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Scanning tunneling microscopy at microwave frequencies
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Ultramicroscopy 42-44 (1992) 379-387 North-Holland
Scanning tunneling microscopy at microwave frequencies W. Seifert, E. G e r n e r *, M. Stachel a n d K. D r a n s f e l d Fakultht fiir Physik, Universitiit Konstanz, W-7750 Konstanz, Germany Received 12 August 1991
We have applied to a scanning tunneling microscope (STM) in addition to the usual DC bias voltage an RF voltage at a frequency f of about 300 MHz, and observed the frequency components of the tip current at the second ( 2 f ) and third harmonic ( 3 f ) of the fundamental frequency f. In order to enhance the detection sensitivity at the higher harmonic frequencies the tip-substrate tunneling gap was part of a re-entrant cavity tuned either to 2 f or 3f. We studied the generation of harmonics using the STM on surfaces of H O P G graphite, gold and semiconducting WSe 2 under atmospheric conditions. T h e origin of the observed generation of higher harmonics turned out to be either the nonlinear current-voltage characteristic of the tunneling gap as we observed on H O P G substrates, or in the case of semiconducting WSe2, a strong distortion of the R F displacement current due to the field-induced change of the space-charge capacitance near the semiconductor surface. Using the generation of harmonics we have been able to image the space-charge density on a semiconductor surface with 15 n m resolution. The experiments reported here are of importance also to the question of whether a microwave STM can be used for the investigation of insulating substrates.
1. Introduction
Scanning tunneling microscopy (STM) has been introduced by Bining and Rohrer [1] as a powerful tool to probe the topology and the electronic properties of conducting surfaces with atomic resolution. At low scanning speed or in the constant-current mode only the low-frequency or the DC component of the tunneling current is generally of interest. Recently, however, several experiments have been reported in which the AC component of the tunneling current has been analyzed (at zero scanning speed) in order to observe also time-dependent processes at a fixed point of the sample: Koch and Hamers [2], for example, found an interesting time-dependent fluctuation of the tunneling current on partially oxidized Si surfaces. These fluctuations were ascribed to electronic or
t Deceased.
ionic charge motion under the tip. M611er et al. [3] found an AC component of the tunneling current on an Ag surface (even in the absence of a DC bias) which gives information about the thermal noise processes in tunneling microscopy. Manassen et al. [4] succeeded in observing the precession of an individual paramagnetic spin in a constant magnetic field by its modulation of the tunneling current at the precession frequency in the microwave range. Time-correlated tunneling of electrons due to the "Coulomb blockade" [5-8] should lead to small voltage oscillations across the junction at a frequency f = I/e with I being the tunnel current. Vice versa, the tunneling process has been shown to be affected in a resonant way by microwave radiation of the same frequency [9-11]. Besides the experiments just mentioned in which the AC component of the tunneling current was observed, Kochanski [12] was the first to apply a microwave voltage to the tunneling gap and study the generation of higher harmonics of
0304-3991/92/$05,00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
380
W. Seifert et al. / S T M at microwal,e frequencies
the tunneling current. He used the generated harmonics to control the feedback loop of a STM. Thus he was able to scan thin isolating films and semiconductors without any DC tunnel current. The physical mechanism for these interesting observations remains unclear. In a second class of time-dependent STM experiments two infrared laser beams of different frequencies were focussed directly on the tunneling gap. The nonlinear dependence of the tunnel current on the applied A C electric field led to the rectification or mixing of the incident radiation up to mixing frequencies in the far-infrared region. As demonstrated by Krieger et al. [13] and more recently by V61cker et al. [14] atomic resolution on graphite ( H O P G ) can be obtained using the emission of the mixing signal at microwave frequencies for the control of the feedback loop during the scanning process. More recently it has been shown that also optical radiation can be rectified by an STM [15,16]. In this paper we have applied high-frequency voltages to the STM in order to study the nature of the current nonlinearity at microwave frequencies. In our search for the physical mechanism responsible for the nonlinearity we used different tip and sample materials. The experiments described here were performed on surfaces of gold, H O P G - g r a p h i t e and tungsten diselenide. As a result we present a new type of scanning microscopy using the generation of higher harmonics for imaging the local space-charge region of semiconductors at variable depths.
2. The nonlinear behaviour of the STM
An important goal of our investigation was to better understand the nature of the current-voltage nonlinearity of the STM which leads to the observed generation of upper harmonics. Before describing our experiments we will here briefly discuss the possible origin of the nonlinearities. Several physical mechanisms could, in principle, explain a nonlinear behaviour between tunnel current and applied voltage. One possible mechanism, for example, could arise from the voltage-dependent elastic defor-
mation of tip and sample by electrostatic forces. Two condenser plates attract each other by a tension P = % E 2 / 2 where E0 and E are the permittivity and the electric field E = ( U ~ + u sin 2:rfi)/d, respectively. Typical electric fields ( E = 1 V / n m ) lead to P = 1 0 7 Pa = 100 k g / c m e. Considering the tip as a charged sphere near a conducting plane [17] we find for this cylindersymmetrical case according to standard elastic theory [18] a deformation of 2(1 + u ) ( 1 -
~z =
c
u)
fo P(r) dr,
where u and c are Poisson's ratio and Young's modulus, respectively. With ~, = 0.23 [19], c = 3.5 × 10 l° N / m 2 [20], a tunnel distance of 10 A and a tip radius of 0.1 /~m the resulting deformation is ~z = 0.1 A [21]. The junction capacitance increases with the absolute value of the tunnel voltage. If the microwave amplitude u exceeds the DC bias voltage U0, surface and tip vibrate towards each other at twice the microwave frequency and a strong third harmonic is expected for the tunnel current [22]. At small tunneling voltages the differential tunnel conductance is proportional to the local density of electronic states [23,24]. For an energy-dependent density of states the tunnel current becomes nonlinear. This nonlinearity is particularly strong in semiconductors with a pinned Fermi level [25]. In the large electric fields around the tip the electronic wavefunctions may also, in principle, be affected directly by the fields leading to a modification of the electronic states which are involved in the tunneling process. For large sinusoidal tunnel currents either the electron gas or the lattice may be periodically heated. In the latter case thermal expansion reducing the tunnel distance and enhancing the tunnel current has been observed for frequencies up to several MHz [26-29]. If AC voltages u of MHz-frequencies f are applied to the STM having a typical gap capacitance C the displacement current I = 2~rfCu exceeds the tunnel current. For example, for f = 160 MHz, C = 10-~6 F and u = 1 V the displacement current would be I = 100 nA, which is two orders
W. Seifertet al. / STM at microwavefrequencies of magnitude higher than the standard tunnel current of 1 nA. Capacitance microscopes [30-33] make use of this displacement current to measure the capacitance between a tip and the sample. If, however, the junction capacitance depends on the voltage, the displacement current becomes a nonlinear function of the applied voltage. The physical origins of a voltage-dependent capacitance and hence of a nonlinear displacement current may be various. Adsorbed polar molecules, for example, may form a dipolar layer leading to a nonlinear polarization and capacitance. When tunneling on semiconductors having a depletion layer the voltage-dependent capacitance Csemicondbetween the space-charge and the semiconductor surface is in series to the gap capacitance and thus determines the total capacitance between tip and sample. A simplified onedimensional model [34] which assumes a constant charge density P in the depletion layer of the semiconductor yields for the capacitance in the semiconductor near the surface
~Q
Csemic°nd- ~V
~
Pee° 2 ( A ( b - V) '
where e, %, Aq~ and V are the dielectric constant of the semiconductor, the permittivity, the difference of the work functions and the applied voltage, respectively. In our experiments described below we could easily measure the voltage dependence of the total junction capacitance by the shift of the cavity resonance frequency when varying the bias voltage at fixed tunneling distance. The voltage-dependent capacitance also leads to higher harmonics of the diplacement current: As can be shown by a Taylor expansion of the displacement current the second harmonic component of the current is proportional to the first derivative of the capacitance with respect to the bias voltage, and the third harmonic component of the current to the second derivative.
3. Experimental procedure The microwave circuit for our experiments on the higher harmonic generation is illustrated in
381
Fig. 1. Set-up of the experiment. An RF voltage of frequency
f / 2 or f/3 is supplied from the generator (G) and after passing through a low-pass filter LF it is applied to the tip of the junction. The sample (S) is mounted inside the 880 MHz re-entrant cavity,characterized by the quality factor (Q = 600). A pick-up loop couples out part of the power at the resonance frequency f. This signal after passing through a high-pass filter and pre-amplifier (PA) is further amplified by a heterodyne amplifier (LO, M and IF) and detected (D). The feedback loop is controlled by the tunnel current (amplifier A). U0 is the DC bias voltage. fig. 1. We use a re-entrant cavity having a resonance frequency f = 870 M H z and a quality factor Q of about 600. The input frequency from the generator G is f / 2 or f / 3 when looking for the second or third harmonic, respectively. For example, if we apply an R F voltage having a frequency f / 2 and the current has a strong component at the second harmonic frequency, it will excite the cavity at its resonance frequency f. The low-pass filter LF suppresses higher harmonics emitted from the generator to - 1 4 0 dB relative to the level of the fundamental frequency at the generator. The coaxial input cable that is connected to the tip is terminated by a 50 f~ resistor to achieve proper impedance matching. D C currents are blocked by two capacitors. An inductive pick-up loop at the bottom of the cavity is by about - 1 0 dB subcritically coupled and its RF-power output is first passed through a high-pass filter (not shown) which prevents the fundamental frequency from reaching the preamplifier PA and the mixer M. The pre-amplified signal is mixed with a signal of slightly different frequency (from the local oscillator LO) and the resulting IF signal is further amplified (with a bandwidth of 0.5 MHz) and detected by a Wiltron 560A scalar network analyzer D. In this way
382
W. Seifert et al. / STM at microwave frequencies
changes of the Upper harmonics corresponding to signal powers of - 1 2 0 dBm (or 10-15 W), close to the thermal-noise limit (k~Tf/Q), could be resolved. If the cavity (resonance frequency f = w/2~-) is excited by a periodic current of amplitude i from the tip the maximum output power Po,, from the cavity into the pre-amplifier can be estimated [35] to be
100
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80
i
~ so
[
C •'--
Q. 40
40
=
Thus the power which can be coupled out of the cavity is proportional to the square of the component of the tunnel current in resonance with the cavity. As an example, for a periodic tunnel current of 1 nA an R F power of 100 fW can be coupled out of the cavity.
4. Experimental results When tunneling with a gold tip on a gold surface a linear I - V characteristic is expected because of the nearly constant local density of states. In this case only the higher harmonics excited by the elastic deformation of the surface might be observable if the deformation is strong enough. However, in our experiments with gold surfaces no higher harmonics could be detected at all. From the sensitivity of our equipment described above we can draw the conclusion that the current component of the second or third harmonic frequency (in resonance with the cavity) is less than 2 nA, for an amplitude of the RF tunnel voltage of 1.5 V. The elastic deformation of the tunneling gap, which would be necessary for this tunnel current, amounts only to 0.3 ,~. This agrees with the theoretical expectations: for fields applied in our experiments a deformation of at most 0.4 ,~ would have been expected. We noticed, however, often a weak rectified tunnel current, if the RF voltage was applied to the A u - A u junction. Interestingly, the efficiency of the rectification depended clearly on the location of the tip: the sample became positive in relation to the tip whenever the topography of
.R
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~ 20 I-
A ;
Pout i2Q/°°C.
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L__I
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Fig. 2. Both the tunnel current (left scale) and the second harmonic power (right scale) show a similar variation with the tunneling distance (as determined from the voltage applied to the piezo controlling the z motion of the tip).
the gold surface is highly convex. For an R F voltage of about 5 V the sample surface charged up to +0.3 V corresponding to a rectifying current of a few hA. We believe that the asymmetry of the tunnel junction arises from sharp protrusions on the gold surface [36]. The ~old surface was prepared by evaporating a 1000 A thick gold film on H O P G graphite and its STM image shows protrusions having lateral dimensions of about 500 A and similar elevations. Thus their radius of curvature is presumably smaller than the tip radius. On pure HOPG-graphite surfaces higher harmonics could best be seen when the tip is close enough to the sample for a high DC tunnel current (o> 10 hA) to flow. At distances larger than 25 A no tunnel current and no higher harmonics were detected as shown in fig. 2. The voltage characteristics of the second and third harmonics are displayed in figs. 3a and 3b, respectively. They can be explained by the D C I - V characteristic shown in fig 3c. For small voltages a Taylor expansion of the current with respect to the tunnel voltage shows that the current component with the second or third harmonic frequency shoul be proportional to the second or third derivative of the I - V curve, respectively. We have checked this relationship between the higher harmonics and the tunnel characteristic
W. Seifert et al. / S T M at microwave frequencies
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383
quantitatively by numerical processing of the data shown in figs. 3a and 3b. We found the nonlinearity of the I - V characteristic effective at R F frequencies to be the same as the one observed under D C conditions as shown in fig. 3c. The generation of higher harmonics in the tunnel gap can be seen directly from the shape of the I - I / curve in fig. 3c. Insert 1 in fig. 3c shows the rectification of a sinusoidal microwave voltage and the generation of a second harmonic at a bias voltage of 0,5 V. The third harmonic (see fig. 3b) shows interesting behaviour with two minima at about U0 = +0.4 V with a maximum located in between at zero bias, This behaviour is in our view related to the curvatures of the I - I / c h a r a c t e r i s t i c shown in fig. 3c changing sign at about U0 = _+0.4 V: at smaller voltages I U0[ the curvature is positive (slope increasing with I U0 I) while at larger bias voltages ([U0l > 0.4 V) the curvature becomes negative (slope decreasing with ]U 0 [) because the tunnel current shows an onset of saturation at high currents. At about +_0.4 V the curvature changes its sign and turns from a positive (at small [U 01) to a negative curvature (for large [U0[). This decreasing slope at high voltages is perhaps caused by the mechanical resistance of adsorbed layers between tip and substrate. Thus qualitatively the intensity of the 3rd harmonic in fig. 3b can be understood from the shape of the DC characteristic shown in fig. 3c. In view of the large AC voltage (of 0.5 V) it is difficult to make more detailed statements about the exact position of the turning points. Thus the nonlinear behaviour of the STM at microwave frequencies on H O P G is a consequence of the nonlinearity of the tunnel characteristic observed also in D C measurements. This nonlinearity may be caused partially by the fieldinduced elastic deformation as discussed above and partially by the local density of states (LDOS) as calculated from first principles using the localdensity approximation [37,38]. The nonlinearity has also been measured by Mizutani et al. [39] up to tunnel currents of 60 nA, and by Krieger et al. [40] up to 800 nA. When applying the RF voltages between the tip and semiconducting WSe 2 surfaces we ob-
384
V£ Seifert et al. / S T M at microwaL~e frequencies -70,
-80
i
-90
i
-100 L
-110
50 100 150 200 Distance between tip and sample [nm]
Fig. 4. Distance dependence of the 3rd harmonic power for the sample of p-doped WSe 2. The distance shown is that derived from the z motion of the tip. The input power was 20 roW. The signal persists to distances of up to 100 rim. Therefore it cannot arise from a tunneling process.
served very strong higher harmonics which remained well visible up to t i p - s a m p l e distances of 100 rim, as shown in fig. 4. They can arise from
tunneling electrons only at very small gaps (in the fingstr6m range). A typical I - V tunneling characteristic of a Pt,/Ir tip at close distance over a sample of p-type WSe 2 is shown in fig. 5a. At larger distances (between about 10 and 100 nm) the observed strong higher harmonics can no longer be caused by the tunneling process. The second and third harmonics observed in the case of large distances show an interesting dependence on the DC bias voltage as demonstrated in figs. 5b and 5c, respectively. This dependence of the higher harmonics on the DC bias voltage can be explained by a voltage-dependent space-charge motion near the surface of the p-type WSe 2 sample. The mobility of holes in p-type WSe 2 (0.014 m 2 / V . s [41]) is sufficiently large that they can follow the microwave fields. If the sample becomes negative in relation to the tip the depletion layer grows and therefore the junction capacitance decreases. Vice
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Fig. 5. Further data on the p-doped sample of WSe 2 (using a P t / I r tip and operating at tunneling distances): the DC tunneling current as a function of the DC bias (a). The 2nd (b) and 3rd (c) harmonic power as a function of the DC bias. The amplitude of the RF voltage was 0.3 and l V, respectively, corresponding to an input power of 1.6 and 40 roW, respectively. The curves (a)-(c) are averaged over 10 voltage sweeps. (d) The tip-sample capacitance versus bias voltage.
W. Seifert et al. / STM at microwave frequencies
versa, for a positive potential of the sample the depletion layer goes to zero and the capacitance reaches its maximum value. (The formation of an inversion layer at a very high negative potential of the sample could not be observed by this method, probably, because the processes of generation and recombination of minority charge carriers is too slow to follow the high frequencies.) The variation of the t i p - s a m p l e capacitance by a D C bias could be easily demonstrated in our cavity: for this purpose we excited the cavity (via the inductive loop) near its resonance frequency where the slope of the resonance peak is steepest. Due to the slight Shift of the cavity resonance while varying the bias voltage we detected a change of the reflected power. Even without a modulation technique we could thus detect changes of the junction capacitance of 2 × 10-18 F. The measured junction capacitance as a function of the D C bias voltage is shown in fig. 5d. The local slope (dC/dU o) and the curvature (d2C/dUl~) of this function depend on the D C bias U 0. If also a microwave voltage (of amplitude u _< 1 V and at the frequency f ) is applied to the tunnel junction the displacement current i = d[C(U 0 + u)]/dt is is expected to contain also u p p e r harmonics since C and u are both time-dependent. The second harmonic (frequency 2f, see fig. 5b) of the current should be proportional to the slope (dC/dV) of the curve in fig. 5d determined by the given D C bias. Indeed, the observed second harmonic power (fig. 5b) exhibits a maximum for a D C bias just below 0.6 V where the slope in fig. 5d is steepest. The third harmonic (frequency 3f, see fig. 5c) should vary with the curvature (d2C/dUo2) of the function shown in fig. 5d. The measured third harmonic power (fig. 5c) shows, as expected, a broad maximum for the DC bias V ~ 0 V, another maximum at V = 1 V and a sharp minimum at V ~ 0.6 V, where the curvature in fig. 5d is zero.
This very good agreement between the theoretical and experimentally determined dependence of the higher harmonics on the D C bias, and the persistence of the strong harmonics at distances up to 100 nm, are convincing evidence
385
that the voltage-dependent space-charge capacitance is responsible for our observations on WSe 2. With the microwave technique described above we have also recorded pictures of the 2nd and 3rd harmonic intensity while scanning across the WSe 2 surface. The tunnel current was controlled to a fixed level, and the topography together with the second or third harmonic were simultaneously recorded. In this way, the local topography (at atomic resolution) and the voltage-dependent space-charge (at submicron resolution) can be imaged at the same time. In our first scanned pictures (not shown here) we found for the WSe 2 sample that in spite of its atomically flat surface the second and third harmonic images show distinct structures with strong intensity variations on a lateral scale of about 150 A. There is a correlation between the fine-structured second harmonic picture and the somewhat coarser third-harmonic image. This structure is presumably caused by local variations of the space-charge density. We suppose that - depending on the DC bias - we have imaged the impurities within about 300 A from the surface.
5. Conclusions
From our studies of the generation of higher harmonics when applying microwaves to a STM we found that for a gold tip on a gold sample no higher harmonic generation could be detected. The second harmonic output was less than 10-~5 W. This is in agreement with a theoretical estimate that for the given fields the elastic deformation of tip and substrate under the influence of the Coulomb forces should not lead to a detectable generation of harmonics. In our experiments on graphite we saw a generation of the 2nd and 3rd harmonic reaching a power level of about 10-~3 W. H e r e the variation of the upper harmonic components with the DC bias clearly shows that the nonlinearity of the D C tunnel characteristic is responsible also for the nonlinear generation of upper harmonics at microwave frequencies.
386
W. Seifert et al. / STM at microwaz~e frequencies
For semiconducting W S e 2 the generation of upper harmonics is still more intense reaching a power of 10-11 W. Interestingly, the upper harmonics remain visible up to tip-sample separations of 100 nm. Thus the tunneling process is not responsible for their generation. It is rather the voltage-dependent depletion layer in the semiconductor leading to a voltage-dependent junction capacity which can account for the generation of the observed strong upper harmonics of the displacement current. Using our technique it is possible to image simultaneously the topography and the local space-charges on semiconductor surfaces with submicron resolution. Because of the differential behaviour mainly the frontier of the space-charge region contributes. By means of the bias voltage we can adjust the depth of the examined layer.
Achnowledgements
One of the authors, Ernst Gerner, died during the early phase of this work. His enthusiasm and his important initial contributions are greatly appreciated. We are grateful also to S. Akari, H. Birk, Ch. Kaiser, B. Koslowski, R. Magerle, R. M611er and T. Schill for many valuable discussions and help. The semiconducting samples were contributed by M. V6gt and K. Friemelt. This investigation has been supported by the Deutsche Forschungsgemeinschaft (DFG, SFB 306).
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W. Seifert et al. / S T M at microwave frequencies [33] H.P. Kleinknecht, J.R. Sandercock and H. Meier, Scanning Microsc. 2 (1988) 1839. [34] S.M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981) p. 248. [35] In order to maintain a constant charge oscillation q0 sin(o~t) in the cavity in spite of the dissipation characterized by a decay time z an external periodic current of amplitude i = d q / d t = q o / r = qoo~/Q has to be added. For critical coupling the maximum power output from the cavity is Pout = q~to/CQ. By eliminating q0 from both equations one finds Pout = i2Q/°~C. [36] N.M. Miskovsky, P.H. Cutler, T.E. Feuchtwang, S.J.
[37] [38] [39]
[40] [41]
387
Shepherd, A.A. Lucas and T.E. Sullivan, Appl. Phys. Lett. 37 (1980) 189. K. Kobayashi and M. Tsukada, J. Vac. Sci. Technol. A 8 (1990) 170. K. Kobayashi, N. Isshiki and M. Tsukada, Solid State Commun. 74 (1990) 1187. W. Mizutani, M. Shigeno, K. Saito, N. Morita, T. Yoshioka, M. Ono and K. Kajimura, J. Microscopy 152 (1988) 547. W. Krieger, T. Suzuki, M. V61cker and H. Walther, Phys. Rev. B 41 (1990) 10229. A. Klein, Diploma Thesis, Universit~it Konstanz (1989).
Ultramicroscopy 42-44 (1992) 379-387 North-Holland
Scanning tunneling microscopy at microwave frequencies W. Seifert, E. G e r n e r *, M. Stachel a n d K. D r a n s f e l d Fakultht fiir Physik, Universitiit Konstanz, W-7750 Konstanz, Germany Received 12 August 1991
We have applied to a scanning tunneling microscope (STM) in addition to the usual DC bias voltage an RF voltage at a frequency f of about 300 MHz, and observed the frequency components of the tip current at the second ( 2 f ) and third harmonic ( 3 f ) of the fundamental frequency f. In order to enhance the detection sensitivity at the higher harmonic frequencies the tip-substrate tunneling gap was part of a re-entrant cavity tuned either to 2 f or 3f. We studied the generation of harmonics using the STM on surfaces of H O P G graphite, gold and semiconducting WSe 2 under atmospheric conditions. T h e origin of the observed generation of higher harmonics turned out to be either the nonlinear current-voltage characteristic of the tunneling gap as we observed on H O P G substrates, or in the case of semiconducting WSe2, a strong distortion of the R F displacement current due to the field-induced change of the space-charge capacitance near the semiconductor surface. Using the generation of harmonics we have been able to image the space-charge density on a semiconductor surface with 15 n m resolution. The experiments reported here are of importance also to the question of whether a microwave STM can be used for the investigation of insulating substrates.
1. Introduction
Scanning tunneling microscopy (STM) has been introduced by Bining and Rohrer [1] as a powerful tool to probe the topology and the electronic properties of conducting surfaces with atomic resolution. At low scanning speed or in the constant-current mode only the low-frequency or the DC component of the tunneling current is generally of interest. Recently, however, several experiments have been reported in which the AC component of the tunneling current has been analyzed (at zero scanning speed) in order to observe also time-dependent processes at a fixed point of the sample: Koch and Hamers [2], for example, found an interesting time-dependent fluctuation of the tunneling current on partially oxidized Si surfaces. These fluctuations were ascribed to electronic or
t Deceased.
ionic charge motion under the tip. M611er et al. [3] found an AC component of the tunneling current on an Ag surface (even in the absence of a DC bias) which gives information about the thermal noise processes in tunneling microscopy. Manassen et al. [4] succeeded in observing the precession of an individual paramagnetic spin in a constant magnetic field by its modulation of the tunneling current at the precession frequency in the microwave range. Time-correlated tunneling of electrons due to the "Coulomb blockade" [5-8] should lead to small voltage oscillations across the junction at a frequency f = I/e with I being the tunnel current. Vice versa, the tunneling process has been shown to be affected in a resonant way by microwave radiation of the same frequency [9-11]. Besides the experiments just mentioned in which the AC component of the tunneling current was observed, Kochanski [12] was the first to apply a microwave voltage to the tunneling gap and study the generation of higher harmonics of
0304-3991/92/$05,00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
380
W. Seifert et al. / S T M at microwal,e frequencies
the tunneling current. He used the generated harmonics to control the feedback loop of a STM. Thus he was able to scan thin isolating films and semiconductors without any DC tunnel current. The physical mechanism for these interesting observations remains unclear. In a second class of time-dependent STM experiments two infrared laser beams of different frequencies were focussed directly on the tunneling gap. The nonlinear dependence of the tunnel current on the applied A C electric field led to the rectification or mixing of the incident radiation up to mixing frequencies in the far-infrared region. As demonstrated by Krieger et al. [13] and more recently by V61cker et al. [14] atomic resolution on graphite ( H O P G ) can be obtained using the emission of the mixing signal at microwave frequencies for the control of the feedback loop during the scanning process. More recently it has been shown that also optical radiation can be rectified by an STM [15,16]. In this paper we have applied high-frequency voltages to the STM in order to study the nature of the current nonlinearity at microwave frequencies. In our search for the physical mechanism responsible for the nonlinearity we used different tip and sample materials. The experiments described here were performed on surfaces of gold, H O P G - g r a p h i t e and tungsten diselenide. As a result we present a new type of scanning microscopy using the generation of higher harmonics for imaging the local space-charge region of semiconductors at variable depths.
2. The nonlinear behaviour of the STM
An important goal of our investigation was to better understand the nature of the current-voltage nonlinearity of the STM which leads to the observed generation of upper harmonics. Before describing our experiments we will here briefly discuss the possible origin of the nonlinearities. Several physical mechanisms could, in principle, explain a nonlinear behaviour between tunnel current and applied voltage. One possible mechanism, for example, could arise from the voltage-dependent elastic defor-
mation of tip and sample by electrostatic forces. Two condenser plates attract each other by a tension P = % E 2 / 2 where E0 and E are the permittivity and the electric field E = ( U ~ + u sin 2:rfi)/d, respectively. Typical electric fields ( E = 1 V / n m ) lead to P = 1 0 7 Pa = 100 k g / c m e. Considering the tip as a charged sphere near a conducting plane [17] we find for this cylindersymmetrical case according to standard elastic theory [18] a deformation of 2(1 + u ) ( 1 -
~z =
c
u)
fo P(r) dr,
where u and c are Poisson's ratio and Young's modulus, respectively. With ~, = 0.23 [19], c = 3.5 × 10 l° N / m 2 [20], a tunnel distance of 10 A and a tip radius of 0.1 /~m the resulting deformation is ~z = 0.1 A [21]. The junction capacitance increases with the absolute value of the tunnel voltage. If the microwave amplitude u exceeds the DC bias voltage U0, surface and tip vibrate towards each other at twice the microwave frequency and a strong third harmonic is expected for the tunnel current [22]. At small tunneling voltages the differential tunnel conductance is proportional to the local density of electronic states [23,24]. For an energy-dependent density of states the tunnel current becomes nonlinear. This nonlinearity is particularly strong in semiconductors with a pinned Fermi level [25]. In the large electric fields around the tip the electronic wavefunctions may also, in principle, be affected directly by the fields leading to a modification of the electronic states which are involved in the tunneling process. For large sinusoidal tunnel currents either the electron gas or the lattice may be periodically heated. In the latter case thermal expansion reducing the tunnel distance and enhancing the tunnel current has been observed for frequencies up to several MHz [26-29]. If AC voltages u of MHz-frequencies f are applied to the STM having a typical gap capacitance C the displacement current I = 2~rfCu exceeds the tunnel current. For example, for f = 160 MHz, C = 10-~6 F and u = 1 V the displacement current would be I = 100 nA, which is two orders
W. Seifertet al. / STM at microwavefrequencies of magnitude higher than the standard tunnel current of 1 nA. Capacitance microscopes [30-33] make use of this displacement current to measure the capacitance between a tip and the sample. If, however, the junction capacitance depends on the voltage, the displacement current becomes a nonlinear function of the applied voltage. The physical origins of a voltage-dependent capacitance and hence of a nonlinear displacement current may be various. Adsorbed polar molecules, for example, may form a dipolar layer leading to a nonlinear polarization and capacitance. When tunneling on semiconductors having a depletion layer the voltage-dependent capacitance Csemicondbetween the space-charge and the semiconductor surface is in series to the gap capacitance and thus determines the total capacitance between tip and sample. A simplified onedimensional model [34] which assumes a constant charge density P in the depletion layer of the semiconductor yields for the capacitance in the semiconductor near the surface
~Q
Csemic°nd- ~V
~
Pee° 2 ( A ( b - V) '
where e, %, Aq~ and V are the dielectric constant of the semiconductor, the permittivity, the difference of the work functions and the applied voltage, respectively. In our experiments described below we could easily measure the voltage dependence of the total junction capacitance by the shift of the cavity resonance frequency when varying the bias voltage at fixed tunneling distance. The voltage-dependent capacitance also leads to higher harmonics of the diplacement current: As can be shown by a Taylor expansion of the displacement current the second harmonic component of the current is proportional to the first derivative of the capacitance with respect to the bias voltage, and the third harmonic component of the current to the second derivative.
3. Experimental procedure The microwave circuit for our experiments on the higher harmonic generation is illustrated in
381
Fig. 1. Set-up of the experiment. An RF voltage of frequency
f / 2 or f/3 is supplied from the generator (G) and after passing through a low-pass filter LF it is applied to the tip of the junction. The sample (S) is mounted inside the 880 MHz re-entrant cavity,characterized by the quality factor (Q = 600). A pick-up loop couples out part of the power at the resonance frequency f. This signal after passing through a high-pass filter and pre-amplifier (PA) is further amplified by a heterodyne amplifier (LO, M and IF) and detected (D). The feedback loop is controlled by the tunnel current (amplifier A). U0 is the DC bias voltage. fig. 1. We use a re-entrant cavity having a resonance frequency f = 870 M H z and a quality factor Q of about 600. The input frequency from the generator G is f / 2 or f / 3 when looking for the second or third harmonic, respectively. For example, if we apply an R F voltage having a frequency f / 2 and the current has a strong component at the second harmonic frequency, it will excite the cavity at its resonance frequency f. The low-pass filter LF suppresses higher harmonics emitted from the generator to - 1 4 0 dB relative to the level of the fundamental frequency at the generator. The coaxial input cable that is connected to the tip is terminated by a 50 f~ resistor to achieve proper impedance matching. D C currents are blocked by two capacitors. An inductive pick-up loop at the bottom of the cavity is by about - 1 0 dB subcritically coupled and its RF-power output is first passed through a high-pass filter (not shown) which prevents the fundamental frequency from reaching the preamplifier PA and the mixer M. The pre-amplified signal is mixed with a signal of slightly different frequency (from the local oscillator LO) and the resulting IF signal is further amplified (with a bandwidth of 0.5 MHz) and detected by a Wiltron 560A scalar network analyzer D. In this way
382
W. Seifert et al. / STM at microwave frequencies
changes of the Upper harmonics corresponding to signal powers of - 1 2 0 dBm (or 10-15 W), close to the thermal-noise limit (k~Tf/Q), could be resolved. If the cavity (resonance frequency f = w/2~-) is excited by a periodic current of amplitude i from the tip the maximum output power Po,, from the cavity into the pre-amplifier can be estimated [35] to be
100
IGraphiteif100.
80
i
~ so
[
C •'--
Q. 40
40
=
Thus the power which can be coupled out of the cavity is proportional to the square of the component of the tunnel current in resonance with the cavity. As an example, for a periodic tunnel current of 1 nA an R F power of 100 fW can be coupled out of the cavity.
4. Experimental results When tunneling with a gold tip on a gold surface a linear I - V characteristic is expected because of the nearly constant local density of states. In this case only the higher harmonics excited by the elastic deformation of the surface might be observable if the deformation is strong enough. However, in our experiments with gold surfaces no higher harmonics could be detected at all. From the sensitivity of our equipment described above we can draw the conclusion that the current component of the second or third harmonic frequency (in resonance with the cavity) is less than 2 nA, for an amplitude of the RF tunnel voltage of 1.5 V. The elastic deformation of the tunneling gap, which would be necessary for this tunnel current, amounts only to 0.3 ,~. This agrees with the theoretical expectations: for fields applied in our experiments a deformation of at most 0.4 ,~ would have been expected. We noticed, however, often a weak rectified tunnel current, if the RF voltage was applied to the A u - A u junction. Interestingly, the efficiency of the rectification depended clearly on the location of the tip: the sample became positive in relation to the tip whenever the topography of
.R
2 nd Harmonic power
~ 20 I-
A ;
Pout i2Q/°°C.
current
•
L 2
L__I
o
__ 3
4
5
Tunnel distance [nm]
Fig. 2. Both the tunnel current (left scale) and the second harmonic power (right scale) show a similar variation with the tunneling distance (as determined from the voltage applied to the piezo controlling the z motion of the tip).
the gold surface is highly convex. For an R F voltage of about 5 V the sample surface charged up to +0.3 V corresponding to a rectifying current of a few hA. We believe that the asymmetry of the tunnel junction arises from sharp protrusions on the gold surface [36]. The ~old surface was prepared by evaporating a 1000 A thick gold film on H O P G graphite and its STM image shows protrusions having lateral dimensions of about 500 A and similar elevations. Thus their radius of curvature is presumably smaller than the tip radius. On pure HOPG-graphite surfaces higher harmonics could best be seen when the tip is close enough to the sample for a high DC tunnel current (o> 10 hA) to flow. At distances larger than 25 A no tunnel current and no higher harmonics were detected as shown in fig. 2. The voltage characteristics of the second and third harmonics are displayed in figs. 3a and 3b, respectively. They can be explained by the D C I - V characteristic shown in fig 3c. For small voltages a Taylor expansion of the current with respect to the tunnel voltage shows that the current component with the second or third harmonic frequency shoul be proportional to the second or third derivative of the I - V curve, respectively. We have checked this relationship between the higher harmonics and the tunnel characteristic
W. Seifert et al. / S T M at microwave frequencies
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383
quantitatively by numerical processing of the data shown in figs. 3a and 3b. We found the nonlinearity of the I - V characteristic effective at R F frequencies to be the same as the one observed under D C conditions as shown in fig. 3c. The generation of higher harmonics in the tunnel gap can be seen directly from the shape of the I - I / curve in fig. 3c. Insert 1 in fig. 3c shows the rectification of a sinusoidal microwave voltage and the generation of a second harmonic at a bias voltage of 0,5 V. The third harmonic (see fig. 3b) shows interesting behaviour with two minima at about U0 = +0.4 V with a maximum located in between at zero bias, This behaviour is in our view related to the curvatures of the I - I / c h a r a c t e r i s t i c shown in fig. 3c changing sign at about U0 = _+0.4 V: at smaller voltages I U0[ the curvature is positive (slope increasing with I U0 I) while at larger bias voltages ([U0l > 0.4 V) the curvature becomes negative (slope decreasing with ]U 0 [) because the tunnel current shows an onset of saturation at high currents. At about +_0.4 V the curvature changes its sign and turns from a positive (at small [U 01) to a negative curvature (for large [U0[). This decreasing slope at high voltages is perhaps caused by the mechanical resistance of adsorbed layers between tip and substrate. Thus qualitatively the intensity of the 3rd harmonic in fig. 3b can be understood from the shape of the DC characteristic shown in fig. 3c. In view of the large AC voltage (of 0.5 V) it is difficult to make more detailed statements about the exact position of the turning points. Thus the nonlinear behaviour of the STM at microwave frequencies on H O P G is a consequence of the nonlinearity of the tunnel characteristic observed also in D C measurements. This nonlinearity may be caused partially by the fieldinduced elastic deformation as discussed above and partially by the local density of states (LDOS) as calculated from first principles using the localdensity approximation [37,38]. The nonlinearity has also been measured by Mizutani et al. [39] up to tunnel currents of 60 nA, and by Krieger et al. [40] up to 800 nA. When applying the RF voltages between the tip and semiconducting WSe 2 surfaces we ob-
384
V£ Seifert et al. / S T M at microwaL~e frequencies -70,
-80
i
-90
i
-100 L
-110
50 100 150 200 Distance between tip and sample [nm]
Fig. 4. Distance dependence of the 3rd harmonic power for the sample of p-doped WSe 2. The distance shown is that derived from the z motion of the tip. The input power was 20 roW. The signal persists to distances of up to 100 rim. Therefore it cannot arise from a tunneling process.
served very strong higher harmonics which remained well visible up to t i p - s a m p l e distances of 100 rim, as shown in fig. 4. They can arise from
tunneling electrons only at very small gaps (in the fingstr6m range). A typical I - V tunneling characteristic of a Pt,/Ir tip at close distance over a sample of p-type WSe 2 is shown in fig. 5a. At larger distances (between about 10 and 100 nm) the observed strong higher harmonics can no longer be caused by the tunneling process. The second and third harmonics observed in the case of large distances show an interesting dependence on the DC bias voltage as demonstrated in figs. 5b and 5c, respectively. This dependence of the higher harmonics on the DC bias voltage can be explained by a voltage-dependent space-charge motion near the surface of the p-type WSe 2 sample. The mobility of holes in p-type WSe 2 (0.014 m 2 / V . s [41]) is sufficiently large that they can follow the microwave fields. If the sample becomes negative in relation to the tip the depletion layer grows and therefore the junction capacitance decreases. Vice
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Fig. 5. Further data on the p-doped sample of WSe 2 (using a P t / I r tip and operating at tunneling distances): the DC tunneling current as a function of the DC bias (a). The 2nd (b) and 3rd (c) harmonic power as a function of the DC bias. The amplitude of the RF voltage was 0.3 and l V, respectively, corresponding to an input power of 1.6 and 40 roW, respectively. The curves (a)-(c) are averaged over 10 voltage sweeps. (d) The tip-sample capacitance versus bias voltage.
W. Seifert et al. / STM at microwave frequencies
versa, for a positive potential of the sample the depletion layer goes to zero and the capacitance reaches its maximum value. (The formation of an inversion layer at a very high negative potential of the sample could not be observed by this method, probably, because the processes of generation and recombination of minority charge carriers is too slow to follow the high frequencies.) The variation of the t i p - s a m p l e capacitance by a D C bias could be easily demonstrated in our cavity: for this purpose we excited the cavity (via the inductive loop) near its resonance frequency where the slope of the resonance peak is steepest. Due to the slight Shift of the cavity resonance while varying the bias voltage we detected a change of the reflected power. Even without a modulation technique we could thus detect changes of the junction capacitance of 2 × 10-18 F. The measured junction capacitance as a function of the D C bias voltage is shown in fig. 5d. The local slope (dC/dU o) and the curvature (d2C/dUl~) of this function depend on the D C bias U 0. If also a microwave voltage (of amplitude u _< 1 V and at the frequency f ) is applied to the tunnel junction the displacement current i = d[C(U 0 + u)]/dt is is expected to contain also u p p e r harmonics since C and u are both time-dependent. The second harmonic (frequency 2f, see fig. 5b) of the current should be proportional to the slope (dC/dV) of the curve in fig. 5d determined by the given D C bias. Indeed, the observed second harmonic power (fig. 5b) exhibits a maximum for a D C bias just below 0.6 V where the slope in fig. 5d is steepest. The third harmonic (frequency 3f, see fig. 5c) should vary with the curvature (d2C/dUo2) of the function shown in fig. 5d. The measured third harmonic power (fig. 5c) shows, as expected, a broad maximum for the DC bias V ~ 0 V, another maximum at V = 1 V and a sharp minimum at V ~ 0.6 V, where the curvature in fig. 5d is zero.
This very good agreement between the theoretical and experimentally determined dependence of the higher harmonics on the D C bias, and the persistence of the strong harmonics at distances up to 100 nm, are convincing evidence
385
that the voltage-dependent space-charge capacitance is responsible for our observations on WSe 2. With the microwave technique described above we have also recorded pictures of the 2nd and 3rd harmonic intensity while scanning across the WSe 2 surface. The tunnel current was controlled to a fixed level, and the topography together with the second or third harmonic were simultaneously recorded. In this way, the local topography (at atomic resolution) and the voltage-dependent space-charge (at submicron resolution) can be imaged at the same time. In our first scanned pictures (not shown here) we found for the WSe 2 sample that in spite of its atomically flat surface the second and third harmonic images show distinct structures with strong intensity variations on a lateral scale of about 150 A. There is a correlation between the fine-structured second harmonic picture and the somewhat coarser third-harmonic image. This structure is presumably caused by local variations of the space-charge density. We suppose that - depending on the DC bias - we have imaged the impurities within about 300 A from the surface.
5. Conclusions
From our studies of the generation of higher harmonics when applying microwaves to a STM we found that for a gold tip on a gold sample no higher harmonic generation could be detected. The second harmonic output was less than 10-~5 W. This is in agreement with a theoretical estimate that for the given fields the elastic deformation of tip and substrate under the influence of the Coulomb forces should not lead to a detectable generation of harmonics. In our experiments on graphite we saw a generation of the 2nd and 3rd harmonic reaching a power level of about 10-~3 W. H e r e the variation of the upper harmonic components with the DC bias clearly shows that the nonlinearity of the D C tunnel characteristic is responsible also for the nonlinear generation of upper harmonics at microwave frequencies.
386
W. Seifert et al. / STM at microwaz~e frequencies
For semiconducting W S e 2 the generation of upper harmonics is still more intense reaching a power of 10-11 W. Interestingly, the upper harmonics remain visible up to tip-sample separations of 100 nm. Thus the tunneling process is not responsible for their generation. It is rather the voltage-dependent depletion layer in the semiconductor leading to a voltage-dependent junction capacity which can account for the generation of the observed strong upper harmonics of the displacement current. Using our technique it is possible to image simultaneously the topography and the local space-charges on semiconductor surfaces with submicron resolution. Because of the differential behaviour mainly the frontier of the space-charge region contributes. By means of the bias voltage we can adjust the depth of the examined layer.
Achnowledgements
One of the authors, Ernst Gerner, died during the early phase of this work. His enthusiasm and his important initial contributions are greatly appreciated. We are grateful also to S. Akari, H. Birk, Ch. Kaiser, B. Koslowski, R. Magerle, R. M611er and T. Schill for many valuable discussions and help. The semiconducting samples were contributed by M. V6gt and K. Friemelt. This investigation has been supported by the Deutsche Forschungsgemeinschaft (DFG, SFB 306).
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W. Seifert et al. / S T M at microwave frequencies [33] H.P. Kleinknecht, J.R. Sandercock and H. Meier, Scanning Microsc. 2 (1988) 1839. [34] S.M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981) p. 248. [35] In order to maintain a constant charge oscillation q0 sin(o~t) in the cavity in spite of the dissipation characterized by a decay time z an external periodic current of amplitude i = d q / d t = q o / r = qoo~/Q has to be added. For critical coupling the maximum power output from the cavity is Pout = q~to/CQ. By eliminating q0 from both equations one finds Pout = i2Q/°~C. [36] N.M. Miskovsky, P.H. Cutler, T.E. Feuchtwang, S.J.
[37] [38] [39]
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