- Email: [email protected]
AlAs double barrier diodes
~
Solid-State Electronics Vol. 37, Nos 4-6, pp. 973-976. 1994 Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1101/94 $6.00+0.00
Pergamon
PHOTOHOLE-INDUCED RESONANT TUNNELING OF ELECTRONS IN SELECTIVELY ETCHED SMALL AREA GaAs/A1As DOUBLE BARRIER DIODES H. BUHMANN,J. WANG, L. MANSOURI,P. H. BETON,L. EAVES, M. HEATHand M. HENINI Department of Physics, University of Nottingham, Nottingham NG7 2RD, England Abstract--The influence of light on the low temperature 1 ( V) characteristics of selectivelyetched small area resonant tunneling diodes (RTD) has been investigated. These diodes have physical dimensions down to 0.5/am and their design allows easy optical access. Under illumination new subthreshold peaks appear in I (V). These peaks are also observed in large area diodes, and are found to be strongly influenced by applying a magnetic field either parallel or perpendicular to the plane of the barriers. We show that our results cannot be explained in terms of resonant tunneling of photo-excited holes and propose an explanation based on the Coulombic electron-hole interaction.
Resonant tunneling diodes (RTDs) are an attractive system for the study of quantum transport since the strong non-linearities observed in their current voltage characteristics, I(V), are a direct consequence of the confinement of carriers within a quantum well[l]. The incorporation of donors within the quantum well (QW) of an RTD leads to the formation of laterally bound hydrogenic-like states which are localized within the plane of the QW. These bound states are lower in energy than the QW continuum and provide an additional channel for resonant tunneling, which in turn leads to additional non-linearities in 1 (V)[2,3]. Resonant tunneling therefore provides a means of detecting the presence of any low energy states which are formed within the QW. In this paper we describe a series of experiments in which we investigate the possibility of using RTDs to probe the presence of holes in the QW. The holes are introduced by photo-excitation and give rise to sub-threshold peaks in I(V). We argue that these peaks are a close analogue of the peaks generated by the presence of donors. Our experiments are conducted on both large (100-400/lm square) mesas and also a range of small area diodes with dimensions down to 0.5/~m. An important element of our work is the development of a fabrication process for a sub-micron RTD which is suitable for optical access. This process is based on optical lithography and wet etching and does not require the use of either dry etching (a possible source of damage) or dielectric layers (which might impair the optical access of the devices) for isolation of bonding pads and metallic tracks. The devices were fabricated from a GaAs/AIAs double-barrier heterostructure grown on a semi-insulating (100) GaAs substrate, using molecular beam epitaxy (MBE). The layer composition of the beterostructure is given in Table I.
To fabricate the small area diodes the GaAs (top contact) layer is selectively etched using NH4OH/H:O2, (5:95), to form a narrow line with a width in the range of 0.5-3/~m. The line is formed between large ohmic contacts (~100/~m x ~ 100/~m). Note that optical lithography is used for pattern definition, so that significant undercut etching is required to achieve sub-micron dimensions. A second (non-selective) etch was used to penetrate the AlAs harriers and reveal the lower GaAs doped (bottom contact) layer. Finally, this buried n-type GaAs layer was also selectively etched to form a freestanding GaAs bridge in t~e. emitter layer. Au/Ge/Ni ohmic contacts were then deposited on the top and bottom contact doped layers. A schematic representation of the final device is shown in Fig. !. Note that the metallised region on the top contact is connected to the active region of the device by the freestanding GaAs bridge. This serves to isolate the bottom contact from the doped region beneath the top contact eliminating any possible parallel conduction path, This novel fabrication route produces small area diodes with low contact resistance which can be easily illuminated. The dimensions of the small area devices discussed below are: I ~ 0.5 x 60#m, II ~ 1.0 x 60/~m and Ill ,,, 3.0 x 60/~m. We have also investigated large area control devices with metal contacts which are sufficiently small for light to penetrate the device. The low temperature current-voltage characteristics (T =4.2 K), I(V), for device I, II and III are shown in Fig. 2(a)). For all measurements the convention of positive bias implies a positive potential applied to the top contact. Comparing the I ( V ) of the small area and large area devices (inset Fig. 2(a)), no significant difference is observed, except for the smallest device (I). The main electron peak positions remain approximately the same, and a small asymme-
973
H. BUHMANNet al.
974
T a b l e I. Sample structure. Growth-direction from bottom to top. T he donor is Si and the M B E growth temperature was 550 C 100.0nm 80.6 nm 50.9 nm 20.4 nm 5.9 nm
GaAs GaAs GaAs GaAs
n = 2 x 10 ~ n = 2 x l0 tn = 2 x 10 ~b
top contact 0
spacer
AlAs
barrier
9.1 nm
GaAs
well
5.9 nm
AlAs
barrier
20.4 nm 50.9 nm 80.6 nm 200.0 nm 7.6 nm
GaAs GaAs GaAs GaAs AlAs
1000.0 nm
GaAs
~
spacer n = 2 x 1016 n = 2 x 10 ~7 n = 2 x 10 ts
-04
0
04
.-------~-=Jll
~
-20
-40
bottom contact etch stop
semi*insulating
Substrate
5 try in the bias region beyond the main resonance is common to all devices. The I ( V ) for the smallest diode, device I, shows a broadening of the main electron resonance together with a shift to higher voltage in forward bias, while in negative bias it exhibits no obvious changes. A similar asymmetry has been observed in gated resonant tunneling devices[4], when the active tunnel area is progressively decreased with increased gatevoltage. This has been explained in terms of the shape of the equipotential close to the tunnel barriers. We may estimate the side wall depletion, d,, in the small area diodes from the value of the peak current, I~,k, of the main resonance from the relation: l~ak =j~,k(l~--ds)lb, where J~ak is the peak current density and l, and lb are defined in Fig. 1. From the values of I ~ k for devices I, II and III we find j ~ k = 0 . 1 7 n A p m -2 and d~=0.4pm. This is in good agreement with the peak current density measured for the corresponding large area d e v i c e s , Jpeak.large = 0.18 nA #m -2. The devices were illuminated in a flow cryostat via an optical fibre. Under constant illumination (PL ~< 100/Z W cm -2) with 670 nm wavelength laser
free standing /x/°hmic t'~ GoAsbridge,,, ~/~.'~onlocts top contact [//~ "~
/bottom contact /A
S
S.I. barriers
Fig. 1. Schematic picture of the small area device.
0
--
11
-5 -10
-0.4
0
V/Volt
0.4
Fig. 2. (a) I(V) characteristics of device I, Ii and III in darkness. Inset: I(V) of a large area devices, 400 × 400/am. (b) I(V) characteristic of device II under illumination, 1: O~W/cm2, 2:1 ~W/cm' and 3:3 ~W/cm2.
light, changes in I (V) are observed. In Fig. 2(b) I (V) for device II is plotted for various levels of illumination. The features which are observed for device II are typical of all devices. The main electron resonance peak position and threshold value shift to lower voltage and n e w resonances (arrowed in Fig. 2(b)) occur below the threshold voltage for the main resonance. The strength of these additional resonances increases with excitation power. In addition to the appearance of these features we also observe an increase in the peak and valley currents of the main resonance with increased illumination. The valley current is greatly enhanced in forward bias. To understand the effects of illumination we refer to the band profiles of the device shown in Fig. 3. The incident light creates electron-hole pairs in the depletion region beyond the collector barrier. The photo-created electrons (majority carriers) are swept into the doped collector region, but the photo-created holes (minority carriers) drift up towards the collector barrier where they form an accumulation layer. This process has been discussed previously in the context of photoluminescence experiments on resonant tunneling diodes[5-7]. The presence of the photo-created holes close to the collector barrier modifies the band bending in the device and accounts for the shift of the threshold and peak of the main resonance to lower voltage. Similar effects have previously been observed in the I ( V ) of large area resonant tunneling diodes under illumination[6,7]
Photohole-induced resonant tunneling of electrons which were attributed to resonant tunneling of photocreated holes. In the remainder of this paper we discuss the dependence of the photo-induced peaks on magnetic field. Our discussion of the magnetic field dependence refers to I (V) for large area diodes, since for these devices we have a more complete set of data, and can make a direct comparison with previous work[6,7]. Figure 4(a) shows I ( V ) up to the threshold voltage for the main resonance for a 400#m square device illuminated with an excitation power PL ~< 10 mW/cm 2 in the presence of a magnetic field B between 0 and 10 T oriented perpendicular to the plane of the barriers. For B = 0 (lowest curve) we observe a sub-threshold resonance in each bias direction at V ~ - l l 0 m V and V ~ I 2 0 m V (peaks marked D in Fig. 4(a)). For B < 4 T this peak remains unaffected by magnetic field, however as B is progressively increased it shifts to larger voltage and its amplitude is reduced. For B > 3 T several more peaks appear which occur at even lower voltage. These are labelled A, B and C on Fig. 4(a). The peaks show a fair degree of symmetry between bias directions, although their amplitude is higher in forward bias (because of an effective difference in the light intensity incident on the depletion region in forward and reverse due to absorption effects). The voltage positions of peaks A, B and C are only weakly dependent on magnetic field, however their amplitude is a strong function of field. At the highest magnetic fields peaks A and B split into two peaks. I(V) for the same diode under illumination in the presence of a magnetic field oriented parallel to the
eaAs
.
.
I
GoAs
/ ' , 4
electron accumulation layer
L \
photoexcited electronhole-pairs
~
oct
1 accumulation layer Fig. 3. Schematic band profile of the device.
20
cl
16
975
"1
A
B
lOT
<= 12 8 4
(a)
0
12
I
B1
11T
0
BI
1
....~
YI ~
-o.1
o V/Volt
o.1
Fig. 4. I(V) characteristics for a 400/am square mesa in (a) perpendicular and (b) in parallel magnetic field configuration. barrier is shown in Fig. 4(b). Note that for our experimental arrangement illumination power is lower than for the perpendicular case and the corresponding photo-induced peaks have smaller amplitude than the data in Fig. 4(a). For B = 0 T we observe two sub-threshold peaks as in Fig. 4(a) (peaks marked D), however as B is increased beyond 3 T another peak appears (peak B). As the magnetic field is increased peak D moves to higher voltage, and a weak splitting is observed. The behaviour of the peak in I(V) corresponding to the main resonance displays quite different behaviour for parallel and perpendicular oriented fields. For a perpendicular field its voltage position and amplitude are only weakly dependent on field, however for a parallel field the threshold moves to higher voltage. Note that peak D in the parallel field moves to a higher voltage at a similar rate to the threshold for the main electron resonance. Thus our data show a series of photo-induced peaks whose amplitude and voltage position are extremely sensitive to magnetic field. We first consider whether the dependence of their amplitude and voltage position on magnetic field is consistent with conventional resonant tunneling of photo-created holes. We focus on peak D since this peak is observed even for B = 0 T. Previous work on p-i-p resonant tunneling diodes[8] shows that the voltage position of the lowest two hole resonances referred to as hhl and lhl (corresponding to resonant tunneling via the
976
H. BUHMANNet al.
lowest heavy and light hole subbands respectively) is almost independent of magnetic field for B < 11 T. Clearly peak D cannot be due to hole resonant tunneling via the hh I or lhl subbands since its voltage position is shifted by a parallel field. Hayden et al. found that the lowest hole subband resonance which has a strong parallel field dependence of its voltage position is hh2, the first excited state heavy hole state. However, firm identification of peak D as the hh2 resonance is not possible, since in that case we would expect to observe a peak in I ( V ) of comparable amplitude at lower voltage corresponding to the lhl resonance as observed by Hayden et al. In addition we have calculated the expected peak positions for electron and hole resonances using a simple model for the band bending of the device which uses the F a n g - H o w a r d wavefunction to model the state in the electron accumulation layer and treats the state in the hole accumulation layer as an Airy function. This model predicts that the hh2 resonance should occur at a higher voltage than the electron resonance. We also note that in similar p - i - n resonant tunneling diodes the hh2 peak always occurs at higher voltage than the lowest electron resonance[9]. Another result established in the study of p - i - p resonant tunneling diodes is that the amplitude and voltage position of the peaks in I ( V ) due to hole resonances are insensitive to the presence of perpendicular magnetic fields for B < 10 T. Certainly nothing comparable with the dramatic magnetic field enhancement of peaks A, B and C in Fig. 4(a) has been observed for p - i - p devices. We are thus unable to account either qualitatively or quantitatively for our data in terms of conventional resonant tunneling of photo-excited holes. We have also investigated these effects in several other wafers which differ from the heterostructure shown in Table 1 only in the thickness of the AlAs tunnel barriers. For barrier widths of 4.5 and 3.0 nm we do not observe such clear additional peaks under illumination, but see a step like behaviour at lower voltage which is highly reminiscent of the data shown in Ref.[7]. For barrier widths 5.9 and 7.5 nm we observe structure similar to that in Fig. 4. Note that the peak current density for our devices, Jp~,k, is two orders of magnitude smaller than that for the material used by Vodjdani et al.[7]. This dependence of the peaks on barrier width clearly complicates the comparison of our data with that previously reported. We have stressed above that our data cannot be explained solely in terms of resonant tunneling of photo-excited holes. Our alternative explanation is that the presence of a hole in the quantum well gives rise to an alternative resonant conduction path which is lower in energy than the quantum well continuum
due to the C o u l o m b interaction of the electron and hole, i.e. tunneling of electrons via an excitonic state. Similar peaks have been observed in I ( V ) for devices in which ionized donors are introduced into the quantum well. The threshold for peak D is approx. 30 mV below that of the main resonance. According to our band bending calculations this corresponds to an energy below the continuum of ~ 5.5 meV. This should be compared with the binding energy of ~ 7 meV for a light hole exciton and ~ 9 meV for a heavy hole exciton. Associating peak D with an excitonic transition is at least consistent with its shift to higher voltage in parallel field. However our model is so far unable to explain the appearance of the lower voltage peaks A, B and C with increasing magnetic field. In conclusion we have observed a series of peaks which appear when a resonant tunneling diode is illuminated. The dependence of these peaks on magnetic field is not consistent with resonant tunneling of holes. We have proposed an alternative explanation based on resonant tunneling via hole-induced excitonic states in the well. Further work, in particular photoluminescence studies, are required to clarify the detailed origin of these peaks. Acknowledgements--Funding for this work was provided in part by ESPRIT Basic Research Grant 7193 PARTNERS and in part by the U.K. Science and Engineering Research Council. REFERENCES
1. L. L. Chang, L. Esaki and R. Tsui, Appl. Phys. Lett. 24, 593 (1974). 2. M. W. Dellow, P. H. Beton, C. J. G. M. Langerak, T. J. Foster, P. C. Main, L. Eaves, M. Henini, S. P. Beaumont and C. D. Wilkinson, Phys. Rev. Lett. 64, 1754 (1992). 3. J. W. Sakai, T. M. Fromhold, P. H. Beton, M. Henini, U Eaves, P. C. Main, F. W. Sheard and G. Hill, Phys. Rev. B 48, 5664 (1993), 4. P. H. Beton, M. W. Dellow, P. C. Main, T. J. Foster, L. Eaves, A. F. Jezierski and M. Henini, AppL Phys. Lett. 60, 2508 (1992). 5. J. F. Young, B. M. Wood, G. C. Aers, R. L. S. Devine, H. C. Liu, D. Landheer, M. Buchanan, A. J. Spring Thorpe and P. Mandeville, Phys. Ret,. Lett. 60, 2085 (1988). 6. C. R. H. White, M. S. Skolnick, L. Eaves, M. L. Leadbeater, M. Henini, O. H. Hughes, G. Hill and M. A. Pate, Phys. Rev. B 45, 6721 (1992). 7. N. Vodjdani, D. C6te, D. Thomas, B. Sermenge, P. Bois, E. Costard and J. Nagle, Appl. Phys. Left. 56, 33 (1989). 8. R. K. Hayden, D. K. Maude, L. Eaves, E. C. Valadares, M. Henini, F. W. Sheard, O. H. Hughes, J. C. Portal and L. Cury, Phys. Rev. Lett. 66, 1749 (1991); R. K. Hayden, thesis, Univ. of Nottingham, 1992. 9. P. M. Martin, R. K. Hayden, C. R. H. White, M. Henini, L. Eaves, D. K. Maude, J. C. Portal, G. Hill and M. A. Pate, Semicond. Sci. Technol. 7, 456 (1992).
Solid-State Electronics Vol. 37, Nos 4-6, pp. 973-976. 1994 Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1101/94 $6.00+0.00
Pergamon
PHOTOHOLE-INDUCED RESONANT TUNNELING OF ELECTRONS IN SELECTIVELY ETCHED SMALL AREA GaAs/A1As DOUBLE BARRIER DIODES H. BUHMANN,J. WANG, L. MANSOURI,P. H. BETON,L. EAVES, M. HEATHand M. HENINI Department of Physics, University of Nottingham, Nottingham NG7 2RD, England Abstract--The influence of light on the low temperature 1 ( V) characteristics of selectivelyetched small area resonant tunneling diodes (RTD) has been investigated. These diodes have physical dimensions down to 0.5/am and their design allows easy optical access. Under illumination new subthreshold peaks appear in I (V). These peaks are also observed in large area diodes, and are found to be strongly influenced by applying a magnetic field either parallel or perpendicular to the plane of the barriers. We show that our results cannot be explained in terms of resonant tunneling of photo-excited holes and propose an explanation based on the Coulombic electron-hole interaction.
Resonant tunneling diodes (RTDs) are an attractive system for the study of quantum transport since the strong non-linearities observed in their current voltage characteristics, I(V), are a direct consequence of the confinement of carriers within a quantum well[l]. The incorporation of donors within the quantum well (QW) of an RTD leads to the formation of laterally bound hydrogenic-like states which are localized within the plane of the QW. These bound states are lower in energy than the QW continuum and provide an additional channel for resonant tunneling, which in turn leads to additional non-linearities in 1 (V)[2,3]. Resonant tunneling therefore provides a means of detecting the presence of any low energy states which are formed within the QW. In this paper we describe a series of experiments in which we investigate the possibility of using RTDs to probe the presence of holes in the QW. The holes are introduced by photo-excitation and give rise to sub-threshold peaks in I(V). We argue that these peaks are a close analogue of the peaks generated by the presence of donors. Our experiments are conducted on both large (100-400/lm square) mesas and also a range of small area diodes with dimensions down to 0.5/~m. An important element of our work is the development of a fabrication process for a sub-micron RTD which is suitable for optical access. This process is based on optical lithography and wet etching and does not require the use of either dry etching (a possible source of damage) or dielectric layers (which might impair the optical access of the devices) for isolation of bonding pads and metallic tracks. The devices were fabricated from a GaAs/AIAs double-barrier heterostructure grown on a semi-insulating (100) GaAs substrate, using molecular beam epitaxy (MBE). The layer composition of the beterostructure is given in Table I.
To fabricate the small area diodes the GaAs (top contact) layer is selectively etched using NH4OH/H:O2, (5:95), to form a narrow line with a width in the range of 0.5-3/~m. The line is formed between large ohmic contacts (~100/~m x ~ 100/~m). Note that optical lithography is used for pattern definition, so that significant undercut etching is required to achieve sub-micron dimensions. A second (non-selective) etch was used to penetrate the AlAs harriers and reveal the lower GaAs doped (bottom contact) layer. Finally, this buried n-type GaAs layer was also selectively etched to form a freestanding GaAs bridge in t~e. emitter layer. Au/Ge/Ni ohmic contacts were then deposited on the top and bottom contact doped layers. A schematic representation of the final device is shown in Fig. !. Note that the metallised region on the top contact is connected to the active region of the device by the freestanding GaAs bridge. This serves to isolate the bottom contact from the doped region beneath the top contact eliminating any possible parallel conduction path, This novel fabrication route produces small area diodes with low contact resistance which can be easily illuminated. The dimensions of the small area devices discussed below are: I ~ 0.5 x 60#m, II ~ 1.0 x 60/~m and Ill ,,, 3.0 x 60/~m. We have also investigated large area control devices with metal contacts which are sufficiently small for light to penetrate the device. The low temperature current-voltage characteristics (T =4.2 K), I(V), for device I, II and III are shown in Fig. 2(a)). For all measurements the convention of positive bias implies a positive potential applied to the top contact. Comparing the I ( V ) of the small area and large area devices (inset Fig. 2(a)), no significant difference is observed, except for the smallest device (I). The main electron peak positions remain approximately the same, and a small asymme-
973
H. BUHMANNet al.
974
T a b l e I. Sample structure. Growth-direction from bottom to top. T he donor is Si and the M B E growth temperature was 550 C 100.0nm 80.6 nm 50.9 nm 20.4 nm 5.9 nm
GaAs GaAs GaAs GaAs
n = 2 x 10 ~ n = 2 x l0 tn = 2 x 10 ~b
top contact 0
spacer
AlAs
barrier
9.1 nm
GaAs
well
5.9 nm
AlAs
barrier
20.4 nm 50.9 nm 80.6 nm 200.0 nm 7.6 nm
GaAs GaAs GaAs GaAs AlAs
1000.0 nm
GaAs
~
spacer n = 2 x 1016 n = 2 x 10 ~7 n = 2 x 10 ts
-04
0
04
.-------~-=Jll
~
-20
-40
bottom contact etch stop
semi*insulating
Substrate
5 try in the bias region beyond the main resonance is common to all devices. The I ( V ) for the smallest diode, device I, shows a broadening of the main electron resonance together with a shift to higher voltage in forward bias, while in negative bias it exhibits no obvious changes. A similar asymmetry has been observed in gated resonant tunneling devices[4], when the active tunnel area is progressively decreased with increased gatevoltage. This has been explained in terms of the shape of the equipotential close to the tunnel barriers. We may estimate the side wall depletion, d,, in the small area diodes from the value of the peak current, I~,k, of the main resonance from the relation: l~ak =j~,k(l~--ds)lb, where J~ak is the peak current density and l, and lb are defined in Fig. 1. From the values of I ~ k for devices I, II and III we find j ~ k = 0 . 1 7 n A p m -2 and d~=0.4pm. This is in good agreement with the peak current density measured for the corresponding large area d e v i c e s , Jpeak.large = 0.18 nA #m -2. The devices were illuminated in a flow cryostat via an optical fibre. Under constant illumination (PL ~< 100/Z W cm -2) with 670 nm wavelength laser
free standing /x/°hmic t'~ GoAsbridge,,, ~/~.'~onlocts top contact [//~ "~
/bottom contact /A
S
S.I. barriers
Fig. 1. Schematic picture of the small area device.
0
--
11
-5 -10
-0.4
0
V/Volt
0.4
Fig. 2. (a) I(V) characteristics of device I, Ii and III in darkness. Inset: I(V) of a large area devices, 400 × 400/am. (b) I(V) characteristic of device II under illumination, 1: O~W/cm2, 2:1 ~W/cm' and 3:3 ~W/cm2.
light, changes in I (V) are observed. In Fig. 2(b) I (V) for device II is plotted for various levels of illumination. The features which are observed for device II are typical of all devices. The main electron resonance peak position and threshold value shift to lower voltage and n e w resonances (arrowed in Fig. 2(b)) occur below the threshold voltage for the main resonance. The strength of these additional resonances increases with excitation power. In addition to the appearance of these features we also observe an increase in the peak and valley currents of the main resonance with increased illumination. The valley current is greatly enhanced in forward bias. To understand the effects of illumination we refer to the band profiles of the device shown in Fig. 3. The incident light creates electron-hole pairs in the depletion region beyond the collector barrier. The photo-created electrons (majority carriers) are swept into the doped collector region, but the photo-created holes (minority carriers) drift up towards the collector barrier where they form an accumulation layer. This process has been discussed previously in the context of photoluminescence experiments on resonant tunneling diodes[5-7]. The presence of the photo-created holes close to the collector barrier modifies the band bending in the device and accounts for the shift of the threshold and peak of the main resonance to lower voltage. Similar effects have previously been observed in the I ( V ) of large area resonant tunneling diodes under illumination[6,7]
Photohole-induced resonant tunneling of electrons which were attributed to resonant tunneling of photocreated holes. In the remainder of this paper we discuss the dependence of the photo-induced peaks on magnetic field. Our discussion of the magnetic field dependence refers to I (V) for large area diodes, since for these devices we have a more complete set of data, and can make a direct comparison with previous work[6,7]. Figure 4(a) shows I ( V ) up to the threshold voltage for the main resonance for a 400#m square device illuminated with an excitation power PL ~< 10 mW/cm 2 in the presence of a magnetic field B between 0 and 10 T oriented perpendicular to the plane of the barriers. For B = 0 (lowest curve) we observe a sub-threshold resonance in each bias direction at V ~ - l l 0 m V and V ~ I 2 0 m V (peaks marked D in Fig. 4(a)). For B < 4 T this peak remains unaffected by magnetic field, however as B is progressively increased it shifts to larger voltage and its amplitude is reduced. For B > 3 T several more peaks appear which occur at even lower voltage. These are labelled A, B and C on Fig. 4(a). The peaks show a fair degree of symmetry between bias directions, although their amplitude is higher in forward bias (because of an effective difference in the light intensity incident on the depletion region in forward and reverse due to absorption effects). The voltage positions of peaks A, B and C are only weakly dependent on magnetic field, however their amplitude is a strong function of field. At the highest magnetic fields peaks A and B split into two peaks. I(V) for the same diode under illumination in the presence of a magnetic field oriented parallel to the
eaAs
.
.
I
GoAs
/ ' , 4
electron accumulation layer
L \
photoexcited electronhole-pairs
~
oct
1 accumulation layer Fig. 3. Schematic band profile of the device.
20
cl
16
975
"1
A
B
lOT
<= 12 8 4
(a)
0
12
I
B1
11T
0
BI
1
....~
YI ~
-o.1
o V/Volt
o.1
Fig. 4. I(V) characteristics for a 400/am square mesa in (a) perpendicular and (b) in parallel magnetic field configuration. barrier is shown in Fig. 4(b). Note that for our experimental arrangement illumination power is lower than for the perpendicular case and the corresponding photo-induced peaks have smaller amplitude than the data in Fig. 4(a). For B = 0 T we observe two sub-threshold peaks as in Fig. 4(a) (peaks marked D), however as B is increased beyond 3 T another peak appears (peak B). As the magnetic field is increased peak D moves to higher voltage, and a weak splitting is observed. The behaviour of the peak in I(V) corresponding to the main resonance displays quite different behaviour for parallel and perpendicular oriented fields. For a perpendicular field its voltage position and amplitude are only weakly dependent on field, however for a parallel field the threshold moves to higher voltage. Note that peak D in the parallel field moves to a higher voltage at a similar rate to the threshold for the main electron resonance. Thus our data show a series of photo-induced peaks whose amplitude and voltage position are extremely sensitive to magnetic field. We first consider whether the dependence of their amplitude and voltage position on magnetic field is consistent with conventional resonant tunneling of photo-created holes. We focus on peak D since this peak is observed even for B = 0 T. Previous work on p-i-p resonant tunneling diodes[8] shows that the voltage position of the lowest two hole resonances referred to as hhl and lhl (corresponding to resonant tunneling via the
976
H. BUHMANNet al.
lowest heavy and light hole subbands respectively) is almost independent of magnetic field for B < 11 T. Clearly peak D cannot be due to hole resonant tunneling via the hh I or lhl subbands since its voltage position is shifted by a parallel field. Hayden et al. found that the lowest hole subband resonance which has a strong parallel field dependence of its voltage position is hh2, the first excited state heavy hole state. However, firm identification of peak D as the hh2 resonance is not possible, since in that case we would expect to observe a peak in I ( V ) of comparable amplitude at lower voltage corresponding to the lhl resonance as observed by Hayden et al. In addition we have calculated the expected peak positions for electron and hole resonances using a simple model for the band bending of the device which uses the F a n g - H o w a r d wavefunction to model the state in the electron accumulation layer and treats the state in the hole accumulation layer as an Airy function. This model predicts that the hh2 resonance should occur at a higher voltage than the electron resonance. We also note that in similar p - i - n resonant tunneling diodes the hh2 peak always occurs at higher voltage than the lowest electron resonance[9]. Another result established in the study of p - i - p resonant tunneling diodes is that the amplitude and voltage position of the peaks in I ( V ) due to hole resonances are insensitive to the presence of perpendicular magnetic fields for B < 10 T. Certainly nothing comparable with the dramatic magnetic field enhancement of peaks A, B and C in Fig. 4(a) has been observed for p - i - p devices. We are thus unable to account either qualitatively or quantitatively for our data in terms of conventional resonant tunneling of photo-excited holes. We have also investigated these effects in several other wafers which differ from the heterostructure shown in Table 1 only in the thickness of the AlAs tunnel barriers. For barrier widths of 4.5 and 3.0 nm we do not observe such clear additional peaks under illumination, but see a step like behaviour at lower voltage which is highly reminiscent of the data shown in Ref.[7]. For barrier widths 5.9 and 7.5 nm we observe structure similar to that in Fig. 4. Note that the peak current density for our devices, Jp~,k, is two orders of magnitude smaller than that for the material used by Vodjdani et al.[7]. This dependence of the peaks on barrier width clearly complicates the comparison of our data with that previously reported. We have stressed above that our data cannot be explained solely in terms of resonant tunneling of photo-excited holes. Our alternative explanation is that the presence of a hole in the quantum well gives rise to an alternative resonant conduction path which is lower in energy than the quantum well continuum
due to the C o u l o m b interaction of the electron and hole, i.e. tunneling of electrons via an excitonic state. Similar peaks have been observed in I ( V ) for devices in which ionized donors are introduced into the quantum well. The threshold for peak D is approx. 30 mV below that of the main resonance. According to our band bending calculations this corresponds to an energy below the continuum of ~ 5.5 meV. This should be compared with the binding energy of ~ 7 meV for a light hole exciton and ~ 9 meV for a heavy hole exciton. Associating peak D with an excitonic transition is at least consistent with its shift to higher voltage in parallel field. However our model is so far unable to explain the appearance of the lower voltage peaks A, B and C with increasing magnetic field. In conclusion we have observed a series of peaks which appear when a resonant tunneling diode is illuminated. The dependence of these peaks on magnetic field is not consistent with resonant tunneling of holes. We have proposed an alternative explanation based on resonant tunneling via hole-induced excitonic states in the well. Further work, in particular photoluminescence studies, are required to clarify the detailed origin of these peaks. Acknowledgements--Funding for this work was provided in part by ESPRIT Basic Research Grant 7193 PARTNERS and in part by the U.K. Science and Engineering Research Council. REFERENCES
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