Extracting the Schottky Barrier Height from the Da- Da-ta

The procedure described in this section was originally developed by Winking [47] for the extraction of the n-type Schottky barrier height. The experimental STS data are analyzed by using the simulated 3D FEM data, which is illustrated in Figure 4.7(a) for the case of a p-type junction. First of all, a constant current isoline is extracted from the topography-normalized STS data. The constant current isoline is taken deep inside the valence band to minimize any influence of charged dopant atoms nearby. In the illustrated case the 𝐼𝐼_𝑇𝑇 isoline is taken at a starting bias voltage of -0.75 V on the flat side of the isoline about 28 nm away from the interface. Since tunneling from the valence band of the free GaAs(11�0) surface into the tip starts at around 𝑉𝑉_{𝑏𝑏𝑖𝑖𝑣𝑣𝑠𝑠}=−0.1 V the tunnel current isoline is taken at about 0.65 eV below the valence band edge.

Figure 4.7: (a) Sketch illustrating how to find the best fit between experimental and simu-lated data [120]. More information can be found in the continuous text. In the lower pan-els the best fits between 𝐼𝐼_𝑇𝑇 and Φ_{𝑉𝑉𝑇𝑇} isolines for the ideal (b) n-type [47] and (c) p-type Fe/GaAs(110) interface are shown.

In a next step, Φ_{𝑉𝑉𝑇𝑇} isolines are extracted from a 3D FEM data set simulated for one par-ticular Schottky barrier height in dependence of the tip-interface distance 𝑥𝑥 and the elec-trostatic potential energy between tip and sample Φ_{𝑇𝑇𝑆𝑆}. One has to keep in mind that the simulated data is plotted in dependence of the electrostatic energy between tip and sample

4.2 Extracting the Schottky Barrier Height from the Data

61 Φ_{𝑇𝑇𝑆𝑆} whereas the experimental data is plotted in dependence of the sample bias voltage 𝑉𝑉_𝑠𝑠. Both quantities are linked by equation (4.2), i.e., the electrostatic potential energy is the sum of the bias voltage and the contact potential difference 𝑒𝑒𝑉𝑉_CPD which is defined as the difference between the work function of the sample and the work function of the tip:

𝑒𝑒𝑉𝑉CPD= Φ𝑆𝑆− Φ𝑇𝑇 (4.15)

Subsequently, the Φ_{𝑉𝑉𝑇𝑇} isoline with the smallest deviation from the constant current iso-line is found. As a measure for the deviation 𝜎𝜎 the square root of the mean squared error is taken:

where 𝑛𝑛 is the number of data points along the 𝑥𝑥 axis, Φ_{𝑆𝑆𝑆𝑆} is the Schottky barrier height for the respective simulated data set, and 𝑉𝑉_sim is the bias voltage along the simulated Φ_{𝑉𝑉𝑇𝑇} isoline. The Φ_{𝑉𝑉𝑇𝑇} isoline starting at a certain value of Φ_{𝑇𝑇𝑆𝑆} on the flat side of the isoline farthest away from the interface with the smallest deviation is the best fit for a particular Schottky barrier height. The deviation of the simulated curve from the experimental curve is obtained for data points up to 1.5 nm off the interface. Closer to the interface, simula-tion and experiment can strongly deviate due to interface effects as can be particularly seen in Figure 4.7(c) for the p-type case.

If one repeats the fitting procedure for simulated data sets of different Schottky barrier heights, one obtains the plots shown in Figure 4.8. For each simulated data set with a particular Schottky barrier height the smallest obtainable deviation is plotted. This yields Schottky barrier heights of Φ_{𝑆𝑆𝑆𝑆}^𝑛𝑛 = 0.94(3) eV [47] and Φ_{𝑆𝑆𝑆𝑆}^𝑝𝑝 = 0.78(2) eV for ideal n-type and p-n-type Fe/GaAs(110) interfaces, respectively. The error is obtained from fitting at different starting voltages inside the bands (±0.1 V) and from fitting at different suita-ble (weakly affected by defects) positions along the interface in 𝑦𝑦 direction. The best fit Φ_{𝑉𝑉𝑇𝑇} isolines together with the tunnel current isolines for the ideal n-type and the p-type junction are shown in Figure 4.7(b) and (c). The simulated isoline for the n-type case describes the experimentally observed space charge region very nicely [47]. Also for the p-type case experimental and simulated isolines are in very good agreement up to 1.5 nm off the interface. The strong deviation at the interface between experiment and simulation are discussed in greater detail in section 4.3.

In the example in Figure 4.7(c) of a p-type junction with an acceptor concentration of 𝑁𝑁_𝐴𝐴= 2.75 × 10¹⁸ cm^-3 the average distance between two acceptors is ~ 7 nm. Therefore, most scan lines in 𝑥𝑥 direction along the space charge region will exhibit acceptor related features. In the tunnel current isoline from Figure 4.7(c) one also finds a weak signature of a Zn acceptor located in proximity to the scan line which is indicated by a small

“bump” at 𝑥𝑥 ≈ −11 nm. However, the extracted Schottky barrier height does not change

62

significantly for fits at different positions along the interface (in 𝑦𝑦 direction) as long as the respective signatures of dopant atoms are weak.

Figure 4.8: Deviation 𝜎𝜎 between experimental and simulated isolines for different Schottky barrier heights Φ_{𝑆𝑆𝑆𝑆} [120] for the ideal (a) n-doped [47] and (b) p-doped [125]

interface.

For the n-type Schottky barrier height the MIGS-and-electronegativity model predicts Φ_{𝑆𝑆𝑆𝑆}^𝑛𝑛 = 0.96 eV [137] which is in excellent agreement with the experimentally obtained value. However, the p-type Schottky barrier height extracted from the XSTS 𝐼𝐼-𝑉𝑉 spectra cannot be explained in the framework of the MIGS-and-electronegativity model which predicts a value of Φ_{𝑆𝑆𝑆𝑆}^𝑝𝑝 = 0.46 eV [137] at room temperature. This deviation between experiment and MIGS-and-electronegativity model for the p-type junction will be dis-cussed in greater detail in chapters 5 and 6.

By finding the simulated Φ𝑉𝑉𝑇𝑇 isoline that has the smallest deviation from the experi-mental constant tunnel current isoline in the way described above, one not only obtains the Schottky barrier height of the system but also the simulated electrostatic energy be-tween tip and sample Φ_{𝑇𝑇𝑆𝑆} that corresponds to the bias voltage in the experiment. There-fore, by using equations (4.2) and (4.15) one can also extract the contact potential differ-ence 𝑉𝑉_CPD between tip and sample [47]. For the n-type contact the best fit yields a contact potential difference of 𝑉𝑉_CPD^𝑛𝑛 = 0.0 V. This is in good agreement with STM barrier height measurements on n-doped GaAs(110) by Teichmann [83]. For the p-type junction a con-tact potential difference of 𝑉𝑉_CPD^𝑝𝑝 = +0.62 V is obtained. This is in the same range found in recent Kelvin probe force spectroscopy measurements on p-doped GaAs(110) [138].

Therefore, the contact potential differences that follow from the best fits are consistent with other most recent measurements.

In an overall perspective the fitting algorithm based on 3D FEM simulations of the elec-trostatic energy along the entire space charge region yields reasonable values for the con-tact potential difference between tip and sample and can therefore be regarded as a relia-ble tool to extract information on the electronic properties of Schottky contacts.