2011 International Conference on Computer Applications and Industrial Electronics (ICCAIE 2011)
A Modular System of Deep Level Transient Spectroscopy Nazreen Rusli Dept. of Information and Communication Technology, Centre for Foundation Studies, International Islamic University Malaysia
[email protected]
Didier Debuf, PhD Dept. of Electrical and Information Engineering The University of Sydney Australia
[email protected]
Abstract— Deep Level Transient Spectroscopy (DLTS) is a technique to determine the electrical characteristics of an electrically active defect in a semiconductor. A measurement system is developed to detect defects in a semiconductor in a LabView environment. A more accurate method namely Fundamental Frequency Deep Level Transient Spectroscopy (FFDLTS) is proposed as one of the methods to analyze the defect level depth.
approach is taken by integrating five off the shelf instruments with the programming written in LabVIEW. The study of electrically active defects in semiconductor devices is continuing and the tools or methods for such an investigation have improved considerably since Lang's [1] development of the DLTS method in 1974. DLTS uses capacitance transient signals resulting from relaxation processes following an abrupt change of bias voltage and temperature control applied to the sample under test [1]. Later, another four refinements of Lang’s original analysis method were developed, which are Fourier Transforms DLTS (FTDLTS) [2], Laplace DLTS (LDLTS) [3], Injection Level Dependent Lifetime Spectroscopy (IDLS) and Temperature Dependent Lifetime Spectroscopy (TDLS) as described in [4]. All of the methods rely on the single-level defect theory of Shockley, Read and Hall (SRH) theory [5]. The general analytic solution to the SRH rate equations that is consistent with multitransient analysis of the numerical solution indicates two fundamental time constants for the single-level defect [6]. Therefore, the usual SRH single time constant expression represents an approximation. The variation of fundamental time constants with excess carrier concentration follows a linear and a non linear region. Thus, in this work, we analyze a unified approach to recombination region by using a new measurement technique based on the multiple-level theory [7][8], where there are m defect levels in the band gap. It is developed from the solution of coupled non-linear differential equations. The governing equation is comprised of linear and non-linear differential components. The solution indicates that the multi exponential decay due to a voltage pulse has m+1 fundamental time constants determined from the linear component of the governing equation. In the transient case, for a single-level-defect for example, it is found that two fundamental time constants are present in decay since these are derived from a second order differential equation, where the non-linear component goes to zero for a particular condition. The total solution for the governing equation comprises an infinite series of mono-exponential terms where the inverse decay constants, for each exponential term, are a linear combination of the inverse of the fundamental time constants [7]. Recently, digital DLTS studies have been presented to replace the previous analog techniques by using digitizers
Keywords—DLTS; FFDLTS; LabVIEW; Defect
I. INTRODUCTION Semiconductor devices are generally formed from a crystal lattice of silicon or Gallium Arsenide and intentionally doped with impurities. In semiconductor processing technologies, the aim is to diminish the process-induced defects. Electrically active defects in semiconductors may dominate device characteristics, for instance in the form of noise in high frequency devices and a shift in the threshold voltage for Field Effect Transistor (FET) type devices. Defects may arise due to some factors such as substitutional and interstitial impurities, vacancies and complexes in the crystal lattice, grain boundaries and interfaces. As a result if a carrier, either electron or hole, comes near to the defect, it may undergo recombination. Recombination is a loss process and removes carriers from the current that reaches the device terminals. The theoretical modeling of defects has been enhanced notably by the measurement technique, namely Deep Level Transient Spectroscopy (DLTS). DLTS has been used to assess the quality of semiconductor device processing and the source material. The method requires forming either a Schottky diode or a p-n junction with a small sample. It is a high-frequency capacitance transient thermal scanning method so as to observe traps in the semiconductor. This technique has the ability to distinguish between majority and minority carrier traps. However, the yield of the small feature size devices warrants a more accurate assessment of semiconductor processing. Hence, in this work, an investigation into a more accurate method namely, Fundamental Frequency Deep Level Transient Spectroscopy (FFDLTS) is performed and LabVIEW is chosen as a platform for the development of the measurement system. A modular
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and digital signal processing equipment. This technique is more flexible as a DLTS system because it is capable of measuring a much wider range of fundamental time constants.
Note that, the expression for in (4), is independent of the fundamental frequencies and the excess carrier concentration Δn(0). The characteristics equation in (1) may be written as equation (5).
II.
FUNDAMENTAL FREQUENCY DEEP LEVEL TRANSIENT SPECTROSCOPY (FFDLTS) A multiple-level-defect theory is given in Ref. [8]. An improved method of defect level depth measurement in the form of Fundamental Frequency Spectroscopy (FFS) for the multiple-level-defect [9] is proposed to unambiguously indicate energy level depth. Consider the case where electrons are the source of the signal response to the applied impulse δ(t). The generalized determinant of the linear simultaneously equation is given in equation (1) for the case of two levels, m=2, resulting in the characteristics equation in ω. Let
Now, is approximately equal to for k = 1,2,3,…..,m where in equation (5) approaching the limit with the magnitude of yields equation (6). (6) The natural logarithm of the left hand side of equation (6) yields equation (7). (7)
(1)
The slope Δ may be found with a relative error of three percent due to the temperature dependence of the intercept b(T). This effect is found for Arrhenius plots where the temperature dependence of the intercept causes a curve to trace out instead of a straight line. The accuracy of the FFDLTS method is evident for multiple-leveldefects where there are m+1 fundamental frequencies, but only m levels, with a direct relationship between the , k = 1,2,3,…, m and a particular level Δ The standard SRH Theory when applied to multiple levels indicates m +1 levels. A similar approach may be taken for the case where holes are the source of the signal response the applied impulse δ(t).
where in order to simplify notation (2a) (2b) (2c) and where the symbols follows:
III. THEORY Defects in the semiconductor material create energy levels in the band gap. A transition of electrons and holes from the conduction band and the valence band, via the defect energy levels, is called Recombination. Recombination is then determined by these deep levels. For a p-n junction of solar cell, the dominant loss mechanism is recombination in the depletion region. Hence, in this work a forward bias pulse is to be applied to a p-n junction reducing the depletion layer width. Thus the defect energy levels within the depletion layer are to be investigated. When a forward bias pulse is applied to a p-n junction, the lightly doped side of a depletion region decreases. Then, electrons and holes fill the defects of the energy level. After the voltage pulse returns to its relaxation value, the trapped carriers start emitting. The defects start to emit trapped carriers due to the thermal emission process. The filling and emitting processes is illustrated in Fig 1.
are now given as (3a) (3b) (3c) (3d)
The rate of concentration,
the
normalized excess , is given by
carrier
(4)
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card represents the sampled record of capacitance meter voltage values versus time. The sampled result follows an exponential or sum of exponential with respect to time. The sampled record is then analyzed [10] for time constants to determine the fundamental decay time constants, τk. The requirement for the experiment is that at each temperature Tj the temperature be kept constant within a certain tolerance and for a certain period of time. This can be done by an MMR technology K-20 temperature controller. MMR K-20 is chosen because it acts as Micro miniature refrigerators and it has a rapid cool-down and warm-up which is less than 15 minutes. It has a precise temperature control, which is about ± 0.1 K. The sample is placed on the MMR K-20 thermal stage connected by a ribbon cable to the temperature controller. Then, this thermal stage is placed in a vacuum chamber whereby the air is evacuated by a vacuum pump and the water vapor and ambient heat is reduced. Then, the thermal stage is now able to be set at a constant temperature. The temperature is set in the range from 80K to 300K with incremental steps of 1K. The constant temperature is needed for a period of time P in order to sample for N records. In this experiment, N is set to 100. These records are then averaged and effective noise is reduced by the square root of N. Smoothing of the uncorrelated samples in each record is not introduced. A timing diagram, indicating the timing relationship between the pulses, is shown in Fig 3.
Figure 1. Filling and Emitting process of holes and electrons
IV.
EXPERIMENTAL INSTRUMENTATION AND SOFTWARE PROCEDURES The analysis of the multi-exponential decay due to the forward bias pulse uses the FFDLTS technique [9] described above in analyzing for defects within the depletion region of a p-n junction. A modular system is chosen and experimental equipment is comprised of a Capacitance Meter, Pulse Generator (PG), Digital Delay Pulse Generator (DG), an Analog to Digital converter (ADC), Rubidium frequency standard and a temperature controller together with a thermal stage and vacuum chamber. Cooling the device is to be done with a JoulesThompson micro-miniature refrigerator. Fig 2 indicates a block diagram of the experimental setup. Control and initialization of the instruments is performed in a LabVIEW environment over IEEE-488 bus.
Figure 2. Filling and Emitting process of holes and electrons
LabVIEW is used as a platform to control all the instruments as well as retrieving the results from the ADC Card. This includes the initialization and setup of instruments with parameters such as the time delay between pulse A and pulse B, Δtd (see Fig 3). LabVIEW is chosen because of its friendlier user interface and it can support the GPIB communication bus interfaces from the instruments used. Since the capacitance transient is measured as a function of time at constant temperature, thus the temperature range is defined to be from 80K (in the range from liquid nitrogen temperature) to room temperature at 300K. However, it has to be kept constant at certain temperature during a measurement, then, incremented by 1K steps. A forward bias voltage pulse is applied to the emitterbase junction, where the emitter is more heavily doped than the lighter doped base, realizing a decrease in the depletion region in the base. When the pulse returns to zero the depletion region relaxes back to equilibrium. The DUT is to be used to calibrate the experimental instrument configuration and the written LabVIEW software. Emission of carriers from the defect level causes the depletion layer edge to decay and the output of the ADC
Figure 3. Timing relationship diagram
A. LabVIEW LabVIEW is used as the interface to control the instruments, namely the Capacitance Meter, Pulse Generator, Delay Generator and ADC Card [11]. LabVIEW is also chosen because it has a large library of drivers for data acquisition hardware and test instruments such as drivers for Delay Generator, Pulse Generator and ADC card. However, drivers for the capacitance meter and temperature controller were developed and programmed in LabVIEW. In LabVIEW, parallel execution of multiple tasks can be handled by placing two independent loops in the diagram and hence allow them to run simultaneously. This is a requirement in this experiment as the reading from the ADC card and delay generator is performed at the same time. During the program development, the issues that arose such as conflicts in time for function calls, nested loops and rapid interrupt by hardware were resolved. In the
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In addition, several interrupts from hardware in rapid succession are implemented with the event control structure in the LabVIEW environment. There are two modes of the interface created, which are manual mode for the detail setting of each instrument and automatic mode. The first mode should be executed for the first time when running the experiment and the second mode can be run later. In the automatic mode, the important parameters are only available to edit or modify during the execution. Fig 4 illustrates the front page of the manual mode.
LabVIEW, one cannot apply the same concept as in the C language for calling functions and nested loops. These are crucial especially when dealing with a real time program. As a result, the most fitting solution is found by using a state diagram. The state diagram can be programmed to wait until one sequence is completed. State diagram architecture can be used to implement complex decisionmaking algorithms and are used in applications where distinguishable states exist. Each state can lead to one or multiple states, and can also end the process flow. The state diagram has been implemented in the program for Delay Generator, Capacitance Meter and Pulse Generator.
Figure 4. The interface for manual configurations
For the second mode which is automatic mode the front panel is shown in Fig 5. Results are plotted on the graph area after the trigger start button is pressed. There are some parameters that can be controlled as well as observed on this
panel. The program is then updated with the automatic and manual modes. The automatic mode is applied if the experiment is required to run a number of cycles continuously.
Figure 5. Automatic Mode
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2) Averaging the number of records By averaging 100 cycles the variance is improved as shown below. A new VI file named as Average.vi is developed in conjunction with the existing software suite developed so that it automatically uploads a bundle of measurement files in order to calculate for the average. However, the file names must be saved with a sequence number in the file name. The test is repeated on the same DUT with the highest data points set. As predicted, the variance is enhanced. Table 3 shows the outcome of the test done for only 8192 data points.
V. TEST Prior to the start the experiment, the system is verified with the oscilloscope and confirmed that the decay values are exactly the same as in the oscilloscope with the right scale of amplitude and time. Then, the first test is done at room temperature of 300K with only one measurement engaged. However, the measurement is taken at three different record lengths that are 1024, 2048 and 4096 data points, in order to determine the accuracy of the system. TABLE I. Test
No. of Points
1
1024
2
2048
3
TIME CONSTANT Time constant (secs)
τ1 = 6.782 E-02 τ2 = 6.522 E-06 τ1 = 4.000 E-02 τ2 = 4.776 E-05 τ3 = 4.266 E-06 τ1 = 4.011 E-01 τ2 = 7.529 E-06 τ3 = 5.407 E-07
4096
Variance 8.562 E-09
TABLE III. No. of Points 8192
7.989 E-09
8.288 E-09
1) Significant digits Initially the significant digits (SD) were set at 6 decimal points. It is expected that the more significant digits that can be generated, the better the variance. Following the large variance found on the first test, the number of decimal places or digits in the data is increased from 6 decimal points to 10 decimal points. The preceding data is truncated. The same tests set at 2048, 4096 and 8192 data points are repeated but with 10 decimal places after the decimal point. The results are shown below.
1 2 3
Variance (10 S.D)
4.000 E-09
2.773 E-09
Variance (Average) 3.5E-11
VI. RESULTS The semiconductor defect test is then continued with the current experimental circumstances. The method has changed from taking the average for 100 cycles at a constant temperature to one measurement per 1 K change along the cooling and heating process. However, it is not linearly changed since the rate of change on temperature of heating process is faster than the cooling process. As a result, these conditions are expected to affect the time constants. The system is kept running automatically throughout the changes in temperature with 1024 and 2048 data points captured separately. The result with resolved time constants, τ are plotted by using Equation (15) in [9].
A. Data Integrity Test
Measurement
Variance (6 S.D)
The output was encouraging since it improves the variance. As a result, the test of 100 cycles at a constant temperature will be applied for future analysis.
There are some variations in the time constants even though the same sampling is repeated at one constant temperature but at different number of points captured. This may be due to a large variance of data measurement. Note that exponentials are non orthogonal and for a large variance different sums of exponentials can be fitted to the data points. Thus, in order to achieve the aim of this experiment, more tests are to be done and data integrity tests are needed [11].
TABLE II.
COMPARISON IN VARIANCE
COMPARISON IN SIGNIFICANT DIGITS
No. of Points 2048 4096 8192
Variance (6 S.D)
Variance (10 S.D)
7.989 E-09 8.288 E-09 4.000 E-09
4.435 E-09 4.217 E-09 2.773 E-09
As clearly can be observed, the variance is decreasing compared to the previous result. The time constant is likely to be more accurate as more significant digits are considered. The increase in significant digits is contributed by the noise. Hence to conclude, the more significant digits the lower the variance obtained for instance it goes from 4E-9 to 2.7E-9 for the 8192 data. However, further tests with different condition, by averaging, is needed and probably the variance may be reduced further.
Figure 6. Resolved fundamental time constants from experimental capacitance decay for 1024 data points
From the graph, a linear form is determined and obviously there is a level appeared in the middle of the band gap labeled as L3. Level L3 has a slope of approximately 0.4838 eV and has a positive slope. It is also near the middle of the band gap where it is an efficient recombination centre. Meanwhile, level L1 has a
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Unfortunately, the method cannot be applied since the temperature control system, as applied in the form of a ramp to the DUT, does not offer the stability in temperature. This is highly important in order to run the test for 100 cycles at one constant temperature and allow the averaging method to be employed.
slope of -0.0799 eV and it has a negative slope. The results are written as follow: TABLE IV. Level L3 L1
ENERGY LEVEL’S DEPTH Energy level 4.838 E-01 7.99 E-01
VII. CONCLUSIONS A defect-level measurement test system is constructed with LabVIEW as a platform to control the instruments. The study on a new method namely Fundamental Frequency Deep Level Transient Spectroscopy cannot be done due the problem of maintaining a constant temperature with current temperature measurement of 100K to 300K. It is proven that there is more than one time constant for each test. Data integrity tests were done at a room temperature in the way to obtain a better result with two orders of magnitude improvement in the variance by averaging the data sets. However, due to ramping in temperature, the average of 100 cycle’s data cannot be done, and hence the result is not as presumed. The averaging concept is expected to produce better result as it improves the variance.
The results indicate that there is a deep level near the middle, which is 0.4838 eV of the band gap which is alleged for a switching transistor. After that, the results for 2048 data points are analyzed [9][10]. The output graph is illustrated in figure 7.
L1
ACKNOWLEDGMENT We would like to express our grateful acknowledgement to School of Physics, The University of Sydney for the contributions of equipment and LabVIEW software.
Figure 7. Energy Level Depth for 2048 points
REFERENCES [1]
D. V. Lang, "Deep-level transient spectroscopy: A new method to characterize traps in semiconductors," in Journal of Applied Physics, vol. 45, pp. 3023-3032, 1974. [2] S. Weiss and R. Kassing, "Deep Level Transient Fourier Spectroscopy (DLTFS)--A technique for the analysis of deep level properties," Solid-State Electronics, vol. 31, pp. 1733-1742, 1988. [3] L. Dobaczewski, et al., "Laplace transform deep-level transient spectroscopic studies of defects in semiconductors," Journal of Applied Physics, vol. 76, pp. 194-198, 1994. [4] S. Rein, et al., "Lifetime spectroscopy for defect characterization: Systematic analysis of the possibilities and restrictions," Journal of Applied Physics, vol. 91, pp. 2059-2070, 2002. [5] W. Shockley and W. T. Read, "Statistics of the Recombinations of Holes and Electrons," Physical Review, vol. 87, p. 835, 1952. [6] K. C. Nomura and J. S. Blakemore, "Decay of Excess Carriers in Semiconductors," Physical Review, vol. 112, p. 1607, 1958. [7] D. Debuf, et al., "General analytic solution to the Shockley-ReadHall rate equations with a single-level defect," Physical Review B, vol. 65, p. 245211, 2002. [8] D Debuf, General Theory of Carrier Lifetime in Semiconductors with Multiple Localized States, J. Appl. Phys., 96:6454 (2004) [9] D. Debuf, "Multiple-Level-Defect Measurements Using Fundamental Frequency Deep Level Transient Spectroscopy," Proceedings 20th European Photovoltaic Solar Energy Conference and Exhibition, CCIB - International Convention Centre, Barcelona, Spain, 6-10 June 2005 [10] J. Alam, Master’s Thesis, The University of Calgary, Alberta, Canada,,1990. [11] N. Rusli, Master’s Thesis, The University of Sydney, Australia, 2010.
Figure 8. Energy Level Depth for 2048 points
Figure 8 shows the FFDLTS analysis of the same data as Figure 7 and indicates the level L1. The magnitude of the slope of the linear portion of the graph, L1, represents the energy level depth of -1.06e-02eV. These two graphs show that only one level is determined which is for L1. There is no energy level appearring in the middle of the band gap for L3 as obtained in figure 6. The results for the two graphs do not agree because the rate of change in the temperature is too high. In the data integrity test section, it is proven that the averaging method offers the better result in variance.
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