Shockley-Read-Hall Model

1. E Hr Magnetic Field Under Resonance Condition (simplest case) EC EC ED ED Pb1 Pb1 EV EV This is a forbidden transition This is an allowed transition Figure 6 Shockley-Read-Hall Model First an electron (hole) is captured at a deep level and then a hole (electron) is captured at the same site. This causes annihilation of the electron and the hole: e- + h+ = 0. The process can be repeated indefinitely. Figure 6 is a graph of SDR amplitude versus Base voltage. The top graph is taken at 9.5 GHz (High field/freq.) while the bottom graph was taken using the low field /freq. system at 58 MHz. Inexpensive Magnetic Resonance on Fully-Processed Devices: Low Field Spin Dependent Recombination Brad Bittel, Corey Cochrane, Thomas Conkling, Patrick Lenahan, Jason RyanThe Pennsylvania State University, University Park, PA 16802 USA Introduction: Spin Dependent Recombination (SDR) is a very sensitive electrically detected magnetic resonance technique that can be used to identify reliability defects in fully processed transistors in IC’s. At the present time these measurements require relatively expensive apparatus and special mounting for the devices. This is so because SDR spectrometers are typically based upon commercially available electron paramagnetic resonance systems. These systems typically use magnetic fields over 3000 G and microwave frequencies above 9 GHz. The high magnetic fields and high frequencies require large expensive magnets, microwave generators, and microwave cavities. These cavities must typically maintain very high quality factors (Q) with the samples loaded inside them. All these factors combine to make the measurements relatively expensive and also limit the ways in which device structures may be packaged. The goal of this project is to develop an inexpensive SDR apparatus which might accommodate fully processed devices in a variety of packages. Top View Side View Figure 5 Figure 1 Results: These preliminary results provide a comparison of high field/freq. SDR to low field/freq. SDR. SDR amplitude versus junction bias clearly demonstrate that the response at high and low field/freq. are the same. All results shown are taken on a 4H SIC BJT roughly 500μm x 500μm in size, supplied by CREE. Figure 2 Electron Paramagnetic Resonance (EPR): EPR is a powerful technique for identifying trapping centers in semiconductor device structures, as it can provide detailed structural and chemical information about trapping centers[1]. In EPR, a sample is exposed to a slowly varying external magnetic field (H) which splits the spin system into two energy levels, called Zeeman levels, (corresponding to spin up and down of the electron) as shown in Figure 1. The sample is then exposed to a second, oscillating magnetic field of frequency ʋ. Resonance occurs when the energy of the oscillating field (h ʋ) equals the Zeeman splitting (∆E), essentially “flipping” the spins. For the simplest case, the resonance condition is defined as h ʋ = gβH. (h = Planck’s constant, ʋ = microwave frequency, H = magnetic field at resonance, β = Bohr magneton, the g depends on the defect structure and orientation in the applied magnetic field. It is essentially a second rank tensor). EPR has a sensitivity of about 1010 spins or about 1010 trapping centers. Since far fewer defects are present in individual transistors, one needs a much higher sensitivity for fully processed transistors. This sensitivity can be provided by SDR. Pauli Exclusion Principle/ EPR A single orbital can only be occupied by two electrons with opposite spin orientation. Figure 3 Figure 7 Figure 7 shows a comparison of SDR results from high field/freq. (top) to low field/freq. (bottom). The high field/freq. system represents a g = 2.0024 +/- 0.0003 at 9.6027 GHz, while the low field/freq represents a g ≈ 2.00 +/- 0.01 at 56.222 MHz. Low Field SDR Apparatus: The Kaplan Solomon Mott Model for SDR predicts the sensitivity is nearly independent of the magnetic resonance field and frequency[3]. This field and frequency independence sensitivity makes it possible for very sensitive SDR measurements at low field and frequency. At low field and frequency the measurements do not require a microwave cavity, only a low Q LC circuit. The device can be placed in a simple coil allowing SDR measurements of devices in any IC package . Expensive magnetic field apparatus is also not required. The low field magnet is comprised of machined brass Helmholtz coils and smaller modulation coils. The RF radiation is coupled into the device via a coil wrapped around a test tube. The transistor is inserted into the test tube and electrically connected to a biasing box. The recombination current is then sent to a pre-amplifier and a lock in amplifier. A computer utilizing Lab-View software performs the data-acquisition. Figure 4 shows a schematic drawling of the apparatus and Figure 5 is a picture of a top and side view of the apparatus. Spin Dependent Recombination (SDR): SDR can be explained qualitatively in terms by the Shockley Read Hall model for recombination (Figure 2), EPR (Figure 1), and the Pauli exclusion principle (Figure 3). In the Shockley Read Hall model, an electron is captured at a deep level defect and is followed by a hole. The electron and hole annihilate which enables the process to be repeated indefinitely. The Pauli exclusion principle tells us that two electrons with the same spin quantum numbers cannot occupy the same orbital. Consider the potential capture of a conduction electron at a paramagnetic site. If both the conduction electron and the deep level paramagnetic site electron have the same spin quantum number the capture event will be forbidden. In EPR, the applied EM energy flips the spin of the deep level electron which enables the process of recombination to occur. This effectively increases the capture cross section of the defect, thereby increasing the recombination current. The magnitude of this current is the basis for SDR. SDR with its high sensitivity of about 102 spins (trapping centers) can be applied to individual BJTs and MOSFETs. In SDR we configure a device so it is dominated by recombination events. With a BJT one can look at recombination centers in the base by examining the recombination in the forward biased emitter-base or collector-base junctions. For SDR with a MOSFET, the device is configured as a gate controlled diode. With the diode slightly forward biased, current is dominated by recombination in the depletion region[2]. Cost: The cost to manufacture the Helmholtz coils is around $500. The cost of the supporting equipment discussed previously is around $12,000, which makes the total cost of our apparatus around $13,000. Commercially available EPR spectrometers typically cost over $200,000. Drawbacks of a low field system: Currently a very low level of resolution of g ≈ +/- 0.01 is available from this system. In high field/frequency systems, the resolution of g = +/- 0.0003. In the future we hope to build a system that uses a field and frequency that are somewhat larger than the current system to increase resolution without sacrificing its advantages. Figure 4 Schematic Diagram : Conclusions: Low field SDR may have the potential to make EPR measurements widely available for reliability studies. References: [1] J.A. Weil, J.R. Bolton, and J.E. Wertz, Electron Paramagnetic Resonance: Elementary Theory and Practical Applications, John Wiley and Sons Inc., New York, NY, 1994 [2] A. Neugroschel, C. T. Sah, K. M. Han, M. S. Carroll, T. Nishida, J. T. Kavalieros, and Y. Lu, IEEE Trans. Electron Devices 42, 1657 _1995_. [3] D. Kaplan, I. Solomon, and N. F. Mott, "Explanation of Large Spin-Dependent Recombination Effect in Semiconductors", Journal De Physique Lettres, 39, pp. L51-L54, (1978)