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Phonoconductivity measurements of the electron-phonon interaction in quantum wire structures
surface science ELSEVIER
Surface Science 361/362 (1996) 660-663
Phonoconductivity measurements of the electron-phonon interaction in quantum wire structures A.J. N a y l o r , K . R . S t r i c k l a n d , A.J. K e n t *, M . H e n i n i Departmentof Physics, Universityof Nottinghant NottinghamNG7 2RD, UK Received 19 June 1995; accepted for pubh'cation 2 August 1995
AImraet We have used a phonoconductivity technique to inve~igate the elcctron-phonon interaction in quantum wires. This interaction has important consequences for certain aspects of device behaviour. The 10/an long wire8 were formed in Ga~/A1C_raAs heterojunctions using sprit-gates. Ballistic phonon pulses, with an approximately Plauckian frequency q3ecmxm, were generated by a resistive film heater on the opposite side of the substrate. The interaction of the phonons with the quantum wire was detected via changes in conductance of the device. Oscillations in the phonoconducfivity were obeerved with increasing (negative) gate bias. The~e oscillations were related to the Fermi level position relative to the one-dimensional subband structure which was determined from electrical transport measurements. We give a qualitative explanation of the results in terms of phonon induced inter- and intra- 1D subband electronic transitions leading to changes in the electron temperature which in turn affvct the conductance. From our results we obtain a value for the effective width of the quantum wire.
Keywords: Electrical transport; Electrical transport measurements; Heterojunctions; Semiconductor heterostructures - gated
1. Introduction The carrier-phonon interaction plays an important role in the behaviour of semiconductor devices. For example, the energy relaxation of hot electrons is by the emission of phonons and this determines the effective electron temperature as well as some other properties in the system with hot electrons. The confinement of carriers in lowdimensional semiconductor structures can lead to a modification of the carrier-phonon interaction owing to restrictions in the available momentum space and changes in the energy spectrum of the carriers. Direct phonon experiments are able to * Correspondingauthor.Fax: +44 115 9515180, e-mail:ppzajk~plmLnott.ac.uk.
give more detailed information regarding the carrier-phonon interaction as has been demonstrated in the case of the two-dimensional electron and hole gases, for a review see Ref. El]. As well as giving information concerning the electron-phonon interaction, phonon methods can also be used to study the low-dimensional electronic states. To date there have been no direct phonon experiments on quasi-one dimensional (1D) electron systems. However, a number of theoretical papers have appeared, see for example Refs. [2,3]. It is expected that the electron-phonon interaction is strongly suppressed owing to the reduction of the momentum space to 1D. For example, ff the electrons are confined in a wire of width w, then the maximum allowed perpendicular momentum component of an absorbed or emitted phonon is,
0039-6028/96/$15.00 Copyright O 1996 El~vier Science B.V. All rights reserved PII S0039-6028 ( 9 6 ) 00494-3
A.J. Naylor et ,d/Surface Science361/362 (1996) 660--663
by the uncertainty principle, about ~/w. For w= 20 nm in GaAs this restricts the interaction to very low frequency, £35 Ghz, modes which are not very effective at exchanging energy between the electron system and the lattice. However, it has also been suggested that electron-electron interactions [4] and possibly the effects of disorder may actually enhance the electron-phonon coupling by relaxing this momentum restriction. The phonoconductivity technique has recently been used to probe edge states in the quantum Hall reTme [5] and excitations in the fractional quontum Hall r e , m e [6]. In this paper we describe the first such measurements on quantum wires in GaAs split-gate structures.
2. Experimental details The experimental arrangement is shown in Fig. 1. A quantum wire was formed in an (001)GaAs/AIGaAs heterojunction using the well known split-gate technique [7,8]. The split-gate was defined by electron beam lithography with a length and gap width of 10/an and 0.4/an, respectively. This was above a two-dimensional electron gas (2DEG) of carrier density and mobitity (both after illumination) of 4.4 x l0 ts m -2 and 100 m 2 V - t s-t, respectively. At the ends of the 2DEG MESA structure, ohmic source and drain contacts were fabricated. The gate characteristics of the sample at a temperature of 1.3 K and drain-source bias current, Ie,, of 100 nA are also shown in Fig. 1. At a gate bias, Vo, of about -0.20 V the
661
regions of 2DEG under the gate were depleted leaving a narrow channel beneath the gap, this channel was further narrowed by increasing the negative gate bias and hence the resistance increased. A distinct kink at RDs ~ 12.9 kl2 is seen at Vo ~ - 1.6 V, indicating that at this bias the channel width and carrier density were such that only one 1D subband was occupied. On the other polished side of the 0.38 mm semiinsulating GaAs wafer, directly opposite the channel was deposited a 100 x 10/an CuNi heater to be used as the phonon source. It was oriented using infrared front-to-back alignment with its long axis perpendicular to the length of the channel. The heater had an impedance of 50 ~ to match the transmission line from the pulse generator. Fig. 2 shows an example of the phonoconductivity signal detected by the device. The heater was excited by a pulse of 1 V amplitude and duration 50 us, and the device parameters were: V o = - 0 . 5 V and I m = 100 hA. The onset of the signal was delayed from the start of the exciting pulse by 120 ns which corresponds to the time of flight for transverse (TA) phonons across the wafer, and is characterised by a rapid rise time, approximately equal to the duration of the heat pulse, followed by a long decay given by the R C time constant of the device and the co-axial cable between the device and the pre, amplifier.
3. Results and discussion Fig. 3 shows the intensity of the phonon signal as a function of the gate bias for two different w
Rvs / k n 20
~V°
hi-Z pre-amp
o
P7
t
-.75 -.5 -.25
0
0.5
1.0
1.5
2.0
GaAs ~ b ~ e Fig 1. The experimentalgeometry,the DC gate characteristics of the deviceare shownin the inset.
Fig 2. Temporal response of the quantum wire to a pulse of non-equilibrium phonotm,the start time of the 50 ns pulse is indicated.
662
A.J. Naylor et H/Surface Science 361/362 (1996) 660-663
," 100
-0.7
-0.6
-0.5
-0.4
zo / v Fig. 3. Boxcar sweep of the phonoconducfivityas a function of the gate bias at heater powers of 20 mW (Th~14 K) and 3~2 mW (The9 K). The position of the intersubband peak is indicated by the vertical arrow. Also shown is the dependence of the deviceconductance on gate bias. heater pulse amplitudes. Also shown in Fig. 3 is the device conductance. The effect of the phonon pulse is to cause a transient increase in the conductance of the channel. The intensity oscillates, with peaks occurring when the Fermi energy, EF, is coincident with the bottom of any 1D band as deduced from the conductance data. At the higher heater power a further peak is deafly seen when EF is in between the bottom of the second and third subbands. This peak becomes dominant at much higher heater power. In the discussion that follows, we make the prior assumption that the electrons in the 1D system are in equilibrium and that we can assign an effective electron temperature, T,. This assumption is commonly used in the ease of 2D and. 3D electron systems. However, we note that it has been suggested that suppression of the electron-electron scattering in quantum wires may, under certain circumstances, lead to the breakdown of thlg assumption I-9]. We postulate that the signals are due to changes in TObrought about by p h o n o n absorption. Steady state measurements of the device conductance as a function of temperature between 1.3 and 4.2 K show the conductance weakly increasing with increasing temperature over the complete range of gate bias. This is consistent with the polarity of the p h o n o n signal. Two possible reasons for this temperature dependence are w e a k loeatisation phenomena and the energy dependence of remote
ionised impurity scattering. In either case the conductance depends only on the electron temperature, and so it seems reasonable to use the conductance as a thermometer to measure TO Taking account of the R C time constant of the system, we can estimate from the size of the phonon signal that To increases by about 2.5 K for a heater power of 3.2 mW. This appears to be quite a large temperature increase, however, it is less than 6.3 K which would be expected if the quantum wire could be treated as a "black body" absorber of phonons. It is also much greater than the increase in substrate temperature caused by thermalisation of the heat pulse which we estimate to be of the order of a few m K (the sample is suspended in liquid helium). We now consider the oscillations in the signal intensity. With the chosen heater geometry the phonons have little momentum component along the length of the quantum wire. This means that the in-line waveveetors, k~ and /q', of the initial and final electron states, respectively, must be close together, see Fig. 4. The low energy phonon absorption will therefore follow the density of states (DOS) at the Fermi energy with strong peaks at the band e d g e . on the other hand, phonon emission processes have no such momentum restriction and, although still dependent on the DoS, the emission will not be as strongly peaked
n=12
-4
3
E
0
+&
Fig. 4. Rloctronenergyband diagram for a quantum wire,intraband (a) and interband (b) phonon absorbing transitions are shown. Transitions involving a large change in k~ (c) are not allowed in our geometry bocausv the phonom have an inmdfcient momentum component along the length of the wire.
A.J. Naylor et al./Surface Science 361/362 (1996) 660-663
as the absorption profile. The balance of these two processes determines the effective electron temperature and so we expect the latter to peak when EF is close to the band edge. The number of available channels for phonon emission due to intersubband transitions decreases as the number of occupied subbands reduces, hence the peaks get stronger. At higher heater temperatures a second phonon absorption process involving near vertical intersubband transitions becomes possible. The probability of such transitions will be a maximum when EF is mid-way between the minima of the lower (filled) and higher (empty) bands. This we believe is the origin of the additional peak occurring when EF is betwoon the 2 nd and 3~d 1D subbands. If the signal is due to interband transitions involving phonons in a narrow range of frequencies, then, following the method used in Ref. [6], we should be able to estimate the subband separation, zt, by measuring the signal as a function of the heater temperature, Th, which is determined by the power supplied to the heater. The signal size is dependent on the number of phonens in the heater spectrum of energy zt, which is proportional to {exp(zt/kTh)-l} -x. By fitting this function to a plot of the signal intensity as a function of Th, we obtain, A=2.7 meV. If we assume a parabolic confining potential this gives an effective channel width of about 20rim at Vo= - 0 . 5 7 V. This result is in good agreement with magnetotransport measurements which give a width of 25 nm at about the same value of gate bias. The interband signal is much weaker for Er between the 1't and 2~ subbands. This is most probably due to the channel narrowing at increased negative gate bias, leading to a larger intersubband energy separation, coupled with the exponential dependence of the signal on the ratio AITh.
4. Conclusions We have presented the first direct phonon measurements of the electron-phonon interactions in a
663
quantum wire using the phonoconductivity technique. We see evidence for phonon induced intrasubband electronic transitions, for which the strength of the phonon absorption follows the density of states at Er. We can also identify near vertical, Akx ~,0, intersubband processes and have made a phonon-spectroscopic measurement of the intersubband energy gap. A qualitative description of the results has been given using as its basis a simple electron temperature model. Further study is required to determine whether this de~'ipfion is appropriate or if a non-equilibrium description of the electron system should be used instead.
Acknowledgements The authors would like to thank Dr M. Blencowe and Prof A. Shik for valuable discussions relating to the theoretical interpretation of our results. The U K Central Microstructure Facility at DRAL for providing e-beam lithography facilities. We would also like to thank EPSRC for support of the NUMBERS programme of wh/ch this project is a part.
References [1] L3. Ch~lli~ and A.J. Kent, in" Physics of Phonons, Eds. T. Paszkiewicz and IC Rapoewicz (Plenum, New York, 1994) p. 159. [2] R. Mickevi~us and C. Milin, Phys. Rev. B 48 (1993) 17194. [3] B. Kramer, T. Brandes, W. HAusler, K. Jauregui, W. Plaff and D. Weinmann, Semicond. SoL TechnoL 9 (1994) 1871. [4] J.1L Senna and S. Dos Sarma, Phys. Rev. Lett. 70 (1993) 2593. [5] DJ. McKitterick, A. Shik, A.J. Kent and M. Henini, Phys. Rev. B 49 (1994) 2585. [6] CJ. MeUor, R.H. Eyles, J.E. Digby, A.J. Kent, K.A. Benedict, LJ. Challis, M. Henini and C.T. Foxon, Phy& Rev. Lett. 74 (1995) 2339. [7] TJ. Thornton, M. Pepper, I-L Ahmed, D. Andrews and G.L Davies, Phys. Rev. Lett. 56 (1986) 1198. [8] I-LZ. Zhang, H.P. Wei, D.C. Tsui and G. Weimann, Phys. Rev. B 34 (1986) 5635. [9] J.P. Leburton, S. Briggs and J. Jovanovic, Superlatt. and Microstz. 8 (1990) 209.
Surface Science 361/362 (1996) 660-663
Phonoconductivity measurements of the electron-phonon interaction in quantum wire structures A.J. N a y l o r , K . R . S t r i c k l a n d , A.J. K e n t *, M . H e n i n i Departmentof Physics, Universityof Nottinghant NottinghamNG7 2RD, UK Received 19 June 1995; accepted for pubh'cation 2 August 1995
AImraet We have used a phonoconductivity technique to inve~igate the elcctron-phonon interaction in quantum wires. This interaction has important consequences for certain aspects of device behaviour. The 10/an long wire8 were formed in Ga~/A1C_raAs heterojunctions using sprit-gates. Ballistic phonon pulses, with an approximately Plauckian frequency q3ecmxm, were generated by a resistive film heater on the opposite side of the substrate. The interaction of the phonons with the quantum wire was detected via changes in conductance of the device. Oscillations in the phonoconducfivity were obeerved with increasing (negative) gate bias. The~e oscillations were related to the Fermi level position relative to the one-dimensional subband structure which was determined from electrical transport measurements. We give a qualitative explanation of the results in terms of phonon induced inter- and intra- 1D subband electronic transitions leading to changes in the electron temperature which in turn affvct the conductance. From our results we obtain a value for the effective width of the quantum wire.
Keywords: Electrical transport; Electrical transport measurements; Heterojunctions; Semiconductor heterostructures - gated
1. Introduction The carrier-phonon interaction plays an important role in the behaviour of semiconductor devices. For example, the energy relaxation of hot electrons is by the emission of phonons and this determines the effective electron temperature as well as some other properties in the system with hot electrons. The confinement of carriers in lowdimensional semiconductor structures can lead to a modification of the carrier-phonon interaction owing to restrictions in the available momentum space and changes in the energy spectrum of the carriers. Direct phonon experiments are able to * Correspondingauthor.Fax: +44 115 9515180, e-mail:ppzajk~plmLnott.ac.uk.
give more detailed information regarding the carrier-phonon interaction as has been demonstrated in the case of the two-dimensional electron and hole gases, for a review see Ref. El]. As well as giving information concerning the electron-phonon interaction, phonon methods can also be used to study the low-dimensional electronic states. To date there have been no direct phonon experiments on quasi-one dimensional (1D) electron systems. However, a number of theoretical papers have appeared, see for example Refs. [2,3]. It is expected that the electron-phonon interaction is strongly suppressed owing to the reduction of the momentum space to 1D. For example, ff the electrons are confined in a wire of width w, then the maximum allowed perpendicular momentum component of an absorbed or emitted phonon is,
0039-6028/96/$15.00 Copyright O 1996 El~vier Science B.V. All rights reserved PII S0039-6028 ( 9 6 ) 00494-3
A.J. Naylor et ,d/Surface Science361/362 (1996) 660--663
by the uncertainty principle, about ~/w. For w= 20 nm in GaAs this restricts the interaction to very low frequency, £35 Ghz, modes which are not very effective at exchanging energy between the electron system and the lattice. However, it has also been suggested that electron-electron interactions [4] and possibly the effects of disorder may actually enhance the electron-phonon coupling by relaxing this momentum restriction. The phonoconductivity technique has recently been used to probe edge states in the quantum Hall reTme [5] and excitations in the fractional quontum Hall r e , m e [6]. In this paper we describe the first such measurements on quantum wires in GaAs split-gate structures.
2. Experimental details The experimental arrangement is shown in Fig. 1. A quantum wire was formed in an (001)GaAs/AIGaAs heterojunction using the well known split-gate technique [7,8]. The split-gate was defined by electron beam lithography with a length and gap width of 10/an and 0.4/an, respectively. This was above a two-dimensional electron gas (2DEG) of carrier density and mobitity (both after illumination) of 4.4 x l0 ts m -2 and 100 m 2 V - t s-t, respectively. At the ends of the 2DEG MESA structure, ohmic source and drain contacts were fabricated. The gate characteristics of the sample at a temperature of 1.3 K and drain-source bias current, Ie,, of 100 nA are also shown in Fig. 1. At a gate bias, Vo, of about -0.20 V the
661
regions of 2DEG under the gate were depleted leaving a narrow channel beneath the gap, this channel was further narrowed by increasing the negative gate bias and hence the resistance increased. A distinct kink at RDs ~ 12.9 kl2 is seen at Vo ~ - 1.6 V, indicating that at this bias the channel width and carrier density were such that only one 1D subband was occupied. On the other polished side of the 0.38 mm semiinsulating GaAs wafer, directly opposite the channel was deposited a 100 x 10/an CuNi heater to be used as the phonon source. It was oriented using infrared front-to-back alignment with its long axis perpendicular to the length of the channel. The heater had an impedance of 50 ~ to match the transmission line from the pulse generator. Fig. 2 shows an example of the phonoconductivity signal detected by the device. The heater was excited by a pulse of 1 V amplitude and duration 50 us, and the device parameters were: V o = - 0 . 5 V and I m = 100 hA. The onset of the signal was delayed from the start of the exciting pulse by 120 ns which corresponds to the time of flight for transverse (TA) phonons across the wafer, and is characterised by a rapid rise time, approximately equal to the duration of the heat pulse, followed by a long decay given by the R C time constant of the device and the co-axial cable between the device and the pre, amplifier.
3. Results and discussion Fig. 3 shows the intensity of the phonon signal as a function of the gate bias for two different w
Rvs / k n 20
~V°
hi-Z pre-amp
o
P7
t
-.75 -.5 -.25
0
0.5
1.0
1.5
2.0
GaAs ~ b ~ e Fig 1. The experimentalgeometry,the DC gate characteristics of the deviceare shownin the inset.
Fig 2. Temporal response of the quantum wire to a pulse of non-equilibrium phonotm,the start time of the 50 ns pulse is indicated.
662
A.J. Naylor et H/Surface Science 361/362 (1996) 660-663
," 100
-0.7
-0.6
-0.5
-0.4
zo / v Fig. 3. Boxcar sweep of the phonoconducfivityas a function of the gate bias at heater powers of 20 mW (Th~14 K) and 3~2 mW (The9 K). The position of the intersubband peak is indicated by the vertical arrow. Also shown is the dependence of the deviceconductance on gate bias. heater pulse amplitudes. Also shown in Fig. 3 is the device conductance. The effect of the phonon pulse is to cause a transient increase in the conductance of the channel. The intensity oscillates, with peaks occurring when the Fermi energy, EF, is coincident with the bottom of any 1D band as deduced from the conductance data. At the higher heater power a further peak is deafly seen when EF is in between the bottom of the second and third subbands. This peak becomes dominant at much higher heater power. In the discussion that follows, we make the prior assumption that the electrons in the 1D system are in equilibrium and that we can assign an effective electron temperature, T,. This assumption is commonly used in the ease of 2D and. 3D electron systems. However, we note that it has been suggested that suppression of the electron-electron scattering in quantum wires may, under certain circumstances, lead to the breakdown of thlg assumption I-9]. We postulate that the signals are due to changes in TObrought about by p h o n o n absorption. Steady state measurements of the device conductance as a function of temperature between 1.3 and 4.2 K show the conductance weakly increasing with increasing temperature over the complete range of gate bias. This is consistent with the polarity of the p h o n o n signal. Two possible reasons for this temperature dependence are w e a k loeatisation phenomena and the energy dependence of remote
ionised impurity scattering. In either case the conductance depends only on the electron temperature, and so it seems reasonable to use the conductance as a thermometer to measure TO Taking account of the R C time constant of the system, we can estimate from the size of the phonon signal that To increases by about 2.5 K for a heater power of 3.2 mW. This appears to be quite a large temperature increase, however, it is less than 6.3 K which would be expected if the quantum wire could be treated as a "black body" absorber of phonons. It is also much greater than the increase in substrate temperature caused by thermalisation of the heat pulse which we estimate to be of the order of a few m K (the sample is suspended in liquid helium). We now consider the oscillations in the signal intensity. With the chosen heater geometry the phonons have little momentum component along the length of the quantum wire. This means that the in-line waveveetors, k~ and /q', of the initial and final electron states, respectively, must be close together, see Fig. 4. The low energy phonon absorption will therefore follow the density of states (DOS) at the Fermi energy with strong peaks at the band e d g e . on the other hand, phonon emission processes have no such momentum restriction and, although still dependent on the DoS, the emission will not be as strongly peaked
n=12
-4
3
E
0
+&
Fig. 4. Rloctronenergyband diagram for a quantum wire,intraband (a) and interband (b) phonon absorbing transitions are shown. Transitions involving a large change in k~ (c) are not allowed in our geometry bocausv the phonom have an inmdfcient momentum component along the length of the wire.
A.J. Naylor et al./Surface Science 361/362 (1996) 660-663
as the absorption profile. The balance of these two processes determines the effective electron temperature and so we expect the latter to peak when EF is close to the band edge. The number of available channels for phonon emission due to intersubband transitions decreases as the number of occupied subbands reduces, hence the peaks get stronger. At higher heater temperatures a second phonon absorption process involving near vertical intersubband transitions becomes possible. The probability of such transitions will be a maximum when EF is mid-way between the minima of the lower (filled) and higher (empty) bands. This we believe is the origin of the additional peak occurring when EF is betwoon the 2 nd and 3~d 1D subbands. If the signal is due to interband transitions involving phonons in a narrow range of frequencies, then, following the method used in Ref. [6], we should be able to estimate the subband separation, zt, by measuring the signal as a function of the heater temperature, Th, which is determined by the power supplied to the heater. The signal size is dependent on the number of phonens in the heater spectrum of energy zt, which is proportional to {exp(zt/kTh)-l} -x. By fitting this function to a plot of the signal intensity as a function of Th, we obtain, A=2.7 meV. If we assume a parabolic confining potential this gives an effective channel width of about 20rim at Vo= - 0 . 5 7 V. This result is in good agreement with magnetotransport measurements which give a width of 25 nm at about the same value of gate bias. The interband signal is much weaker for Er between the 1't and 2~ subbands. This is most probably due to the channel narrowing at increased negative gate bias, leading to a larger intersubband energy separation, coupled with the exponential dependence of the signal on the ratio AITh.
4. Conclusions We have presented the first direct phonon measurements of the electron-phonon interactions in a
663
quantum wire using the phonoconductivity technique. We see evidence for phonon induced intrasubband electronic transitions, for which the strength of the phonon absorption follows the density of states at Er. We can also identify near vertical, Akx ~,0, intersubband processes and have made a phonon-spectroscopic measurement of the intersubband energy gap. A qualitative description of the results has been given using as its basis a simple electron temperature model. Further study is required to determine whether this de~'ipfion is appropriate or if a non-equilibrium description of the electron system should be used instead.
Acknowledgements The authors would like to thank Dr M. Blencowe and Prof A. Shik for valuable discussions relating to the theoretical interpretation of our results. The U K Central Microstructure Facility at DRAL for providing e-beam lithography facilities. We would also like to thank EPSRC for support of the NUMBERS programme of wh/ch this project is a part.
References [1] L3. Ch~lli~ and A.J. Kent, in" Physics of Phonons, Eds. T. Paszkiewicz and IC Rapoewicz (Plenum, New York, 1994) p. 159. [2] R. Mickevi~us and C. Milin, Phys. Rev. B 48 (1993) 17194. [3] B. Kramer, T. Brandes, W. HAusler, K. Jauregui, W. Plaff and D. Weinmann, Semicond. SoL TechnoL 9 (1994) 1871. [4] J.1L Senna and S. Dos Sarma, Phys. Rev. Lett. 70 (1993) 2593. [5] DJ. McKitterick, A. Shik, A.J. Kent and M. Henini, Phys. Rev. B 49 (1994) 2585. [6] CJ. MeUor, R.H. Eyles, J.E. Digby, A.J. Kent, K.A. Benedict, LJ. Challis, M. Henini and C.T. Foxon, Phy& Rev. Lett. 74 (1995) 2339. [7] TJ. Thornton, M. Pepper, I-L Ahmed, D. Andrews and G.L Davies, Phys. Rev. Lett. 56 (1986) 1198. [8] I-LZ. Zhang, H.P. Wei, D.C. Tsui and G. Weimann, Phys. Rev. B 34 (1986) 5635. [9] J.P. Leburton, S. Briggs and J. Jovanovic, Superlatt. and Microstz. 8 (1990) 209.