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DLTS: Deep level transient spectroscopy
Deep levels in semiconductors influence both the electrical and the optical properties of the material. There are a number of optical techniques for the characterisation of deep level defects in semiconductors. However, one of the main shortcomings of these techniques is that they cannot measure or predict the electrical properties. Since most semiconductor applications rely on the electrical properties of the semiconductor, it is important to know the electrical properties of a deep level defect. Furthermore, many of the processes that occur in deep levels that influence device performance are nonradiative, and cannot be observed by optical techniques. Deep level transient spectroscopy (DLTS) is one of the most versatile techniques used to determine the electrical properties of defects.
The DLTS technique
As described by Lang (1974), the DLTS technique uses a fast, sensitive capacitance meter to measure the capacitance of a reverse-biased Schottky, MOS or p–n junction. According to Equation (2.11), the capacitance of a reverse-biased diode can be related to the width of the depletion region, which in turn depends on the charge in the depletion region, due to dopants as well as deep levels. The DLTS technique measures the change in the capacitance of the junction due to the emission of carriers by defects in the depletion region, as described by Equation (2.29). By processing the capacitance signal with a weighting function, the emission rate of the defect in the depletion region is obtained.
Consider the case of a Schottky contact on an n-type semiconductor, as shown in Figure 3.1(A). The semiconductor contains a low concentration of a defect that causes a deep electron trap with energy ET . In the figure the bulk of the semiconductor containing free carriers is indicated by the shaded area, while the depletion region is left unshaded. Filled and open circles indicate filled and empty traps respectively. For simplicity, we assume that, initially, all the traps in the depletion region are empty, while all the traps in the bulk of the semiconductor are filled.
At the start of the DLTS cycle, a smaller reverse bias (or even a forward bias) pulse is applied across the diode. [Figure 3.1(B)]. This bias pulse reduces the width of the depletion region, increasing the capacitance of the Schottky diode drastically. The reduction in the width of the depletion region fills the traps up to a distance of approximately the depletion width below the surface of the semiconductor.
After the filling pulse, the reverse bias is returned to its quiescent level [Figure 3.1(C)]. This increase in reverse bias increases the width of the depletion region again. However, since some of the deep level traps in the depletion region are now filled, the charge density in the depletion region is less than it was in (A), therefore the depletion region is slightly wider and the capacitance slightly lower than was the case in (A).
Since the filled traps in the depletion region are above the Fermi level, they now emit carriers by means of thermal processes, as described in Section 2.2. This causes the charge density in the depletion region to increase, reducing its width and increasing the capacitance of the junction.
If it is assumed that N T ≪ ND , the depletion region width will not change significantly during the emission of carriers. Under these circumstances, it is reasonable to assume that the emission of carriers from the depletion region may be described by an exponential decay, as in Equation (2.29). The capacitance of the Schottky diode is then also described by an exponential decay function
where l is the decay rate and C¥ is the steady state capacitance of the diode.
If it is assumed that all the defects from the depletion region edge to the interface are filled by the filling pulse and subsequently emptied, the defect concentration may be calculated from the amplitude of the exponential decay function by applying Equation (2.11
It is possible to obtain an activation energy and a capture cross-section associated with the emission of the carriers from the defect by measuring the decay time constant as a function of temperature, as described in Section 2.2.1.
In the above explanation, it has been assumed that the defect level is empty in the depletion region and full in the bulk. Since the defect level typically lies much deeper in the band than the dopant level, the defect level intersects the Fermi level a distance l shallower than the depletion region edge, as shown in Figure 3.2.
University of Pretoria etd – Meyer, W E (2007)
Figure 3.1 A schematic illustration describing the origin of the DLTS transient. (A): Quiescent state,
(B): Filling pulse; (C) Reverse bias; (D) Exponential decay as carriers are emitted. The graphs in the middle show the applied bias VD and the change in the capacitance of the diode DC as a function of time. (After Miller, 1977.)
Figure 3.2 An energy band diagram showing the relationship between the depletion region edge and the position where the defect level intersects the Fermi level.
If a constant dopant concentration ND is assumed, then the distance l is independent of the width of the depletion region, and is given by
The result is that the DLTS measurement does not probe the region at the depletion region edge, but a region a distance l shallower, as shown in Figure 3.3. This effect has to be taken into account when the DLTS technique is used to determine the depth profile of defects or the electric field experienced by the defects is calculated. Furthermore, during the transient, charges are removed a distance l from the depletion region edge, therefore Equation (3.2) is not strictly valid, and a more careful analysis needs to be performed in order to obtain quantitatively correct values. DLTS depth profiling and the precautions that need to be taken are discussed in detail by Zohta (1982)
Figure 3.3 Filling (top) and subsequent emission (bottom) of electrons from a deep level in the depletion region, assuming a constant Fermi level. In the top diagram, the filling of the defect during the filling pulse is shown. Note that due to band bending and the depth of the defect level, the defect level is filled to a depth l shallower than the depletion region edge. After the filling pulse, the width of the depletion region increases by an amount Dw . Carriers are now emitted from a band of defects with a width Dw a distance l shallower than the depletion region edge.
University of Pretoria etd – Meyer, W E (2007)
Analysis of the DLTS transient
In the idealised case, the DLTS capacitance transient obtained from a sample with a single defect level is an exponential decay function of the form where A is the amplitude, l is the decay rate and C¥ is the capacitance of the junction at equilibrium. Many physical processes are described by such an exponential decay process, and in principle determining the values of A, l and C0 is reasonably straightforward.
However, it frequently occurs that there is more than one defect level in the semiconductor and that these defects have closely spaced decay constants, or even a continuous band of decay constants. In this case, the capacitance transient can be described as the sum of a number of exponential decay functions. Many techniques have been developed for the deconvolution of such a multi-exponential function. However, there are significant problems associated with all of the techniques, and the analysis generally becomes unreliable in the presence of noise.
Analogue techniques
The original method used to analyse the DLTS transient was a double boxcar proposed by Lang (1974). According to this method, the DLTS signal is obtained by subtracting the capacitance measured at time t2 from the capacitance at time t1 (both times measured relative to the filling pulse). Qualitatively the process may be described as follows: Assume that the sample is at a low temperature and therefore there is a slow transient. Because the capacitance does not change much, the DLTS signal
As an alternative to the above method, it is possible to keep the temperature constant and rather change the frequency of the LIA. This technique is referred to as isothermal DLTS or frequency scanned DLTS (Henry, 1985). Isothermal DLTS is usually implemented using digital signal processing, where a fast analogue to digital converter (ADC) connected to a computer is used to capture and analyse the data.
Both the boxcar and lock-in amplifier techniques can be successfully implemented using a fast ADC and a computer. Using a computer to analyse the transient has the further advantage that analysis at a number of lock-in amplifier frequencies can be done simultaneously, thereby saving a considerable amount of time. Furthermore, a much wider range of emission rates (especially low emission rates) can be accessed by such systems, allowing defects to be studied over a wider temperature range. However, the main advantage of digital signal processing is that modern techniques to analyse multi-exponential decay functions such as the Gaver-Stehfest method (Istratov, 1997) and various methods for calculating numerical inverse Laplace transforms (e.g. Dobaczewski, 1994) may be used.
Digital processing of DLTS transients
The major shortcoming of the DLTS technique is that, even for emission from a single defect level at a single decay rate, the DLTS peaks as obtained by boxcar and LIA analysis are broad, compared to the typical spacing between defects. This is in stark contrast to optical techniques, which, especially at low temperatures, yield very sharp lines. Although the broad DLTS peaks are not a serious handicap if only a single level is present, it is difficult to accurately determine the emission rate of defects with emission rates spaced less than an order of magnitude apart when both are present in the same spectrum. In fact, analysis by more advanced techniques has shown that DLTS peaks that were previously regarded as a single peak actually consist of a number of discrete peaks that could not be observed due to the limited resolution of LIA DLTS (Dobaczewski, 1992).
Istratov (1998) compares a number of different weighting functions. Some of them reduce peak widths by almost a factor of three compared to widths obtained by LIA DLTS, but at the cost of decreasing the signal to noise ratio by more than an order of magnitude. Using weighting functions based on the Gaver-Stehfest algorithm, Istratov (1997) has shown that it is possible to decrease the peak width by almost a factor 5 (compared to a lock-in amplifier), while still keeping the signal to noise requirements of the input signal realistic.
Another approach to improve the resolution of the DLTS technique is to assume that the sample emits a spectrum of emission rates with a spectral density function F (t ) , so that the capacitance transient
Differential DLTS
The depth range sampled by the DLTS technique depends on the applied reverse bias and the filling pulse, which respectively determine the maximum and minimum of the depth range that is observed. By recording DLTS transients under different biasing conditions and then subtracting these transients, it is possible to observe defects that lie in a limited depth range only. Such techniques are generally used to measure defect concentration depth profiles, see Lefèvre (1977) or Zohta (1982).
However, this technique is not limited to the measurement of concentration depth profiles. As described by Equation (2.8), the electric field in the depletion region also changes with depth; therefore, defects at different depths beneath the surface experience different electric fields. Thus, by restricting the measurement to only a limited depth range, it is possible to observe the behaviour of the defect under the electric field present at that depth. By applying different bias voltages, it is possible to vary the electric field in the depletion region from approximately zero to almost the breakdown field of the semiconductor. If samples with different doping levels are used, it is possible to study the behaviour of a defect under electric fields that vary by several orders of magnitude, and a variety of phenomena described in Section 2.2.3 may be observed.
1 Introduction
2 Some concepts in semiconductor physics
2.1 Metal-semiconductor junctions
2.1.1 The Schottky model
2.1.2 The ideal case
2.1.3 Behaviour of the barrier under forward and reverse bias
2.1.4 Calculation of the electric field in a Schottky barrier
2.2 Defects and deep levels in semiconductors
2.2.1 Emission and capture of carriers from defects
2.2.2 Defect occupation as a function of time
2.2.3 Field dependence of the emission rate
3 DLTS: Deep level transient spectroscopy
3.1 The DLTS technique
3.2 Analysis of the DLTS transient
3.2.1 Analogue techniques
3.2.2 Digital processing of DLTS transients
3.3 Differential DLTS
4 Planning of the digital DLTS set-up
4.1 Acquisition of the capacitance signal
4.1.1 Random noise
4.1.2 Response time, sampling rate and resolution
4.1.3 Periodic noise
4.1.4 Stability
4.2 Selection and characterisation of the instrumentation
4.2.1 Digitiser
4.2.2 Capacitance meter
4.2.3 Pulse generator
4.2.4 Rise and fall times
4.2.5 Sample mounting and temperature control
4.3 Other hardware
4.3.1 Fast pulse interface
4.3.2 Synchronisation
4.4 Software
5 Experimental
5.1 Introduction
5.2 Sample preparation:
5.2.1 Gallium Arsenide
5.2.2 Silicon
5.2.3 Gallium Nitride
5.3 IV and CV characterisation
6 Characterisation of the EL2 and E2 defects in n-GaAs
6.1 Introduction
6.2 The EL2 and E2 defect levels in n-
6.3 Experimental
6.4 Results and discussion
6.5 Conclusions
6.6 Publications
7 Field dependence of the thermally activated emission rate
7.1 Introduction
7.2 Publications
8 DLTS observation of the transformation of bistable defects
8.1 Introduction
8.1.1 Configurationally bistable defects
8.1.2 Charge state controlled metastability
8.1.3 Characterisation of metastable defects
8.1.4 Example: The C–C pair in Si
8.2 Experimental
8.2.1 Introduction
8.2.2 Sample preparation
8.2.3 Determining the defects’ DLTS signatures
8.2.4 Determination of the transformation kinetics
8.2.5 Discussion
8.3 Publications:
9 Negative-U defects in n-GaN
9.1 Introduction
9.1.1 What is U?
9.1.2 Mechanisms leading to negative-U behaviour
9.1.3 Properties of negative-U defects
9.2 DLTS of a negative-U defect
9.2.1 Behaviour of a negative-U defect under changing Fermi level
9.2.2 DLTS of a negative-U defect
9.3 Negative U properties observed in a sputter-deposition induced defect in n-GaN.
9.3.1 Introduction
9.3.2 Experimental
9.3.3 Results and discussion
9.3.4 Conclusion Publications
10 Conclusions
References
