Figure 8.4. Depletion layer below an n-type semiconductor surface: (a) band bending showing ionized donors above the Fermi level EF ; (b) charge density r(z); and (c) potential variation V(z) in the Schottky approximation.

hand, as devices get smaller, such eVects can be pervasive throughout the whole device, and the unwanted statistical distribution of impurities may well pose a limit to device dimensions in future.

8.1.3Techniques for analyzing semiconductor interfaces

Classical experiments to determine the depth of the depletion layer and the barrier heights include C±V pro®ling, where the same types of arguments as used above show

that C22 is linearly proportional to the bias voltage V, with an intercept which gives fB, and the photo-electron yield or photocurrent, where the square root of the yield versus

photon energy gives a straight line with intercept fB (Sze 1981, Schroder 1998). By biasing the sample with a d.c. oVset, and using a.c. techniques for probing and detect-

ing, more subtle techniques including deep level transient spectroscopy (DLTS) have been developed, and used to study the distribution of electrically active defects with depth. An example related to point defects produced during InGaAs thin ®lm growth is given by Irving & Palmer (1992); but it is noticeable that deductions about the nature of the defects responsible are at best rather indirect.

Semiconductor devices are very demanding in terms of analytical techniques, since one would like to know the density and depth distribution of the dopants, and of other impurities (Schroder 1998). Of the wide range of surface analytical techniques available, so far only secondary ion mass spectrometry (SIMS) has been widely applied; although it is destructive, it does have the necessary sensitivity, and it speci®cally identi®es the elements in question. The calculation in section 8.1.2 above can be used to estimate the sensitivity needed: to detect 1014 cm23 dopants in a depletion layer of thickness 400 nm, over 1 mm2 sample area means detecting and quantifying 43 107 atoms. A determination of the depth distribution of (delta-doped) Be dopants in GaAs by SIMS is shown in ®gure 8.5. Note that deductions about the eVects of annealing temperature and `knock-on' eVects during implantation have been made (reliably) from pro®les containing a maximum of only 200 counts/channel (Schubert 1994).

Although STM and related spectroscopies (STS) have revolutionized surface imaging since the early 1980s, it is perhaps less clear whether similar advances in

Figure 8.6. (a) Schematic set-up of a BEEM experiment, indicating tunneling and collector currents It and Ic and the tip voltage Vt; (b) energy level diagrams for forward BEEM at an n-type (top) and p-type collector (bottom) (after von Känel et al. 1995, reproduced with permission).

arrangement is shown in ®gure 8.6. BEEM can be understood as a hot electron triode, in which the tunneling current (It) into the metal serves as the source for the collected current (Ic) in the semiconductor. BEEM images can then be obtained by scanning the tip, and compared with STM images of the same area, as shown for a thin metallic CoSi2 layer on Si(111) by von Känel et al. (1995). The application of STM and BEEM to study silicides is reviewed by Bennett & von Känel (1999).

The corresponding spectroscopy (BEES) is possible, also spatially resolved at the nanometer scale, and has become a very powerful means of determining local values of the Schottky barrier height, as indicated in ®gure 8.7. Here Ic is plotted against the tip voltage Vt for constant It, and goes to zero as 2 Vt approaches fB. These fB values are at least as good as those produced by large area electrical methods: a quite remarkable achievement (Meyer & von Känel (1997).

It is a current research topic to understand the contrast mechanisms in both the microscopy and spectroscopy. If the metal base electrode is featureless on the lateral scale of interest, then BEEM contrast is thought to arise largely through eVects occurring at the metal±semiconductor interface, though diVerences in experimental arrangements may have lead to inconsistencies between diVerent groups. It is notable that transmission through the base layer as a function of thickness oVers a direct measurement of the inelastic mean free path (imfp) for low energy electrons, well below the minimum in the imfp curves discussed earlier in section 3.3.4. For example, Ventrice et al. (1996) show that for Au ®lms on Si(100) had li ,13 nm at room temperature and 15 nm at 77 K, for an injected energy of around 1 eV above the Fermi level. It is thus reasonable to use base electrodes with thickness up to tens of nanometers in these techniques.

268 8 Surface processes in thin ®lm devices

Vt

Figure 8.7. Ballistic electron emission spectra Ic(Vt) normalized to the tunneling current, taken on top of (open circles) or next to (®lled circles) an interfacial point defect. Ic is higher on the defect for Vt close to the barrier height fB. The inset shows the 2/5 power of Ic, yielding a value of fB50.66 6 0.01 eV (after Meyer & von Känel 1997, reproduced with permisison).

One of the possibilities of BEEM is to identify the defects responsible for surface states. The images of mis®t dislocations in the CoSi2/Si(111) interface can be seen at high resolution to consist of a `string of pearls' as shown in ®gure 8.8(b), rather than a continuous line image which one might expect from a dislocation line. In the same images there are also isolated point defects in the vicinity of the interface, and a sensitivity of below 1012 cm22 is claimed (Meyer & von Känel, 1997); the hypothesis is that it is point defects trapped in the vicinity of dislocations, rather than the dislocations themselves, which are electrically active.

This sensitivity level is particularly inviting in relation to the SiO2/Si and related interfaces. One of the main reasons why the various MOS and CMOS silicon device technologies work is the low density of surface states at the Si-SiO2 interface, where values below 1012 cm22 (i.e. ,1023 ML, or 1010 on 1 mm2, or 104 on 1 mm2), can be consistently achieved. However, it is extremely diYcult to deduce what these defects actually are; the technologist is primarily interested in getting rid of them, and often the only means of assessing them are the same electrical properties which one is trying to optimize: a sure recipe for a black art.

Recently, it has been shown that BEEM can address such problems. Using a base electrode of thin granular Pt, electrons can be injected into, and can be trapped in, a 25 nm thick insulating ®lm of SiO2 on Si. Trapping of very few (,10) electrons results in a decrease of the BEEM current which can then be readily measured (Kaczer et al. 1996). A complementary (broad area) tool is electron spin resonance (ESR), which is

Figure 8.8. (a) STM topography image of a 2.8 nm thick CoSi2 ®lm on Si(111), showing a 0.06 nm high line due to the strain ®eld of an interface dislocation (dashed line);

(b) corresponding BEEM image showing interfacial point defects, S and P, and those trapped in the core of the interface dislocation D, which comprises empty (E) and occupied (O) regions (after Meyer & von Känel 1997, reproduced with permisison).

very good for detecting unpaired electrons; these are typically the centers which give rise to electron traps in SiO2, some of which are indicated in ®gure 8.9. These centers, for example the Pb center, which is an electron trapped on a Si dangling bond, are diVerent in detail on surfaces of diVerent orientation (Helms & Poindexter, 1994). Another sensitive wide beam technique is called Total re¯ection X-ray Fluorescence (TXRF), which, by using glancing incidence X-rays, can detect below 1010(cm22) metal atoms on ¯at surfaces. It is now highly valued for examining the cleanliness of silicon wafers in production plant environments (Schroder 1998, section 10.4).