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Evidence for non-equilibrium free electron density in AlGaAs at low temperatures
Solid State Communications, Vol. 78, No. 2, pp. 159-162, 1991. Printed in Great Britain.
0038-1098/91 $3.00 + .00 Pergamon Press plc
EVIDENCE FOR NON-EQUILIBRIUM FREE ELECTRON DENSITY IN A1GaAs AT LOW TEMPERATURES* C. Ghezzi Dipartimento di Fisica, Universitfi degli Studi di Parma, Viale delle Scienze, 43100 Parma, Italy and R. Mosca, A. Bosacchi, S. Franchi, E. Gombia and L.E. Vanzetti Istituto MASPEC del Consiglio Nazionale delle Ricerche, Via Chiavari 18/A, 43100 Parma, Italy (Received 10 September 1990 by R. Fieschi)
Due to the strong temperature dependence of the capture rate, the DX centre in AIGaAs is expected to show non-equilibrium occupancy at low temperatures. Results of Thermally Stimulated Capacitance and Capacitance-Voltage measurements, carried out at 77K on Au-AlxGa~_xAs (x = 0.25) Schottky barriers, are strongly influenced by the cooling rate. This demonstrate that in practical experiments the free electron density commonly observed at low temperature is far from thermodynamical equilibrium.
IN RECENT years much attention has been devoted mal equilibrium due to the vanishingly small capture to the main electron trap observed in n-type cross section of the DX centre. This hypothesis is AlxGal_xAs for x > 0.22, the so-called DX centre consistent with capture time data reported by Mooney [1-3]. It is now generally agreed that the DX centre is et al. [11]. In fact the observation of long trapping related to a substitutional donor [5], whose features times actually leaves out that in practical experiments are strongly influenced by the x-dependent structure the DX centre occupancy may reach at low temperaof the conduction band. The electrical conductivity of ture values corresponding to thermal equilibrium. The n-type A1GaAs is strongly affected by the presence of well known persistent photoconductivity (PPC) effect the DX centre. Hall effect measurements carried out itself is evidence for this; however, after the first obseras a function of temperature for different x values vation of PPC in A1GaAs [12], several papers [8, 13[6-8] show a decrease in the Hall carrier concentration 15] dealt with the DX centre assuming an equilibrium as the temperature is decreased. Between 300 K and free electron density at low temperatures. As a matter about 150 K the electron freeze-out to DX centres is of fact, although it has been suggested that low temdescribed by an exponential function of the reciprocal perature data depend on the sample cooling rate [16], temperature, whereas at lower temperatures, the Hall to our knowledge no systematic studies of this effect electron concentration reaches values which are con- have been carried out. stant or only weakly temperature dependent, dependIn this paper we report Thermally Stimulated ing on x. To explain this effect Spring-Thorpe et al. [6] Capacitance (TSCap) and low temperature C-V invoked the onset of impurity band conduction or, measurements carried out upon cooling the sample owing to the high mobility values, the presence of a with different cooling rates. Our results clearly demonbackground shallow donor level. Chand et al. [7] and strate that the low temperature free electron density Schubert and Ploog [8] proposed that the observed depends on the cooling procedure in agreement with saturation orginates from the shallow F- related level the expected absence of thermodynamical equilibrium introduced by the dopant impurity itself. Kunzel et al. in the DX centre occupancy. [9, 10] suggested that the saturation effect can be The Hall free electron density reduction, observed caused by electronic equilibrium lagging behind ther- when cooling AlxGa I xAs (x > 0.22), is commonly attributed to carrier freeze out to the DX centre * This work has been partially supported by the [7-10]. Owing to its thermally activated nature, the Finalized Project of the Consiglio Nazionale delle capture process is described by a time constant tc Ricerche (CNR) "Materials and Devices for Solid which is strongly temperature dependent. For instance, State Electronics". extrapolation of the results reported by Mooney et al. 159
160
N O N - E Q U I L I B R I U M F R E E E L E C T R O N D E N S I T Y IN AIGaAs
[11] suggests that in a x = 0.27 sample, tc should vary from l0 6-10-SS at 300K to about 10tlS at 78K, so that at low temperature the DX centre occupancy can be considered completely quenched. Since the capture time t, increases when the sample temperature decreases, if the time At necessary for the temperature decrease is much larger than the corresponding increase in the capture time Ate, the DX centre occupancy can be considered to be at equilibrium. This is usually the case for high temperature (e.g. 300 K). On the contrary, if At is smaller than Ate, the occupancy factor f is lower than the equilibrium factor f0 and electronic equilibrium lags behind thermal equilibrium. The faster the cooling rate, the higher is the temperature T* at which the difference f-f0 becomes significant and the larger also is the low temperature value of f-f0. Since the electron concentration n is expected to decrease monotonically with increasing f, the presence of non-equilibrium conditions should result in different free electron densities when the sample is cooled with different cooling rates. We have therefore measured the capacitance of Schottky barriers prepared on A1GaAs epitaxial layers by using different cooling procedures. The samples were Si-doped AlxGal_xAs (with x = 0.25) layers grown by MBE on either conducting or semiinsulating substrates. In this paper we refer to a representative sample, consisting of a n ÷ -substrate, a 0.3/~m thick n+-GaAs buffer layer, a 7pm thick n-AIGaAs layer and a 200 A thick undoped GaAs cap that was removed by etching in H2SO4:H202:HzO (40:1 : 1) for 20 s. Ohmic contacts were obtained by alloying indium on the backside of the samples and Schottky barriers were fabricated by evaporating Au dots with a 0.26 mm 2 area. C- V measurements carried out at 77 K (LNT) under saturated PPC conditions show that the uncompensated donor density in the AIGaAs layer is 1.29 x 10iScm -3. To check the dependence of the capacitance at 77 K on the cooling rate, three different cooling procedures (a)-(c) were examined: (a) 77 K attained in 203 min with a nearly constant rate; (b) 77 K attained in 5 min and (c) the sample was directly immersed in liquid nitrogen (LNz). During procedure (c) the temperature could not be accurately measured during the scan: the cooling time from room temperature (RT) to LNT was estimated as 10 s. The sample was always kept in the dark. In order to minimize the contribution to the space charge density due to the DX centres, which near the metal/semiconductor interface are fully positively ionized, we reduced band bending during cooling by keeping the Schottky barrier forward biased (Va = 0.8V). Figure 1 shows the C - T curves obtained during the cooling scan under f o r -
Vol. 78, No. 2
direct Immerelon Into LN 2
(v,:o.8 v)
w
a')
~
~ ~
I~t~"
direct
soc
3
Immerlllon [[
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/
z
40C
,;o
,;o
~o Temperature
2~o
I
300
(K)
Fig. 1. TSCap measurements performed with applied voltage Va = 0 V after cooling in (a) 203 min and (b) in 5 min. The curves (a') and (b') refer to the respective cooling scans carried out with Va = 0.8V. The capacitance values as measured at 77 K after direct immersion into LN: are also indicated.
ward bias (a; b') and those obtained during the warm up scan with no applied voltage (a, b). Such curves have been observed to be very reproducible when the cooling scans are repeated. The capacitance values for Va = 0.8V and V~ = 0V as obtained at 7 7 K with procedure (c) are also indicated in Fig. 1. As it can be seen, for temperatures higher than 180 K the C - T curves are not affected by the cooling rate, suggesting an equilibrium occupancy of the D X centre. In contrast, when T < 180 K the capacitance depends on the cooling procedure: faster cooling rates correspond to higher capacitance values measured at 77 K. This is expected since when the cooling rate is increased, the temperature T* at which a given deviation from equilibrium is achieved increases. As a consequence, the fraction of unoccupied DX centres at 77 K becomes higher. In order to obtain quantitative information about the DX centre occupancy at 77K, we used C - V measurements. Double integration of Poisson's equation, carried out under the depletion approximation, gives:
2e(Vbi-k-
FDX -- q[N+x(~) -- N a ] W 2,
V~) =
(1)
where w
Fox
2q I z[U+x(Z) -- N + x ( ~ ) ] d z '
(2)
0
e is the dielectric constant, Vbithe built-in potential, V~ the bias used for the 77 K C - V measurement, Na the
Vol. 78, No. 2
N O N - E Q U I L I B R I U M F R E E E L E C T R O N D E N S I T Y IN A1GaAs
acceptor concentration, Nt~x(z) the ionized D X centre density at a distance z from the contact, Nr~x(oo) is the value of Nr~x(Z) in the asymptotic flat band region and W the width of the space charge region. If the charge state of the DX centre is quenched, the term Fox is independent on V, being only determined by the bias Va applied while cooling and, to a minor extent, by the cooling procedure [16]. Therefore, equation (1) predicts a linear relation between I/C 2 and V,, with slope related to the net ionized DX centre density in the flat band region, namely N~x(OO) - Na. It is worth noting that the bias V~, applied during the cooling, has no effect on the slope, since it influences, through the Fox term, only the value of the apparent built-in voltage as determined by extrapolating to zero the 1/C 2 line. In deriving the above equations we neglected the contribution o f the shallow donors and we assumed that the charge state of the DX centre is neutral when occupied and singly positively charged otherwise. It is straightforward, however, to account for hypothetical shallow donors [18] or to reformulate equations (1) and (2) assuming a negative U character for the D X centre with a singly positive or singly negative charge state, depending on whether the Fermi level is lower or higher than the proper occupancy level for the DX centre [19, 20]. It is therefore possible to quantitatively determine the influence of the cooling procedure on the DX centre occupancy at low temperature. In Fig. 2 we show the 1/C 2 vs V, curves obtained at 77 K following the three cooling procedures (a)-(c). The corresponding free electron densities n are listed in Table 1. With the conventions employed n is equal to N~x(OO) - Na, so that it is evident that in the fiat band region the net ionized DX centre concentration depends on the cooling rate increasing by about 50% when the cooling time is reduced from 203 min to 10sec. This finally demonstrates that the data obtained at low temperature depend on the cooling rate, as a consequence of the thermally activated nature of the capture process. Table 1 . Free electron density n and apparent built-in voltage as determined by fitting the 1/C 2 vs V~ curves shown in Fig. 2. With the convention employed n is equal to N+x(OO) - N, in equations 1-2
Cooling time 203 min 5 min 10s
n
Vr(1/C 2 = 0)
( 10 '7 cm - 3)
(Volt)
2.02 2.45 2.92
0.786 0.827 0.866
161
2
A
~
A B mln o d i r e c t Immersion Into LN 2
j O,B
0
-O,B Vr
-1
-1.8
(V)
Fig. 2. 1/C 2 v s Vr as determined at 77 K after cooling the sample following the three cooling procedures (a)-(c) described in the text. The present results suggest that the Hall electron density saturation observed at low temperature is caused by the lag of electronic equilibrium behind thermal equilibrium. Moreover, the observed dependence on x of the saturation effect [8] seems to be explained by the x dependence of the capture time activation energy E~ [11]. In fact, different Ec values imply that significant deviations from equilibrium occupancy conditions are achieved at different temperatures T*, the lower the capture energy, the lower T*. Along the same lines, a few comments should be made in reference to the dependence on x of the PPC effect. The latter has been observed to be maximum for x = 0.35 [7]. This has been simply explained in terms of ionization energy, which is maximum at x = 0.35, without taking into account the capture time activation energy, which has been shown to be minimum for x = 0.35 [11]. At this AlAs molar fraction, for a given net donor density and a given cooling rate, the low temperature dark electron density should reach its minimum value since both the equilibrium density and the deviations from equilibrium conditions are expected to be minimized. As a consequence, the PPC effect reaches its maximum value: the capture time activation energy is then expected to amplify the x dependence of the PPC effect. As a final comment it is worth noting that at low temperature the electron gas is far from equilibrium only with respect to the DX centre, that is the lowest energy state of the donor atom. On the contrary, it is expected to be in equilibrium with excited states such as the F or X related shallow levels. Experimental evidence for electron freeze-out to these states was in fact recently given by Mizuta [21]. In summary, it has been shown that the DX centre occupancy at low temperature depends on the cooling rate. This is a further experimental demonstration that
162
NON-EQUILIBRIUM FREE ELECTRON DENSITY IN AIGaAs
at low temperatures the DX centre shows a non equilibrium occupancy originated by the thermally activated nature of the capture process.
Acknowledgement - The authors wish to thank Mr P. Allegri for technical assistance in the MBE growth.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
D.V. Lang & R.A. Logan, Phys. Rev. Lett. 39, 6354 (1977). D.V. Lang, R.A. Logan & M. Jaros, Phys. Rev. B19, 1015 (1979). D.V. Lang, in Deep Centres in Semiconductors, (Edited by S.T. Pantelides), p. 489, Gordon and Breach, New York (1986). P.M. Mooney, J. Appl. Phys. 67, RI (1990). M. Mizuta, M. Tachikawa, H. Kukimoto & S. Minomura, Jpn. J. Appl. Phys. 24, L143 (1985). A.J. Spring-Thorpe, F.D. King & A. Becke, J. Electron. Mater. 4, 101 (1975). N. Chand, T. Henderson, J. Klein, W.T. Masselink, R. Fischer, Y. Chang & H. Morkoc, Phys. Rev. B30, 4881 (1984). E.F. Schubert & K. Ploog, Phys. Rev. B30, 7021 (1984).
9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
21.
Voi. 78, No. 2
H. Kunzel, K. Ploog, K. Wunstel & B.L. Zhou, J. Electron. Mater. 13, 281 (1984). H. Kunzel, A. Fischer, J. Knecht & K. Ploog, Appl. Phys. A32, 69 (1983). P.M. Mooney, N.S. Caswell & S.L. Wright, J. Appl. Phys. 62, 4786 (1987). R.J. Nelson, Appl. Phys. Lett. 31, 351 (1977). B. El Jani, K. Kolher, K. N'Guessan, A. Bel Hadj & P. Gilbart, J. Appl. Phys. 63, 4518 (1988). T. Ishikawa, T.Maeda & K. Kondo, Appl. Phys. Lett. 53, 1926 (1988). P.W.M. Blom, P.M. Koenraad, F.A.P. Blom & J.H. Wolter, J. Appl. Phys. 66, 4269 (1989). E. Munoz & E. Calleja, Physics o f D X Centres in GaAs Alloys, (Edited by J. Bourgoin), p. 99, Sci-Tech. Publ. (1989). R. Mosca, unpublished. M.F. Li, Y.B. Jia, P.Y. Yu, J. Zhou & J.L. Gao, Phys. Rev. B40, 1430 (1989). D.J. Chadi & K.J. Chang, Phys. Rev. B39, 10063 (1989). J.M. Langer, J.E. Dmochowski, L. Dobaczewski, W. Jantsch & G. Brunthaler, in Physics of DX Centres in GaAs Alloys, (Edited by J.C. Bourgoin), p. 233, Sci-Tech. Publ. (1989). M. Mizuta, in Physics of DX Centres in GaAs Alloys, (Edited by J.C. Bourgoin), p. 65, SciTech. Publ. (1989).
0038-1098/91 $3.00 + .00 Pergamon Press plc
EVIDENCE FOR NON-EQUILIBRIUM FREE ELECTRON DENSITY IN A1GaAs AT LOW TEMPERATURES* C. Ghezzi Dipartimento di Fisica, Universitfi degli Studi di Parma, Viale delle Scienze, 43100 Parma, Italy and R. Mosca, A. Bosacchi, S. Franchi, E. Gombia and L.E. Vanzetti Istituto MASPEC del Consiglio Nazionale delle Ricerche, Via Chiavari 18/A, 43100 Parma, Italy (Received 10 September 1990 by R. Fieschi)
Due to the strong temperature dependence of the capture rate, the DX centre in AIGaAs is expected to show non-equilibrium occupancy at low temperatures. Results of Thermally Stimulated Capacitance and Capacitance-Voltage measurements, carried out at 77K on Au-AlxGa~_xAs (x = 0.25) Schottky barriers, are strongly influenced by the cooling rate. This demonstrate that in practical experiments the free electron density commonly observed at low temperature is far from thermodynamical equilibrium.
IN RECENT years much attention has been devoted mal equilibrium due to the vanishingly small capture to the main electron trap observed in n-type cross section of the DX centre. This hypothesis is AlxGal_xAs for x > 0.22, the so-called DX centre consistent with capture time data reported by Mooney [1-3]. It is now generally agreed that the DX centre is et al. [11]. In fact the observation of long trapping related to a substitutional donor [5], whose features times actually leaves out that in practical experiments are strongly influenced by the x-dependent structure the DX centre occupancy may reach at low temperaof the conduction band. The electrical conductivity of ture values corresponding to thermal equilibrium. The n-type A1GaAs is strongly affected by the presence of well known persistent photoconductivity (PPC) effect the DX centre. Hall effect measurements carried out itself is evidence for this; however, after the first obseras a function of temperature for different x values vation of PPC in A1GaAs [12], several papers [8, 13[6-8] show a decrease in the Hall carrier concentration 15] dealt with the DX centre assuming an equilibrium as the temperature is decreased. Between 300 K and free electron density at low temperatures. As a matter about 150 K the electron freeze-out to DX centres is of fact, although it has been suggested that low temdescribed by an exponential function of the reciprocal perature data depend on the sample cooling rate [16], temperature, whereas at lower temperatures, the Hall to our knowledge no systematic studies of this effect electron concentration reaches values which are con- have been carried out. stant or only weakly temperature dependent, dependIn this paper we report Thermally Stimulated ing on x. To explain this effect Spring-Thorpe et al. [6] Capacitance (TSCap) and low temperature C-V invoked the onset of impurity band conduction or, measurements carried out upon cooling the sample owing to the high mobility values, the presence of a with different cooling rates. Our results clearly demonbackground shallow donor level. Chand et al. [7] and strate that the low temperature free electron density Schubert and Ploog [8] proposed that the observed depends on the cooling procedure in agreement with saturation orginates from the shallow F- related level the expected absence of thermodynamical equilibrium introduced by the dopant impurity itself. Kunzel et al. in the DX centre occupancy. [9, 10] suggested that the saturation effect can be The Hall free electron density reduction, observed caused by electronic equilibrium lagging behind ther- when cooling AlxGa I xAs (x > 0.22), is commonly attributed to carrier freeze out to the DX centre * This work has been partially supported by the [7-10]. Owing to its thermally activated nature, the Finalized Project of the Consiglio Nazionale delle capture process is described by a time constant tc Ricerche (CNR) "Materials and Devices for Solid which is strongly temperature dependent. For instance, State Electronics". extrapolation of the results reported by Mooney et al. 159
160
N O N - E Q U I L I B R I U M F R E E E L E C T R O N D E N S I T Y IN AIGaAs
[11] suggests that in a x = 0.27 sample, tc should vary from l0 6-10-SS at 300K to about 10tlS at 78K, so that at low temperature the DX centre occupancy can be considered completely quenched. Since the capture time t, increases when the sample temperature decreases, if the time At necessary for the temperature decrease is much larger than the corresponding increase in the capture time Ate, the DX centre occupancy can be considered to be at equilibrium. This is usually the case for high temperature (e.g. 300 K). On the contrary, if At is smaller than Ate, the occupancy factor f is lower than the equilibrium factor f0 and electronic equilibrium lags behind thermal equilibrium. The faster the cooling rate, the higher is the temperature T* at which the difference f-f0 becomes significant and the larger also is the low temperature value of f-f0. Since the electron concentration n is expected to decrease monotonically with increasing f, the presence of non-equilibrium conditions should result in different free electron densities when the sample is cooled with different cooling rates. We have therefore measured the capacitance of Schottky barriers prepared on A1GaAs epitaxial layers by using different cooling procedures. The samples were Si-doped AlxGal_xAs (with x = 0.25) layers grown by MBE on either conducting or semiinsulating substrates. In this paper we refer to a representative sample, consisting of a n ÷ -substrate, a 0.3/~m thick n+-GaAs buffer layer, a 7pm thick n-AIGaAs layer and a 200 A thick undoped GaAs cap that was removed by etching in H2SO4:H202:HzO (40:1 : 1) for 20 s. Ohmic contacts were obtained by alloying indium on the backside of the samples and Schottky barriers were fabricated by evaporating Au dots with a 0.26 mm 2 area. C- V measurements carried out at 77 K (LNT) under saturated PPC conditions show that the uncompensated donor density in the AIGaAs layer is 1.29 x 10iScm -3. To check the dependence of the capacitance at 77 K on the cooling rate, three different cooling procedures (a)-(c) were examined: (a) 77 K attained in 203 min with a nearly constant rate; (b) 77 K attained in 5 min and (c) the sample was directly immersed in liquid nitrogen (LNz). During procedure (c) the temperature could not be accurately measured during the scan: the cooling time from room temperature (RT) to LNT was estimated as 10 s. The sample was always kept in the dark. In order to minimize the contribution to the space charge density due to the DX centres, which near the metal/semiconductor interface are fully positively ionized, we reduced band bending during cooling by keeping the Schottky barrier forward biased (Va = 0.8V). Figure 1 shows the C - T curves obtained during the cooling scan under f o r -
Vol. 78, No. 2
direct Immerelon Into LN 2
(v,:o.8 v)
w
a')
~
~ ~
I~t~"
direct
soc
3
Immerlllon [[
tv.:o v)//
/
z
40C
,;o
,;o
~o Temperature
2~o
I
300
(K)
Fig. 1. TSCap measurements performed with applied voltage Va = 0 V after cooling in (a) 203 min and (b) in 5 min. The curves (a') and (b') refer to the respective cooling scans carried out with Va = 0.8V. The capacitance values as measured at 77 K after direct immersion into LN: are also indicated.
ward bias (a; b') and those obtained during the warm up scan with no applied voltage (a, b). Such curves have been observed to be very reproducible when the cooling scans are repeated. The capacitance values for Va = 0.8V and V~ = 0V as obtained at 7 7 K with procedure (c) are also indicated in Fig. 1. As it can be seen, for temperatures higher than 180 K the C - T curves are not affected by the cooling rate, suggesting an equilibrium occupancy of the D X centre. In contrast, when T < 180 K the capacitance depends on the cooling procedure: faster cooling rates correspond to higher capacitance values measured at 77 K. This is expected since when the cooling rate is increased, the temperature T* at which a given deviation from equilibrium is achieved increases. As a consequence, the fraction of unoccupied DX centres at 77 K becomes higher. In order to obtain quantitative information about the DX centre occupancy at 77K, we used C - V measurements. Double integration of Poisson's equation, carried out under the depletion approximation, gives:
2e(Vbi-k-
FDX -- q[N+x(~) -- N a ] W 2,
V~) =
(1)
where w
Fox
2q I z[U+x(Z) -- N + x ( ~ ) ] d z '
(2)
0
e is the dielectric constant, Vbithe built-in potential, V~ the bias used for the 77 K C - V measurement, Na the
Vol. 78, No. 2
N O N - E Q U I L I B R I U M F R E E E L E C T R O N D E N S I T Y IN A1GaAs
acceptor concentration, Nt~x(z) the ionized D X centre density at a distance z from the contact, Nr~x(oo) is the value of Nr~x(Z) in the asymptotic flat band region and W the width of the space charge region. If the charge state of the DX centre is quenched, the term Fox is independent on V, being only determined by the bias Va applied while cooling and, to a minor extent, by the cooling procedure [16]. Therefore, equation (1) predicts a linear relation between I/C 2 and V,, with slope related to the net ionized DX centre density in the flat band region, namely N~x(OO) - Na. It is worth noting that the bias V~, applied during the cooling, has no effect on the slope, since it influences, through the Fox term, only the value of the apparent built-in voltage as determined by extrapolating to zero the 1/C 2 line. In deriving the above equations we neglected the contribution o f the shallow donors and we assumed that the charge state of the DX centre is neutral when occupied and singly positively charged otherwise. It is straightforward, however, to account for hypothetical shallow donors [18] or to reformulate equations (1) and (2) assuming a negative U character for the D X centre with a singly positive or singly negative charge state, depending on whether the Fermi level is lower or higher than the proper occupancy level for the DX centre [19, 20]. It is therefore possible to quantitatively determine the influence of the cooling procedure on the DX centre occupancy at low temperature. In Fig. 2 we show the 1/C 2 vs V, curves obtained at 77 K following the three cooling procedures (a)-(c). The corresponding free electron densities n are listed in Table 1. With the conventions employed n is equal to N~x(OO) - Na, so that it is evident that in the fiat band region the net ionized DX centre concentration depends on the cooling rate increasing by about 50% when the cooling time is reduced from 203 min to 10sec. This finally demonstrates that the data obtained at low temperature depend on the cooling rate, as a consequence of the thermally activated nature of the capture process. Table 1 . Free electron density n and apparent built-in voltage as determined by fitting the 1/C 2 vs V~ curves shown in Fig. 2. With the convention employed n is equal to N+x(OO) - N, in equations 1-2
Cooling time 203 min 5 min 10s
n
Vr(1/C 2 = 0)
( 10 '7 cm - 3)
(Volt)
2.02 2.45 2.92
0.786 0.827 0.866
161
2
A
~
A B mln o d i r e c t Immersion Into LN 2
j O,B
0
-O,B Vr
-1
-1.8
(V)
Fig. 2. 1/C 2 v s Vr as determined at 77 K after cooling the sample following the three cooling procedures (a)-(c) described in the text. The present results suggest that the Hall electron density saturation observed at low temperature is caused by the lag of electronic equilibrium behind thermal equilibrium. Moreover, the observed dependence on x of the saturation effect [8] seems to be explained by the x dependence of the capture time activation energy E~ [11]. In fact, different Ec values imply that significant deviations from equilibrium occupancy conditions are achieved at different temperatures T*, the lower the capture energy, the lower T*. Along the same lines, a few comments should be made in reference to the dependence on x of the PPC effect. The latter has been observed to be maximum for x = 0.35 [7]. This has been simply explained in terms of ionization energy, which is maximum at x = 0.35, without taking into account the capture time activation energy, which has been shown to be minimum for x = 0.35 [11]. At this AlAs molar fraction, for a given net donor density and a given cooling rate, the low temperature dark electron density should reach its minimum value since both the equilibrium density and the deviations from equilibrium conditions are expected to be minimized. As a consequence, the PPC effect reaches its maximum value: the capture time activation energy is then expected to amplify the x dependence of the PPC effect. As a final comment it is worth noting that at low temperature the electron gas is far from equilibrium only with respect to the DX centre, that is the lowest energy state of the donor atom. On the contrary, it is expected to be in equilibrium with excited states such as the F or X related shallow levels. Experimental evidence for electron freeze-out to these states was in fact recently given by Mizuta [21]. In summary, it has been shown that the DX centre occupancy at low temperature depends on the cooling rate. This is a further experimental demonstration that
162
NON-EQUILIBRIUM FREE ELECTRON DENSITY IN AIGaAs
at low temperatures the DX centre shows a non equilibrium occupancy originated by the thermally activated nature of the capture process.
Acknowledgement - The authors wish to thank Mr P. Allegri for technical assistance in the MBE growth.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
D.V. Lang & R.A. Logan, Phys. Rev. Lett. 39, 6354 (1977). D.V. Lang, R.A. Logan & M. Jaros, Phys. Rev. B19, 1015 (1979). D.V. Lang, in Deep Centres in Semiconductors, (Edited by S.T. Pantelides), p. 489, Gordon and Breach, New York (1986). P.M. Mooney, J. Appl. Phys. 67, RI (1990). M. Mizuta, M. Tachikawa, H. Kukimoto & S. Minomura, Jpn. J. Appl. Phys. 24, L143 (1985). A.J. Spring-Thorpe, F.D. King & A. Becke, J. Electron. Mater. 4, 101 (1975). N. Chand, T. Henderson, J. Klein, W.T. Masselink, R. Fischer, Y. Chang & H. Morkoc, Phys. Rev. B30, 4881 (1984). E.F. Schubert & K. Ploog, Phys. Rev. B30, 7021 (1984).
9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
21.
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