- Email: [email protected]
Still a hot season for US compounds …thanks especially to the DoD
m
m RTD2 F E A T U R E
I
the by M. Henini, T.M. Fromke
D.P. S
e4uen
In recent years there has been a revival of experimental and theoretical interest in resonant tunnelling devices, largely motivated by the impressive progress achieved in MBE. Following on from our previous issue this article concludes our update of some of the recent advances in resonant tunnelling and presents several topics concerning the DBRTS. ,~Nr-.aU area DIlRTS The composition of a conventional large-area DBRTS is shown schematically in Fig. 6(a). The yellow strips represent layers of high band-gap semiconductor material which act as two potential barriers. When an electron is confined within the quantum well formed by the two barriers, the energy associated with motion perpendicular to the layer interfaces is quantised into discrete energy levels. The separation AE between adjacent energy levels is inversely related to the well width w by AE~ 1/w2 For typical well widths of around 20 nm, AE is sufficiently large (,-~ 100 meV), that resonant tunnelling into the quantised energy levels produces well-resolved peaks in the currentvoltage characteristics, I-V. Of course, an electron in the quantum well is also confined laterally (in the plane of the layers) by the side walls of the mesa. However for conventional DBRTS, the mesa diameter d is so large (> 100 t~m) that even at liquid helium temperatures, the spacing of quantised energy levels produced by the lateral confinement, AElat- or 1/d 2 is around five orders of magnitude smaller than the thermal broadening of the emitter Fermi energy. Consequently, resonant effects originating from lateral quantisation cannot be
(a)
(b)
ETCH
d< llim le--,.--el
Iw
BARRIEr
d>lOO~m Figure 6. Schematic diagrams o f (a) a large area D B R T S and (b) a sub-micron diameter DBRTS. The transfer o f electrons between the contacts and the quantum well is equivalent to charging the two serial capacitors shown in (b).
resolved in large-area DBRTS. However, AElat can be made comparable with the thermal broadening by reducing the mesa diameter to submicron dimensions. One way of doing this is illustrated in Fig. 6. First a small etch resistant
096,,290/94j,700 ,994 E,sevierSc,ence Ltd Pa0e,01
lVo,No4
cap (red) is deposited on the top surface of the device. The mesa is then etched down through the two barrier layers and into the bottom contact. The etch resist protects a thin pillar which forms a sub-micron DBRTS as shown in Fig. 6(b). This
j[
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l"ik,ure 7. l-l" characterislics o/ a .,uh-micron D B R T S /})r a range o / t e m p e r a t u r e s T. ~It htieh T (blue curve) a sin gh" peak {s oh~erved (j~,rectl arrow) due Io resonant lu/lnelli/t£~ into the/ou.c.s'l quasi-hotold stale :~/ lhc Q w. 4t 7 I K (red curve) additional s'uh-rcvonance~ arc revealed ,'hh!ck arrow~ /, (r£/i 9).
technique |\)r fabricating small-area devices was first reported by Reed et aL, (9). When sourcc and drain ohmic contacts arc evaporated onto the upper and lower surfaces of the structure, the I-V characteristics can be measured. The blue curve m Fig. 7 shows the I-V characteristics of a 0. I l-tm diameter DBRTS measured at temperature T-100 K. Resonant tunnelling into the lowest quantised energy level in the quantum well, El, produces a single resonance peak when thc applied bias voltage V is approximately 0.75 V (green arrow). If the temperaturc is lowered to 1 K, as in the red curve, additional subresonances are revealed (black arrows). Reed and co-workers attributed these extra fealures to quantisation of the lateral motion in the q u a n t u m well. An alternative e x p l a n a t i o n , based on C o u l o m b blockade of the tunnelling process, was suggested by Groshev e't el., (10). The basic physics of the Coulomb blockade effect can bc understood by m o d e l l i n g the D B R T S with an equivalent circuit consisting of two scrial capacitors each of wtlue C c~ d e, as shown in Fig. 6(b). Suppose that wc transfer one clectron from the emitter contact into the quantum well. The chargc transfer process is equivalent to adding a single electro-
nic charge e to cach of the two capacitors. The energy E c - e 2 / C associated with the charging process must be supplied by t t e external voltage source. If the applied voltage is insufficient to supply the charging energy, the charge transfer process is blocked. As the applied voltage is raised, it can only supply the charging energy required for an additional electron to tunnel into the quantum well at discrete voltage ~alues with constant spacing AV - e/C Each time an extra electron is transferred to the quantum well, the number of electrons which contribute to the tunnel current from the well into the collector contact increases. Regular resonant features are therefore expected in I-V, with a voltage period V (e/C).:x. 1/d 2 [:or largearea devices, AV is too small to be resolved. However, for sub-micron mesa diameters, z~V-_- 1 mV is sufficiently large that the observation of C o u l o m b blockade effects can be anticipated. As shown above, the two competing models proposed by Reed et al., and Groshev to explain the origin of the additional subresonant peaks, predict that the voltage spacing of the resonances will increase as the mesa diameter decrea ses.
Page 47
Vol 7 No 4
To investigate whether the subresonances could be due either to lateral quantisation or to Coulomb blockade effects, Dellow et al., (11) fabricated a three-terminal DBRTS in which the effective diameter d can be controlled by biasing a lateral gate. The construction of the threeterminal devices is shown schematically in Fig. 8 (top inset). A square pillar of width 1 #m is fabricated by etching the top surface of the mesa. A metallic lateral gate is then deposited around the perimeter of the pillar. When a negative bias voltage is applied to the lateral gate, the conduction electrons are repelled from it and so the effective area of the conducting channel can be reduced in a controlled way. By applying a source-drain voltage Vsj) to O h m i c contacts on the top and bottom surfaces of the device, the current-voltage characteristics l-Vsr) can be measured. The blue curve in Fig. 8 shows the I-VsD plot obtained when the lateral gate is unbiased. Thc single resonance peak (arrowed) is due to tunnelling into the lowest quantised energy level El in the quantum well. The additional current-voltage curves, in order of decreasing peak height, show the effect of increasing the magnitude of the negative lateral gate voltage V~. As V~, is made morc negative, the tunnel curren! falls because the area of the conducting channel is further constricted. In addition, the l-VsD plots become increasingly asymmetrical with respect to reversal of the source-drain bias (11). However, the most interesting features are revealed in the low-voltage regime VsD< 50 mV (12). To see these effects, the portion of the I-VsD plot for V~ - 0V enclosed by the green box is shown enlarged in the lower inset to Fig. 8. The black arrows indicate a n u m b e r of additional peaks which are observed under both forward and reverse bias conditions. The additional peaks are referred to as sub-threshold resonances because they are observed tBr values of Vso far below the threshold voltage required for resonant tunnelling into the energ,' level E~ The key experimental feature of the sub-threshold resonances is that the peak positions and spacings along the VsD axis are both totally independent of" the lateral gate voltage Vg. Conse-
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Figure 8. l(Vso) plots for a laterally-gated DBRTS with a range of negative gale voltages Vs between 0 V (blue curve) and 5 V (red curve). Green arrows indicate the main resonance. Top inset: schematic diagram of the DBRTS. Bottom inset: Portion of I(VsD) plot for Ve = OV (enclosed by green box in main figure) showing a number @sub-threshold resonances, (refs. 11 and 12).
quently they cannot originate either from lateral quantisation or Coulomb blockade effects. One possible explanation for the sub-threshold features suggested by the Nottingham group, is that during the growth process donors segregate from the contacts into the quantum well. The donors are ionised, and the attractive potential produced by the positive ion core gives rise to an additional bound state in the well. Calculations by Greene and Bajaj (13) show that the donor bound state energy depends on the position of the donor in the quantum well and is approximately 12 meV below E~, when the well width w ' 1 0 nm. According to this model, the sub-
threshold resonances originate from resonant tunnelling through zerodimensional (0D) bound states of the donor impurities which are localised in all three spatial directions. Because the donor bound state energy varies with the position of the donor in the well, tunnelling through different donors is expected to produce resonant peaks at different values of VSD, as in the experiment. To s y s t e m a t i c a l l y investigate whether this donor-assisted tunnelling process could indeed account for the sub-threshold resonances, one of the authors (M. Henini at Nottingham) grew a number of DBRTS, each containing a &-doping layer of Si donors (concentration 4 x
Pa0e.l lv°,N°4
109 cm -2) at the centre of the quantum well. The influence of the donors on the current-voltage characteristics was studied by comparison with undoped control samples (14).The red curve in Fig. 9 shows the I-V curve of one of the &-doped samples. The main resonance occurs at about 175 mV. However, an additional subthreshold resonance (black arrow) is also observed, just as for the laterallygated device. To show this subthreshold feature more clearly, a region of the I-V plot is shown enlarged in the inset (red curve). The donor-assisted peak (black arrow) is observed in both forward and reverse bias, and is emphasised in the conductance plot dI/dV (green curve). The I-V plot of the undoped control sample (blue curve) contain no trace of the sub-threshold resonance which must therefore be directly related to tunnelling via the donor impurities. To further study the sub-threshold resonances in the ~-doped samples, the amplitude Ip of the donor-assisted peak was measured as a function of magnetic field B, applied parallel to the barrier interfaces. The full red circles in Fig. 10 show the magnetic field dependence of the natural logarithm of Ip. The amplitude of the donor-assisted peak decreases with increasing B, and the peak is totally quenched when B ~ 11T. To investigate whether this behaviour is consistent with resonant tunnelling via localised donor states, Fromhold et at. (15), calculated the current flowing into a single donor impurity as a function of the in-plane magnetic field B (15). In Fig. 10, the solid black curve shows the natural logarithm of the calculated peak donor-assisted current Ip(B). The good quantitative agreement between the theoretical Ln{Ip(B)} plot and the experimental data further supports the donor-assisted model for the sub-threshold resonances. In addition, the calculations show that the shape of the Ip (B) plot provide a direct measure of the Fourier transform of the donor wavefunction, from which the wavefunction itself can, in principle, be reconstructed. Resonant magnetotunnelling from a two-dimensional electron gas into any 0D bound state therefore has potential as a new experimental technique with which to probe the 0D wavefunction (15).
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Acknowledgements
=0
::
The authors are grateful for many helpful discussions with Prof. L. Eaves, Drs. P.H. Beton, P.C. Main, F.W. Sheard, M.W. Dellow and Mr. J.W. Sakai.
-,50
E V m
-100 -160
1
. . . . . -80 0
80
160
V(mV)
References 9. M.A. Reed et al. Phys. Rev, Lett., 60, 535, (1988). 10. A. Groshev et al. Phys. Rev. B, 42, 5895, (1990). 11. M. Dellow et al. Electron. Lett., 27, 134, (1991). 12. M.W. Dellow et al. Phys. Rev. Lett., 68, 1754, (1992). 13. R.L. Greene and K.K. Bajaj, Solid St. Commun., 45, 825, (1983). 14. J.W. Sakai et al. Phys. Rev. B, 48, 5664, (1993)• 15. T.M. Fromhold et al. Acta Physica Polonica A, 82, 737, (1992). 16. S.M. Sze, "Physics of semiconductor devices", (Wiley, New York, 1961), chapter 11.
....
J
I
0
200
I
M
400
I
800
600
v(mv) Figure 9. I ( V ) curve o f a large-area D B R T S with Si g-doping at the well centre. Black arrow indicates a weak resonant feature at a voltage V ~ 8 0 mV, far below the threshoM of the main resonance, lnset: enlarged 1(V) plot (red curve) showing sub-threshold resonances (black arrows) which are emphasised in dl/dV (green curve). The I ( V ) plot o f a control sample (blue curve) in which the Q W is not intentionally doped reveals no trace of the sub-threshold peaks, (ref 14).
~
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Conclusion Numerous additional devices involving D B R T S are currently under consideration. In particular, resonant tunnelling devices with multiple N D R regions are of potential interest for a variety of circuits which could be realised with reduced complexity, including multiple valued logic, bit checkers, ultra high speed analog-todigital converters and frequency dividers. So far, none of the exotic devices presented in this article have been used in electronic applications. Most of the work on these devices has c o n c e n t r a t e d on the use o f new structures and material systems and on studies of the fundamental physical processes which take place in D B R T S . In addition, the device applications of D B R T S has been explored, especially in the field of high speed electronics, i.e.. microwave systems. In our view, it is likely that this decade will indeed see the commercial exploitation of resonant tunnelling devices. However, let us conclude by quoting from the wellknown book by Sze (16)
3
2
4B(6sla)8"re
10
12
Figure 10. Full circles." Natural logaritJ~m o f the peak donor-assisted current 1~, measured as a function o f magnetic' field B applied parallel to the plane o f the well. Black curve: corresponding theoretical plot. (ref 15).
Page 49
[lii ii
i:~i
jvo,, No4
m RTD2 F E A T U R E
I
the by M. Henini, T.M. Fromke
D.P. S
e4uen
In recent years there has been a revival of experimental and theoretical interest in resonant tunnelling devices, largely motivated by the impressive progress achieved in MBE. Following on from our previous issue this article concludes our update of some of the recent advances in resonant tunnelling and presents several topics concerning the DBRTS. ,~Nr-.aU area DIlRTS The composition of a conventional large-area DBRTS is shown schematically in Fig. 6(a). The yellow strips represent layers of high band-gap semiconductor material which act as two potential barriers. When an electron is confined within the quantum well formed by the two barriers, the energy associated with motion perpendicular to the layer interfaces is quantised into discrete energy levels. The separation AE between adjacent energy levels is inversely related to the well width w by AE~ 1/w2 For typical well widths of around 20 nm, AE is sufficiently large (,-~ 100 meV), that resonant tunnelling into the quantised energy levels produces well-resolved peaks in the currentvoltage characteristics, I-V. Of course, an electron in the quantum well is also confined laterally (in the plane of the layers) by the side walls of the mesa. However for conventional DBRTS, the mesa diameter d is so large (> 100 t~m) that even at liquid helium temperatures, the spacing of quantised energy levels produced by the lateral confinement, AElat- or 1/d 2 is around five orders of magnitude smaller than the thermal broadening of the emitter Fermi energy. Consequently, resonant effects originating from lateral quantisation cannot be
(a)
(b)
ETCH
d< llim le--,.--el
Iw
BARRIEr
d>lOO~m Figure 6. Schematic diagrams o f (a) a large area D B R T S and (b) a sub-micron diameter DBRTS. The transfer o f electrons between the contacts and the quantum well is equivalent to charging the two serial capacitors shown in (b).
resolved in large-area DBRTS. However, AElat can be made comparable with the thermal broadening by reducing the mesa diameter to submicron dimensions. One way of doing this is illustrated in Fig. 6. First a small etch resistant
096,,290/94j,700 ,994 E,sevierSc,ence Ltd Pa0e,01
lVo,No4
cap (red) is deposited on the top surface of the device. The mesa is then etched down through the two barrier layers and into the bottom contact. The etch resist protects a thin pillar which forms a sub-micron DBRTS as shown in Fig. 6(b). This
j[
j~
I%
15
10~, m
5 100 T(K)
0 0.5
0.0
u.,
-'-
v (v)
l"ik,ure 7. l-l" characterislics o/ a .,uh-micron D B R T S /})r a range o / t e m p e r a t u r e s T. ~It htieh T (blue curve) a sin gh" peak {s oh~erved (j~,rectl arrow) due Io resonant lu/lnelli/t£~ into the/ou.c.s'l quasi-hotold stale :~/ lhc Q w. 4t 7 I K (red curve) additional s'uh-rcvonance~ arc revealed ,'hh!ck arrow~ /, (r£/i 9).
technique |\)r fabricating small-area devices was first reported by Reed et aL, (9). When sourcc and drain ohmic contacts arc evaporated onto the upper and lower surfaces of the structure, the I-V characteristics can be measured. The blue curve m Fig. 7 shows the I-V characteristics of a 0. I l-tm diameter DBRTS measured at temperature T-100 K. Resonant tunnelling into the lowest quantised energy level in the quantum well, El, produces a single resonance peak when thc applied bias voltage V is approximately 0.75 V (green arrow). If the temperaturc is lowered to 1 K, as in the red curve, additional subresonances are revealed (black arrows). Reed and co-workers attributed these extra fealures to quantisation of the lateral motion in the q u a n t u m well. An alternative e x p l a n a t i o n , based on C o u l o m b blockade of the tunnelling process, was suggested by Groshev e't el., (10). The basic physics of the Coulomb blockade effect can bc understood by m o d e l l i n g the D B R T S with an equivalent circuit consisting of two scrial capacitors each of wtlue C c~ d e, as shown in Fig. 6(b). Suppose that wc transfer one clectron from the emitter contact into the quantum well. The chargc transfer process is equivalent to adding a single electro-
nic charge e to cach of the two capacitors. The energy E c - e 2 / C associated with the charging process must be supplied by t t e external voltage source. If the applied voltage is insufficient to supply the charging energy, the charge transfer process is blocked. As the applied voltage is raised, it can only supply the charging energy required for an additional electron to tunnel into the quantum well at discrete voltage ~alues with constant spacing AV - e/C Each time an extra electron is transferred to the quantum well, the number of electrons which contribute to the tunnel current from the well into the collector contact increases. Regular resonant features are therefore expected in I-V, with a voltage period V (e/C).:x. 1/d 2 [:or largearea devices, AV is too small to be resolved. However, for sub-micron mesa diameters, z~V-_- 1 mV is sufficiently large that the observation of C o u l o m b blockade effects can be anticipated. As shown above, the two competing models proposed by Reed et al., and Groshev to explain the origin of the additional subresonant peaks, predict that the voltage spacing of the resonances will increase as the mesa diameter decrea ses.
Page 47
Vol 7 No 4
To investigate whether the subresonances could be due either to lateral quantisation or to Coulomb blockade effects, Dellow et al., (11) fabricated a three-terminal DBRTS in which the effective diameter d can be controlled by biasing a lateral gate. The construction of the threeterminal devices is shown schematically in Fig. 8 (top inset). A square pillar of width 1 #m is fabricated by etching the top surface of the mesa. A metallic lateral gate is then deposited around the perimeter of the pillar. When a negative bias voltage is applied to the lateral gate, the conduction electrons are repelled from it and so the effective area of the conducting channel can be reduced in a controlled way. By applying a source-drain voltage Vsj) to O h m i c contacts on the top and bottom surfaces of the device, the current-voltage characteristics l-Vsr) can be measured. The blue curve in Fig. 8 shows the I-VsD plot obtained when the lateral gate is unbiased. Thc single resonance peak (arrowed) is due to tunnelling into the lowest quantised energy level El in the quantum well. The additional current-voltage curves, in order of decreasing peak height, show the effect of increasing the magnitude of the negative lateral gate voltage V~. As V~, is made morc negative, the tunnel curren! falls because the area of the conducting channel is further constricted. In addition, the l-VsD plots become increasingly asymmetrical with respect to reversal of the source-drain bias (11). However, the most interesting features are revealed in the low-voltage regime VsD< 50 mV (12). To see these effects, the portion of the I-VsD plot for V~ - 0V enclosed by the green box is shown enlarged in the lower inset to Fig. 8. The black arrows indicate a n u m b e r of additional peaks which are observed under both forward and reverse bias conditions. The additional peaks are referred to as sub-threshold resonances because they are observed tBr values of Vso far below the threshold voltage required for resonant tunnelling into the energ,' level E~ The key experimental feature of the sub-threshold resonances is that the peak positions and spacings along the VsD axis are both totally independent of" the lateral gate voltage Vg. Conse-
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.
.
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.
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,
,
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%00 -100
0 100 200 VSD (mV)
Figure 8. l(Vso) plots for a laterally-gated DBRTS with a range of negative gale voltages Vs between 0 V (blue curve) and 5 V (red curve). Green arrows indicate the main resonance. Top inset: schematic diagram of the DBRTS. Bottom inset: Portion of I(VsD) plot for Ve = OV (enclosed by green box in main figure) showing a number @sub-threshold resonances, (refs. 11 and 12).
quently they cannot originate either from lateral quantisation or Coulomb blockade effects. One possible explanation for the sub-threshold features suggested by the Nottingham group, is that during the growth process donors segregate from the contacts into the quantum well. The donors are ionised, and the attractive potential produced by the positive ion core gives rise to an additional bound state in the well. Calculations by Greene and Bajaj (13) show that the donor bound state energy depends on the position of the donor in the quantum well and is approximately 12 meV below E~, when the well width w ' 1 0 nm. According to this model, the sub-
threshold resonances originate from resonant tunnelling through zerodimensional (0D) bound states of the donor impurities which are localised in all three spatial directions. Because the donor bound state energy varies with the position of the donor in the well, tunnelling through different donors is expected to produce resonant peaks at different values of VSD, as in the experiment. To s y s t e m a t i c a l l y investigate whether this donor-assisted tunnelling process could indeed account for the sub-threshold resonances, one of the authors (M. Henini at Nottingham) grew a number of DBRTS, each containing a &-doping layer of Si donors (concentration 4 x
Pa0e.l lv°,N°4
109 cm -2) at the centre of the quantum well. The influence of the donors on the current-voltage characteristics was studied by comparison with undoped control samples (14).The red curve in Fig. 9 shows the I-V curve of one of the &-doped samples. The main resonance occurs at about 175 mV. However, an additional subthreshold resonance (black arrow) is also observed, just as for the laterallygated device. To show this subthreshold feature more clearly, a region of the I-V plot is shown enlarged in the inset (red curve). The donor-assisted peak (black arrow) is observed in both forward and reverse bias, and is emphasised in the conductance plot dI/dV (green curve). The I-V plot of the undoped control sample (blue curve) contain no trace of the sub-threshold resonance which must therefore be directly related to tunnelling via the donor impurities. To further study the sub-threshold resonances in the ~-doped samples, the amplitude Ip of the donor-assisted peak was measured as a function of magnetic field B, applied parallel to the barrier interfaces. The full red circles in Fig. 10 show the magnetic field dependence of the natural logarithm of Ip. The amplitude of the donor-assisted peak decreases with increasing B, and the peak is totally quenched when B ~ 11T. To investigate whether this behaviour is consistent with resonant tunnelling via localised donor states, Fromhold et at. (15), calculated the current flowing into a single donor impurity as a function of the in-plane magnetic field B (15). In Fig. 10, the solid black curve shows the natural logarithm of the calculated peak donor-assisted current Ip(B). The good quantitative agreement between the theoretical Ln{Ip(B)} plot and the experimental data further supports the donor-assisted model for the sub-threshold resonances. In addition, the calculations show that the shape of the Ip (B) plot provide a direct measure of the Fourier transform of the donor wavefunction, from which the wavefunction itself can, in principle, be reconstructed. Resonant magnetotunnelling from a two-dimensional electron gas into any 0D bound state therefore has potential as a new experimental technique with which to probe the 0D wavefunction (15).
r
I
i
I
'
I
~
"... a useful solid-state device is one which can be used in electronic applications or can be used to study the f u n d a m e n t a l physical p a r a meters".
I
100 2
50 E
<
2
Acknowledgements
=0
::
The authors are grateful for many helpful discussions with Prof. L. Eaves, Drs. P.H. Beton, P.C. Main, F.W. Sheard, M.W. Dellow and Mr. J.W. Sakai.
-,50
E V m
-100 -160
1
. . . . . -80 0
80
160
V(mV)
References 9. M.A. Reed et al. Phys. Rev, Lett., 60, 535, (1988). 10. A. Groshev et al. Phys. Rev. B, 42, 5895, (1990). 11. M. Dellow et al. Electron. Lett., 27, 134, (1991). 12. M.W. Dellow et al. Phys. Rev. Lett., 68, 1754, (1992). 13. R.L. Greene and K.K. Bajaj, Solid St. Commun., 45, 825, (1983). 14. J.W. Sakai et al. Phys. Rev. B, 48, 5664, (1993)• 15. T.M. Fromhold et al. Acta Physica Polonica A, 82, 737, (1992). 16. S.M. Sze, "Physics of semiconductor devices", (Wiley, New York, 1961), chapter 11.
....
J
I
0
200
I
M
400
I
800
600
v(mv) Figure 9. I ( V ) curve o f a large-area D B R T S with Si g-doping at the well centre. Black arrow indicates a weak resonant feature at a voltage V ~ 8 0 mV, far below the threshoM of the main resonance, lnset: enlarged 1(V) plot (red curve) showing sub-threshold resonances (black arrows) which are emphasised in dl/dV (green curve). The I ( V ) plot o f a control sample (blue curve) in which the Q W is not intentionally doped reveals no trace of the sub-threshold peaks, (ref 14).
~
l
0
2
r
I
r
T
r
I
r
f
Conclusion Numerous additional devices involving D B R T S are currently under consideration. In particular, resonant tunnelling devices with multiple N D R regions are of potential interest for a variety of circuits which could be realised with reduced complexity, including multiple valued logic, bit checkers, ultra high speed analog-todigital converters and frequency dividers. So far, none of the exotic devices presented in this article have been used in electronic applications. Most of the work on these devices has c o n c e n t r a t e d on the use o f new structures and material systems and on studies of the fundamental physical processes which take place in D B R T S . In addition, the device applications of D B R T S has been explored, especially in the field of high speed electronics, i.e.. microwave systems. In our view, it is likely that this decade will indeed see the commercial exploitation of resonant tunnelling devices. However, let us conclude by quoting from the wellknown book by Sze (16)
3
2
4B(6sla)8"re
10
12
Figure 10. Full circles." Natural logaritJ~m o f the peak donor-assisted current 1~, measured as a function o f magnetic' field B applied parallel to the plane o f the well. Black curve: corresponding theoretical plot. (ref 15).
Page 49
[lii ii
i:~i
jvo,, No4