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Intrinsic sequence in the breakdown of the quantum Hall effect
Surface Science 229 (1990) 57-59 North-Holland
INTRINSIC
SEQUENCE
IN THE BREAKDOWN
P.C. van SON, G.H. KRUITHOF
OF THE QUANTUM
HALL EFFECT
and T.M. KLAPWIJK
Department ofApplicd Physics, University ofGroningen, 974 7 AG Groningen, The Netherlands Received I1 July 1989; accepted for publication 14 September 1989
The breakdown of the quantum Hall effect in high-mobility Si-MOSFETs occurs in a series of resistance steps as the current is increased beyond a critical value. These steps, that correspond to the successive breakdown of spatially localized parts of the sample, are not determined by inhomogeneities but have an intrinsic origin. We also observe that the breakdown always starts in the corner where the electrons enter the ZDEG. This asymmetry implies the need for a microscopic approach.
The zero-resistance state of a two-dimensional electron gas (ZDEG) in the quantum Hall regime is destroyed when the current exceeds a critical value [ I]. In wide structures (widths larger than 10 pm) one usually finds that the resistance appears in a series of steps that correspond to the successive breakdown of spatially localized parts of the sample as the current is increased. This behaviour may be due to inhomogeneities (weak spots) in the sample. We performed measIlrements on high-mobility Si-MOSFETs with 200-/lrn-wide 2DEG channels and find that the breakdown sequence is an intrinsic effect. Namely the sequence that we observe does not depend on the absolute location of the voltage contacts along the sample edge but on their relative location with respect to the corner in which the electrons are injected into the 2DEG. Moreover we conclude that the resistive state of the 2DEG originates in the corner where the electrons are injected and that with increasing current it spreads out from there. The explanation of this asymmetry between the current injection and extraction point will require a microscopic approach also for breakdown in wide channels. The measurements were performed on Si-MOSFETs with standard Hall-bar geometry (see fig. 1). The 2DEG is 200 pm wide and 600 pm long and the separation of the voltage contacts is 200 pm; the peak electron mobility is 2 m2/V-s. The breakdown measurements were done at T= 1.2 K and B= 12 T. The gate voltage was adjusted for the first Landau level 0039-6028/90/$03.50 ( Nosh-Holland )
0 Elsevier Science Publishers B.V.
(a)
4
5
6
(b)
4
5
6
Fig. 1. Current dist~butions in the 2DEG channel for at1 polarities of magnetic field and current. The dot indicates the comer in which the electrons are injected into the ZDEG. The dimensions of the channel and the positions of the voltage contacts are according to the indicated scale.
to be completely filled (filling factor u = 4 due to spin and valley degeneracy). A direct current and a small ( 100 nA) alternating current modulation is sent from source (s) to drain (d). The differential resistance R, between voltage contacts i and j is measured with a lock-in amplifier as a function of the direct current. Fig. I shows the idealized current distributions in the 2DEG; the dot indicates the point where the electrons are injected from the current contact into the 2DEG. By reversing the direction of the current and/ or the direction of the magnetic field, the injection point of the electrons can be placed in any of the four corners of the ZDEG. Fig. 2 shows results of the differential resistance between three different sets of voltage contacts for
P.C. van Son et al/The breakdown of the quantum Hall effect
58
J -40
-20
0
20
40 I,,(d)
Fig. 2. Differential resistance versus direct current for a Si-MOSFET at the v=4 QHE-plateau, showing the similarity between breakdown curves for different sets of voltage contacts. (a) Rlz with the direction of the magnetic field and the direction of the positive current as shown in fig. la. (b) R,, with positive current corresponding to fig. lc. (c) R,, with positive current corresponding to fig. 1b. The curves have been shifted upward for clarity.
three different combinations of magnetic field and current directions. The voltage contacts have been chosen in such a way that they have the same relative position with respect to the injection point: for negative current the injection point is as close as possible to the voltage contacts while for positive current it is in the opposite corner of the 2DEG. The three breakdown curves are the same, apart from small differences that may be due to inhomogeneities. Other samples with the same geometry show very similar structure. This means that there must be an intrinsic mechanism that determines the structure of these curves. Note that the observed asymmetry is not due to hysteresis. Fig. 3 shows how the breakdown developes across the sample. For negative current the current distribution is that of fig. lb. Resistance first appears between voltage contacts 1 and 2 and subsequently between contacts 4 and 5 and contacts 5 and 6. For a positive current (corresponding to fig. la) breakdown first occurs between contacts 5 and 6 and almost simultaneously between contacts 4 and 5 and contacts 1 and 2. This clearly shows that the resistive state of the 2DEG originates in the corner in which the electrons are injected into the 2DEG and spreads out from there all the way to the opposite corner. The
Lo
-20
0
20
40 Id< (PA)
Fig. 3. Differential resistance versus direct current for a Si-MOSFET at the v=4 QHE-plateau, showing how the breakdown spreads out across the sample. The direction of the magnetic field and the direction of the positive current are as shown in fig. la. (a) RL2. (b) R,,. (c) R56. The curves have been shifted upward for clarity.
structure in a single breakdown curve seems to be related to the appearance of resistance in other parts of the sample. The resistance rise at ZdC= + 18 ,uA in fig. 3c coincides with breakdown of the zero-resistance state between the drain contact and contact 3 (not shown), while the rise at Z,,= + 23 ,uA coincides with breakdown between contacts 4 and 5 (fig. 3b). The resistance tail for positive current in fig. 3a may be due to the fact that for high (Hall) voltages in the plane of the 2DEG, the effective gate voltage varies across the sample. The width of the o = 4 zeroresistance state in terms of gate voltage is 0.1 V which is equal to the Hall voltage for ZdC= 16 PA. The (a- ) symmetries in the breakdown curves have not been reported before probably because the voltage contacts are usually located much further from the current contacts. Then the intrinsic asymmetry is small and is easily dominated by the effect of inhomogeneities. Apart from the intrinsic nature of the breakdown sequence, we want to emphasize one other point. The asymmetry between the current injection and extraction points cannot be explained in a macroscopic equilibrium theory (like e.g. a heating model [ 21) because there the points are equivalent. Btittikers approach [ 3 ] is a good starting point to discuss nonequilibrium effects, but he predicts the dissipation to occur in the “wrong” corner. From our measurements we conclude that the elec-
P.C. van Son et al./The breakdown of the quantum Hall effect
tron injection point plays a crucial role in the breakdown of the quantum Hall effect in Hall-bar samples. Therefore a careful microscopic description of the electron injection process [4] will be essential for an explanation of our results.
59
References [ 1] G. Ebert, K. van Klitzing, K. Ploog and G. Weimann, J. Phys. C 16 (1983) 5441; M.E. Cage, R.F. Dziuba, B.F. Field and E.R. Williams, Phys. Rev. Lett. 51 (1983) 1374. [ 2 ] S.Komiyama, T. Takamasu, S. Hiyamizu and S. Sasa, Solid State Commun. 54 ( 1985) 479. [3] M. Biittiker, Phys. Rev. B 38 (1988) 9375. [4] P.C. van Son and T.M. Klapwijk, to be published.
INTRINSIC
SEQUENCE
IN THE BREAKDOWN
P.C. van SON, G.H. KRUITHOF
OF THE QUANTUM
HALL EFFECT
and T.M. KLAPWIJK
Department ofApplicd Physics, University ofGroningen, 974 7 AG Groningen, The Netherlands Received I1 July 1989; accepted for publication 14 September 1989
The breakdown of the quantum Hall effect in high-mobility Si-MOSFETs occurs in a series of resistance steps as the current is increased beyond a critical value. These steps, that correspond to the successive breakdown of spatially localized parts of the sample, are not determined by inhomogeneities but have an intrinsic origin. We also observe that the breakdown always starts in the corner where the electrons enter the ZDEG. This asymmetry implies the need for a microscopic approach.
The zero-resistance state of a two-dimensional electron gas (ZDEG) in the quantum Hall regime is destroyed when the current exceeds a critical value [ I]. In wide structures (widths larger than 10 pm) one usually finds that the resistance appears in a series of steps that correspond to the successive breakdown of spatially localized parts of the sample as the current is increased. This behaviour may be due to inhomogeneities (weak spots) in the sample. We performed measIlrements on high-mobility Si-MOSFETs with 200-/lrn-wide 2DEG channels and find that the breakdown sequence is an intrinsic effect. Namely the sequence that we observe does not depend on the absolute location of the voltage contacts along the sample edge but on their relative location with respect to the corner in which the electrons are injected into the 2DEG. Moreover we conclude that the resistive state of the 2DEG originates in the corner where the electrons are injected and that with increasing current it spreads out from there. The explanation of this asymmetry between the current injection and extraction point will require a microscopic approach also for breakdown in wide channels. The measurements were performed on Si-MOSFETs with standard Hall-bar geometry (see fig. 1). The 2DEG is 200 pm wide and 600 pm long and the separation of the voltage contacts is 200 pm; the peak electron mobility is 2 m2/V-s. The breakdown measurements were done at T= 1.2 K and B= 12 T. The gate voltage was adjusted for the first Landau level 0039-6028/90/$03.50 ( Nosh-Holland )
0 Elsevier Science Publishers B.V.
(a)
4
5
6
(b)
4
5
6
Fig. 1. Current dist~butions in the 2DEG channel for at1 polarities of magnetic field and current. The dot indicates the comer in which the electrons are injected into the ZDEG. The dimensions of the channel and the positions of the voltage contacts are according to the indicated scale.
to be completely filled (filling factor u = 4 due to spin and valley degeneracy). A direct current and a small ( 100 nA) alternating current modulation is sent from source (s) to drain (d). The differential resistance R, between voltage contacts i and j is measured with a lock-in amplifier as a function of the direct current. Fig. I shows the idealized current distributions in the 2DEG; the dot indicates the point where the electrons are injected from the current contact into the 2DEG. By reversing the direction of the current and/ or the direction of the magnetic field, the injection point of the electrons can be placed in any of the four corners of the ZDEG. Fig. 2 shows results of the differential resistance between three different sets of voltage contacts for
P.C. van Son et al/The breakdown of the quantum Hall effect
58
J -40
-20
0
20
40 I,,(d)
Fig. 2. Differential resistance versus direct current for a Si-MOSFET at the v=4 QHE-plateau, showing the similarity between breakdown curves for different sets of voltage contacts. (a) Rlz with the direction of the magnetic field and the direction of the positive current as shown in fig. la. (b) R,, with positive current corresponding to fig. lc. (c) R,, with positive current corresponding to fig. 1b. The curves have been shifted upward for clarity.
three different combinations of magnetic field and current directions. The voltage contacts have been chosen in such a way that they have the same relative position with respect to the injection point: for negative current the injection point is as close as possible to the voltage contacts while for positive current it is in the opposite corner of the 2DEG. The three breakdown curves are the same, apart from small differences that may be due to inhomogeneities. Other samples with the same geometry show very similar structure. This means that there must be an intrinsic mechanism that determines the structure of these curves. Note that the observed asymmetry is not due to hysteresis. Fig. 3 shows how the breakdown developes across the sample. For negative current the current distribution is that of fig. lb. Resistance first appears between voltage contacts 1 and 2 and subsequently between contacts 4 and 5 and contacts 5 and 6. For a positive current (corresponding to fig. la) breakdown first occurs between contacts 5 and 6 and almost simultaneously between contacts 4 and 5 and contacts 1 and 2. This clearly shows that the resistive state of the 2DEG originates in the corner in which the electrons are injected into the 2DEG and spreads out from there all the way to the opposite corner. The
Lo
-20
0
20
40 Id< (PA)
Fig. 3. Differential resistance versus direct current for a Si-MOSFET at the v=4 QHE-plateau, showing how the breakdown spreads out across the sample. The direction of the magnetic field and the direction of the positive current are as shown in fig. la. (a) RL2. (b) R,,. (c) R56. The curves have been shifted upward for clarity.
structure in a single breakdown curve seems to be related to the appearance of resistance in other parts of the sample. The resistance rise at ZdC= + 18 ,uA in fig. 3c coincides with breakdown of the zero-resistance state between the drain contact and contact 3 (not shown), while the rise at Z,,= + 23 ,uA coincides with breakdown between contacts 4 and 5 (fig. 3b). The resistance tail for positive current in fig. 3a may be due to the fact that for high (Hall) voltages in the plane of the 2DEG, the effective gate voltage varies across the sample. The width of the o = 4 zeroresistance state in terms of gate voltage is 0.1 V which is equal to the Hall voltage for ZdC= 16 PA. The (a- ) symmetries in the breakdown curves have not been reported before probably because the voltage contacts are usually located much further from the current contacts. Then the intrinsic asymmetry is small and is easily dominated by the effect of inhomogeneities. Apart from the intrinsic nature of the breakdown sequence, we want to emphasize one other point. The asymmetry between the current injection and extraction points cannot be explained in a macroscopic equilibrium theory (like e.g. a heating model [ 21) because there the points are equivalent. Btittikers approach [ 3 ] is a good starting point to discuss nonequilibrium effects, but he predicts the dissipation to occur in the “wrong” corner. From our measurements we conclude that the elec-
P.C. van Son et al./The breakdown of the quantum Hall effect
tron injection point plays a crucial role in the breakdown of the quantum Hall effect in Hall-bar samples. Therefore a careful microscopic description of the electron injection process [4] will be essential for an explanation of our results.
59
References [ 1] G. Ebert, K. van Klitzing, K. Ploog and G. Weimann, J. Phys. C 16 (1983) 5441; M.E. Cage, R.F. Dziuba, B.F. Field and E.R. Williams, Phys. Rev. Lett. 51 (1983) 1374. [ 2 ] S.Komiyama, T. Takamasu, S. Hiyamizu and S. Sasa, Solid State Commun. 54 ( 1985) 479. [3] M. Biittiker, Phys. Rev. B 38 (1988) 9375. [4] P.C. van Son and T.M. Klapwijk, to be published.