Essay Example on EBIC Technique in SEM: A Comprehensive Investigation

Introduction

The electron beam induced current (EBIC) is a technique for semi-conductor analysis. This procedure can be conducted through a scanning transmission electron microscope (STEM) or a scanning electron microscope (SEM) (Haney, Yoon, Gaury, & Zhitenev, 2016). Through the analysis, it is possible to identify the buried junctions or the defects in the semi-conductors and other carrier properties of the materials. The EBIC technique in SEM is the focus of this investigation, which has been widely used in the assessment of semi-conductor materials to evaluate the defects in materials that are electrically active. The aim of this experiment was to investigate the properties of a - junction using Electron Beam Induced Current (EBIC) microscopy in Scanning Electron Microscope (SEM).

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Theory

A highly focused beam that is less than 3 nm, tested in an SEM instrument tends to dissipate energy through heating (generation of phonons) and break the chemical bond. The process of heating and breaking the chemical bond tends to create an electron-hole pair located within the energy dissipation volume under the electron beam (Haney, Yoon, Koirala, Collins, & Zhitenev, 2015). In this regard, the interaction volume of the electron-solid could be considered to be a point of source for the excess carriers. These number of carriers can be determined by the use of average formation of the energy for the electron-hole pair ef, by the electrons as shown in the equation below.

ef ≈ 3Eg + 0.5 … (1)

From the equation above, is the bandgap of the semi-conductor. G, which is the generation factor for the electron-hole pairs, is given by the equation below.

G = Eo(1-η)ef …(2)From the equation, 2 above, Eo is the electron energy while η is the backscattered electron coefficient. It should be noted that the electron-hole pairs on the electron excitation diffuse through the lattice which thermalizes on the edges of bands. The process takes around ~10−12 seconds. When the injected carriers diffuse into the vicinity of a - junction, the “built-in” contact potential across the space charge region forms a strong electric field that can separate the electron-hole pairs to produce a collection (EBIC) current. The relationship between the EBIC and the SEM beam current Ib is demonstrated in equation 3 below.

EBIC = … (3)

From equation 3 above, Ncc is the charge collection efficiency across the - junction. Equation 4 below shows the differential equation for the diffusion of excess minority carriers.

D∇2Δn+ GIb – Δnτ = 0…(4) From equation 4 above τ is the minority carrier lifetime and D is the minority carrier diffusion. Considering that GIb is equal zero throughout except for the small interaction volume that is under the incident electron beam, and the fact that =√, then the equation can be illustrated as shown below.

∇2Δn– ΔnL2 = 0…(5) When equation 5 above is solved in one dimension with an assumption of spherical symmetry, the following equation 6 is obtained.

EBIC = EBICmax−/ … (6)

From the equation, it is demonstrated that the current collection EBIC tends to decay exponentially within a distance r that is from the junction with L as the diffusion length and the EBICmax as the maximum collection current that occurs within the region of depletion. In this regard, the width of the depletion layer expressed as a function of reverse bias VRB is given by equation 7 below.

W = 2εVRB+VCPqNA+ND…(7)Where is the dielectric constant of the semi-conductor ( = 0), and are the concentration of ionized acceptor and donor dopants, respectively, is the electronic charge and is the internal contact potential of the - junction (0.7 V for Si).

Materials and Methods

The scanning electron microscope (SEM) instrument was used to set up the electron beam induced current (EBIC). In the experiment, the EBIC line scans were collected across the - junction as a function of the reverse bias, by use of a cross-sectioned IN4002 power diode and an electron beam accelerating voltage of 25 kV. Also, all of the EBIC profiles were measured with a beam current of 1.0 nA measured with a Faraday cup. Finally, the Si diode used had a contact potential of 0.7v. The findings from the experiment were provided in the MS Excel template with a summary shown in the results section below.

Results

Table 1: Data for Silicon

Band Gap () Formation Energy () Relative Permittivity () Backscattered Coefficient ()

1.1 V 3.6 V 11.8 0.1

Table 2: Scanning from the N to P side of the diode left to right sample data

Line Scan EBIC current (µA) reverse bias

r (µm) 0V 2V 10V 15V 20V 25V

0.00 0.004 1.906 2.725 3.451 4.201 4.871

0.24 0.009 1.911 2.730 3.456 4.201 4.881

0.49 0.004 1.911 2.730 3.461 4.211 4.886

79.83 0.151 2.053 4.334 4.976 4.334 4.976

The electron-hole pair formation energy, .

ef≈3Eg+0.5, Eg≈1.1eVef≈31.1eV+0.5∴ ≈3.8eVThe minority carrier diffusion length, .

IEBIC=NccGIbIEBIC=IEBICMAX* e-rLIEBICIEBICMAX=e-rLlnIEBICIEBICMAX=-rLRearranging gives the gradient to the Linearized EBIC plot, and thus we can solve for L:

1L=lnIEBICIEBICMAX-rFrom excel data, IEBICMAX≈10.6μm, 1L=0.0658 (Figure 2) ∴L≈15.2μm for 25V.

The total dopant concentration, ( + ).

W=2ε(VRB+VCP)q(NA+ND)Rearranging depletion width formula to find NA+ND:

W2=2ε(VRB+VCP)q(NA+ND)NA+ND=2ε(VRB+VCP)W2qWe are given VRB=25V, VCP=0.7V, ε=1.4E10, q=1.6E19C, W≈4.9μm (from data)

NA+ND=2(1.4E10)(25+0.7)4.92*1.6E19C∴ NA+ND = 2.3 x 10-4

Discussions and Conclusions

The aim of the experiment was to investigate the properties of a - junction using Electron Beam Induced Current (EBIC) microscopy in Scanning Electron Microscope (SEM). From the procedures and results obtained, it was established that an electron beam induced current is a technique that is suitable in the analysis of the electrical properties of semi-conductor materials. When a sample is exposed to an electron beam of energy, there is a flow of an electric current (Luke, 1998). In this regard, the material properties of a - junction in semi-conductor materials are obtained in this experiment by measuring the flow of the electric current. The experiment showed that the electron-hole pair formation energy, was 3.8eV.

This demonstrates that there is substantial energy that flows across the junction of the semi-conductor material. The electric current EBIC was exposed across various distances of the material to study the behavior of the flow in different sections. The data obtained was used to draw a graph of EBIC current against distance, with the peak current obtained at between 20 to 30 µm of material distance. The highest voltage demonstrated the highest overall current. Finally, the set up was able to investigate the total dopant concentration, ( + ), which was equal to 2.3 x 10-4. From the results obtained, it is evident that the electric properties of a - junction can be analyzed using the EBIC technique in the SEM instrument.

References

Haney, P., Yoon, P., Gaury, B., and Zhitenev, B., 2016. Depletion region surface effects in electron beam induced current measurements. Journal of Applied Physics, 120(9): pp.095702. DOI: 10.1063/1.4962016

Haney, P., Yoon, P., Koirala, P., Collins, R., and Zhitenev, B. 2015. Electron beam induced current in the high injection regime. Nanotechnology, 24(26): pp. 295401. doi: 10.1088/0957-4484/26/29/295401

Luke, K., 1998. Electronbeam induced current characterization of backsurface field solar cells using a chopped scanning electron microscope beam. Journal of Applied Physics, 55: pp.555. https://doi.org/10.1063/1.333062