Exploring the Electron Tunneling Behavior of Scanning Tunneling Microscope (STM) tip and n-type Semiconductor

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1 Page 110 Exploring the of Scanning Tunneling Microscope (STM) tip and n-type Seiconductor M. A. Rahan * and J. U. Ahed Departent of Applied Physics, Electronics & Counication Engineering, University of Chittagong, Chittagong , Bangladesh * Corresponding author: ashikbd89@yahoo.co Abstract: Scanning Tunneling Microscope (STM) is a treendous and revolutionary innovation that facilitates one to get iages with atoic resolution of the surfaces of etal and seiconductor crystals which enables to generate nano-technological based applications, surface science studies and also anipulation of atos, etrological applications etc. Hence, one has to know the electron tunneling behavior of STM-tip and etal/seiconductor contact. In this paper, a theoretical odel has been developed to explore the electron tunneling behavior of the STM tip and n-type seiconductor. A Schottky barrier contact has been considered and the I-V curves were calculated for a variety of barrier height, barrier thickness, teperature and filled electrons ξ. Transission probability and current density were recognized fro the Poisson equation (for obtaining the potential energy), the static Schrodinger equation (to copute the transission coefficient) and the Feri-Dirac distribution function (for calculating the current density). The study reveals that I-V curve just follows the standard diode perforance when the therionic current doinates the tunneling current contribution (sall, large, high, large ξ) between the STM tip and n-type seiconductor contact. However, the reverse current begins to appear and thereby reverse the rectifying perforance of the usual diode when the tunneling current is the ajor source of the current (large, sall, low, sall ξ). Keywords: STM, electron tunneling, explore, Schottky barrier, n-type seiconductor. 1. INTRODUCTION Even though, Scanning Tunneling Microscope (STM) is a well-established and widely used surface-science technique [1,2], there are still soe unanswered questions connected to the electron tunneling through STM junction. In any ways, it can be copared to a black box - it works, and it is by now known how to use it, but the finer details are still lacking. Since tunneling is a standard textbook probles, this ay see surprising [3]. However, the real proble is very coplex for the following reasons: The syetry of the electron tunneling is very hard to calculate absolute nubers for, e.g., tunneling conductance, gap widths, barrier heights and corrugations etc [4]. It is not clear how to odel the tip, as the exact coposition and geoetry are unknown and furtherore, it often changes during operation [5]. Electronic effects, tip-surface interactions, and the strong electrical field cannot be neglected. Very little is known about the relative iportance of these coplications [6]. Hence even though STM iages are interpreted as topographic aps of the surface, it is soeties far fro clear what they really represent. In order to investigate the nano-scale devices, STM is used with a sharp etal tip which can ove accurately within a few nanoeters. With the atoically sharp etal tip, the current and the voltage are easured [7]. Although any experients depending on the tip-saple easureent has been done, the behavior of the electron tunneling between the tip-saple gap has reained relatively unexplored. Hence, research has to be done in order to elucidate the tunneling behavior of the tip-saple gap. In this paper, we have developed a theoretical odel in order to investigate the electron tunneling behavior of tip-saple gap region. In our theoretical odel, Schottky contact is fored at the contact between the etal tip and the n-type seiconductor saple and I-V curves are calculated for various paraeters to siulate the behavior of electron tunneling. In order to obtain the transission coefficient, at first we focused on coputing the Poisson equation to calculate the potential energy barrier, then solved nuerically the static Schrödinger equation with the calculated potential function while keeping charge density constant through the depletion layer. P-ID 51 International Conference on Physics Sustainable Developent & Technology (ICPSDT-2015) Departent of Physics, CUET.

2 Page 111 Finally, the current density is calculated using the calculated transission coefficient and the Feri-Dirac distribution function. Eventually, to be sure about the calculation, the current density was calculated for the square barrier potential. Our MATLAB siulation reveals for the spherical Schottky barrier that I-V curve just follows the standard diode behavior when the therionic current doinates the tunneling current contribution and deonstrates viceversa when the tunneling current is the ajor source of the current. 2. THEORETICAL ANALYSIS 2.1 Developing the Model of Spherical Shape Schottky Barrier Contact To explore the electron tunneling behavior, a theoretical odel has been developed, a STM tip and the saple which is assued to be n-type seiconductor. The study of a p-type seiconductor is alost the equivalent as the n-type one. The standard geoetry of the STM tip easureent is siilar to the Fig. 1(a). If the Feri energy of the n-type seiconductor is higher than that of the STM tip, Schottky contact is fored (Fig. 1-b). The electron oves to the STM etal tip side; therefore the positively charged depletion region is fored around the tip [8]. Fig. 1: (a) Geoetry & Siplified odel with spherical contact and (b) Energy diagra of Schottky contact. Fro Fig. 1(b), before the contact is fored, the Feri energy of the n-type seiconductor is higher than that of the STM etal tip. When the two becoes contact each other, slight aount of electron oves to the STM etal tip side, so the Feri energies of both sides becoe equivalent and the Schottky barrier is fored. While the bias voltage is applied, the difference of the Feri energies becoes [9]. In the proposed odel, a spherical tip front with a radius ' ' is assued for the nuerical siplicity, [10]. 2.2 Potential Energy Barrier Calculation throughout the Poisson Equation Assued that the charge density at the depletion layer is constant. Therefore, the Poisson equation ( ) is to be solved where electric potential is syetric ( ( ) ); So Poisson equation becoes- ( ) (1) Multiplying by and taking integration, ( ) (2) And, if we divide by and taking integration, (3) At the end of the depletion layer, putting ; (4) So (where the electric field vanishes) and (by setting ground potential as ). Hence, the electric potential of Schottky contact, { { (5) with the constraint [11], where intrinsic potential drop, and the applied bias voltage. P-ID 51 International Conference on Physics Sustainable Developent & Technology (ICPSDT-2015) Departent of Physics, CUET.

3 Page Transission Probability Coputation through the Schrodinger Equation Usually, the transission probability can be coputed by solving tie-independent Schrodinger equation. 2 2 d ( x) U( x) ( x) E ( x) 2 E E (where * effective ass of electron) (6) E 2* dx Accordingly we can write the result as a cobination of the incident, the transitted and the reflected wave as { When an incident wave approaches to the barrier, a part is transitted through the barrier and the other part is reflected back [11]. With the priary circustance, we obtain { Now, integrate the Eq.(6) nuerically and get and at the point. Set where coefficients are just required to eet the constraint,.therefore, copute and as follows: (7) (8) { (9) Subsequently, calculating the transission probability as- (10) 2.4 Current Density Calculation Fro the Feri-Dirac distribution and the tunneling probability, Current density can be calculated. Let's consider the incident wave advancing fro the left side is transitted and reflected at the potential barrier. If we put, the noralized wave function is specified by- { Therefore while the boundary condition ( ) is applied, the possible values for a set of discrete nubers, and the unit length of -space becoes. In general, current density of the left-advancing case is su over the all possible k values ties Feri function factor [11]. ( ) (12) where Feri function factor ( ) is the probability that the state k is in used on the left side, and factor ( ) is the probability that the state k is unoccupied on the right side of the barrier. Thus, factor in the front begins fro the spin degree of freedo for each values. Transfor it into the integral representation, ( ) (13) Consequently, the total current is the difference of the two contributions. ( ) (14) 3. NUMERICAL ANALYSIS AND RESULT Applying the theoretical odel, I-V curves at the STM tip and n-type seiconductor contact is nuerically calculated for both square and spherical shape Schottky potential barrier. (11) Fig. 2: (a) Square barrier Energy band diagra and (b) Spherical shape Schottky barrier Energy band diagra. P-ID 51 International Conference on Physics Sustainable Developent & Technology (ICPSDT-2015) Departent of Physics, CUET.

4 Page 113 Fro Fig.2, the paraeters for the calculation are identifies as: Barrier Width ; Barrier Height ; Bias Voltage ; Feri Energy on the Left/Right ; Conduction Band Botto on the Left/Right ; ; Hence obtain =. 3.1 Square Barrier Whenever two different aterials turn into contact with each other, the Feri energies of those aterials becoe the sae. Then, if the bias voltage is applied, electron can flow but the Feri energies turn out to be different, as given by and (' ' is the energy of the electron) (15) The foreost thing to note is the dependence of the barrier thickness. Fig. 3 illustrates that I-V characteristic curves were calculated for a variety of the barrier thicknesses as,,, and. The other paraeters were set to be the sae for each calculation as =, l = r =, T = 300 K. Table-1. Observation on various barrier width B. Thicknesses Hard for electrons to penetrate Characterize Ohic behavior Ohic behavior is observed Fig. 3: I-V curves for various values of barrier thickness. Fro the observation of electron tunneling behavior, the study reveals that when the barrier is thick, it is hard for electrons to penetrate throughout the tunneling barrier (Table-1). Accordingly the electrons can tunnel through the barrier only when the high enough bias voltage is applied. In Fig. 4, a coparable trend can also be viewed in the calculation for a variety of teperatures (30 K, 300 K, 3000 K, and K). The other paraeters were set to be the sae as =, l = r =, = 1 n. It is clear fro Fig. 4 that for extreely high teperature the I-V characteristic curves turn into linear where involveent of the current coes ostly fro the therionic eission. On the other hand, in the low teperature region, like 30 K and 300 K, ost of the current coes fro the tunneling electrons whose energy is coparatively low. At 3000 K, there are enough electrons whose energy is alost at the STM tip of the barrier; therefore they can tunnel directly (Table-2). Ohic behavior is observed Table-2. Observation on teperature dependence Tep. T Fig. 4: Teperature dependence of the I-V curves. 30 K Current coes fro tunneling electrons whose energy is low 300 K Tunneling electrons energy is low 3000 K Quantu interference effect occurs K Ohic behavior is observed Next, what we have to be considered is the barrier height dependence of the I-V curves (Fig. 5). At this tie, the additional paraeters (T = 300 K, l = r=, = 1 n) were set to be the sae for each calculation. P-ID 51 International Conference on Physics Sustainable Developent & Technology (ICPSDT-2015) Departent of Physics, CUET.

5 Page 114 Table-3. Observation on different barrier height B. Height - Ohic behavior is observed Shows quantu interference effect Quantu interference effect occurs Hard for electrons to penetrate Fig. 5: I-V curves for the different values. The first representation, = eans the free space; hence, for no barrier case, the I-V curves viewed linear. As the barrier height increases, the I-V curves show a curvature. Especially for the = 0 case, quantu interference effect occurs and showing a funny shape of the I-V curve (Table-3). 3.2 Spherical Schottky Barrier The foreost thing to note is the dependence of the barrier thickness/diode size (should not be confused with barrier thickness ' ' in the previous study for Square barrier ). In spherical shape Schottky barrier contact, the thickness of barrier is ' '. In Fig. 6, I-V curves were calculated for the diode sizes,, and respectively. The other paraeters were set to be the sae as, l = r = 2 ev, T= 300K. Table-4. Observation on various barrier thickness B. Thicknesses (r d ) Hard for electrons to penetrate Quantu interference effect occurs Ohic behavior starts to appear Fig. 6: I-V curves for various values of barrier thickness. Fro above entioned tunneling behavior, it can be revealed that as the diode size becoes saller it coes to follow the Ohic characteristics. It was also revealed that for a thicker barrier, it is hard for a electron to tunnel through the barrier; electrons can tunnel through the barrier only when high enough bias voltage is applied (Table-4). Now, we represent the teperature dependence of the I-V curves as shown Fig. 7. Here, the additional paraeters were set to be the sae as = 6, l = r=, = 1 n. At low teperature (e.g. 30 K and 300 K), electron close to the Feri surface satisfy the interference condition. Hence the tunneling current doinates the therionic current, thereby the reverse current is observed. Otherwise, when the teperature is high enough, ost of the current coes fro the therionic eission (Table-5). Ohic behavior is observed P-ID 51 International Conference on Physics Sustainable Developent & Technology (ICPSDT-2015) Departent of Physics, CUET.

6 Page 115 Table-5. Observation on teperature dependence Tep. T Fig. 7: I-V curves for teperature dependence. 30 K Reverse current is observed 300 K Reverse current is observed 3000 K Diode behavior starts to appear K Ohic behavior is observed The interesting trend can be seen when the barrier height dependence of the I-V curves were observed (Fig. 8). In this case, all the additional conditions were also set to be the sae as T = 300 K, l = r =, = 1 n. Table-6. Observation on various barrier heights Fig. 8: I-V curves for a variety of barrier height values. B. Height Ohic behavior is observed Diode-behavior is observed Reverse current starts to appear Reversing the rectifying behavior of the Schottky diode When the barrier height is low the I-V curve is Ohic; which is insignificant because alost all of the current coes fro the therionic eission. On the contrary, whenever the barrier height turns into larger, the diode behavior is observed. As the barrier height becoes larger, the reverse current coes into view, thereby reversing the rectifying behavior of the Schottky diode (Table-6). Finally, another otivating perforance is shown in I-V curves for the different r values (see Fig. 9). In this case, the additional paraeters were also set to be the sae as T = 300K, l =, = 1 n, Table-7. Observation on a variety of r values Filled Electrons ξr Fig. 9: I-V curves for the various r values. Rectifying behavior is reversed Therionic currents contribute Diode behavior starts to appear Usual diode behavior is observed It is clear fro these tunneling behavior that the I-V curves showed the reverse rectifying behavior of the diode for r=1ev. In this regie the tunneling current doinates the therionic current. As r increases, the therionic eission current starts to contribute; thus the usual diode behavior of the Schottky barrier is observed (Table-7). P-ID 51 International Conference on Physics Sustainable Developent & Technology (ICPSDT-2015) Departent of Physics, CUET.

7 Page CONCLUSION In this paper, we have developed a theoretical odel in order to explore the electron tunneling behavior of STM tip and n-type seiconductor as a Schottky contact barrier. Fro this study, it was observed that the I-V curve just follows the standard diode characteristics when therionic current doinates the tunneling current contribution (sall, large, high, large ξ) between the STM tip and the n-type seiconductor. It was also found that when tunneling current is considered only the ajor source of the current (large, sall, low, sall ξ), the rectifying perforance of the usual diode was reversed. Teperature dependence of the I-V charateristic curves of the tip-saple gap also presented here; for extreely high teperature the I-V characteristic curves turn into linear where involveent of the current coes ostly fro the therionic eission; on the other hand, for relative low teperature the current ostly coes fro the tunneling electrons whose energy is coparatively low. Hence, it can be concluded that the current at the STM tip is coposed of both therionic and tunneling current, and even if these two contributions are ixed up, it would explore the I-V characteristics curve of half-like standard diodes. REFERENCES 1. G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel. Surface studies by scanning tunneling icroscopy. Phys. Rev. Lett. 49, (1982) [Journal] 2. G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel. Tunneling through a controllable vacuu gap. Appl. Phys. Lett. 40, (1982) [Journal] 3. L. Olesen, K. Hansen, E. Lægsgaard, I. Stensgaard, and F. Besenbacher, Experiental Studies of Tip- Surface Interactions, To appear in Proceedings of the NATO Advanced Research Workshop on Nanowires, Madrid, 1996 [Proceedings] 4. K W Hipps, Handbook of Applied Solid State Spectroscopy, Washington University, USA (2005)[Book] 5. J. A. Stroscio and D. M. Eigler. Atoic and olecular anipulation with the scanning tunneling icroscope. Science 254, (1991). [Journal] 6. R. Wiesendanger, Scanning Probe Microscopy and Spectroscopy (Cabridge University Press, Cabridge, 1994). [Book] 7. G. Binnig and H. Rohrer. Scanning tunneling icroscopy fro birth to adolescence. Rev. Mod. Phys. 59, (1987) [Journal] 8. Dongwook Go, Modeling of the Contact between the Metal Tip and n-type Seiconductor as a Schottky Barrier, Institute of Solid State Physics, Technical University of Graz, (2013) [Thesis] 9. Winfried Monch, Mechaniss of Schottky barrier foration in etal-seiconductor contacts, Laboratoriufur Festk6rperphysikand., Universitdt Duisbur, Gerany (1988) [Journal] 10. Shanna Crankshaw, A icroscopic odel of resonant double-barrier tunneling in a quantu syste, Departent of Physics, University of Florida,Gainesville, Florida (2011) [Journal] 11. B. Ven Zeghbroeck, Principles of Seiconductor Devices (Accessed: 18 May 2014) [Online Textbook] P-ID 51 International Conference on Physics Sustainable Developent & Technology (ICPSDT-2015) Departent of Physics, CUET.