“apparatus” electron beam microtomography in sem

V. V. ARISTOV et al.: Electron Beam Microtomography in SEM 21 1

phys. stat. sol. (a) 150, 211 (1995)

Subject classification: 61.14; S1.3; S5.11

Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences, Chernogolovka‘)

“Apparatus” Electron Beam Microtomography in SEM

BY V. V. ARISTOV, E. I. RAU, and E. B. YAKIMOV

(Received April 5, 1995)

Dedicated to Professor Dr. JOHANNES HEYDENREICH on the occasion of his 65th birthday

The methods of SEM “apparatus” tomography for layer-by-layer reconstruction of composition, electrical and optical properties are discussed. It is shown that the energy dispersive detection of backscattering electrons or the study of the dependence of the backscattering coefficient on primary electron energy can be considered as examples of such methods. It is shown that the methods of modulated CL and modulated EBIC allow to reconstruct the depth distribution of electrical and optical properties in semiconductor structures. The depth resolution of all methods discussed can achieve 10 nm.

1. Introduction

Tomographic methods are widely used for the reconstruction of the internal structure of an object under study and for the reconstruction of the three-dimensional distribution of its properties [I]. In microelectronics applications most objects to be characterized are multilayer planar structures in which the thickness of layers is much smaller than their lateral dimensions. Therefore, the methods for the characterization of such structures should have high spatial resolution in one direction only. For conventional scanning electron microscopy (SEM) methods the lateral resolution usually is varied from a few nm to a few pm depending on primary electron energy and the method used. The results obtained on samples inhomogeneous in depth allow to evaluate some effective values of their parameters only because in general it is impossible to reconstruct the three-dimensional distribution from the two-dimensional images. In other words, since an unknown function describing the distribution to be measured depends on three variables, while the signal does only on two, for the successful reconstruction it is necessary to introduce an additional parameter as a third variable. In the SEM methods in many cases the most suitable parameter for this purpose is the primary electron energy. Then, using computer tomography and a set of images obtained at different energies it is possible to reconstruct the three-dimensional distribution of physical parameters with an enhanced spatial resolution [2 to 41.

In the backscattering electron (BSE) mode the possibilities of reconstruction of the internal structure of objects under study and of layer-by-layer sectioning were studied analytically [ S to 71 and using Monte-Carlo simulation of electron backscattering processes [S]. The dependence of the BSE coefficient on the primary electron energy, the orientation of the

I ) 142432 Chernogolovka, Moscow district, Russia.

14*

212 V. V. ARISTOV, E. I. RAU, and E. B. YAKIMOV

probing beam, and the detection angle was studied experimentally in [9 to 111. The results obtained show that the BSE mode can be used for layer-by-layer tomography, but the inverse problem, i.e. the problem of reconstruction of the three-dimensional distribution on the basis of a set of BSE images, has not been solved yet. Therefore, it is important to develop some “apparatus” methods for internal structure reconstruction.

For the reconstruction of the distribution of electrical and optical properties measurements in the electron beam induced current (EBIC) and cathodoluminescence (CL) modes can be used. The solution of the inverse problem for these methods was discussed in [3, 41. It was shown that it is an ill-posed problem which can be solved by well-developed regularization techniques [12]. The only question is that this procedure is very sensitive to noise and needs high enough precision of measurements. Therefore, in this case the development of an “apparatus” tomography approach, i.e. methods for the selection of signals from narrow internal layers and the reconstruction of the distribution of electrical and optical properties by means of a specially designed set-up, is also very useful.

In the present paper such an approach is illustrated by two in situ differential methods: by EBIC with modulation of the depletion region width and by CL with modulation of energy and intensity of the electron beam, and by tomography in the BSE mode. All methods demonstrate usual for SEM methods lateral resolution and enhanced depth resolution and allow to reconstruct nondestructively the depth distribution of composition, electrical and optical properties.

2. “Apparatus” Tomography in the BSE Mode

As shown in [7, 10, 13 to 151 information about the depth distribution of density in the object under study, i.e. layer-by-layer tomography, can be obtained from measurements of the dependence of the BSE coefficient on the primary electron energy E,. For multilayer structures the layers with densities lower or higher than that of the matrix lead to the appearance of some peculiarities in such dependences which, in principal, allow to obtain the thickness of the layers and their depth. The experiments carried out allow to estimate the minimum thickness which can be measured by this method. It was found to be about 10 nm for layers with rather different densities (Al-Cu-Si structure) and about 100 nm for those with close densities (Al-Si0,-Si structure). It was shown that Cu layers a in A1 or Si matrix give peaks in the dependence of the BSE coefficient on Eb whose number is equal to the number of these layers. It should be also noted that for layers containing heavier elements there is a range of &, in which the signal from the deeper layer is larger then that from shallower ones. This allows, by optimizing the energy of primary electrons, to inspect any specific layer in multilayer structures.

The other possibility to reconstruct the internal structure from measurements in the BSE mode is the spectroscopy of BSE energy. As theoretical and experimental investigations have shown [16 to 191 the electrons reflected from a near-surface layer practically do not lose their energy and the energy of backscattered electrons decreases with increasing depth of the layer on which they were reflected. Thus the detection of BSE with energy in a narrow energy window allows to obtain information about the depth and thickness of layers with chemical composition (and therefore density) different from those of the matrix [20, 211. The narrower the energy window used, the better is the depth resolution which can be achieved. Therefore, for this method the most important parameter determining the

“Apparatus” Electron Beam Microtomography in SEM 213

depth resolution is the energy resolution of the spectrometer used. For our investigations a new spectrometer well adapted to the SEM with improved energy resolution has been designed [22]. The construction of this spectrometer will be described in the next section.

2.1 BSE energy spectrometer

The configuration of designed BSE energy spectrometer is presented in Fig. 1. It consists of an electrostatic sectional toroidal condenser in axial symmetry with the SEM optical axis and that of the detector. As a detector we use a semiconductor ring detector or a modified Robinson scintillator ring detector [22] . Backscattered electrons enter into the space between two electrodes with curvature radius rl and r2 through the ring slit S, symmetric to the SEM axis OZ at an angle CI with respect to this axis. Then they are deflected by the electric field of a toroidal deflector. As a result, only electrons with specific energy determined by the potential +_ V applied between the electrodes can pass through the exit slit S,. The geometry of the energy analyzer was optimized using computer simulation. As a result, an energy resolution about 1 % is achieved and the working distance is about 25 mm.

2.2 Experimental results obtained in the energy dispersive BSE mode

Examples of BSE energy spectra obtained are presented in Fig. 2. It is seen that the BSE spectrum for the structure consisting of a bulk AI-60 nm Cu-360 nm A1 (curve 3) differs essentially from those of pure A1 (curve 1) and Cu (curve 2). The spectrum calculated for the same structure is also shown (curve 4). The energy dependence of BSE contrast, i.e. the

I I I r.

Fig. 1. Left part of the diagram of a sectional toroidal BSE Spectrometer. 0 is the object under study, s, the entrance slit, S, the exit slit, D the detector


c 1 4

W

z -

3

2

1

0

E / E b - 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

I 1 I I--*‘

b 1 * - D o * : 4 t # *

8

5.0 10.0 12.5 15.0 17.5 20.0 i;- *** *.c. ,’*- ’ E ( k e V ) -

Fig. 2. RSE energy spectra measured on pure bulk samples of Al (1) and Cu (2), on structures bulk AIL60 nm (3-360 nm A1 (3) and bulk Cu-200 nm AlLlO nm Cu (6); (4) spectrum for the structure 3 obtained by Monte-Carlo simulation, ( 5 ) dependence of contrast on the energy of detected electrons for the same structure; E, = 20 keV

difference between curves 3 and 1 normalized to the signal for pure A1 (curve 1) is described by curve 5. From this dependence the depth of different layers can be estimated. It should be noted that the contrast can change sign in some energy range. The spectrum 6 is measured on the structure consisting of a layer with lower density in a denser matrix (bulk Cu-200 nm AIL10 nm Cu).

The detection of BSE with an energy in the chosen window allows to separate the signals formed in different layers and to realize layer-by-layer tomography. Such layer-by-layer images of a test structure consisting of three 20 nm Au layers evaporated step-by-step by shifting a square mask on Si substrate are presented in Fig. 3. The upper layers are separated by 500 nm polymer films. The diagram of the structure is shown in Fig. 4. In the case presented the separation of images of every layer is achieved by a simple “apparatus” method - by selection of the BSE energy before its detection. If the energy of detected electrons E , is chosen near the primary electron energy E , = 28 keV, the image of the upper layer is observed (Fig. 3 b). Detection of electrons with energy E , = 22 keV allows to obtain the image of the middle layer (Fig. 3c) and at energy about 15 keV the lower Au layer is observed (Fig. 3d). The images presented in Fig. 3 and 4 allow to reconstruct any section of the three-dimensional structure.


Fig. 3. a) The image of the test structure in the conventional BSE mode and b) to d) layer-by-layer images of the same structure obtained in the energy dispersive BSE mode. The BSE energy is b) 28, c) 22, and d) 15 keV; E, = 30 keV

Fig. 5 illustrates the possibility to reveal the phosphorus-doped regions and to separate the regions with different doping depth. The phosphorus concentration in the doped layers is about 5 x lo1’ cmP3 and the thickness of the doping layers is about 1 pm in Fig. 5b and about 2.2 pm in Fig. 5c.

A

Fig. 4. The diagram of the test structure the images of which are presented in Fig. 3


Fig. 5. The images of Si locally doped by phosphorus on 1 and 2.2 pm obtained in a) the BSE mode and b), c) the energy dispersive BSE mode. The BSE energy is b) 13 and c) 10 keV; E, = 15 keV

3. Methods for Electrical and Optical Property Reconstruction

For the characterization of semiconductor structures in many cases it is necessary not only to obtain the dimensions of different layers but also to measure the electrical and optical properties and to reconstruct the depth distribution of these properties. It seems that for these purposes two in-situ differential methods, i.e. EBIC with depletion region width modulation [23, 241 and CL with energy and current modulation [25 to 271, will be very promising. The depth resolution in the both methods is much better than the electron range and is determined by modulation parameters, measurement precision, and characteristics of the structure under study [28]. It should be noted that these methods are very suitable for the characterization of microelectronics structures because they have high depth resolution (up to 10 nm) and lateral resolution about a few pm.

3.1 Modulated EBIC

The collected current in the EBIC mode I , in samples with homogeneous distribution of diffusion length L changes as exp ( - s /L ) , where s = z - W is the distance between the collected junction and the depth of electron-hole pair generation z , W is the depletion region (DR) width. From this expression it follows that the diffusion length can be obtained from the dependence of I , on s. Usually for planar structures with collecting junction perpendicular to the e-beam s is changed by changing the depth of generation, for ex- ample, by variation of the primary electron energy. However, s can be changed also by varying of the DR width. The precision of such measurements can be improved when the DR width W is modulated by applying of a small ac voltage. In this modulated EBIC method the first harmonic of the signal selected by a lock-in amplifier is proportional to the first derivative of the collected current, dI,/dW. As shown in [23] measurements of the first derivative of the collected current allow to obtain the diffusion length in the region adjacent


to the DR. Indeed, the value-.of L at depth z = W can be obtained as

where

y (z, W ) is the one-dimensional carrier collection probability and it represents the collected current produced by a unit charge generated at depth z, h(z) is the depth dependent excess carrier generation function. It should be stressed that in the method discussed dI,( W)/d W and I,( W ) can be measured independently, therefore Q ( W ) can be easily calculated using the experimental data. If the D R width is changed by varying of applied bias, the L(z) distribution can be reconstructed on the basis of such measurements. This method allows to reconstruct the diffusion length depth distribution with resolution determined by measurement precision, modulation amplitude, and doping level, and can achieve values much smaller than the electron range R. The results of the reconstruction of the L distribution in dry etched Si and GaAs by modulated EBIC were presented in [29].

As shown in [24] this technique can be used also for local measurements of W at any applied bias and therefore for the reconstruction of the dopant depth distribution. For this purpose it is necessary to measure dI,( W)/d W and I,( W ) at two different beam energies. The depth resolution of the method discussed can be comparable with that of the widely used C-I/ method, but the high lateral resolution allows to map dopant and diffusion length distributions separately.

Thus this technique allows to measure L and dopant concentration in layers situated at different depths or in different layers of multilayer structures. This allows to consider it as an “apparatus” technique for layer-by-layer tomography of electrical properties. It should be stressed that the diffusion length value can be evaluated even in the case when the layer thickness is much smaller than L.

3.2 Modulated CL

In the modulated cathodoluminescence mode electron energy E , and electron beam current I , are modulated with frequency w as E , = Eo(l + a , sin wt) and I, = 1,(1 + u2 sin cot), respectively. Under the assumption that minority carrier diffusion, non-radiative surface recombination, and light absorption inside the sample can be neglected and the sample consists of layers infinite in lateral direction and its characteristics are constant inside every layer, the CL signal detected at wavelength 1 can be presented as [26]

where SI is the coefficient in the dependence R - EZ (u = 1.75), Ai(lJ is a constant depending on the parameters of the i-th layer, zi is the depth of the interface between the layers i and


i + 1, n is the number of layers, and f ( z / R ) = Rh(z, E,). The signal measured on the first or second harmonic can be expressed in a similar form [26],

where k = j for the j-th harmonic of the CL signal, a = a,/a,, R, is the electron range at E , = E,. The expressions for fkw(z /R, a) for the first and second harmonics of the modulated CL signal were given in [26, 271. It is very important to stress that while f ( z / R ) is positive at all z,f,(z/R, a) is equal to zero at one point and f,,(z/R, a) is equal to zero at two points in the range 0 < z < R. Therefore, it is possible [26] to choose the a and E , values such that the signals on the first harmonic from any layer of a two-layer structure or the signals on the second harmonic from any two layers of a three-layer structure can be made equal to zero. This allows to select the CL signal from any layer of two- or three-layer structures.

To measure the CL spectrum from any layer of two- or three-layer structures it is possible to use computer simulation of the signals to choose the conditions for the signals from the other layers to be equal to zero. If at least one line from the spectra associated with the layer is known, the conditions which allow to eliminate the signal from this layer can be obtained experimentally. An influence of charge carrier diffusion and surface recombination, as shown in [26], can also be taken into account.

Acknowledgement

This work was partially supported by Russian Foundation of Fundamental Research (Grant NO. 93-02-2293).

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“apparatus” electron beam microtomography in sem

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