A New Method of Scanning Tunneling Spectroscopy for Study of the Energy Structure of Semiconductors and Free Electron Gas in Metals

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1 SCANNING Vol. 19, 59 5 (1997) Received April 1, 1997 FAMS, Inc. Accepted May, 1997 A New Method of Scanning Tunneling Spectroscopy for Study of the Energy Structure of Semiconductors and Free Electron Gas in Metals A. PAVLOV AND H. IHANTOLA Laboratory of Electronics and Information Technology, University of Turku, Turku, Finland Summary: In this study, a new method for the scanning tunneling spectroscopy (STS) of direct and indirect gap semiconductors and free electron gas in metals is proposed. Band structures of Si, porous Si, and Ge were studied. The tunneling current-voltage characteristics of Si and porous Si surfaces were measured over different voltage intervals from tens of mv to V under incident light from an Xe lamp and those of a Ge surface in the dark. The correlation between the shapes of the I-V curves and band structure of the materials was calculated. It was found that the curves are linear if measured in the voltage range V < E g /(e) and nonlinear when V > E g /(e) (in the measurements the applied voltage was changed from -V to V ). The method was used for the observation of a new effect of tunneling of free electron gas having thermal energies from a metal tip to a band gap state of the semiconductor. The energy spectrum of free electron gas was measured. Key words: scanning tunneling microscopy, tunneling spectroscopy Introduction Several powerful spectroscopy methods such as Fourier transform infrared, Raman scattering, optical time-resolved, and photo-emission spectroscopy have been developed to study the energy structure of solid materials. These methods give macroscopic spectra averaged on the sample surface. By using scanning tunneling spectroscopy (STS), the density of states (DOS) of the specimen can be investigated from the tunneling current-voltage characteristics measured through a small (several Å) gap between the scanning tunneling microscope (STM) tip and the surface of the sample. The tip position can be controlled rather precisely, and the spectroscopic Presentation of this paper was made possible through the support of the Foundation for Advances in Medicine and Science, Inc. Address for reprints: A. Pavlov Laboratory of Electronics and Information Technology University of Turku 1 Turku, Finland measurements are made on a very small area of the sample. This method makes it possible to get energy spectra of very small objects at the surface. This can be used in the microelectronics industry, for example, to control electrical properties of transistors, especially those of a very small size. The band structures of direct semiconductors such as Ge, n-gaas, and Ga/Si have been successfully investigated using STS. Feenstra suggested that DOS be calculated from the normalized conductance (di/dv)/(i/v) (Feenstra 1991). The measurements were presented for Ge(111), Si(111) (Feenstra 1991), n-gaas (Feenstra 199), Ga/Si(1) (Sakama et al. 199), and some other substances. However, the accuracy of this method is not satisfactory at small voltages. The problem appeared in the calculations of DOS, because the normalized conductance is divergent at I/V= since I/V converges to zero faster than di/dv. To resolve this problem, a broadening of I/V is needed (Feenstra 1991, 199; Sakama et al. 199) and the analysis becomes complicated. Another problem arises when the I-V curve is measured over a large voltage range, say 1 V, and the calculated energy band gap can be larger than the real band gap. Indeed, the distance l between the STM tip and the surface remains constant during the measurement of an I-V curve. However, the DOS can change significantly over the large energy interval in semiconductors, even more than one order of magnitude, and the features near the band gap edges and inside the band gap, especially near the Fermi level, may not present in the I-V curve. Materials and Methods In this paper we suggest a method for the measurement of the energy spectra of direct and indirect gap semiconductors using STM spectroscopy, and investigate in particular cases of Si, porous Si, and Ge. Our approach improves the accuracy of STS, especially in the region near the band gap edges and inside the band gap. We avoid the problems which appeared in Feenstra s method, as pointed out above; in addition, our calculations are simpler. It is well known that the electrical conductance in metals is described according to the properties of electrons near the Fermi level (it is reciprocal to the Fermi impulse of the electron). We assume that only electrons at the Fermi level of the metal tip establish the main tunneling current because of the tunneling transitions between the sample and the Fermi level

2 Scanning Vol. 19, 7 (1997) of the tip. Bardeen (19) showed that the tunneling matrix element M is determined by a surface integral on a separation surface between the tip and the specimen φ m φ s + φ m M = h m χ Ψ dz Ψχ * dz ds where Ψ and χ are the wavefunctions of the two electrodes. The rate of electron transfer is determined by the Fermi golden rule. The probabilityw of an electron in the state Ψ at energy level E ψ tunneling to a state χ of energy level E χ obeys the following equation: (1) (a) φ β E g φ s w = π h M δ( E Ψ E χ ) () The delta function in this equation indicates that only the states of the same energy level in both electrodes can tunnel into each other. Figure 1 shows a schematic band diagram of a metal tip and semiconductor sample. By using the Fermi distribution function for electron states in a metal tip, and supposing that kt << E g, where E g is a band gap of the semiconductor, one can correlate the tunneling transition with the Fermi level of the metal tip as shown by the dashed line in the diagrams. When a tunneling voltage, is applied, the Fermi levels are shifted at the rate from each other. Consider the case when corresponds to a state in the band gap of a semiconductor shown in Figure 1(a). The tunneling current will be zero if there are no states in the band gap. When forward bias exceeds the value, the energy difference between the valence band edge and the Fermi level in the semiconductor, then electrons tunnel from the metal tip to the valence band of the semiconductor. On the other hand, under reverse bias, an electron transition from the semiconductor to the tip can take place if >, where is the energy difference between the conduction band edge and the Fermi level, on condition that electrons also occupy the corresponding state in the conduction band. In our experiments with indirect semiconductors, we used incident light from an Xe lamp to create electrons in the conduction band, as shown in Figure 1b d. The tunneling current starts to increase when the forward voltage exceeds the valence band edge (Fig. 1b) or when the reverse voltage exceeds the conductance band edge (Fig. 1c). The band bending upward in these diagrams originates from the surface states, accumulating negative charge. Figure 1d shows an energy band diagram where surface photovoltage V SPV establishes a positive surface charge. This corresponds to the band bending downward. The surface photovoltage (SPV) decreases the barrier height f b by SPV which is equal to - SPV. This results in the flow of the tunneling current at V=. To compensate for V SPV, a bias V=-V SPV is needed and the tunneling current is zero at this voltage value. Figure 1(b) shows a band diagram with a negative charge at the surface states. The SPV is established in the (b) (c) (d) φ β l SPV + SPV FIG. 1 Schematic band diagram of a tunneling contact under different applied voltages between a semiconductor sample and a metal STM tip with a gap l between the tip and the surface. Incident light illumination produces a significant photovoltage SPV. hυ hυ

3 A. Pavlov and H. Ihantola: New method of scanning tunneling spectroscopy 1 depletion layer of the semiconductor and does not depend on the distance l between the STM tip and the surface. Therefore, it is possible to measure the value of V SPV by recording I-V curves at a different l. This was entirely in agreement with the experimental data when the I V curves crossed at a single point corresponding to V= V SPV. A tunneling current is described by the equation 1 exp ξ SPV l E gn exp ξ SPV where SPV can be positive or negative. This is negative (positive) when a positive (negative) charge is accumulated at the surface. For an intrinsic semiconductor, Eq. (3) will have the form 1 l sinh ξ SPV E g / The I-V curves calculated for p-si and porous Si from Eqs. (3) and () are shown in Figure by solid lines. A derivative of the tunneling current can be expressed by the Bardeen formula (Bardeen 19, Chen 1993) (3) () porous Si from Eq. (7), and in Figure for Ge from Eq. (7). In the following we consider the situation when tunneling transitions occur to the states inside the band gap of the semiconductor near the Fermi level. The tunneling current between the two electrodes is determined by the equation (Bardeen 19). Tunneling current (na) 8 8 I ρ s ( + E)ρ T ( + E)dE p-si (8) d dv ρ s ( ) (5) (a) 1 V SPV 1 where ρ s is the DOS of a material. For the characterization of the energy structure inside the band gap, it is more convenient to use the relation between the DOS at the Fermi level and the DOS at a chosen state, because this relation is independent of the distance l. We use the function f(e)=1 (di/dv) /(di/dv). The derivative (di/dv) corresponds to the energy + SPV and the energy E is referred to this level. For n- or p-type semiconductors, f(e) can be deduced from Eq. (3) f (E) = 1 exp ξ E E + exp ξ () Tunneling current (na) Porous-Si For intrinsic semiconductor we obtain from Eq. () E f (E) = 1 1 / cosh ξ E g / It can be seen that f.5 (for intrinsic semiconductor f =.5) when E =,, ±E g /. The curves f(e) are shown by solid lines in Figure 3a for p-si from Eq. (), in Figure 3(b) for (7) (b) V SPV FIG. Tunneling I-V curves measured for p-type Si (a) and porous Si (b) at different distances l. Solid lines are calculated from Eq. (3) for p-si and from Eq. () for porous Si. The zero tunneling current is shifted by V SPV. This voltage value is needed to compensate for the surface photovoltage.

4 Scanning Vol. 19, 7 (1997) where is the applied voltage, and ρ s (E) and ρ T (E) are the density of states of the sample and the STM tip, respectively. Here we assume that the tunneling matrix element is constant as was accepted in Bardeen (19), and we omit this in the analysis. When a metal tip is used, then the Fermi distribution describes the DOS of the tip. In calculations of the tunneling current, a good approximation is obtained using a step function instead of the Fermi function (Bardeen 19, Chen 1993, Giaever 19). Indeed, the value of kt at room temperature,., is small when compared with the accuracy usually needed in STS. The derivative conductance di/dv is correlated with the DOS of the sample on these conditions in accordance with Eq. (5). However, when the voltage range is small, the equation for the tunneling current should be corrected taking into account the difference between the step function and the Fermi distribution. The total tunneling current can be presented as a sum of two components, =I 1 +I. The first component, due to the tunneling process, correlated only with the DOS of the sample; the DOS of the metal tip is assumed to be constant. This component, I 1, given by Eqs. (3) and (), dominates at energies near the band gap edges and inside the bands, that is, far from the Fermi level of the semiconductor. The second component is an additional tunneling current from the states inside the band gap due to the electrical properties of the STM tip and correlated with the energy of free electron gas. It follows from Eq. (8) that both densities of states enter into the formula in a symmetric way. It is also seen from Eqs. () and (7) that ρ s (E) is almost constant near the Fermi level of the semiconductor. Now we investigate a small energy interval where the above assumption is valid, and we assume ρ s (E) ρ s ( ). Then the derivative of the tunneling current at small voltages is given by di / dv ρ s ( )ρ m ( ) (9) 1 (dl/dv) / (dl/dv) p-si and the derivative conductance becomes the function of the metal DOS. We show that, at small distances between the metal STM tip and the semiconductor surface, an additional tunneling current can flow due to the tunneling of free electron gas having thermal energies. This current can be described by the electron tunneling through a square barrier with a height of and a width l, the distance between the surface and the tip. The probability density is Ψ*Ψ exp(-kl), where Ψ is an eigenfunction of an electron, k = (m( E)).5 / h, E is a thermal energy, and m is the mass of the electron. Two parameters influence the probability density, the distance l, and the Coulomb barrier, which can be adjusted so that the probability value is enough to observe the tunneling current (a). Energy E () (dl/dv) / (dl/dv).8... Porous-Si 1 (dl/dv) / (dl/dv).8... Ge (b) Energy E () 1 3 Energy E () FIG. 3 Relative density of states f(e)=1-(di/dv) /(di/dv) between the energy + SPV and at the energy distance E from it. Experimental data are obtained from f(e)=1-(di/dv) min /(di/dv) =E and shown by triangles for p-si (a) and by circles for porous Si (b). The theoretical curves are calculated from Eqs. () and (7) and are shown by solid lines. FIG. Relative density of states between the Fermi level and at the energy distance E from it for Ge. Experimental I-V curves were measured in the dark and values of f(e)=1-(di/dv) min /(di/dv) =E are shown by squares. The theoretical curve was calculated from Eq. (7) where SPV = and is shown by a solid line.

5 A. Pavlov and H. Ihantola: New method of scanning tunneling spectroscopy 3 of thermal electrons. Then the thermal tunneling can be written as (1) When the energy barrier is large, then I is decreased due to the small value of ΨΨ *. On the other hand, at very small, much less than kt, the integral is almost zero. This may seem strange because the barrier height is zero. However, the tunneling of thermal electrons occurs in two opposite directions, resulting in zero total tunneling current. A saturation value of thermal tunneling current will be observed when V approaches zero. When the voltage V is positive, then the value will be positive, corresponding to the thermal tunneling of electrons. When V is negative, then holes having thermal energies can tunnel in a similar way, and a negative saturation value will be observed. The main tunneling current, described by Eq. () for Ge at I =, is shown by the dashed curve 1 in Figure 5. When both components are present, when the tip is closer, then the tunneling current has a shape shown by the dotted curve in Figure 5. An interesting region is the area between two turning points. The probability density ΨΨ * can be considered as a constant in Eq. (1), and the tunneling current is completely determined by the density of states of the free electron gas. Results I ρ s l ( ) ΨΨ ρ m (E )de Measurements have been performed on the STM working in a spectroscopic mode in an ambient atmosphere. In our experiments we used lightly doped p-si (1) wafer and porous Tunneling current (na) FIG. 5 Current-voltage characteristics (curves 1 and ) measured at the surface of Ge in the dark. Curve has been measured at a smaller distance between the STM tip and the surface. Curve 3 was calculated from Eq. (), and Curve was calculated as a sum of two components, the previous one (Curve 3) and additional current described by Eq. (1). Ge 1 3 Si prepared by electrochemical etching of p-si of resistivity 5 Ω cm in a solution of ethanol, hydrofluoric acid (HF), and water. The etching time was 1 min. The porous Si sample exhibited a strong photoluminescence. The I-V curves were measured from the illuminated p-si and porous Si specimens using a platinum STM tip. It was observed that the I-V curves measured over small voltage intervals were almost linear, as shown by the triangles in Figure a for Si and Figure b for porous Si. However, the regions where I-V curves are linear differ for Si and porous Si. This linear behavior is a consequence of the condition that, near the Fermi level in the semiconductor, ρ s ( +) constant and I-V curves exhibit metallic-like behavior at small voltages. The conductance is very small in this case, but the tunneling current can be observed by decreasing the distance between the tip and the sample. This is an important detail in our measurements, because at smaller distances l we observe more accurately the features in I-V curves near the Fermi level. By increasing the voltage range, the nonlinearity first increased slightly, and when the voltage range exceeded the value of ( - ) for reverse and ( - ) for forward voltages, the nonlinearity increased dramatically, as shown by the squares and circles in Figure for both materials. The fitting curves using Eqs. (3) and () are shown by solid lines. From Eq. (3) for p-si we obtain =., =.5 corresponding to data in Figure a. We used the experimental SPV =.35. The value of the parameter ξ is For porous silicon, we obtain an almost symmetric curve; this is described by Eq. () as shown by solid lines in Figure b, where E g =1.8 and SPV =.. The porous Si behaves as an intrinsic semiconductor with a negative charge at the surface states and a positive charge in the depletion layer. The band in this case will bend upward. The barrier φ b will be increased by SPV and positive voltage = - SPV is needed to compensate for the SPV. We have obtained the following values for the band gaps: 1.1 for Si and 1.8 for porous Si. These are in agreement with the values measured by other techniques and reported in the literature (Canham 199, Sze 1991). The Fermi level in our porous Si sample lies near the center of the band gap, which is consistent with the data obtained by ultrasoft UHV photoemission spectroscopy (Aprelev 199). Using the fitting functions for the tunneling current, the relative DOS values are calculated from Eqs. () and (7). The solid line in Figure 3 shows the function f(e) = 1 (di/dv) /(di/dv) for Si (Fig. 3a) and porous Si (Fig. 3b); here E is calculated from + SPV. Experimental values of the function f(e) are calculated from the following procedure. At a given value V i, the distance l i is adjusted so that the tunneling current = I (in practice I = 1 na). Then an I-V curve is measured in the interval -V oi <V<V oi and a value 1- (di/dv) min /(du/dv) max is calculated for this curve. The maximum of the derivative (di/dv) max is usually observed near two points, V=-V i and V=V i, so we obtain two experimental points f(e i- ) and f(e i+ ), E i- - = - i, and E i+ - = oi. Energy E i- corresponds to the state below the Fermi level and E i+ to that above the Fermi level. By changing the starting voltage V oi and repeating the measurement procedure N

6 Scanning Vol. 19, 7 (1997) times, we obtain N curves for i = 1...N and N experimental points. The experimental data are presented by triangles for Si and circles for porous Si. The accuracy of our approach is limited to kt and related to the Fermi region width in a metal tip. The method described above is also applicable to direct semiconductors. In this case, no incident illumination is needed and I-V curves can be measured in the dark. The energy structure of Ge is depicted in Figure, where the theoretical curve is calculated from Eq. (7) using SPV =. We get E g =.7, and the Fermi level position is in the center of the band gap. For the spectroscopy of free electron gas we used a platinum tip and Ge sample. This choice was made because Ge is a direct semiconductor with the band gap much larger than kt. Therefore, the condition ρ s (E), being constant near the Fermi level of the semiconductor, is satisfied with good accuracy. Figure shows two experimental curves measured at different distances l. The tunneling of electrons with energies of kt is observed only at smaller distances. Figure shows similar measurements in the energy interval from.1 to.1. Curve 1 of this figure contains no details of thermal tunneling and exhibits linear behavior due to di/dv = ρ s =constant. This shows that the conditions of the observation of thermal tunneling are very strict; the free path of electrons must be larger than the distance l. Curve of Figure exhibits both the main tunneling current linearly increasing along the voltage and the region between two dashed lines where the tunneling conductance is larger because of the tunneling of free electron gas of thermal energies. The tunneling current is zero at.53, which corresponds to the value of kt at room temperature. An expected shift should be kt, because the Boltzmann energy distribution for free electron gas gives this value. The additional value of kt in the shift resulted from the surface states of the semiconductor. It seems that the electrical charge at surface states produces the electrical field which compensates for the thermal movement of electrons and holes at the Fermi level in the semiconductor. Thus, there can be band bending upward or downward depending on the dominating concentration of electrons or holes near the surface. This produces an additional shift of the Fermi region in the metal tip at I-V curves. The position of the Fermi level is shown by the dotted line in Figure corresponding to the value.5 V. The derivative of the tunneling current in the region bounded by dashed lines in Figure, excluding a small constant due to the tunneling of the main current, gives the density of states ρ m (E) of free electron gas as shown in Figure 7. An interesting result is that the energy spectrum of free electron gas is discrete. The dashed line in Figure 7 corresponds to the derivative df/de of the function F(E) = 1/(exp((E- )/kt)+1). This function is similar to the Fermi distribution, but the energy (E- ) is multiplied by. The energy of the free electron gas is mainly concentrated inside the interval from -. to.. Discussion When a semiconductor is illuminated by light, then the SPV is created between the charge at the surface states and the opposite charge in the depletion layer. Surface photovoltage measurements using STS can give detailed information on the surface properties. The SPV in porous Si has a complicated structure. It was observed that there are discrete values of photovoltage presented at the porous Si surface (Pavlov and Pavlova 199). Both positive and negative SPV values have been measured from the same specimen. This can be associated with the influence of hydrogen and oxygen on the electrical potential of the surface. The influence of hydrogen on the band bending of Si(111) in SPV has been reported(mcellistrem et al. 1993). It is known that a SiO lay- 1 8 Tunneling current (na) 1 ρ m (arb. units) FIG. The I-V curves measured at the surface of Ge in the dark at room temperature. The dotted line corresponds to the Fermi level.... E ().. FIG. 7 The energy spectrum of the free electron gas calculated from the data of Figure. The dashed line is the derivative df/de of the function F(E) = 1/(exp((E- )/kt + 1) which is similar to the Fermi distribution.

7 A. Pavlov and H. Ihantola: New method of scanning tunneling spectroscopy 5 er exposed on Si accumulates negative charge (Munakata 1988). On the other hand, trapped hydrogen in SiO generates a positive oxide trap (Feigl et al. 1981). It was shown for thermally oxidized silicon that a positive charge correlated with holes is accumulated at the Si-SiO interface and that the electrons are trapped in the SiO layer (Stathis et al. 1993, Young et al. 1979). These effects can be present in porous Si. The new approach described in this paper allows us to measure band structure of direct and indirect gap semiconductors and free electron gas energies of the metal STM tip. In the second case, a semiconductor surface is used as a probe and the STM tip plays the role of the sample. It was observed that when the additional tunneling current due to tunneling of free electrons that have thermal energies becomes of the order of the main tunneling current, then images of the surface become smooth. This means that it is impossible to observe small details of the surface structure where the thermal tunneling occurs. This is consistent with the uncertainty principle that results in the resolution, more than 1Å, of the surface structure at an energy resolution less than kt. The system of a metal surface and a metal STM tip can also be described by the method presented in this paper. A strong nonlinear effect in I-V curves has also been observed at small voltages, explained by the fact that the energy densities of both materials are not constant near the Fermi level. More experimental data are needed to describe this system in detail. Conclusion We have suggested a new scanning tunneling microscopy spectroscopic model to study the energy structure of semiconductors by measuring tunneling I-V curves at different voltage intervals. From the nonlinearity of the curves, the band gap and the position of the Fermi level can be calculated. Light emission was used to excite electrons into the conduction band for p-type Si and porous Si. Using the model proposed in the paper, the energy structures of p-type Si, porous Si, and Ge were calculated. A new effect of the tunneling of free electron gas of thermal energies was measured for platinum. This effect is described using the model proposed in the paper. The energy spectrum of the free electron gas is presented. Acknowledgments The authors would like to thank Dr. R. Laiho for the possibility of working with STM equipment. References Aprelev A, Lisachenko A, Laiho R, Pavlov A, Pavlova Y: UV (hv=8.3 ) photoelectron spectroscopy of porous silicon near Fermi level. E-MRS 199 Spring Meeting: Symposium L, June 7 199, Strasbourg, France (accepted in J Thin Solid Films) Bardeen J: Tunneling fron a many-body point of view. Phys Rev Lett, (19) Canham LT: Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers. Appl Phys Lett 57, 1, 1,8 (199) Chen CJ:Introduction to Scanning Tunneling Microscopy. Oxford University Press, New York (1993) Feenstra RM: Band gap of the Ge(111) x1 and Si(111) 1 surface by scanning tunneling spectroscopy. Phys Rev B, 13,791 13,79 (1991) Feenstra RM: Tunneling spectroscopy of the (11) surface of direct-gap III V semiconductors. Phys Rev B 5,,51,57 (199) Feigl FJ, Young DR, DiMaria DJ, Lai SK, Calise JA: The effects of water on oxide and interface trapped charge generation in thermal SiO films. J Appl Phys 5, 5,5 5,8 (1981) Giaever I: Energy gap in superconductors measured by electron tunneling. Phys Rev Lett 5, (19) McEllistrem M, Haase G, Chen D, Hamers RJ: Electrostatic sample-tip interactions in the scanning tunneling microscope. Phys Rev Lett 7,,71,7 (1993) Munakata C: Analysis of ac surface photovoltages in accumulation region. Jpn J Appl Phys 7, (1988) Pavlov A, Pavlova Y: Investigation of surface topography of light emitting nanostructures of porous Si and related photovoltaic effect by photoassisted scanning tunnelling microscopy. E-MRS 199 Spring Meeting: Symposium L, June 7, 199, Strasbourg, France. J Thin Solid Films 97,13 13 (1997) Sakama H, Kawazu A, Sueyoshi T, Sato T, Iwatsuki M: Scanning tunneling microscopy on Ga/Si (19). Phys Rev B5, 8,75 8,7 (199) Sze SM: Physics of Semiconductor Devices. A Wiley-Interscience Publication (1981) Stathis JH, Buchanan DA, Quinlan DL, Parsons AH, Koteck DE: Interface defects of ultrathin rapid-thermal oxide on silicon. Appl Phys Lett,,83,8 (1993) Young DR, Irene EA, DiMaria DJ, De Keersmaecker RF, Massoud HZ: Electron mapping in SiO at 95 and 77 K. J Appl Phys 5,, 3,37 (1979)