
%..'.".. r-.4L_*,
Ec
!2--22_--:-.'~E,= 3 ----~.---.
EV Et3
w
2. TRAP FILLING DYNAMICS The essential features of the trap-filling dynamics during a capacitance transient measurement of deep levels can be described with reference to the energy-band diagrams in Fig. 1 for a Schottky-barrier contact on an n - t y p e semiconductor. (Most of the symbo!s in this figure have been defined previously5.) The Schottky diode is shown under a reverse bias VR in Fig. l(b) and at the of a zero- bias trap filling pulse in Fig. l(a). States in the shaded regions of the band gap are occupied with electrons. For brevity three selected energies, Eti (i = 1-.3), in a continuous distribution of gap states are identified in the semiconductor band gap. Trap filling involves the capture of free electrons into gap states in the unshaded region below the Fermi level EF in Fig. l(a); in thermal equilibrium EF identifies the energy at which the electron capture and emission rates are equal. In the space-charge layer, the free-electron density n(x) decreases exponentially with electric potential ¢ from its bulk value no:
beginning
steady-state
n(x) = no e x p [ - q ¢ ( x ) / k T ] ,
(1)
where q is electronic charge, k is Boltzmann's constant, and T is the absolute temperature. Therefore, in this region the characteristic time for gap states to capture free electrons, %, increases exponentially with ¢ and is given by ,rc(X) = [OrnVthn(X)]- 1 ,
(2)
where en is the capture cross-section (assumed to be a constant in the present discussion) and Vth iS the mean thermal velocity of free carriers in the extended states of the conduction band. For x >_ WO, n = no and Tc is a constant. In doped a-Si:H devices, the capture time typically varies from nanoseconds for x > W 0 to hundreds of seconds near the metal- semiconductor contact (i.e., at x = 0 +). As an aside, it should be noted that since fully saturated trap emission requires the
Charge transient and optical absorption measurements
149
attainment of equilibrium during zero-bias trap filling, these extremely long trap-filling times should be at least partially responsible for commonly observed "soft" saturation under long pulse-width conditions in deep-level transient measurements. This should be especially true in the current transient mode which is maximally sensitive to interface trap filling8. If the dependence of n on ~ is ignored in a pulse - width measurement, then this dependence will appear in a n (see Eq. (2)), yielding an effective capture cross-section, eeff, which decreases exponentially with ¢. Equivalently, if the principal of detailed balance is invoked, the relation between the emission coefficient and the capture cross-section is 7n = °'nVthNc,
(3)
where 7n is the attempt-to-escape frequency and NC is the effective density of states in the conduction band. Ignoring the ~ - dependence of n will yield an effective frequency Yeff which similarly decreases exponentially with !/,. In Fig. l(a), at a given trap depth, Eti, the spatial interval over which traps are to be filled is bounded by the occupation crossover points (i.e., Xoti and xti), which a r e defined in Ref. 5. The distance of this interval from the interface (i.e., from x = O) decreases as the trap depth increases. Therefore, fewer free electrons are available to fill the deeper levels. If this qualitative feature of the trap filling dynamics is ignored, an effective capture cross- section which decreases essentially exponentially with trap depth will result. The energy-band diagrams in Fig. 1 further illustrate that for small reverse biases, representative of those quoted in Refs. 1 - 3, nearly all of the traps to be filled are located within the region of band bending under zero applied bias (i.e., Xti < Wo). Consequently, the trap filling dynamics are entirely dominated by a spatially varying capture rate. Furthermore, a more complete analysis indicates that the magnitude of the exponential energy dependence of the emission prefactor found in Ref. 1 is also consistent with neglecting the spatial dependence of trap filling9. Finally, it has previously been noted 1° that due to the high g a p - state densities in amorphous semiconductors, the capture rate may also display a significant time dependence, which should also be considered when analyzing trap filling data. 3. ENERGY SCALE COMPRESSION In the previous section, a plausible physical mechanism was described which would yield an effective attempt- t o - escape frequency that decreased exponentially with trap depth even when the actual Yn is constant. This functional dependence of Yeff on trap depth E, measured relative to the conduction- band mobility edge, may be generally expressed as follows:
Charge transient and optical absorption measurements
150
7elf = 70 exp( - E/ET),
(4)
where 7o is the actual attempt - to - escape frequency and Ey is the decay constant. Furthermore, from the coefficient for thermal emission, the energy of emitting centers E increases with time during the trap emission cycle of a d e e p - level transient measurement as follows: E = kT In(¥nt),
(5)
where t is the time after the onset of trap emission and 7n E 70 in the present discussion. If 7eff instead of 7o is substituted for 7n in Eq. (5), the following effective energy Eelf is obtained: Eeff
= (1 + kT/E7)- 1 kT In(7ot) = (1 + kT/E¥)- 1 EactuaI .
(6)
The decay constant E 7 is estimated to be 57 meV at T = 297 K from Ref. 1. When these values are substituted into Eq. (6), an actual trap depth Eactual = 0.80 eV corresponds to an effective depth Eeff = 0.55 eV. In other words, a peak in the gap-state distribution at 0.8 eV, as found in the present study 5,9, would appear at 0.55 eV if the apparent a t t e m p t - t o - e s c a p e frequency possessed, either artifactually or in reality11, the functional form of Eq. (4). In addition, from Ref. 1 the prefactor in Eq. (4) is estimated to be 7o = 1.5X1012 sec-1, which is in close agreement with the magnitude of 7n determined in the present study. 4. CORRELATED MEASUREMENTS The accuracy of the assumptions used in capacitance transient spectroscopy was tested by comparing transient voltage spectroscopy, photothermal deflection spectroscopy, and photoconductivity measerements on c o - deposited samples, with doping concentrations (i.e., [PH3]/[SiH4]) of 4X10 -7 to 2X10 -5. While thermal- emission and optical- excitation energies are fundamentally different 12, it is expected that the difference in magnitudes is small in comparison to the ~ 300 meV discrepancy which exists between the peak - energy placement in Ref. 1 and in other studies 5,6. The density at the peak in the characteristic gap-state distribution, g(Ep), as measured by the electrical versus optical techniques is shown in Fig. 2, with phosphorus doping concentration as the implicit parameter. Within exporimental uncertainty, a satisfactory o n e - t o - one correspondence is obtained indi(~ating that subgap absorption is dominated by the characteristic peak. By comparing the energy of the subgap absorption with gap-state densities, it was found that the results of the present study are self-consistent with a peak at 0.8+0.05 eV, 7n ~-- 1X1012 sec-1 (at 295 K), and a value of ~1.2X10 -16 cm -2 for the optical cross-section 5,9,13.
Charge transient and optical absorption measurements
1016
I
r
151
I
i
,
I T
a - Si:H
FIGURE 2 Electrically versus optically measured gap-state density g at the peak energy (with Ep ~. 0.8 eV) of the characteristic deep-level distribution in a-Si:H. The material is doped over a range of phosphorus concentrations.
13
:
>.
1o1,
Phosphorus Doped
•
T /
-
_,:
_
10 TM
5'
10TM
~
2
J_
L
I
J
j
5 1017 2 5 Optical g(Ep) (eV -1 crn 3)
10 TM
5. CONCLUSIONS This study concludes that ignoring the spatially varying capture rate in a pulse - width measurement will yield, especially for small reverse biases, an effective capture cross- section, or equivalently an effective attempt- t o - escape frequency, which decreases exponentially with trap depth even if the actual value is a constant. It was also shown that this yields an effective trap energy which is less that the actual trap depth of emitting centers in a capacitance transient measurement. Given the above observations, the transient capacitance data of Ref. 1 appear in agreement with the self - consistent electrical and optical results summarized in this paper. A final consequence of these observations is that only a single defect, rather than the two - defect model proposed in Refs. 3 and 7, is needed to account for the deep-level density of states measured in phosphorus doped a-Si:H. ACKNOWLEDGMENT The authors are pleased to acknowledge helpful discussions with D. K. Biegelsen, R. A. Street, M. Stutzmann, and M. J. Thompson and to thank R. Lujan, R. Thompson, and B. Walker for assistance with sample preparation. The work was partially supported by SERI. REFERENCES 1) H. Okushi, Y. Tokumaru, S. Yamasaki, H. Oheda, and K. Tanaka, Phys. Rev. B25 (1982) 4313.
152
Charge transient and optical absorption measurements
2) H. Okushi, T. Takahama, Y. Tokumaru, S. Yamasaki, H. Oheda, and K. Tanaka, Phys. Rev. B27 (1983) 5184. 3) K. Tanaka, Defects in a-Si:H, these proceedings. 4) A. Zylbersztejn, Appl. Phys. Lett. 33 (1978) 200. 5) N. M. Johnson, Appl. Phys. Lett. 42 (1983) 981. 6) D. V. Lang, J. D. Cohen, and J. P. Harbison, Phys. Rev. B25 (1982) 5285. 7) S. Yamasaki, H. Oheda, A. Matsuda, H. Okushi, and K. Tanaka, Jpn. J. Appl. Phys. 21 (1982) L539. 8) R. S. CrandaU, J. Electron. Mater. 9 (1980) 713. 9) N. M. Johnson and W. B. Jackson, to be published. 10) N. M. Johnson, J. Non-Cryst. Solids 59 (1983) 265. 11) N. M. Johnson, J. Vac. Sci. Technol. 21 (1982) 303. 12) J. A. Van Vechten and C. D. Thurmond, Phys. Rev. B14 (1976) 3539. 13) W. B. Jackson and N. M. Amer, Phys. Rev. B25 (1982) 5559.
147
CHARGE TRANSIENT AND OPTICAL ABSORPTION MEASUREMENTS OF CHARACTERISTIC GAP STATES IN PHOSPHORUS DOPED a - S i : H * N. M. JOHNSON and WARREN B. JACKSON Xerox Pale Alto Research Center, Palo Alto, CA 94304 Recent electron capture experiments claim that the emission prefactor Yn decreases exponentially with trap energy and that the characteristic peak in the gap-state distribution of a-Si:H is ~0.5 eV below the conduction band, rather than at ~0.8 eV as found in other studies. Arguments are presented demonstrating that an exponential dependence of 7n on energy can result from an overly-simplified analysis of the trap filling process in a capacitance transient measurement. Furthermore, it is shown that within experimental uncertainty electrical and optical measurements yield the same peak densities over a range of phosphorus doping concentrations. 1. INTRODUCTION The energy of the characteristic peak in the gap-state distribution of a-Si:H has become controversial with reports t -3 from electron capture data that the prefactor 7n of the thermal emission coefficient decreases exponentially with energy in the band gap and has a magnitude in the range of 109 sec- 1. These results place the peak at approximately 0.5 eV below the conduction - band mobility edge. This paper presents a brief summary of arguments showing that the exponential dependence of 7n on energy is due to an overly- simplified analysis of the dynamics of trap filling in an amorphous semiconductor which specifically ignores the spatial and temporal dependences of the capture rate. Spatially-varying capture rates are known to affect the pulse-width measurement of capture cross-sections for discrete levels in crystalline semiconductors 4. When this effect is considered, the results of the capture-rate measurements in Ref. 1 are found to be in good agreement with other studies5,6. Furthermore, both electrical and optical measurements of the subgap defect profiles yield consistent estimates of the magnitude and location in energy of the peak in the gap-state distribution. Consequently, only a single defect, rather than a two-defect model 7, is needed to account for the measured gap-state distribution.
* This article was inadvertently omitted from Vol. 66, nos. 1,2 containing the Proceedings of the International Topical Conference on Transport and Defects in Amorphous Semiconductors, Bloomfield Hills, Michigan, U.S.A., March 1984.
0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
148
Charge transient and optical absorption measurements (a) Metal* ~ - ~
Semiconductor
~ T ~ P
FIGURE 1 Energy - band diagrams for a Schottky- barrier diode with deep levels in the semiconductor band gap: (a) zero applied bias at the onset of trap filling and (b) reverse bias VR in steady state.
~g"(x,
~ x
Xot3
%..'.".. r-.4L_*,
Ec
!2--22_--:-.'~E,= 3 ----~.---.
EV Et3
w
2. TRAP FILLING DYNAMICS The essential features of the trap-filling dynamics during a capacitance transient measurement of deep levels can be described with reference to the energy-band diagrams in Fig. 1 for a Schottky-barrier contact on an n - t y p e semiconductor. (Most of the symbo!s in this figure have been defined previously5.) The Schottky diode is shown under a reverse bias VR in Fig. l(b) and at the of a zero- bias trap filling pulse in Fig. l(a). States in the shaded regions of the band gap are occupied with electrons. For brevity three selected energies, Eti (i = 1-.3), in a continuous distribution of gap states are identified in the semiconductor band gap. Trap filling involves the capture of free electrons into gap states in the unshaded region below the Fermi level EF in Fig. l(a); in thermal equilibrium EF identifies the energy at which the electron capture and emission rates are equal. In the space-charge layer, the free-electron density n(x) decreases exponentially with electric potential ¢ from its bulk value no:
beginning
steady-state
n(x) = no e x p [ - q ¢ ( x ) / k T ] ,
(1)
where q is electronic charge, k is Boltzmann's constant, and T is the absolute temperature. Therefore, in this region the characteristic time for gap states to capture free electrons, %, increases exponentially with ¢ and is given by ,rc(X) = [OrnVthn(X)]- 1 ,
(2)
where en is the capture cross-section (assumed to be a constant in the present discussion) and Vth iS the mean thermal velocity of free carriers in the extended states of the conduction band. For x >_ WO, n = no and Tc is a constant. In doped a-Si:H devices, the capture time typically varies from nanoseconds for x > W 0 to hundreds of seconds near the metal- semiconductor contact (i.e., at x = 0 +). As an aside, it should be noted that since fully saturated trap emission requires the
Charge transient and optical absorption measurements
149
attainment of equilibrium during zero-bias trap filling, these extremely long trap-filling times should be at least partially responsible for commonly observed "soft" saturation under long pulse-width conditions in deep-level transient measurements. This should be especially true in the current transient mode which is maximally sensitive to interface trap filling8. If the dependence of n on ~ is ignored in a pulse - width measurement, then this dependence will appear in a n (see Eq. (2)), yielding an effective capture cross-section, eeff, which decreases exponentially with ¢. Equivalently, if the principal of detailed balance is invoked, the relation between the emission coefficient and the capture cross-section is 7n = °'nVthNc,
(3)
where 7n is the attempt-to-escape frequency and NC is the effective density of states in the conduction band. Ignoring the ~ - dependence of n will yield an effective frequency Yeff which similarly decreases exponentially with !/,. In Fig. l(a), at a given trap depth, Eti, the spatial interval over which traps are to be filled is bounded by the occupation crossover points (i.e., Xoti and xti), which a r e defined in Ref. 5. The distance of this interval from the interface (i.e., from x = O) decreases as the trap depth increases. Therefore, fewer free electrons are available to fill the deeper levels. If this qualitative feature of the trap filling dynamics is ignored, an effective capture cross- section which decreases essentially exponentially with trap depth will result. The energy-band diagrams in Fig. 1 further illustrate that for small reverse biases, representative of those quoted in Refs. 1 - 3, nearly all of the traps to be filled are located within the region of band bending under zero applied bias (i.e., Xti < Wo). Consequently, the trap filling dynamics are entirely dominated by a spatially varying capture rate. Furthermore, a more complete analysis indicates that the magnitude of the exponential energy dependence of the emission prefactor found in Ref. 1 is also consistent with neglecting the spatial dependence of trap filling9. Finally, it has previously been noted 1° that due to the high g a p - state densities in amorphous semiconductors, the capture rate may also display a significant time dependence, which should also be considered when analyzing trap filling data. 3. ENERGY SCALE COMPRESSION In the previous section, a plausible physical mechanism was described which would yield an effective attempt- t o - escape frequency that decreased exponentially with trap depth even when the actual Yn is constant. This functional dependence of Yeff on trap depth E, measured relative to the conduction- band mobility edge, may be generally expressed as follows:
Charge transient and optical absorption measurements
150
7elf = 70 exp( - E/ET),
(4)
where 7o is the actual attempt - to - escape frequency and Ey is the decay constant. Furthermore, from the coefficient for thermal emission, the energy of emitting centers E increases with time during the trap emission cycle of a d e e p - level transient measurement as follows: E = kT In(¥nt),
(5)
where t is the time after the onset of trap emission and 7n E 70 in the present discussion. If 7eff instead of 7o is substituted for 7n in Eq. (5), the following effective energy Eelf is obtained: Eeff
= (1 + kT/E7)- 1 kT In(7ot) = (1 + kT/E¥)- 1 EactuaI .
(6)
The decay constant E 7 is estimated to be 57 meV at T = 297 K from Ref. 1. When these values are substituted into Eq. (6), an actual trap depth Eactual = 0.80 eV corresponds to an effective depth Eeff = 0.55 eV. In other words, a peak in the gap-state distribution at 0.8 eV, as found in the present study 5,9, would appear at 0.55 eV if the apparent a t t e m p t - t o - e s c a p e frequency possessed, either artifactually or in reality11, the functional form of Eq. (4). In addition, from Ref. 1 the prefactor in Eq. (4) is estimated to be 7o = 1.5X1012 sec-1, which is in close agreement with the magnitude of 7n determined in the present study. 4. CORRELATED MEASUREMENTS The accuracy of the assumptions used in capacitance transient spectroscopy was tested by comparing transient voltage spectroscopy, photothermal deflection spectroscopy, and photoconductivity measerements on c o - deposited samples, with doping concentrations (i.e., [PH3]/[SiH4]) of 4X10 -7 to 2X10 -5. While thermal- emission and optical- excitation energies are fundamentally different 12, it is expected that the difference in magnitudes is small in comparison to the ~ 300 meV discrepancy which exists between the peak - energy placement in Ref. 1 and in other studies 5,6. The density at the peak in the characteristic gap-state distribution, g(Ep), as measured by the electrical versus optical techniques is shown in Fig. 2, with phosphorus doping concentration as the implicit parameter. Within exporimental uncertainty, a satisfactory o n e - t o - one correspondence is obtained indi(~ating that subgap absorption is dominated by the characteristic peak. By comparing the energy of the subgap absorption with gap-state densities, it was found that the results of the present study are self-consistent with a peak at 0.8+0.05 eV, 7n ~-- 1X1012 sec-1 (at 295 K), and a value of ~1.2X10 -16 cm -2 for the optical cross-section 5,9,13.
Charge transient and optical absorption measurements
1016
I
r
151
I
i
,
I T
a - Si:H
FIGURE 2 Electrically versus optically measured gap-state density g at the peak energy (with Ep ~. 0.8 eV) of the characteristic deep-level distribution in a-Si:H. The material is doped over a range of phosphorus concentrations.
13
:
>.
1o1,
Phosphorus Doped
•
T /
-
_,:
_
10 TM
5'
10TM
~
2
J_
L
I
J
j
5 1017 2 5 Optical g(Ep) (eV -1 crn 3)
10 TM
5. CONCLUSIONS This study concludes that ignoring the spatially varying capture rate in a pulse - width measurement will yield, especially for small reverse biases, an effective capture cross- section, or equivalently an effective attempt- t o - escape frequency, which decreases exponentially with trap depth even if the actual value is a constant. It was also shown that this yields an effective trap energy which is less that the actual trap depth of emitting centers in a capacitance transient measurement. Given the above observations, the transient capacitance data of Ref. 1 appear in agreement with the self - consistent electrical and optical results summarized in this paper. A final consequence of these observations is that only a single defect, rather than the two - defect model proposed in Refs. 3 and 7, is needed to account for the deep-level density of states measured in phosphorus doped a-Si:H. ACKNOWLEDGMENT The authors are pleased to acknowledge helpful discussions with D. K. Biegelsen, R. A. Street, M. Stutzmann, and M. J. Thompson and to thank R. Lujan, R. Thompson, and B. Walker for assistance with sample preparation. The work was partially supported by SERI. REFERENCES 1) H. Okushi, Y. Tokumaru, S. Yamasaki, H. Oheda, and K. Tanaka, Phys. Rev. B25 (1982) 4313.
152
Charge transient and optical absorption measurements
2) H. Okushi, T. Takahama, Y. Tokumaru, S. Yamasaki, H. Oheda, and K. Tanaka, Phys. Rev. B27 (1983) 5184. 3) K. Tanaka, Defects in a-Si:H, these proceedings. 4) A. Zylbersztejn, Appl. Phys. Lett. 33 (1978) 200. 5) N. M. Johnson, Appl. Phys. Lett. 42 (1983) 981. 6) D. V. Lang, J. D. Cohen, and J. P. Harbison, Phys. Rev. B25 (1982) 5285. 7) S. Yamasaki, H. Oheda, A. Matsuda, H. Okushi, and K. Tanaka, Jpn. J. Appl. Phys. 21 (1982) L539. 8) R. S. CrandaU, J. Electron. Mater. 9 (1980) 713. 9) N. M. Johnson and W. B. Jackson, to be published. 10) N. M. Johnson, J. Non-Cryst. Solids 59 (1983) 265. 11) N. M. Johnson, J. Vac. Sci. Technol. 21 (1982) 303. 12) J. A. Van Vechten and C. D. Thurmond, Phys. Rev. B14 (1976) 3539. 13) W. B. Jackson and N. M. Amer, Phys. Rev. B25 (1982) 5559.