Internal Photoemission Spectroscopy Methods

4 Internal Photoemission Spectroscopy Methods

As has already been discussed in Chapters 2 and 3, inelastic scattering of photoinjected charge carriers entering the collector results in their thermalization at a distance of about a few nanometres from the surface of the photoemitter. Rapid thermalization effectively erases any information about the initial energy distribution of the injected carriers, making most electron spectroscopy approaches used in external photoemission inapplicable. Under these circumstances, reliable information about the electron states involved in the internal photoemission (IPE) process can be obtained only from the quantum yield value, which corresponds to the total number of carriers escaped the emitter (cf. Chapter 3). Nevertheless, because the carriers contributing to the IPE signal are transported in a ballistic regime from the point of their optical excitation to the surface of the emitter and further, towards the image-force barrier top, their energy distribution is reflected in the escape probability value which, in turn, determines the quantum yield. As a result, not only can the IPE threshold energy be found from the yield spectra, but also all the other processes potentially affecting the quantum yield (optical singularities, scattering thresholds, etc.) can also be characterized. In addition, optical excitation of the occupied electron states in the collector allows one to obtain information about the bandgap width of the materials and about electron states with the electron energy levels inside the collector bandgap. By combining these approaches, one can extract a vast amount of information about the uppermost occupied and lowest unoccupied electron states in the emitter
collector system. Worth adding here is that these portions of the electron state spectrum determine the most important electron transport properties of the interfaces and heterostructures. The latter makes IPE spectroscopy the most relevant method of analysis. In this chapter several major IPE spectroscopy methods will be discussed: G

G

G

G

G

the spectral threshold determination which allows quantification of energy band offsets at the emitter
collector interface; the total yield spectroscopy enabling observation of the optical transitions in the surface layer of the emitter; the scattering spectroscopy revealing onsets of electron energy-loss processes both in the emitter and in the collector; the intrinsic photoconductivity (PC) spectroscopy addressing the electron excitations involving the band-type states in the collector; spectroscopy of photoionization (PI) that enables characterization of gap states in the collector.

Internal Photoemission Spectroscopy. DOI: http://dx.doi.org/10.1016/B978-0-08-099929-6.00004-X © 2014 Elsevier Ltd. All rights reserved.

110

4.1 4.1.1

Internal Photoemission Spectroscopy

IPE Threshold Spectroscopy Contributions of Different Bands to IPE

Determination of spectral thresholds of different photoinjection processes represents the most widely used application of IPE spectroscopy to characterization of interfaces. In this method, the energy barrier height at the interface is associated with the spectral threshold Φ determined as the minimal photon energy necessary for injection of a charge carrier into the collector. The basic idea of this technique is related to description of the IPE yield dependence on the photon energy as a fingerprint of the initial density of states (DOS) in the emitter weighted by the escape probability and integrated over all the carrier energies exceeding the interface barrier height (cf. Eq. (3.1a)). As the result, the IPE yield spectrum will represent the replica of the photoemitter DOS integrated over energy and weighted by the carrier escape probability. If several occupied electron bands are present in the photoemitter, each of them will give rise to the corresponding component in the IPE spectrum. The separate contributions stemming from different bands of the emitter will be referred to as the photoemission band, similar to the optical absorption bands or luminescence bands in conventional optical spectroscopy. In the most straightforward way, the application of this description can be illustrated by the IPE yield spectra from a heavily doped n-type semiconductor in which two contributions to the density of occupied electron states can be separated: wide distribution in the valence band (VB) of the semiconductor and a narrow band of filled states at the bottom of the conduction band (CB). Examples of the corresponding spectra have been shown in Chapters 2 and 3 for the case of electron IPE from n1-Si(100) into Al2O3 (cf. Figs 2.4, 3.7 and 3.11). To demonstrate quantitatively the correspondence between the electron density in the particular band and the IPE yield, in Fig. 4.1, the IPE spectral curves for n1-Si (100)/SiO2 interfaces and two different concentrations (nd) of phosphorus donors in a silicon photoemitter: nd  (1
2) 3 1019 cm23 (top panel) and nd  5 3 1020 cm23 (bottom panel) are shown. These measurements were performed under different strengths of the electric field in the oxide, which was controlled externally by applying the corresponding bias voltage to the semitransparent field electrode (a 15-nm thick Au layer) on top of a 124- (top panel) or a 15-nm thick (bottom panel) thermally grown oxide layer. The IPE spectra are seen to contain two bands: the one with a low yield and spectral threshold at around 3 eV, and another one, with much a higher quantum yield and the spectral onset at around 4 eV. By comparing the yield spectra from a low-doped Si and the heavily doped n-type material (cf. Fig. 3.11), the low-energy IPE band can be associated with optical excitation of electrons from the occupied states in the CB of silicon to unoccupied states of the SiO2 CB. At approximately 1 eV, higher photon energy starts the second IPE band associated with photoemission of electrons from the silicon VB into the oxide CB. Because the electron DOS in the VB of silicon is independent on the dopant concentration, one can normalize the spectra to the same yield value at hν 5 6 eV at

Internal Photoemission Spectroscopy Methods

10–6

10–8 10–9

0.20 0.36 0.55 0.77 1.17 1.57

0.5 0.0

3.0

F(MV/cm):

3.5 hν (eV)

nd ~ (1–2) x 1019 cm–3

10–10

Y1/3 x 103

Yield (relative units)

10–7

ΦeC

1.0

10–11 dox = 124 nm

10–12

(relative units)

Y x 1010 (relative units)

10–5

111

n –Si(100)/SiO2 3

ΦeC

ΦeV

E2

6 E1

4 2 0

+

10–13

8

3 4

4 hν (eV) 5 5

6

Y x 109 (relative units)

Photon energy (eV)

10–5

10–7

1 0 2.0

F(MV/cm): 2.5

3.0

3.5

hν (eV)

10–9 dox = 15 nm 10–10

n+–Si(100)/SiO2 2

3

Φ eV

8

nd ~ 5 x 1020 cm–3

(relative units)

10–8

0.7 1.0 1.3 2.7 4.0 5.3

2

Y1/3 x 103

Yield (relative units)

10–6

3

6 4 2 0

4 Photon energy (eV)

3

4 hν (eV) 5 5

6

Fig. 4.1 IPE quantum yield as a function of the photon energy for two heavily phosphorousdoped n-type (100)Si/SiO2/Au(15 nm) structures with a concentration of donors of nd  (1
2) 3 1019 cm23 (top panel) and nd  5 3 1020 cm23 (bottom panel) as measured at indicated strengths of the electric field in the thermally grown oxide. Determination of the spectral thresholds of electron IPE from the conduction (ΦeC) and VB (ΦeV) of silicon into the oxide CB using Y 2 hν and Y1/3 2 hν plots is illustrated in the top left and bottom right inserts in both panels, respectively. The arrows indicate the spectral thresholds as well as the energies of optical singularities E1 and E2 of the Si crystal.

F 5 1.5 MV/cm to account for the enhanced electron
electron scattering in the heavily n-doped Si. In this case one can notice that the IPE yield from the silicon CB increases by a factor of about 20 in the heavier-doped sample, which agrees with the increase in the density of electrons expected from a higher donor concentration.

112

Internal Photoemission Spectroscopy

IPE threshold (eV)

4.5

Fig. 4.2 The Schottky plot of spectral thresholds electron IPE from the CB (ΦeC) and VB (ΦeV) of silicon into the oxide CB as measured in the n1-(100)Si/SiO2/Au (15 nm) samples with different concentrations of phosphorus donors in silicon. Lines illustrate the determination of zero-field barrier heights corresponding to the fundamental band offsets at the interface.

ΦeV(F = 0) = 4.25 eV

4.0

ΦeV

3.5 ΦeC(F = 0) = 3.20 eV 3.0

ΦeC 2.5 0.0

0.5

1.0

1.5

2.0

2.5

3.0

(Electric field)1/2 (MV/cm)1/2

Next, to determine the exact band offset values at the Si/SiO2 interface, one should first find the corresponding spectral thresholds at different field strengths and then obtain their zero-field value using extrapolation in the Schottky coordinates. According to Table 3.1, the quantum yield of IPE from an energetically narrow distribution of electron states should increase linearly above the spectral threshold (Powell, 1970) as, indeed, is observed in the linear plot of the IPE yield shown in the upper left inserts in both panels in Fig. 4.1. Then, the corresponding spectral threshold ΦeC can be analysed using the Schottky plot shown in Fig. 4.2 (the bottom line) resulting in the zero-field barrier value of 3.20 6 0.05 eV. This barrier height directly corresponds to the CB offset at the Si/SiO2 interface. In turn, the yield of electron IPE from the semiconductor VB is expected to follow the YB(hν2Φ)3 spectral dependence (Powell, 1970). Determination of the corresponding spectral threshold ΦeV requires linear extrapolation in the Y1/3
hν plot, which is exemplified in the lower right insert in Fig. 4.26. However, the spectra are seen not to be perfectly linear but exhibit a dip at around hν 5 4.3
4.4 eV. This behaviour is related to significant variation in optical properties of the Si emitter in the vicinity of the E2 singularity (hν 5 4.4 eV) associated with excitation of direct optical transitions between points of high symmetry in the Brillouin zone of the Si crystal (Allen and Gobeli, 1966; DiStefano and Lewis, 1974). Therefore, only a limited portion of the spectral curve can be used to determine the corresponding IPE threshold ΦeV. Similarly, the linear fit of the IPE spectra from the silicon CB shown in the upper left insert in Fig. 4.26 is also limited to the photon energy range hν , 3.4 eV because of E1 optical singularity occurring at this energy. To resolve the problem associated with these optical effects, Powell introduced analysis of the voltage dependences of IPE current measured at different photon energies by using linear extrapolation in the Y1/3
V1/2 co-ordinates (Powell, 1970). This method potentially allows one to exclude the influence of optical effects because only the shape of the Y1/3
V1/2 curve is analysed. However, this method suffers from the influence of scattering effects in the low-field range and, therefore, requires application of a high electric field. In addition, the ideal image-force barrier behaviour is assumed for the field-dependent barrier height, which greatly

Yield (relative units)

Internal Photoemission Spectroscopy Methods

(IPE yield)1/3 (relative units)

12 10 8

0

F(MV/cm): 1.0 2.0 3.0 4.0 5.0 6.4

Φ1

1

2

3

6

113

4

Φ3

hν (eV)

Φ2 6H-SiC/SiO2

4 2 0

Φ1

2

3

4 5 Photon energy (eV)

Fig. 4.3 IPE quantum yield as a function of the photon energy for an n-type 6H-SiC/ SiO2(22 nm)/Au(15 nm) capacitor at different strengths of the electric field in the oxide indicated in the figure. The spectral thresholds of three observed IPE bands are indicated for clarity. The lines represent a guide for the eye, not the curve fitting.

6

limits the applicability of the Powell’s approach. Instead, while keeping in mind the limited accuracy of threshold determination, we can find the thresholds by extrapolating yield in the photon energy range below E2 5 4.4 eV by using highresolution IPE spectra, as shown in the bottom panel in Fig. 4.1. The corresponding values of ΦeV are plotted in Fig. 4.2 (upper plots) and, by using linear extrapolation to zero electric field, one can estimate the energy offset between the VB of Si and the CB of SiO2 as ΦeV(F 5 0) 5 4.25 6 0.05 eV. The observed  1-eV difference between the barriers for electron IPE from the VB and CB states of silicon accounts well for the bandgap width in this semiconductor (1.12 eV at room temperature) although some gap narrowing is expected to occur in the heavily doped n-type semiconductor (Goodman, 1966a). From the slope of the Schottky plots using Eq. (2.29) one may estimate the effective imageforce constant εi to be close to 2, which is consistent with the expected value εi  n2 5 2.1. This example clearly shows how different parts of the emitter DOS can be traced both on the basis of their energy thresholds and on the relative quantum yield which is proportional to the initial charge carrier density. It needs to be added that the observed IPE thresholds are not necessarily associated with DOS of the emitter electrode but may also contain contributions of other states located near the interface or inside the collector layer itself. For instance, the electron IPE yield spectra of 6H-SiC/SiO2 interface shown in Fig. 4.3 as Y1/3
hν plots exhibit three spectral thresholds indicated by arrows. Only the lowest threshold Φ1 and the upper Φ2 are field dependent, as illustrated by the Schottky plots shown in Fig. 4.4. Observation of Schottky barrier lowering suggests the relationship of these thresholds to excitation of the occupied electron states of the SiC emitter. The change of SiC polytype from 6H-SiC to other (3C-, 15R-, 4H-) is found to affect the lower IPE threshold in accordance with the polytype-specific value of the SiC bandgap width (Afanas’ev et al., 1996a, 2004) varying from 2.38 eV in 3C-SiC to 3.25 eV in 4H-SiC (Choyke, 1990). This effect and the

114

Internal Photoemission Spectroscopy

IPE threshold (eV)

6

Φ3

5

Φ2

4 SiC/SiO2

Φ1 3

Fig. 4.4 The Schottky plot of IPE spectral thresholds as functions of the electric field strength in the oxide at the interfaces of different SiC polytypes (3C, 6H, 15R, 4H) with thermally grown SiO2 layers. Lines illustrate the determination of zero-field barrier heights.

4H 6H,15R 3C

2 0

1

2

(Electric field)1/2 (MV/cm)1/2

observed difference in the relative quantum yield value allows interpretation of the SiC/SiO2 IPE spectra as the electron IPE from the VB with the threshold Φ3 and the electron emission from the CB of SiC with the polytype-sensitive threshold Φ1 (Afanas’ev et al., 1996a). The remarkable feature here is the considerable CB IPE, even from a moderately doped (nd 5 4 3 1016 cm23) SiC, which is indicative of a large photoelectron escape depth. Indeed, as the maximal kinetic energy of electrons in the CB is equal in this case to hν, it appears to be below the bandgap width of the semiconductor (3.02 eV for 6H-SiC), resulting in a reduced rate of electron
electron scattering in the emitter. As far as the spectral threshold Φ2 is concerned, which is also clearly seen in the IPE spectra in Fig. 4.3, its field dependence appears to be below the spectral resolution limit in all the studied samples, as can be seen in Fig. 4.4. This behaviour suggests that the electron excitations at hν . Φ2 correspond to the final state spatially located inside the SiO2 collector in which case no image force is present. Therefore, these states can be associated with some imperfections at the interface of SiC with SiO2 or inside the near-interfacial oxide layer. As no measurable decay of the photocurrent is observed after prolonged illumination with hν . Φ2, it was concluded that these electron states can communicate electronically with SiC substrate by tunnelling, which limits their location to a tunnelling distance in SiO2 from the surface of emitter, i.e., to a few nanometres. The origin of these states can be traced down to clusters of carbon created during oxidation of SiC because of incomplete removal of carbon in the form of volatile oxides species (Afanas’ev et al., 1996a,c, 1997). This conclusion is based on the observed similarity between the trap-related component of the SiC/SiO2 IPE spectra and the IPE spectra observed from thin a-C:H layers deposited onto SiO2 (Afanas’ev et al., 1996a,b, 1997). The example of the electron IPE spectra from the a-C:H into SiO2 is shown in Fig. 4.5 for the carbon films of three compositions characterized by different optical bandgap width. The graphitic carbon appears to give spectral thresholds of IPE at around 3 eV, whereas sp2-bonded carbon clusters of smaller size give the zero-field threshold at around 4.5 eV, i.e., close to the value observed as the

Internal Photoemission Spectroscopy Methods

115

(IPE yield)1/3 (relative units)

12 10 8

F = 4.0 MV/cm

6 a-C:H

SiO2 Eg(a-C:H) (eV):

4

3.0

Fig. 4.5 Electron IPE yield as a function of photon energy for the as-deposited a-C:H layers with different bandgap widths
3.0, 1.74 and 0.70 eV
measured at the strength of the electric field in a SiO2 collector layer of 4 MV/cm. The scheme of the observed electron transitions is illustrated in the insert.

1.74

2

0.70 0

3

4

5

6

Photon energy (eV)

threshold Φ2 in SiC/SiO2 structures. In turn, on the C-rich interfaces formed by oxidation of (000 1) faces of hexagonal SiC polytypes, the IPE spectra appear to resemble those of the IPE from graphitic carbon (Afanas’ev et al., 1996a, 1997). This example of IPE study demonstrates the importance of field-dependent barrier analysis in identifying electron transitions contributing to the photocurrent.

4.1.2

The Field-Dependent Barrier Analysis

The field-dependent measurements of IPE threshold can also be used to reveal the character of the interface barrier perturbation if it deviates from the ideal imageforce behaviour. For instance, it is found that incorporation of H1 protons or Li1 ions to the Si/SiO2 interface by annealing at an elevated temperature results in formation of a positive charge (Afanas’ev and Stesmans, 1998a,b, 1999a). This charge causes significant lowering of the potential barrier for electron IPE from the silicon VB into the oxide CB, suggesting the location of the ionic charges in close vicinity of the injecting interface. This effect is exemplified by the IPE yield spectral plots shown in Fig. 4.6 for control (uncharged) sample (filled circles) and for samples containing the annealing-induced H1 or Li1 charges (open symbols). To obtain more information about the character of the barrier perturbation, the field-dependent spectral thresholds Φ0 (control samples) and ΦQ (charged samples) were compared using the Schottky plot shown in the insert. When positive charge is present (x,&) the lowest IPE threshold ΦQ is seen to follow the Schottky law but with a significantly increased slope. This effect can be understood in the framework of the model considering the image-force barrier modification by the Coulomb potential of the individual charge centre discussed in Section 2.2.5. In particular, the case of the charge location close to the surface of the emitter appears to be in a good agreement with the observed barrier lowering values (Afanas’ev and Stesmans, 1999a). Numerical fit of the shown Schottky plots allows evaluation of the average distance between the ion and the Si surface to be 0.2 6 0.1 nm for both H1 and Li1,

116

Internal Photoemission Spectroscopy

106

IPE yield (relative units)

104 103 102

Φ (eV)

4.0

105

Φ0 ΦQ

3.5

3.0

0

1

2

(F)1/2(MV/cm)1/2

ΦQ Φ0

101 100 3.0

3.5

4.0

4.5

5.0

Photon energy (eV)

Fig. 4.6 Spectral curves of the IPE quantum yield from (100)Si into SiO2 in the control sample (K), a H2-annealed sample (x) exhibiting positive a charge density of 5 3 1012 q/cm2 and in a Li-diffused sample (&) exhibiting a positive charge density of 4 3 1012 q/cm2. All the curves are measured using an externally applied electric field of 2 MV/cm, with the metal biased positively. The arrows indicate the spectral thresholds of IPE at 2 MV/cm in the control (Φ0) and charged (ΦQ) samples. The insert shows the Schottky plot of the IPE spectral thresholds in the control sample (K), a H2-annealed sample (x) exhibiting a positive charge density of 5 3 1012 q/cm2, a Li-diffused samples exhibiting a positive charge density of 4 3 1012 q/cm2 (&) and B2 3 1013 q/cm2 (Δ), and in a sample containing 1.3 3 1015 Na1/cm2 (r) according to (DiStefano and Lewis, 1974). The solid line represents the calculated barrier lowering for the Coulomb attractive centre located in the plane of the interface; dashed lines result from fitting of the ideal image-force barrier behaviour (Φ0), and the barrier lowering in the presence of a ˚ above the Si surface plane (ΦQ). Coulomb attractive centre in SiO2 at 2 A

suggesting these ions are attached to the first layer of oxygen atoms bonded to the Si crystal surface (the SiaO bond length in SiO2 is approximately 0.15 nm). Interestingly, in the earlier studied case of Na1 ions diffused from the outer SiO2 surface through the oxide towards its interface with Si (DiStefano and Lewis, 1974), an even larger barrier reduction is observed as also shown by triangles in the insert in Fig. 4.6. A weaker dependence of the spectral threshold on electric field suggests that a considerable portion of these ions remain in SiO2 and produce attractive potential for electrons. The latter adds to the externally applied field and weakens the barrier lowering measured as a function of the external electric field. This effect can also be seen as related to the overlap of long-range Coulomb potentials of ions in an insulator with a low dielectric constant, εD 5 3.9 for SiO2 (Sze, 1981). To summarize, IPE threshold spectroscopy appears to represent a unique experimental tool in characterizing the interface barrier behaviour not only in ideal image-force barriers but also in the presence of the perturbing charges.

Internal Photoemission Spectroscopy Methods

4.1.3

117

Separation of Different Contributions to Photocurrent

The examples presented of IPE threshold determination make use of knowledge that the observed IPE current is related to photoinjection of electrons into SiO2. This identification becomes immediately possible because of the observed sensitivity of the IPE current to electron density in the CB of silicon substrate or inside the a-C:H layer. Hole IPE from Si into SiO2 can safely be excluded because the energy barriers for electron injection at the interfaces of silicon dioxide with metals and semiconductors are usually significantly lower than the barriers for hole injection (Adamchuk and Afanas’ev, 1984, 1992a,b), with the only noticeable exception being wide-bandgap SiC polytypes (Afanas’ev and Stesmans, 2000). Initially, the conclusion about dominance of the electron IPE was reached on the basis of several experiments including optical interference analysis (Powell, 1969), the observed insensitivity of the IPE current measured under positive bias to the anode material (Williams, 1965) and negative charge trapping (the photocharging) in the oxide observed after a prolonged photoinjection (Adamchuk and Afanas’ev, 1985). Direct determination of the electron and hole IPE barriers at the Si/SiO2 interface using the photocharging technique gives values of 4.3 and 5.7 eV, respectively, for silicon oxidized in pure O2 (Adamchuk and Afanas’ev, 1984, 1992a,b). In a general case, however, it is hard to exclude the possibility that several processes may simultaneously contribute to the photocurrent, as illustrated in Fig. 3.14. Therefore, as the first step in the analysis, one must address identification of the injected charge carrier type that provides the dominant contribution to the photocurrent in the particular IPE band. There are several approaches to determine the charge sign of the injected carrier or, which is equivalent, to identify the injecting interface. First, one may use the already mentioned photocharging of the insulating collector to determine the injected carrier sign by observing the sign of the trapped charge using methods that will be discussed in the next chapter. However, this technique faces a problem that it may be selectively sensitive to the charge carriers of one type. For instance, trapping of holes in the thermal oxides on Si is many orders in magnitude more efficient than electron trapping. This property can be used to detect IPE of holes from silicon on the background of much more intense electron IPE from a metal gate electrode (Adamchuk and Afanas’ev, 1985, 1992a,b). However, identification of electron IPE requires photocharging measurements to be conducted over the whole spectral range of the photocurrent observations, making this analysis extremely laborious (Adamchuk and Afanas’ev, 1985). Second, as an alternative, one may consider tracing the impact of electron DOS change in one of the electrodes of the metal
insulator
semiconductor (MIS) or metal-insulator-metal (MIM) capacitor on the IPE yield spectra: Once the IPE curves are observed to sense variations in the bandgap width or the doping level of a semiconductor electrode or the shift of the Fermi energy of a metal, the identification of the IPE current source becomes obvious. Conversely, the lack of sensitivity to the DOS in one of the electrodes may be considered as suggesting that the IPE signal stems from the opposite contact. Taking into account that charge carriers of only one sign may be injected under a certain orientation of the electric field in the insulating

118

Internal Photoemission Spectroscopy

collector, ensuring their drift away from the injecting interface, the identification of the injecting interfaces automatically provides the sign of the injected charge carrier. One may also attempt to find experimental configuration(s) enabling IPE at one interface only. In this case the sign of the injected charge carriers will be uniquely determined by the orientation of the electric field, which must be attractive to enable photoinjection. This can be realized in samples with a thick collector when the electric field required for IPE transitions is present only in the barrier region, or by using the blocking electrolyte contact because its conductivity is determined by ions rather than by electrons. This last approach was used, for instance, to observe IPE of holes from Si into SiO2 using the photocurrent measurements (Goodman, 1966b). Amorphous carbon represents another choice of blocking electrode material (Adamchuk and Afanas’ev, 1992a), characterized by extremely low quantum yield of electron IPE. A similar approach has recently been used by applying a single-layer graphene as the top gate to the Si/SiO2 and Si/Al2O3 structures enabling detection of hole IPE from silicon using photocurrent measurements (Yan et al., 2012, 2013). An example of application of several approaches to separate the IPE and PC contributions to the photocurrent as well as the electron and hole IPE signals can be given using the IPE/PC spectra for (100)Si/HfO2 structures with a thin (1 nm) SiON or Si3N4 interlayer and semitransparent Al or Au field electrodes. Using the spectral plots shown in Fig. 4.7 (Afanas’ev et al., 2002a) one may reach several conclusions. First, in the high photon energy range (hν . 5.9 eV) the photocurrent yield appears to be insensitive to the orientation of the electric field in the oxide, to the type of interlayer between Si and HfO2 (SiON or Si3N4), and to the metal used as the field electrode material (Au or Al). This behaviour suggests (Williams, 1965) a relationship of this current to the photogeneration of charge carriers inside the HfO2 collector layer. Taking into account the high quantum efficiency of this generation process, which approaches unity, it can be reliably associated with intrinsic photogeneration of electron
hole pairs in HfO2 with the spectral threshold corresponding to the (lowest) HfO2 bandgap, indicated by arrows in all four panels in Fig. 4.7. Next, as the low-energy portions (hν , 5 eV) of the spectra measured under the positive metal bias appear to be insensitive to the metal electrode material and, at the same time, remain different from those taken at negative bias, they can be associated with IPE of electrons from Si substrate into HfO2. This interpretation is supported by observation of kinks in the spectral curves occurring at photon energies around 3.4 and 4.4 eV, which correspond to the already mentioned optical singularities E1 and E2 of Si crystal (indicated by dashed lines in Fig. 4.7). Therefore, the energy barrier between the top of the Si VB and the bottom of HfO2 CB can be determined from the spectral onset of photocurrent measured when applying a positive bias to the metal electrode. Furthermore, when analysing the IPE spectra measured under negative bias on the metal field electrodes, as shown panels (c) and (d), one may notice that the replacement of the Au electrode by Al one leads to a large “red shift” in the photocurrent threshold. This can be immediately associated with an up-shift of the Fermi level, indicating the metal to be the source of carriers (electrons). However, this logic is valid only for Al: An increase of the quantum yield in the Au-gated samples

Internal Photoemission Spectroscopy Methods

106 105

119

(100)Si/SiON/HfO2

(100)Si/SiON/HfO2/Au

V>0

V<0

104 103 102

Φe(Si)

Φe(Al)

Yield (relative units)

101 Eg(HfO2)

100 10–1

(A)

106 105

Eg(HfO2) Al

(C)

Au (100)Si/Si3N4/HfO2

(100)Si/Si3N4/HfO2/Au

V<0

V>0

104

Φh(Si)

103 102

Φe(Si)

Φe(Al)

101 Eg(HfO2)

100

3

4

Eg(HfO2)

E2

E2

E1

10–1

(B) 5

Al

Au

6 2 3 Photon energy (eV)

(D) 4

5

6

Fig. 4.7 IPE yield as a function of photon energy in n-Si/SiON/HfO2(10 nm)/Au (A) and n-Si/Si3N4/HfO2(10 nm)/Au (B) capacitors measured under positive voltage on the Au electrode of 1.0 (x), 1.5 (&), 2.0 (Δ) and 2.5 V (r); filled symbols correspond to the samples additionally oxidized for 30 min in O2 at 500 (¢) and 650 C (£), measured with a metal bias of 12.0 V. Panels (C) and (D) show IPE yield as a function of photon energy in the as-deposited p-Si/SiON/HfO2(9 nm) and p-Si/Si3N4/HfO2(10 nm) capacitors with Au (x) and Al (&) electrodes measured under negative voltages of 22.0 and 22.5 V, respectively; filled symbols correspond to the samples additionally oxidized for 30 min in O2 at 500 (¢) and 650 C (£), measured under 22.0 V bias on Au electrodes. Arrows and dashed lines indicate the spectral thresholds and the energies of optical singularities of the Si substrate crystal, respectively.

at hν . 3.6 eV is also visible in the structures with Al electrodes on the background of electron IPE from the aluminium. Because no such photoemission is seen to occur when Au is biased positively (panels (a) and (b)), the corresponding current must be related to the IPE of holes from Si into HfO2. The corresponding spectral threshold is equal to the energy barrier between the top of the HfO2 VB and the bottom of Si CB, as shown in Fig. 3.14. Association of the IPE band with spectral threshold of 3.6 eV with the hole photoinjection from Si gains further ground from the observation of its modulation at the energy corresponding to E2 singularity of Si. Furthermore, the significant attenuation of this current found in samples subjected to

120

Internal Photoemission Spectroscopy

supplemental thermal oxidation (filled symbols in Fig. 4.7) indicates that formation of a SiO2-like interlayer, which results in a barrier of large height that, as already mentioned, is expected for holes injected from silicon. Thus, it is possible to separate contributions of different IPE transitions by combining measurements in samples with different field electrode materials, different emitter
collector combinations, as well as opposite orientations of the electric field in the insulating collector. Additionally, in collector PC or bulk defect PI, one may consider analysis of the photocurrent as a function of the collector thickness because, for photon energies close to the intrinsic optical absorption edge of the collector, this signal must scale linearly with the photoexcited material volume (Williams, 1965). To complete this overview of interface barrier determination, it is worth mentioning that the experiments described so far concern single-photon IPE processes. It has also been suggested that two- and three-photon absorption can be used to photo-inject charge carriers from a semiconductor into an insulator, offering the possibility of evaluating the corresponding barrier height (Marka et al., 2003; Lei et al., 2012a,b). Because multi-photon excitation requires illumination of the sample with laser pulses of high power, it cannot be used to excite MIS or MIM samples because of free-electron absorption in a metal. Instead, multi-photon IPE is observed through variations in the second harmonic generation (SHG), reflecting built-in electric fields in the gate-free semiconductor/insulator structure. The energy onset of the multi-photon IPE is determined in this case as the laser photon energy corresponding to the transition from a single-photon IPE to the two-photon excitations or to the three-photon transitions. Because the charge accumulation in the samples with the floating potential of the insulator surface is affected by adsorption of ions, for example O22 (Marka et al., 2003; An et al., 2013), the strength of the electric field and the variation of the electrostatic potential across the insulating layer appear to be out of control. This factor not only excludes meaningful analysis of the barrier lowering by external field but may also introduce systematic error to the barrier heights measured as the energy onset of multi-photon SHG optical signal. For example, the barrier height of 4.5 eV found at the (100)Si/SiO2 interface using the SHG technique (Marka et al., 2003) appears to be higher by 0.25 eV than that found using conventional IPE in the Si/SiO2/metal capacitor (cf. Fig. 4.2), which suggests an additional contribution to the barrier originating from the O22 ions adsorbed at the surface of the oxide. Although one may try to overcome this difficulty by applying bias to the sample during SHG measurements using corona discharge (Vanbel et al., 2013), the multi-photon IPE still provides much less flexibility than the single-photon IPE mostly addressed in this book.

4.2

IPE Yield Spectroscopy

The IPE spectral curves discussed in the previous sections are often seen to exhibit modulation of the quantum yield at the photon energies corresponding to excitation of direct optical transitions specific to the particular crystal emitter. For instance,

(IPE yield)1/3 (relative units)

Internal Photoemission Spectroscopy Methods

(100)Si/ZrO2

(100)Si/Al2O3 4

121

δ(hν) = 0.02eV

E2

E2

Φe

E1 Si OxMe 2

Φe(ZrO2)

Φe(Al2O3)

0

E1

Φe(SiO2) 3

4

3

4

5

Photon energy(eV)

Fig. 4.8 The cube root of the IPE yield as a function of photon energy for MOS structures with different dielectrics. Left panel shows results for as-deposited 5-nm thick Al2O3 (x) or supplementally oxidized at 650 C for 30 min (&) compared with a 4.1-nm thick thermal SiO2 (Δ). Right panel shows IPE spectra of electrons from Si into as-deposited 7.4 nm ZrO2 (x) or additionally oxidized at 650 C for 30 min (&). All curves are measured under an applied electric field of 2 MV/cm in the insulating layer closest to Si. Arrows E1 and E2 indicate onsets of direct optical transition in the Si crystal. The spectral thresholds Φe are indicated for different oxides. The error in the IPE yield determination is smaller than the size of the symbol.

this effect can be seen in Figs 4.1 and 4.7 for the silicon crystal as well as results reported in several earlier studies (Allen and Gobeli, 1966; DiStefano and Lewis, 1974). Association of these features with properties of electron states of the emitter is easily proved by observation of their same spectral position in samples with a different collector: One may compare the IPE results for Si/SiO2 (Fig. 4.1) and Si/HfO2 (Fig. 4.7) interfaces with the spectra obtained when using Al2O3 or ZrO2 collector layers, as illustrated in Fig. 4.8. In all the cases the IPE yield increase deviates from the cube increase with photon energy at around hν 5 3.4 eV (E1 feature), whereas around hν 5 4.4 eV (E2 feature) the quantum yield decreases in its absolute value which cannot be explained using the simple IPE theory: Integrals (3.1) or (3.1a) can never have a negative first derivative on the photon energy. Therefore, some additional physical process has to be invoked to explain the observations.

4.2.1

Physical Mechanism of the Yield Spectra Modulation

The explanation of the IPE yield decrease with increasing photon energy in the vicinity of the E2 point (hν 5 4.4 eV) can easily be found when comparing the absolute energies of the final excited electron states in the X4 !X1 and, somewhat weaker, Σ4 ! Σ1 direct optical transitions responsible for the E2 feature with the energy electron needs to be injected into SiO2 or another wide-bandgap metal oxide, as shown in Fig. 4.9. From the band diagram of Si crystal (Cardona and

122

Internal Photoemission Spectroscopy

Energy (eV)

10

Eg(Si)

5

EC

X1

0 X4

5 10

L

Γ

X

EV Si

SiO2

Fig. 4.9 Electron energy band structure of silicon crystal (Cardona and Pollak, 1966) with the energy band diagram of Si/SiO2 interface shown in the same energy scale. Bold arrow indicates X4 !X1 direct optical transitions occurring at photon energy of 4.4 eV responsible for the E2 feature in the optical spectra of Si. The final electron state in this transition (X1) is seen to be energetically well below the oxide CB bottom, making photoinjection of electrons impossible.

Pollak, 1966; Adachi, 1988) it is seen that the final states involved in the E2 transition lie energetically close to the bottom of the Si CB (see the bold arrow in Fig. 4.9), i.e., the photogenerated electrons are B3 or B2 eV below in energy than the bottom of the CB in SiO2 or HfO2, respectively. As the result, the X4 !X1 and Σ4 ! Σ1 transitions strongly contribute to optical absorption but give no corresponding contribution to the electron IPE (Adamchuk and Afanas’ev, 1992a). Therefore, the decrease in the observed quantum yield is caused by a combination of two factors. First, the reflectivity of silicon strongly increases when photon energy approaches the energy of the E2 feature, causing reduction in the external quantum yield (cf. Eq. (3.2)). Second, the excitation of direct transitions accounts for the very large value of the optical absorption coefficient of silicon approaching α  2.5 3 106 cm21 at 4.4 eV (Aspnes and Studna, 1983), leading to substantial light attenuation at a depth comparable to the mean photoelectron escape depth. In other words, the high oscillator strength of the X4 !X1 and Σ4 !Σ1 direct optical transitions allows them to “scavenge” the incident photons and in this way effectively “screen” excitations to the energetically higher states which may potentially contribute to the IPE. In a similar way, the transitions between Λ3 and Λ1E-k branches responsible for the E1 feature in the optical spectra of Si at hν 5 3.4 eV (Pollak and Rubloff, 1972) also give no contribution to the electron IPE because of insufficient energy of electrons in the final state. The modulation of the IPE spectral curves by optical features of the emitter can be observed not only for silicon but also for other materials. For instance, “saturation” of the electron IPE yield from amorphous carbon into SiO2 in the spectral range hν . 5.5 eV shown in Fig. 4.5 is probably caused by π !π excitations in the chains or rings of π-bonded carbon atoms (Afanas’ev et al., 1996 a,b). Remarkably, in the graphite-rich layers (&,W) this feature is seen to be shifted to a lower energy (4.5
5 eV), which is consistent with the expected decrease of the π
π splitting with increasing the size of the π-bonded carbon cluster

Internal Photoemission Spectroscopy Methods

IPE/PC yield (relative units)

106

123

(100)Ge/Si/SiOx /HfO2

105

104 (100)Ge/GeN O /HfO x y 2 103 Eg(HfO2)

102

5.6 eV

101 100 10

E'0

1

2

3

E2

4 5 Photon energy (eV)

Fig. 4.10 IPE yield as a function of photon energy measured with 11 V bias on the Au electrode in n-Ge/ HfO2 (10 nm)/Au capacitors with interlayers of different composition indicated. Arrows indicate the spectral threshold of intrinsic oxide PC Eg(HfO2) and the energies of direct optical transitions in the Brillouin zone of Ge crystal, E 0 0 and E2, respectively.

6

(Lee et al., 1994). On the other hand, an example very similar to the Si pattern is provided by IPE experiments on Ge interfaces with HfO2, as shown in Fig. 4.10 for samples with interlayers of different chemical composition (Afanas’ev and Stesmans, 2006). The quantum yield of electron IPE is seen to exhibit features at photon energies of 3.2
3.3 and 4.4 eV, which are consistent with energies of direct optical transitions in Ge (Cardona and Pollak, 1966; Adachi, 1988). Interestingly, the depth of the yield modulation is seen to be different in the Ge/ HfO2 samples with GeNxOy or Si/SiOx interlayers. The weaker impact of the E 0 0 and E2 transitions on the yield in the latter case may be associated with a symmetry lowering of the Ge crystal lattice at the surface caused by the strain induced by the overgrowth of the 1.2-nm thick Si capping layer. This observation would be consistent with the high sensitivity of the IPE to the surface layer of the emitting material as only the optical transitions occurring within the IPE signal formation depth (i.e., mean photoelectron escape length) will contribute to the spectral features observed on the IPE spectra shown in Fig. 4.10.

4.2.2

Application of the IPE Yield Modulation to Si Surface Monitoring

The sensitivity the IPE yield to the intensity of optical transitions in the very surface layer of the emitter makes its analysis a promising technique to evaluate the crystalline quality of semiconductor surfaces. An example of such an application can be given for silicon interfaces with different oxide insulators, which represents an issue highly relevant for several practical microelectronic applications of this semiconductor (Wilk et al., 2001). Upon disordering, the peak in the optical reflectivity and absorption spectra at hν 5 4.3
4.4 eV (the E2 singularity) typical for the single-crystal silicon disappears, leading to featureless spectra of Si optical parameters in the photon energy range from 4 to 4.7 eV (Philipp, 1971; Jan et al., 1982). Potentially, the conventional optical absorption spectroscopy also allows one to monitor the electron transitions in the vicinity of the E2 point. However, direct optical measurements have poor sensitivity to the very surface/interface layer

124

Internal Photoemission Spectroscopy

Fig. 4.11 Spectral dependences of electron IPE from the VB of (100) Si into 5-nm thick thermal SiO2 measured in Si/SiO2/Au structures with different positive bias applied to the metal electrode. The arrow indicates the energy of the E2 transition.

(IPE yield)1/3 (relative units)

(100)Si/SiO2 (5 nm) 10 V (Volt): 1.0

E2

1.5 5

2.0 2.5 3.0

0 3.5

4.0 4.5 Photon energy (eV)

5.0

of the semiconductor because the light absorption occurs at a depth of about 1/α (α is the optical absorption coefficient of a solid) thus yielding a probing depth of 100 2 40 nm for Si in the photon energy range 3.0
4.5 eV (Aspnes and Studna, 1983). By contrast, monitoring of the intensity of the E2-singularity related feature in the IPE spectra allows one to trace the processing-induced distortion of the lattice with the probing depth comparable to the mean photoelectron escape length at hν 5 4.4 eV, i.e., in the order of only few nanometres. The principle of using IPE for monitoring Si surface optical properties was discussed earlier (Fig. 4.9) by using the electron energy band diagram of Si at its interface with SiO2. The X4 ! X1 excitation indicated by the arrow provides an excited electron in a final state well below the oxide CB edge, which makes it emission of this electron into SiO2 impossible. The corresponding distortion of the IPE spectra is expected to be proportional to the partial absorption coefficient of electron transitions in the E2 peak. The character of the of IPE spectral distortion in the spectral range corresponding to emission of an electron from the VB of (100)Si into a 5-nm thick thermal oxide is illustrated in Fig. 4.11. As predicted by the theory (cf. Table 3.1), in the vicinity of the spectral threshold the IPE spectral curves must obey the cubic law Y  A(hν 2 Φ)3, where A is a constant and Φ is the IPE spectral threshold. The shift of the threshold Φ towards lower energy is caused by the Schottky lowering of the Si/SiO2 potential barrier, consistent with that predicted by Eq. (2.29). At around hν  4.2 eV the spectral curves begin to deviate from the theoretical dependence. The spectral position of this feature is seen to be insensitive to the electricfield-induced shift of the IPE spectral threshold. The latter importantly indicates that it originates from the field-independent optical excitation, which can be associated with the E2 feature in the optical characteristics of the Si crystal substrate. To ensure the correct assignment of the feature observed in the IPE spectra to the peak in the optical constants of Si crystal, it was attempted to reduce the intensity of the dominant X4 ! X1 transition by high-dose implantation of a donor impurity (phosphorus). As can be seen from Fig. 4.9, the final state of the optical transition at point X1 of the silicon Brillouin zone lies very close to the bottom of

Internal Photoemission Spectroscopy Methods

125

Fig. 4.12 Spectral dependences of electron IPE yield from the VB of (100)Si into 85-nm thick thermally grown SiO2 for the low-doped n-type Si substrate (x) and for the phosphorus-implanted (D 5 1 3 1016 P/cm2 at E 5 80 keV) one (&). The arrow indicates energy of the E2 transition in Si crystal.

104

IPE yield (relative units)

No implantation 103

E2

1 1016 P /cm2

102 101 100 10

1

10

2

3

4

5

Photon energy (eV)

the Si CB, and, in heavily P-doped n-type Si, it will be occupied by electrons. The latter will reduce the oscillator strength of the optical transitions because they become impossible between the points of high symmetry and, therefore, must occur at slightly different wave vector values. The IPE spectra shown in Fig. 4.12 indicate that for the P-implanted Si(100)/SiO2 sample a high density of electrons is present in the Si CB (they account for the IPE from the Si CB at low photon energies similarly to the case discussed in the beginning of the previous section) and the feature at hν 5 4.4 eV is greatly reduced in comparison to the control (unimplanted) sample. Therefore, the observed modulation of the IPE spectra can firmly be associated with excitation of X4!X1 transitions not only on the basis of the same energy position but also using the exposed sensitivity to the conduction electron density in silicon. Furthermore, the remarkable sensitivity of the IPE spectra to Si surface processing is illustrated by the IPE spectra shown in Fig. 4.13(a) for (100)Si oxidized in dry O2 at 1000 C for various times resulting in different oxide thickness. It is clearly seen that, with increasing oxide thickness, the depth of the yield spectrum modulation in the vicinity of the E2 singularity decreases, approaching nearly zero value similar to that attained in the phosphorous-implanted samples (curve (4) in Fig. 4.13(a)). To make a meaningful comparison between the intensities of the direct optical transitions at the interfaces of silicon with differently prepared insulators, one must find a way to characterize the distortion of the IPE spectral curves in a quantitative way. Assuming that the dependence of the IPE yield on photon energy Y0(hν) is a monotone function of hν, one may define the deviation function S(hν) characterizing the normalized spectrum distortion (Adamchuk et al., 1988; Adamchuk and Afanas’ev, 1992a): SðhνÞ 5

Y0 ðhνÞ 2 YðhνÞ ; Y0 ðhνÞ

ð4:1Þ

126

Internal Photoemission Spectroscopy

(IPE yield)1/3 (relative units)

Si(100)/SiO2

10

1 2 3 4

5

(A) 0 dox(nm):

0.2

23.5

S

46 55 84 100 148

0.1

Fig. 4.13 (A) Cube root plot of the spectral dependences of electron IPE from the VB of (100)Si into thermally grown SiO2 layers of different thickness obtained by oxidation of the crystal in dry O2 at 1000 C (in nm): 55 (1), 100 (2) and 160 (3) compared with the samples with a 100-nm thick oxide implanted with high dose of phosphorous before oxidation (4). The curves are measured using Si/SiO2/Au structures, with the average strength of the electric field in the oxide being 1 MV/cm with the metal biased positively. (B) The relative deviation of the quantum yield from the cube law S(hν) as a function of photon energy for (100)Si/SiO2 samples with different oxide thicknesses.

(B) 0.0 4.0

4.2 4.4 4.6 Photon energy (eV)

4.8

where Y(hν) is the experimentally observed IPE yield, and Y0(hν) is obtained by extrapolation of the yield measured at hν , E2 to the higher photon energies. In the simplest case, when E2 lies slightly above the spectral threshold Φ from the semiconductor VB, one may approximate Y0 as a power function (Powell, 1970), obtaining SðhνÞ 5 1 2

YðhνÞ ; Cðhν2ΦÞ3

ð4:2Þ

where the constant C is determined from the slope of the near-threshold part of the linear Y1/3 2 hν plot or may be taken from a reference sample. The S(hν) curves derived for (100)Si/SiO2 interfaces with different thicknesses of the thermal oxide layer are compared in Fig. 4.13(b). Their shape is very similar to the E2 optical absorption peak of Si crystal due to the X4!X1 and Σ4!Σ1 transitions, which are gradually attenuated with increasing oxidation time. Importantly, this optical feature appears to be much less pronounced for the oxidized Si surfaces than for the clean cleaved ones (see, e.g., Allen and Gobeli, 1966), suggesting that the oxidation of the Si surface leads to some kind of crystal symmetry reduction

Internal Photoemission Spectroscopy Methods

(IPE yield)1/3 (relative units)

15

(100)Si/Al2O3 (50 nm)

127

Fig. 4.14 Spectral dependences of electron IPE from the VB of (100) Si into a 50-nm thick as-deposited Al2O3 layer (x) and after 10-min post-deposition oxidation in pure O2 at 950 C (&). The arrows indicate the energies of transitions E1 and E2.

E2

as-deposited 950°C 10 min 10

E1 5

0 2.5

3.0

3.5

4.0

4.5

5.0

Photon energy (eV)

and to a decrease of the oscillator strength of the X4!X1 and Σ4!Σ1 direct optical transitions (Adamchuk et al., 1988; Adamchuk and Afanas’ev, 1992a). As most simple way to compare different surfaces of Si, the maximum modulation depth of the IPE spectrum can be determined as the peak value Smax of the S(hν) function. For comparison, the IPE results for Al2O3 on (100)Si grown using atomic-layer deposition at 300 C are shown in Fig. 4.14. For the as-deposited alumina layer (x), the E2 feature is much more pronounced than in thermal SiO2/Si structures, which is also consistent with the IPE spectra shown in Figs 4.7 and 4.8 for other metal oxides deposited at relatively low temperature (300
350 C). However, a substantial increase is observed in the IPE spectral threshold energy after 10 min oxidation of the Al2O3/Si sample in O2 at 950 C (&), which suggests formation of an aluminosilicate layer at the interface. Most importantly, the modulation depth of the IPE spectrum at point E2 drops drastically after this oxidation, indicating a substantial perturbation (disordering) of the Si crystal surface structure. The results of the IPE total yield analysis in the vicinity of E2 optical singularity are illustrated in Fig. 4.15 by comparing values of Smax for different insulating layers on (100)- and (111)-oriented Si crystals. As the reference S value, one may use S  0.35 determined from the external photoemission spectra of a clean cleaved (111) Si crystal (Allen and Gobeli, 1966) and S 5 0 for amorphous Si (Jan et al., 1982). It is clearly seen that in thermal SiO2 growth, the silicon surface crystallinity degrades with increasing oxide thickness (oxidation time). In contrast, the crystallinity of the (100) Si surface with deposited Al2O3, ZrO2 or HfO2 is approximately independent of the overlayer thickness and, at least for the same deposition method (results for the atomic-layer deposition are shown in Fig. 4.15), on the composition of the deposited oxide. The corresponding Smax values even higher than the value Smax 5 0.35 obtained after (111) Si crystal cleavage (Allen and Gobeli, 1966), pointing towards the presence of atomic steps on the clean surface as a possible disordering factor or on the influence of Cs adsorbate used to reduce the silicon work function.

128

Internal Photoemission Spectroscopy

0.6 MeOx 0.4

(111)Si

Smax

Cleaved SiO2 0.2

Al2O3

SiO2

ZrO2 HfO2 0.0 1

4.2.3

10 Oxide thickness (nm)

Fig. 4.15 Maximum modulation depth of the IPE spectrum at the E2 point versus insulator thickness for SiO2 layers (circles) thermally grown on (100) (x) and (111) (K) Si, and for low-temperature deposited Al2O3 (&), ZrO2 (W) and HfO2 (X) layers on Si(100). Arrow indicates the Smax value evaluated from the external photoemission yield spectra of the clean cleaved (111)Si (Allen and Gobeli, 1966). Lines guide the eye.

100

Model for the Optically Induced Yield Modulation

The results presented above demonstrate the mechanism of IPE spectral distortion by optical features of the emitter crystal but provide no immediate link to the measurable values of the optical absorption coefficient or the optical reflectivity. To quantify the influence of optical singularities one may use a simple model describing attenuation of incident light at a depth comparable to the mean photoelectron escape depth λe (Adamchuk and Afanas’ev, 1992a). In this case the internal quantum yield is related to the optical absorption coefficient α(hν) and the escape depth λe, assumed to be energy independent, by the relationship (Berglund and Spicer, 1964): Y  ðhνÞ 5 Yðhν; ΦÞ

αðhνÞλe ; 1 1 αðhνÞλe

ð4:3Þ

where Y (hν) is the spectral dependence of the quantum yield obtained neglecting the optical effects, e.g., given in Table 3.1. In the limiting case of strong electron scattering, α(hν)λe{1, Eq. (4.3) leads to expression (2.9) for the external quantum yield. In the absence of any optical singularities, the light absorption at the surface of the emitter may be characterized by the energy-independent coefficient α0, which would scale the internal quantum yield by a constant factor: Y0 ðhνÞ 5 Yðhν; ΦÞ

α0 λ e : 1 1 α0 λ e

ð4:4Þ

The external quantum yield can be calculated from Eq. (4.4) by multiplying by a factor [1 2 R], where R is the optical reflectivity of the sample (cf. Eq. (3.2)). Next, assume that at certain photon energy hν 0 . Φ an excitation of additional interband electron transitions occurs leading to an increase of the optical absorption

Internal Photoemission Spectroscopy Methods

129

coefficient by α (hν), which adds to the energy-independent optical absorption α0. If the conventional procedure of the quantum yield determination by normalizing to the incident photon flux is still used, this additional optical absorption will modify the yield curves because the variation of the optical constants is neglected when calculating Y. Two cases are possible, depending on the energy of the final electron state Ef in the additional interband transitions (Adamchuk and Afanas’ev, 1992a). If Ef . Φ the additionally excited electrons will contribute to the IPE and the real quantum yield will be determined by the total optical absorption [α0 1 α (hν)]: Y1 ðhνÞ 5 ½1 2 RYðhν; ΦÞ

½α0 1 α ðhνÞλe : 1 1 ½α0 1 α ðhνÞλe

ð4:5Þ

Therefore, there will be a photon-energy-dependent enhancement of the quantum yield compared with the predicted Y(hν,Φ)  C(hν 2 Φ)p dependence, which can be characterized by the relative deviation function S(hν) constructed in a similar way as the function given by Eq. (4.1). This function can now be expressed as follows, assuming that the contribution of the optical reflectivity [1 2 R] remains unchanged: SðhνÞ 5

Y1 ðhνÞ 2 Y0 ðhνÞ ðα ðhνÞ=α0 Þ 5 : Y0 ðhνÞ 1 1 ½α0 1 α ðhνÞλe

ð4:6Þ

If Ef , Φ the additionally excited electrons will contribute only to the light attenuation but not to the IPE and the real quantum yield is still be determined by the optical absorption α0: Y1 ðhνÞ 5 ½1 2 RYðhν; ΦÞ

α0 λe ; 1 1 ½α0 1 α ðhνÞλe

ð4:7Þ

suggesting a decrease of the quantum yield compared with the “no-singularity” case. For the spectral deviation function (4.1) one obtains now the following expression: SðhνÞ 5

Y0 ðhνÞ 2 Y1 ðhνÞ α ðhνÞλe 5 : Y0 ðhνÞ 1 1 ½α0 1 α ðhνÞλe

ð4:8Þ

The character of the IPE spectral plot distortion is illustrated in Fig. 4.16 by simulation of the Lorentz-type absorption peak influence on the Y1/p 2 hν plot with the final states of additional transitions states contributing to the IPE (Ef . Φ) and providing no charge carriers at an energy sufficient for the interface barrier surmount (Ef , Φ). It is obvious that both the enhancement and attenuation of the external IPE yield can be observed. It must be added, however, that construction of the spectral deviation function S(hν) seems to be the more appropriate method because Eqs. (4.6) and (4.8) indicate that the spectral shape of this function closely resembles the spectral dependence of the partial absorption coefficient α (hν) of the additionally excited interband transitions (cf. Fig. 4.13(b)).

130

Internal Photoemission Spectroscopy

hν0

4

Ef > Φ

c

s on

ta

nt

α

(Yield) 1/p

3

2

Ef < Φ

Fig. 4.16 Simulation of the IPE yield changes caused by the Lorentz absorption peak centred at photon energy hν 0 (α (max) 5 α0; α0λe 5 0.2) with the energy of the final electron state above and below the interface barrier height Φ.

1 Φ 0

(IPE yield)1/3 (relative units)

Photon energy

X7

GaAs(111)B/SrF2

Fig. 4.17 Cube root of the electron IPE quantum yield as a function of photon energy measured at the interface of GaAs (111)B with a 120-nm thick epitaxially grown layer of SrF2. The strength of the electric field in the fluoride during measurements was 0.4 MV/cm, with the Au field electrode biased positively. Arrows indicate the energy position of direct optical electron transitions in GaAs crystal.

X6

4 3 2 1 Γ8 0 3.0

3.5

4.0

Γ7 4.5

5.0

5.5

Photon energy (eV)

It is worth illustrating the predicted positive and negative deviations of the quantum yield with respect to the idealized power law by the experimental IPE spectrum of electron IPE from the VB of GaAs(111)B into the epitaxially grown SrF2 collector (Afanas’ev et al., 1991, 1992a,b) layer shown in Fig. 4.17. As can easily be noticed, the quantum yield obeys cube behaviour predicted by Powell’s theory over the energy range of  1 eV above the spectral threshold. When the photon energy increases further, the yield increases faster than expected, yielding a “hump” on the spectral curve at hν  4.4 eV. Further increase of the photon energy leads to a rapid decrease of the quantum yield at around hν  4.8 eV below the line obtained by extrapolating the initial nearly ideal portion of the spectral curve. The insensitivity of the spectral positions of these features to the strength of the electric field in the fluoride layer (Afanas’ev et al., 1991) indicates their optical origin. Accordingly, they may be associated with direct optical excitation of Γ8!Γ7 transitions in GaAs, yielding electrons with energies above the CB edge of SrF2, and with X7!X6 excitations, which give no contribution to IPE because their final state appears to lie well below the interfacial barrier top. Potentially, if the photoelectron escape depth is known from an independent source, this kind of measurement is capable of providing quantitative information about the strength of direct optical transitions at the surface of the photoemitter.

Internal Photoemission Spectroscopy Methods

4.3

131

Spectroscopy of Carrier Scattering

In IPE, the excited charge carrier must travel from the point of its optical excitation in the emitter to some point behind the maximum of the potential barrier in a collector without experiencing any substantial energy loss. Therefore, variations in the inelastic scattering rate in the emitter or collector will affect the probability of the carrier escape and, therefore, the IPE quantum yield value. If this change in the scattering rate occurs in the carrier energy range above the spectral threshold of IPE, this transport-induced variation of the quantum yield will then be reflected in the IPE spectral characteristics, enabling one to determine the energy onset(s) of the inelastic scattering process(es). In this way, one may attempt to identify the dominant scattering mechanisms. Obviously, the transport properties of the emitter and collector affect different steps of the IPE process, and scattering in these materials should be analysed separately.

4.3.1

Scattering in the Emitter

The scattering of charge carriers on their way from the point of excitation to the surface of the emitter affects the quantum yield by modulating the photoelectron escape depth λe, which is largely determined by the rate of inelastic electron
electron scattering. In the most simple case of a large, compared with λe, light penetration depth α21, the quantum yield is proportional to λe, as can be seen from Eq. (2.9). The principle of observing the energy loss mechanism during electron IPE from a wide bandgap emitter like SiC is illustrated in Fig. 4.18 (Afanas’ev and Stesmans, 2003). For a photon of energy hν , Eg(SiC) exciting an electron in the SiC CB by transition indicated by arrow A, the excited carrier can experience only the quasi-elastic scattering by phonons because its energy remains insufficient to excite a valence electron to the SiC CB. When the photon energy exceeds Eg (transition B), the generation of new electron
hole pairs during transport of excited electrons towards the emitter surface becomes possible. As the result of a pair generation, the initially excited electron loses its energy and cannot be injected into SiO2 anymore. Therefore, the rate of inelastic scattering of the excited electrons sharply increases when hν becomes larger than Eg, which, in turn, reduces the photoelectron escape probability and the rate of the IPE yield increase with photon energy. Then the energy position of the loss feature observed in the IPE spectra can be directly associated with the onset of electron
hole pair generation process, i.e., with the bandgap of the emitter Eg representative of the SiC surface layer of thickness comparable to the mean photoelectron escape depth (a few nanometres). The essential condition to observe such effects in IPE from a semiconductor CB can be expressed as Φ , Eg(emitter){Eg(collector). This would enable detection of the scattering-modulated IPE signal well below the spectral threshold of PC, which has much higher quantum yield than the IPE. In IPE from the VB of a semiconductor, the largest kinetic energy of an electron will be equal to hν 2 Eg(emitter), leading a different condition for observation of inelastic scattering effects in IPE: Φ , 2Eg(emitter){Eg(collector).

132

Internal Photoemission Spectroscopy

B

Fig. 4.18 Electron energy band diagram of a SiC/SiO2 interface with the schemes of electron transitions contributing to the IPE in the spectral range hν , Eg(SiC) (process A) and hν . Eg(SiC) with the additional electron
electron scattering process B shown.

A

Ec Eg Ev SiO2

SiC

103

Φ3

IPE yield (relative units)

6H-SiC Eloss

102

Φ2 101 100 10–1 Φ1 10–2

2

3

Field (MV/cm) 1.0 2.0 3.0 4.0 5.0 6.4 4 5 Photon energy (eV)

Fig. 4.19 IPE yield as a function of photon energy for a 6H-SiC MOS structure at different strengths of the electric field in the oxide (in MV/cm): 1.0 (x), 2.0 (&), 3.0 (W), 4.0 (X), 5.0 (e) and 6.4 (hexagons). The arrow Eloss indicates the position of the electron energy loss peak.

6

The experimental evidence for quantum yield reduction when the excited carrier energy exceeds the inelastic scattering energy threshold is provided by the electron IPE spectral curves shown using the logarithmic yield scale in Fig. 4.19 for the 6H-SiC/SiO2 interface. One might notice that the quantum yield above the threshold of electron IPE from the CB of SiC, shown as Φ1, shows a drop at around hν  3.1 eV indicated by the arrow Eloss. For the photons with energy higher than this value, the rate of further yield increase appears to be much reduced, suggesting a smaller IPE probability. As the energy point at which the IPE yield decrease is observed appears to be insensitive to the strength of the electric field in the oxide (which is seen to cause a shift of the spectral threshold to lower photon energy because of the Schottky effect) this feature is clearly related to the processes occurring inside the SiC emitter. At the same time, the optical absorption and reflectivity of 6H-SiC in the spectral range around hν 5 3 eV do not exhibit variation strong enough to explain the yield decrease by the influence of direct optical transitions discussed in the previous section because of the indirect nature of the SiC bandgap. Therefore, the onset of inelastic electron
electron scattering in the SiC crystal represents the only feasible explanation of the observed yield behaviour. Further support for this interpretation is provided by the results presented in Fig. 4.20(a
c), which shows the spectra of electron IPE into SiO2 from three SiC polytypes: 4H, 15R and 3C, respectively. For the first two polytypes, the spectra exhibit the feature similar to than the 6H-SiC data (cf. Fig. 4.19), also indicated by

Internal Photoemission Spectroscopy Methods

102

133

Fig. 4.20 IPE yield as a function of photon energy for the 4H-(A), 15R(B) and 3C-SiC (C) MOS structure at different strengths of the electric field in the oxide (in MV/cm): 0.3 (x), 0.5 (&), 1.0 (W), 2.0 (X) and 3.0 (e). The arrow marked Eloss indicates the position of the electron energy loss peak.

4H-SiC Eloss

101 100 10–1

IPE yield (relative units)

(A) 10–2 102 15R-SiC Eloss

101 100 10–1

(B)

10–2 102

3C-SiC

101 100 10–1 (C) 10–2

2

3

4 5 Photon energy (eV)

6

arrows as Eloss. Although it is less pronounced in the 4H-SiC sample than in 6H-SiC, its energy position seems also to be insensitive to the strength of applied electric field. In the case of 3C-SiC (cf. Fig. 4.20(c)) no modulation of the IPE spectrum is observed. The latter is consistent with the discussed mechanism of the excited electron scattering through excitation of another electron across the SiC bandgap: In 3C-SiC the bandgap width of 2.38 eV (Choyke, 1990) is considerably lower that the threshold of IPE from the CB, i.e., for any electron contributing to the IPE process, inelastic scattering is possible and its energy threshold remains unobservable. In Fig. 4.21 the energy position of the Eloss scattering peak is shown as a function of the optical bandgap width of the corresponding SiC polytype (Choyke, 1990). The loss is seen to occur at an energy slightly ( 0.1 eV) above the SiC bandgap value; however, apart from this, the correlation between the two energies is clear. The value of the shift of the loss peak to a higher energy is close to the energy of the longitudal optical (LO) (970 cm21) and transversal optical (TO) (790 cm21) optical phonons h ω in SiC (Engelbrecht and Helbig, 1993). Apparently, phonon emission facilitates the transition of the secondary electron from the top of the SiC VB to the SiC CB bottom.

4.3.2

Scattering in the Collector

As already discussed in Chapter 2, scattering of charge carriers in the image-force potential well, i.e., in the spatial region between the surface of the emitter and the

134

Internal Photoemission Spectroscopy

Electron energy loss (eV)

3.4

Fig. 4.21 Spectral position of the electron energy loss peak in the IPE spectra as a function of the optical bandgap width of the corresponding SiC polytype according to Choyke (1990). Lines guide the eye.

4H-

3.3 3.2

Eloss = Eg + hω Eloss = Eg

15R6H3.1 3.0 2.9 2.9

3.0

3.1 3.2 3.3 SiC bandgap width (eV)

3.4

Fig. 4.22 Mean free path of an electron ‘ at the Si/SiO2 interface as a function of the difference between exciting phonon energy hν and the interface barrier height Φ. The points show the experimental data for (111) Si/SiO2 (Berglund and Powell, 1971; Przewlocki et al., 2012) and (100)Si/ SiO2 (Afanas’ev, 1991); the dashed line is the results predicted by Monte Carlo simulations assuming only an LO phonon scattering mechanism.

Mean free path (nm)

15 Berglund and Powell (1971) Afanas’ev (1991) 10

5

Przewlockietal. (2012)

MC simulation

Experiment 0 0.0

Si/SiO2

0.5

1.0

1.5

hν–Φ (eV)

top of the potential barrier xm shown in Fig. 2.8, modulates the quantum yield by a term exp[ 2 xm/‘] (cf. Eq. (2.31)). Using the field dependence of xm given by Eq. (2.30), one can determine the mean electron thermalization length ‘ by fitting the low-field portion of the IPE yield versus the field curve with Eq. (3.11) while keeping the photon energy hν constant. An example of the results obtained using this approach is presented in Fig. 4.22, which shows the mean electron thremalization length ‘ as a function of excess photon energy over the Si(100)/SiO2 interface barrier (Afanas’ev, 1991). Experimental points are obtained by fitting the IPE current
voltage characteristics using Eq. (2.30) with p 5 3 corresponding to the case of electron IPE from the VB of the semiconductor (Powell, 1970). For comparison literature results for (111)Si/SiO2 interfaces are also shown (Berglund and Powell, 1971; Przewlocki et al., 2012). In the range of the small excess energy of electrons, i.e., (hν 2 Φ) , 0.3 eV, the themalization length strongly increases, indicating a lower electron scattering rate. The constant thermalization length model (Berglund and Powell, 1971) is seen to be a realistic approximation in the excess electron energy range from 0.3 to 1 eV. At excess energies higher than 1 eV ‘ is suggested

Internal Photoemission Spectroscopy Methods

135

to increase approximately as ‘B(hν 2 Φ)1/2 (Afanas’ev, 1991), which is supported by recent results (Przewlocki et al., 2012). These experimental results can be compared with the results of the Monte Carlo simulation of electron transport across the image-force barrier region assuming electron interaction with LO phonon modes (h ω1 5 0.063 eV and h ω2 5 0.15 eV), which are also shown in Fig. 4.22 by a dashed line (Afanas’ev, 1991). The Monte Carlo simulations performed using the electron
phonon scattering parameters of bulk SiO2 (Fitting and Friemann, 1982; Fitting and Boyde, 1983) are seen to reproduce the experimental data on electron scattering quite well. Importantly, they also reveal a reduction in scattering rate in the low electron energy range, which can now be explained in some more detail. Analysis of electron trajectories indicates that most of the electron
phonon interactions occur in the immediate vicinity of the potential barrier top because electrons are travelling there with a minimal normal velocity and, therefore, are dwelling for the longest time in this spatial region. When the energy of electron is smaller than the phonon energy h ω, no scattering with phonon emission is possible, resulting in transport with almost no energy loss. This effect appears to be particularly pronounced in emission from the silicon VB because of the triangular shape of the excited electron distribution in IPE from the VB (cf. Table 3.1) contains a large portion of the low-energy charge carriers. These carriers provide the most significant contribution to the increase of ‘ because the latter is averaged over the whole energy spectrum of the electrons entering the oxide. These results indicate the inelastic interaction with LO phonons, primarily with h ω2 5 0.15 eV mode, to be the dominant mechanism of electron thermalization at the Si/SiO2 interface. At the same time the Monte Carlo simulation results predict that the energy onsets of this scattering process can also be observed. This would naturally lead to determination of the scattering mode energy, i.e., they will allow one to determine the energy spectrum of phonons in the near-interface layer of the collector. However, analysis of current
voltage curves of electron IPE from the VB is unsuitable for this purpose because, in addition to the broad energy distribution of electrons passing through the barrier region, the barrier height at the interface is also a function of the electric field (cf. Eq. (2.29)) and it changes in the course of the IPE current
voltage curve recording at a constant hν. The way to the phonon mode spectroscopy was paved by IPE experiments using degenerately doped n-type Si in which electrons occupy a narrow energy range close to the bottom of the semiconductor CB (Afanas’ev, 1991). For donor concentrations that are not too high, optical excitation of the conduction electrons results in a nearly mono-energetic flux of charge carriers arriving at the Si/SiO2 interface, as illustrated in the insert in Fig. 4.23(a). The spectral curves of electron IPE presented in this figure using a linear yield plot (cf. Table 3.1) exhibit nonmonotonous yield increase with increasing energy of the photons. This might look similar to the scattering-related features observed in the electron IPE spectra of SiC/SiO2 interface shown in Figs 4.19 and 4.20. However, in contrast to the SiC/ SiO2 case, in n1-Si/SiO2 structures the spectral position of the yield deviations from the linear increase is seen to be affected by the strength of the electric field in the oxide. This behaviour is consistent with the prediction that electron scattering

136

Internal Photoemission Spectroscopy

0.063 eV 0.15 eV (B)

(A) IPE yield (relative units)

n+-Si 0.5

0.0 2.7

SiO2

0.5

Scattering probability

1.0

1.0

0.0 2.8

2.9 3.0 3.1 3.2 Photon energy (eV)

0.0

0.1 0.2 0.3 Electron energy (eV)

Fig. 4.23 (A) The quantum yield of electron IPE from the CB of n1-Si(100) into SiO2 as a function of photon energy as measured under different strengths of the electric field in the oxide (in MV/cm): 0.3 (x), 0.5 (&), 1.0 (W), 1.5 (X) and 2.2 (e). The insert shows the scheme of the observed electron transitions. (B) The electron scattering probability as a function of its kinetic energy above the potential barrier top obtained from the corresponding spectral curves shown on panel (a). Three upper curves are shifted along the vertical axis for clarity. Dashed lines indicate the energy of SiO2 LO phonon modes.

occurs in the vicinity of the field-dependent potential barrier maximum. Moreover, for the spectral curve measured at the highest strength of the electric field in the oxide of F 5 2.2 MV/cm (e) deviations from linearity are seen to be weak. The latter is, again, in agreement with the reduction in the scattering probability caused by a progressive shift of the barrier maximum towards the emitter surface with increasing electric field. The electron scattering probability may be quantified by constructing the spectral deviation function of type given by Eq. (4.1) (Afanas’ev, 1991; Adamchuk and Afanas’ev, 1992a): P½hν 2 ΦðFÞ; F  5 1 2

Yðhν; FÞ ; C½hν 2 ΦðFÞ

ð4:9Þ

in which the constant C is determined by the slope of the spectral curve less affected by the scattering (curve (e) in Fig. 4.23(a)). The results of scattering probability calculations are illustrated in Fig. 4.23(b) in which the energies of the dominant LO phonon modes in SiO2 are indicated for comparison. The onset of scattering is seen to be well correlated with the lowest LO mode (h ω1 5 0.063 eV) while the contribution of the higher phonon mode (h ω2 5 0.15 eV) can also be distinguished on curves corresponding to IPE spectra taken at relatively high electric field strength (W) and (X) in Fig. 4.23. One may significantly improve the spectral resolution in the measurements of this by using laser excitation. This point is illustrated in Fig. 4.24, which shows the

Internal Photoemission Spectroscopy Methods

Photo current (pA)

10

Fig. 4.24 (A) Photocurrent as a function of the electric field as measured in n1-Si(100)/SiO2/Au structures using 2.84-eV laser excitation. The current originates from the electron IPE from the CB of Si doped with phosphorus with concentration nD 5 5 3 1018 cm23 (x) and nd 5 2 3 1019 cm23 (&). (B) First derivative of the IPE current
voltage curve versus strength of applied electric field. The arrows indicate the position of electron scattering-related features.

hν = 2.84 eV

nd (cm–3) 5

137

5 x 1018 2 x 1019 (A)

dI/dV (relative units)

0 40

30

20

10 (B) 0 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Electric field (MV/cm)

electric field dependence of electron IPE current from n1-Si into SiO2 excited by Cd-vapour laser (hν 5 2.84 eV). The increase in the IPE current under constant hν with increasing field is associated with the barrier lowering (the Schottky effect) and with the shift of its maximum closer to the injecting interface. The curves shown for two dopant concentrations exhibit undulations associated with onsets of inelastic electron scattering. These onsets are more clearly seen in Fig. 4.24(b), which shows the first derivative of the photocurrent on voltage for the sample with nd 5 2 3 1019 cm23 as a function of applied field. The peaks are observed at the strength of the electric field corresponding to the excessive energy of electrons of 0.03 and 0.06 eV, which is close to the energy of acoustic and optical phonons in SiO2, respectively. In this measurement mode, the IPE scattering spectroscopy closely resembles the inelastic tunnelling spectroscopy in which the impact of scattering on the electron tunnelling current is analysed. Similar to the tunnelling spectroscopy technique, further improvement of the energy resolution may be attained when the measurement temperature is lowered because of reduction in the thermal width of the energy distribution of the initial electron states in the CB of the n1doped semiconductor. By analysing electron scattering probability in the barrier region, one may also obtain information about the influence of static scattering impurities on the thermalization length. This is exemplified in Fig. 4.25, which shows ‘(hν 2 Φ) curves obtained from the electron IPE experiments in Si/SiO2 structures prepared by

138

Internal Photoemission Spectroscopy

Mean free path (nm)

(nm)

4

10

3 2 1 0

0

1 (1020 cm–3)

2

5

0 0.0

0.2

0.4 hν–Φ (eV)

0.6

Fig. 4.25 Mean free path of an electron ‘ at the Si/SiO2 interface as a function of the difference between exciting phonon energy hν and the interface barrier height Φ derived from the IPE measurements in the samples with different Ge content in the starting Si crystal (in cm23): 0 (x), 8 3 1018 (&) and 2.5 3 1020 (W). The insert shows the dependence of ‘ in the plateau region on Ge concentration.

0.8

thermal oxidation of Ge-doped Si crystals (Afanas’ev et al., 1992b). The overall shape of the curves remains approximately the same, suggesting that LO phonon scattering dominates the electron energy dissipation process. At the same time, a considerable reduction in the thermalization length is seen to occur progressively with increasing Ge concentration in the samples, as illustrated in the insert. Apparently, elastic scattering of electrons by Ge ions in the near-interface oxide layer results in the electrons dwelling for an effectively longer time in the potential barrier region. This would lead to a higher probability of energy loss through electron
phonon scattering. The described spectroscopy of energy losses in IPE spectroscopy is somewhat similar to the conventional energy loss spectroscopy used in external photo- and secondary electron spectroscopy methods. However, at least in spectroscopy of carrier scattering in the collector, one observes predominantly the scattering events taking place in the spatial region close to the top of the image-force barrier maximum.

4.4

Spectroscopy of Intrinsic PC

The photocurrent (or photocharging) signal that is detected in IPE experiments may be generated not only by the IPE-type electron transitions across the interfacial barrier but also by optical excitation of free charge carriers inside the collector. Two types of transition can be considered: the intrinsic PC associated with band-to-band electron transitions in the collector and the PI of defect or impurity states with energy levels inside the collector bandgap. The spectroscopy of PC and PI enables one to obtain additional information about energy distribution and density of electron states in the collector, which is of particular importance when characterizing thin layers of solids and their interfaces. In this section the description of the PI/PC methods will be split in two parts, depending on type of electron states participating in the primary optical excitation. The electron transitions between fundamental band states of the collector leading to PC will be considered first; in the next

Internal Photoemission Spectroscopy Methods

(PC yield)1/2 (relative units)

1500

1000 Si Ox 500

0 3

4

Au

139

Fig. 4.26 PC spectra of (100)Si/ oxide/Au samples with various highpermittivity oxide insulators: ZrO2 HfO2 atomic-layer chemically vapour deposited Al2O3, ZrO2, HfO2, Ta2O5 Nb2O5 and TiO2, and for Nb2O5 grown using liquid-source mist deposition Ta2O5 measured at a strength of the electric TiO2 field in the oxide of 1 MV/cm with the metal biased negatively. Lines Al2O3 illustrate the procedure of PC threshold determination. Insert shows electronic transitions in the 5 6 7 oxide responsible for PC.

Photon energy (eV)

section the processes involving localized states in the collector resulting in PI will be addressed. In turn, the discussion on PI will also be separated into two parts. The “real” PI of electron states well isolated electrically from the collector contacts represents the most simple case, whereas, in electron exchange between localized states and the contact, i.e., in localized electron states in the immediate vicinity of the interface, the aforementioned “pseudo-IPE” excitations will be analysed. In contrast to IPE, intrinsic PC is expected to be insensitive to the orientation of the electric field in the collector or to the materials used as the semiconductor or the metal electrode. In turn, for the same strength of electric field, the IPE current is expected to be insensitive to the insulator thickness as long as the carrier trapping probability remains low and the trapping has no measurable influence on the current density. By contrast, the PC current is expected to increase with the thickness of the collector (d) in the range d , 1/α, where α is the optical absorption coefficient in the analysed spectral range. Therefore, analyses of the photocurrent dependence on insulator thickness, electrode material and orientation of the electric field are the experimental criteria to be considered when attributing the observed photocurrent to the IPE or the PC process. Assuming the mean free path of photogenerated charge carriers to be larger than the thickness of the collector layer, the PC current will be proportional to the joint density of states (J-DOS) for optical transitions. In amorphous insulators this dependence is experimentally observed to be close to IphB(hν 2 Eg)2 (DiStefano and Eastman, 1971; Afanas’ev and Stesmans, 2004, 2007), which allows determination of Eg by extrapolation of the current normalized to the incident photon flux nph to zero using (Iph/nph)1/2
hν plot. The applicability of this procedure is illustrated in Fig. 4.26 which compares the PC spectra of samples with six different high-permittivity oxide insulators of 6
20 nm thickness deposited on (100)Si (Afanas’ev and Stesmans, 2004). Being plotted in the (Iph/nph)1/2
hν co-ordinates, the spectra show a well-defined linear portion, which allows determination of the oxide bandgap as the intrinsic PC threshold. One of the remarkable features to be mentioned here is significant bandgap narrowing observed in low-temperature deposited alumina, in which the

140

Internal Photoemission Spectroscopy

Fig. 4.27 PC spectra of (100)Si/ ZrO2/Au samples with different thickness of the oxide (in nm): 10 (x), 50 (&) and 100 (W) measured at a strength of the electric field in the oxide of 1 MV/cm with the metal biased negatively.

4000 (PC yield)1/2 (relative units)

Si(100)/ZrO2/Au 3000

dZrO2(nm): 10

2000

50 100

1000

0 4.5

5.0

5.5 6.0 Photon energy (eV)

6.5

bandgap width appears to be approximately 30% smaller than in the Al2O3 crystal, which amounts 8.7 eV (Bortz and French, 1989; French, 1990). These results indicate that the fundamental electronic structure of the deposited oxides is not necessarily identical to that of the bulk crystal of chemically the same oxide. Again, like the case of IPE, the exponent of the PC spectral dependence can be considered as an independent parameter corresponding to the energy dependence of J-DOS (intrinsic PC) or to the energy dependence of PI cross-section. By using the found exponent one can associate the observed PC with a particular type of optical transition in the same way as is done for optical absorption edge spectra (see, e.g., Pankove, 1975). The important portion of the PC spectra is the sub-threshold region, which potentially might reveal intrinsic or extrinsic band-tail states of the amorphous (or liquid) collector material. Fig. 4.27 shows the PC spectra of the ZrO2 layers of different thickness deposited at 300 C, all exhibiting the same spectral threshold at 5.5 eV (Afanas’ev and Stesmans, 2004). With increasing oxide thickness, a progressively intense sub-threshold PC is observed, suggesting excitation of some states in the bulk of the oxide. As annealing at 800 C is found to have no measurable effect on the relative intensity of the sub-threshold PC, one can exclude the possible presence of different crystalline phases in the zirconia film as the origin of the complex PC spectrum because the phase composition of the film is strongly affected by the high-temperature treatments (Houssa et al., 2001). This result suggests the relationship of the sub-threshold PC to some defect or impurity incorporated into the film during the deposition process. Sub-threshold PC may also originate from excitation of electron states concentrated predominantly near one interface. In this case the spectra of photocurrent obtained with a different orientation of the electric field in the collector may also differ because transport of electrons and holes will not be identical: The carriers of one type will be transported more easily than other if the latter are left in some state with the collector bandgap. An example of such behaviour is provided by near-threshold PC spectra of SiO2 thermally grown on Si(100) (Adamchuk and

Internal Photoemission Spectroscopy Methods

PC yield (relative units)

F (MV/cm)

Si(100)/SiO2

4

141

6.80

3

5.50 3.70 2.27

2

1.36 0.63

1

Fig. 4.28 PC yield (photocurrent per incident photon) as a function of photon energy as measured in a Au/SiO2(55 nm)/Si(100) structure under negative bias on the metal electrode corresponding to the strength of the electric field in the oxide indicated in the figure.

0.18 0 7

8

9 Photon energy (eV)

10

Yield (relative units)

2

Q/I (R. U.)

1.0 0.5 0.0 8

1

9 hν(eV)

10

Si(100)/SiO2

0 8.0

8.5

9.0 9.5 Photon energy (eV)

Fig. 4.29 Spectral curves of quantum yield of photocurrent (x) and positive photocharging (&) measured in the vicinity of intrinsic PC threshold of SiO2 in Au/SiO2(160 nm)/Si(100) structures with positive bias on the metal field electrode. The latter corresponds to the average strength of the electric field in the oxide of 1.1 MV/cm. The insert shows the photocharging/photocurrent ratio as a function of the photon energy.

10.0

Afanas’ev, 1992a,b). Although the spectra obtained with positive bias of the field electrode of Au/SiO2/Si capacitor exhibit a clear shoulder at around hν 5 8.5
9 eV, shown in Fig. 4.28, no such sub-threshold PC is seen if the measurements are repeated in the same sample when the metal electrode is biased negatively. In the last case the PC yield increases as (hν 2 Eg)2, leading to the intrinsic PC threshold of 8.9 eV which is in good agreement with earlier observation (DiStefano and Eastman, 1971). The inference that the PC signal measured at hν , 9 eV originates not from the intrinsic PC but from excitations of some other type is also supported by comparison of photocurrent to photocharging exemplified by the data shown in Fig. 4.29. The spectral dependence of the positive photocharging rate (&) is observed to follow that of the photocurrent (x) only for hν . 9.3 eV, which can logically be explained by generation of holes in SiO2 followed by their drift towards Si substrate and subsequent capture by the “detecting” defects
hole traps. It is likely that these processes occur in the same way if photons are absorbed in the bulk of the SiO2 collector layer. At lower photon energies a reduced value of the photocharging/photocurrent ratio is found, as shown in the insert. The latter indicates a

142

Internal Photoemission Spectroscopy

lower efficiency of the positive charge trapping, suggesting that photogeneration of holes in the spectral range below 9 eV occurs not in the VB of the SiO2 layer but in a somewhat different way. A large photocurrent signal without a corresponding hole trapping rate suggests that most of the current is carried by electrons while the holes are apparently left close to Si substrate and neutralized by electron tunnelling (Adamchuk and Afanas’ev, 1992b). Thus, the sub-threshold PC in Si/thermal oxide structures is associated with excitation of near-interface defects and energy levels close to the top of the oxide VB. The example of the collector PC analysis in Si/SiO2 structures demonstrates the most complex problem of the method, which consists in identification of the observed PC threshold with the oxide bandgap or, alternatively, with the ionization energy of some imperfection-related state. As a general way of reasoning, one may argue that the imperfection-related states must be much more sensitive to the details of fabrication and processing of the collector layer (and of the whole sample) than the intrinsic (fundamental) properties. Indeed, in the case discussed of Si oxidation, the change of technological parameters is seen to affect the subthreshold PC drastically (cf. fig. 41 in Adamchuk and Afanas’ev (1992a)). An even more striking example of sensitivity of the sub-threshold PC to the collector processing details is provided by PC spectra of SrxTi12xO3 films crystallized by annealing on top of SiOx or TiNx underlayers. The spectral curves shown in Fig. 4.30 indicate that the intrinsic PC observed in the spectral range hν . 3.5 eV is marginally sensitive to the bottom electrode composition yielding the same bandgap width of 3.3 eV, as illustrated in the insert. At the same time, the sub-threshold PC signal is enhanced by two orders of magnitude in the sample annealed on top of the oxygen-free TiNx electrode. The latter effect may be related to the generation of O-deficiency related centres in the insulator during crystallization anneal with an energy level at Et 5 0.8
0.9 eV below the CB of SrTiO3 (Manger et al., 2009). This example shows how the criterion of reproducibility between different material fabrication technologies can be used to separate fundamental excitations from those that are imperfection or impurity related.

10–3

Au/Sr0.54Ti0.46Oz/SiO3/Si Au/Sr0.63Ti0.37O3/TiNx/Si d (SrTiO3) = 27 nm

10–5

V = –2 V

10–6 0.0008

10–7

Eg = 3.3+/–0.1 eV

0.0006

10–8

Et = 0.8 – 0.9 eV

0.0004

10–9

0.0002 Y 1/2

Yield (relative units)

10–4

10–10

0.0000 2.0

2.5

3.0

10–11 2

3

4 5 Photon energy (eV)

3.5 hν (eV)

6

Fig. 4.30 Spectral curves of the photocurrent yield as measured on 27-nm thick SrTiO3 films deposited on top of SiOx (x) or TiOx (&) underlayers and subsequently crystallized by 1.5 s annealing in N2 at 650 C. The measurements are made under 22 V bias applied to the top Au electrode. The insert illustrates determination of the PC spectral thresholds using Y1/2
hν plots.

Internal Photoemission Spectroscopy Methods

143

One may also try to analyse the field-dependent PC to obtain additional information about the origin of the final electron state in the corresponding optical transition. For instance, the simple model of electron escape from the potential well of a hole it leaves behind (cf. Fig. 3.4) predicts exponential behaviour of the photocurrent on the inverse square root of the electric field, as given by Eq. (3.14) (Adamchuk and Afanas’ev, 1992a). By using this model one can extract the mean free path of a carrier ‘ with respect to thermalization as a function of photon energy. For the discussed example of SiO2 PC the procedure of ‘ determination is illustrated in Fig. 4.31(a), which shows the logarithmic plot of photocurrent as a function of (F)21/2 as observed at different energies of the exciting photons. The corresponding plot of ‘ as a function of photon energy shown in Fig. 4.31(b) reveals a remarkable feature, namely a much larger mean free path of electron found in the spectral range hν , 9.3 eV than at a higher photon energy. This behaviour would indicate that the average kinetic energy of electrons excited in the former spectral range is higher than of electrons dominating the photocurrent at, say, hν  10 eV. Such a “decrease” in the average energy of electrons with increasing photon energy is only possible if optical excitation in the low photon energy range is dominated by transitions from some electron state in the oxide bandgap, thus supporting the above analysis of the sub-threshold PC in the Si/SiO2 structures. Interestingly, if assuming the electron mean free path ‘ to be determined by energy losses caused by interaction with LO phonons in SiO2 as it happens in electron IPE from a contact, one may determine the threshold of the fundamental PC from analysis using a constant LO phonon emission rate above the threshold of (B) /2

8 SiO2

~(

6 Eg (SiO2) 4

5 4

2 1

0

0.5

6

3

h ν(eV): 8.86 9.16 9.23 2 9.68 10.18 10.81

0.0

hν

)1 g –E

Mean free path (nm)

log (photocurrent) (relative units)

(A)

1.0

1.5

2.0

(Field)–1/2(MV/cm)–1/2

8.5

9.0

0 9.5 10.0 10.5 11.0 11.5 Photon energy (eV)

Fig. 4.31 (A) PC current per incident photon as a function of the inverse square root of the electric field in the oxide of Au/SiO2(160 nm)/Si(100) structures measured under excitation by photons of different energy hν. Lines indicate the linear fit used to determine the mean free path of an electron ‘. (B) The mean free path of an electron ‘ as a function of photon energy in the vicinity of spectral threshold of SiO2 PC. The solid line shows the approximation of the intrinsic PC portion of the curve by the function ‘B(hν 2 Eg)1/2. This fit yields the oxide bandgap width Eg(SiO2) 5 8.9 eV indicated by the arrow.

144

Internal Photoemission Spectroscopy

their excitation (Fitting and Friemann, 1982). In this case the probability of phonon emission will be proportional to the time an electron remains in the potential well of a hole, which will decrease with electron energy as the first power of its velocity in the CB of SiO2. Therefore, one may write ‘B(hν 2 Eg)1/2, which expression fits well the high-energy portion of the curve shown in Fig. 4.31 yielding Eg 5 8.9 eV. The advantage of this method consists of the insensitivity of the results to the substantial variation of optical constants of SiO2 in the used photon energy range. However, the proposed simple description of electron
hole dissociation relies on the ballistic character of electron transport after optical excitation and may not necessarily be valid in an arbitrary collector material.

4.5

PI Spectroscopy

The optical ionization of localized electron states in the collector with energy levels corresponding to the collector bandgap may lead to generation of photocurrent that bears information about defects or impurities present in the collector material. This kind of measurement may be of particular value if the research is focussed on the properties of the collector itself because the energies of the found states can be directly compared to the band diagram of the emitter
collector-field electrode structure found from the IPE and PC experiments. The major difficulty here consists in the identification of the electron transition involved in the PI, in other words in the determination of charge sign of the carrier photoexcited from the localized state into the transport band of the collector. In the most straightforward way this problem can be resolved by directly observing the variation of electric charge in the collector caused by the PI transitions by measuring the shift of the capacitance
voltage curves of MIS structures (Mehta et al., 1972; Jacobs and Dorda, 1977a,b; DiMaria et al., 1978). One may apply more sophisticated tools aimed at monitoring the collector surface potential, ranging from the conventional Kelvin probe to techniques enabling lateral resolution like scanning tunnelling microscope (Im et al., 1999) or photoelectron emission microscope (Siegrist et al., 2004).

4.5.1

PI of Bulk Traps

In the core of PI analysis lies the assumption of linear dependence of the process rate on the photon flux nph(hν) and the number of localized states (traps) Nt(hν) available for optical excitation at a given photon energy hν: @Nt 5 σph ðhνÞnph ðhνÞNt ðhνÞ; @t

ð4:10Þ

where σph(hν) represents the cross-section of PI. The problem with direct application of Eq. (4.10) is related to the fact that σph(hν) is also a function of the electron

Internal Photoemission Spectroscopy Methods

145

level energy Et and is usually expressed as a function (hν 2 Et), see, e.g., eqs. (5.2.40
5.2.42) in Landsberg (1991) or figs 1 and 2 in Lucovsky (1965). Therefore, if a trap distribution Nt(Et) is present in the sample, the PI rate normalized to the photon flux (i.e., the PI quantum yield) will be proportional to the integral over the distribution of traps lying within the energy of hν from the edge of the band to which charge carriers are excited (see, e.g., DeKeersmaecker and DiMaria, 1980): Yph ðhνÞ ~

ð hν

Nt ðEt Þσph ðhν 2 Et ÞdEt ;

ð4:11Þ

0

where zero energy corresponds to the edge of the band. From Eq. (4.11) one can easily see that the PI signal is actually proportional to the convolution of the trap energy distribution and the energy-dependent PI cross-section, which excludes simple analysis and necessitates additional experimental efforts. Potentially, one may consider two modes when measuring PI as a function of photon energy: the “fast” and “slow” spectral sweep (Kapoor et al., 1977a,b). In the “fast” hν sweep mode the occupancy of initial states of the PI process is assumed to remain unchanged during the whole measurement time. The resulting PI yield in this case, both in terms of current and charge, can be expressed using the integral given by Eq. (4.11). The only information available in this case is the energy onset of the PI process, which can be considered either as the energy level of the localized state (if a well-defined state structure is discussed) or as the upper edge of the localized state distribution. An example of experimental results corresponding to the former case is shown in Fig. 4.32, in which the photocurrent yield is shown for the Si(100)/SiO2 structure before (x) and after incorporation (&) of a large density of H-passivated Si dangling bond defects (O3RSiaH entities) into the oxide by exposing it to 10-eV photons (Afanas’ev and Stesmans, 1997a). The control (pre-irradiation) spectrum shows two spectral thresholds Φ1 and Φ0

105

Yield (relative units)

104

Si(100)/SiO2

103 102 Φ0

101 100

Φ1

Φ1 Φ2

10–1

Et Φ2

10–2 3

Φ0 4 5 Photon energy (eV)

6

Fig. 4.32 Photocurrent quantum yield as a function of photon energy measured at the electric field strength in the oxide of 4 MV/cm under positive metal bias in the control Si/SiO2(66 nm)/Al structure (x) and in those exposed to 1 3 1019 10-eV photons cm22 without (&) and with subsequent H2 anneal at 400 C (Δ) followed by injection of 1018 electrons/cm2 from Si. The arrows indicate the observed IPE and PI spectral thresholds whose schemes are clarified in the insert.

146

Internal Photoemission Spectroscopy

corresponding to the excitation of electrons from the near-interface defects generated during oxide growth and from the VB of Si crystal, respectively. Incorporation of defects to the oxide and filling them by electrons using their avalanche injection from Si results in considerable negative charge accumulation. Subsequent exposure to a monochromatic light reveals additional photocurrent with spectral threshold Φ2, which may be correlated with a decrease of the negative charge. As the latter is observed to occur at both bias polarities and irrespectively of the strength of the electric field in the oxide, the excitation of electrons from the negatively charged centres to the SiO2 CB represents the most logical way to describe the process. Assuming that the defects of the same atomic structure, i.e., O3RSiaH, have the same energy level of the trapped electron, one may simply determine the energy of this level with respect to the SiO2 CB by extrapolating the PI current to zero in the YPI1/2
hν co-ordinates, which appear to fit experimental data reasonably well, as shown in Fig. 4.33. However, in addition to the threshold Φ2 5 3.1 eV, one also finds there a significant increase of the PI signal above 4 eV, which is indicative of the second transition threshold from the same (O3RSiaH)2 or to an additional defect bath. The same trend is observed both in the PI current and charge measurements (cf. Fig. 4.33(b)), and all the trapped electrons can be removed during extended illumination by photons with hν , 4 eV. Then the excitation of second transition, possibly from a SiaH bond in the negatively charged O3RSiaH entity appears to be the likely explanation of the second PI threshold. What is important here is that the PI spectrum recorded in the “fast” hν sweep mode cannot be seen as a replica of the localized state energy distribution in the collector bandgap. In this sense PI differs from the IPE significantly. (A)

(B)

(Yield)1/2 (relative units)

3

4 Charge 3

2 2

Traps Si

1

SiO2 1 Current

0

0 3

4

5 3 4 Photon energy (eV)

5

Fig. 4.33 (A) Photocurrent quantum yield as a function of photon energy in the Si/ SiO2(66 nm)/Al structure exposed to 1 3 1019 10-eV photons cm22, annealed in H2 (400 C, 30 min) and subjected to the avalanche electron injection from Si to the dose of 1018 electrons/cm2. The points are taken at the electric field strength in the SiO2 of 0.5 (x), 1.0 (&) and 2.0 MV/cm (Δ) with the metal biased positively. (B) Photocurrent quantum yield as a function of photon energy in the same structure measured for an oxide field of 1 MV/cm with the metal biased positively (x) or negatively (&) and the PI (the photodischarging) yield measured with F 5 3 MV/cm (Δ) under positive metal bias.

Internal Photoemission Spectroscopy Methods

147

To obtain information about the energy distribution of the ionized localized states, not being weighted by their energy-dependent σph, Thomas and Feigl (1970) introduced the “slow” photon energy sweep mode in which the measurement time Δt at each spectral point is postulated to exceed by far the time constant of the (quasi-)exponential PI current decay. This condition actually means integration of the PI response over the time Δt which allows one to collect at every measurement point a significant portion of charge available for PI at a given photon energy. The problem with this kind of measurement is in the necessity to detect a low photocurrent over an extended period of time, which makes it highly sensitive to the dark (leakage) current and to the drift of the measurement equipment. As an extreme case of the “slow” sweep method, it was proposed to perform the optical (dis)charging measurements not in the small-signal mode as described in Chapter 3 (cf. Eq. (3.23)) but by tracing the charge kinetics to its saturation at incremental photon energies (Afanas’ev and Stesmans, 1999b). An example of such a trace obtained in a SiO2 sample containing charged Si clusters is presented in Fig. 4.34, which shows the kinetics of flatband voltage shift measured in a Si/ SiO2/Au capacitor under the condition of hν increment once less than 20% relative variation of the de-trapped charge is attained. The latter would mean that nearly all the traps depopulated at the selected photon energy are energetically located in a narrow spectral window equal to the increment of the photon energy with respect to the preceding PI step. This allows immediate determination of the trap spectral density per unit sample area, thus providing the most straightforward DOS results (Afanas’ev and Stesmans, 1999b). Moreover, from the PI kinetics at each hν, one directly extracts the PI cross-section which is now also relevant to the narrow “slice” of the localized state energy distribution. In this way a complete characterization of the electron state through its PI parameters can be achieved. Another advantage of direct charge monitoring consists of the possibility of separate PI transitions originating from electron states with different signs or values for the initial charge. This possibility is exemplified in Fig. 4.35 by DOS

ΔVFB (Volt)

10

Fig. 4.34 Shift of the flatband voltage VFB on the capacitance
voltage curve in a Si/SiO2/Au sample with the oxide containing Si clusters as a function of the illumination time (Afanas’ev and Stesmans, 1999b). The photon energy hν increases from 3.25 to 3.52 eV in B0.1 eV steps.

Clusters Si SiO2

5

hν (eV): 3.25

3.42

3.33

3.52

0 0

100

200

300

Illumination time (min)

400

148

Internal Photoemission Spectroscopy

60

(A)

Fig. 4.35 Density of oxide gap states in Si/SiO2/Au samples with SiO2 layers containing clusters of different size as determined from PI measurements using 0/1 (dashed line) and 2/0 (dotted line) transitions as a function of energy below the SiO2 CB. The cluster size is characterized by electron capture radii of 2, 3, 1 and 0.5 nm in samples (A
D), respectively (see Afanas’ev and Stesmans (1999b) for details).

–/0

40 0/+

20 0 60

–/0

(B)

DOS (1011 cm–2 eV–1)

40

0/+

20 0 20

–/0

(C)

0/+ x5

10 x1 0 6

(D) 0/+

4

0

x1

–/0

2 2

x50

3

4

5

E – EC (SiO2) (eV)

histograms of Si clusters determined in the course of the exhaustive PI measurements just discussed (Afanas’ev and Stesmans, 1999b). Panels (a
d) correspond to the SiO2 layers containing clusters of different effective radius characterized through their electron capture cross-section. The dashed distributions correspond to the PI of clusters resulting in the generation of positive charge in the initially electrically neutral oxide, i.e., to the 0/ 1 transition of the cluster. The dotted curves correspond to the neutralization of negative charge trapped on the clusters in the course of pre-PI electron injection, i.e., these transitions correspond to 2/0 cluster transition or to the compensation of its charge by the positive charge of the neighbouring cluster. The results reveal nearly the same energy onsets of the 0/1 and 2/0 transitions in all the cases except the sample (d) with the smallest clusters, suggesting the transitions are dominated by some common electron state likely to be associated with some defect at the cluster/oxide interface. Remarkably, the energy onset of the PI transitions is seen to be close to the earlier discussed threshold (Φ2 5 3.1 eV) of trapped electron emission from the negatively charge O3RSiaH fragment in SiO2. Only in the smallest clusters in sample (d) are the shallow electron states expected from the quantum confinement considerations observable in 2/ 0 transitions, suggesting that the small cluster surface area makes only a few O3RSiaH states available.

Internal Photoemission Spectroscopy Methods

(A)

149

Fig. 4.36 (A Illuminationinduced charge density variation in (100)Si/SiO2(4 nm)/ γ-Al2O3(20 nm)/Au(15 nm) capacitors in the neutral state (’) and after electron injection (W) as a function of photon energy. The samples were exposed to monochromatic light for 3 h at each photon energy. (B) SCD corresponding to the trap energy distribution as a function of trap energy below the CB of alumina layer as inferred from the photodepopulation spectra.

1

Charge (μC cm–2)

0 Uncharged After electron trapping

–2

γ-Al2O3

–4

–6

Spectral charge density (1012 cm–2 eV–1)

(B) 20

10

0

–10

Uncharged After electron trapping 0

1

2 3 4 Photon energy (eV)

5

6

Although the above results indicate great potential for exhaustive PI spectroscopy of electron states in the collector material, the applicability of this method depends on the possibility of preserving the desired charge of the analysed electron state without significant changes during the time needed for PI spectral measurements. This limits the possible collector materials to the wide-bandgap insulating layers of sufficient quality. Nevertheless, this method enables one to determine the trap-related DOS in absolute terms of density per unit area per electron volt, as is demonstrated in Fig. 4.35. Although the demonstrated concept of exhaustive photodepopulation spectroscopy has initially been proposed to characterize electron states that belong to clusters imbedded in the insulating matrix, there are no reasons for not using this technique to find the density of electron states related to defects in the collector layers. In several recent studies (Wang et al., 2009, 2012; Zahid et al., 2010) it has been shown that the energy distribution of trapped electrons can be determined using essentially the same PI approach. To illustrate the potential of this method, Fig. 4.36 shows the illumination-induced oxide charge variations (top panel) and the spectral charge density (SCD) distributions (bottom panel) measured in (100)Si/ SiO2(4 nm)/γ-Al2O3(20 nm)/Au samples. One of the samples has been analysed in the neutral pristine state (filled symbols) whereas the other was injected by

150

Internal Photoemission Spectroscopy

electrons using Fowler
Nordheim tunnelling through the 4-nm thick SiO2 barrier layer (open blue symbols) when applying a 120 V pulse to the top metal electrode. As is observed from the shift of the flatband voltage point (VFB) on the capacitance
voltage curves, electron injection leads to accumulation of negative charge indicating the presence of traps in the alumina layer. Upon subsequent illumination under 11 V metal bias the density of trapped electrons decreases. The absence of any significant charging of the control neutral sample indicates that there is no charge compensation due to PI of donor states and, therefore, the removal of negative charge can be associated with photodepopulation of electron traps. Because the photodepopulation results shown in the top panel of Fig. 4.36 are obtained by a stepwise (0.3 eV) increase of photon energy from 1.3 to 6.5 eV and the saturation of the VFB shift was reached at every photon energy, the amount of trapped electron charge “lost” at every illumination step corresponds to the density of trapped electrons in the given 0.3-eV energy interval below the γ-Al2O3 CB. This allows one to convert the charge variations into the SCD values and plot them inside the corresponding energy interval as is shown in the bottom panel, resulting in the distribution diagram of trap depth energy. The remarkable feature of this result, also reproduced in several different deposited oxide insulators (Wang et al., 2009, 2012; Zahid et al., 2010), consists of a very broad (2 eV wide) energy distribution of the trap energy levels. Basically, one should consider the presence of a continuum of trapping levels in the insulating film rather than the discrete energy levels conventionally invoked in classic solid-state physics.

4.5.2

PI of Near-Interface States in the Collector: The Pseudo-IPE Transitions

In the previous section the PI process was described under assumption that the excited localized electron states with energy levels in the bandgap of the collector cannot communicate electrically with the emitter or with a conducting field electrode. This approximation is likely to be valid in emitter/collector and the field/electrode collector interfaces of high quality and with high defect or impurity density in the bulk of the collector. It is possible, however, that chemical interactions at the interfaces of the collector or their contamination in the process of fabrication will lead to an enhanced density of electron energy levels within the collector bandgap. These states will be constantly re-filled by electron tunnelling from an electrode and, at the same time, may contribute to the PI transitions without, however, being exhausted by a prolonged PI (cf. Fig. 1.9). An important feature of this kind of PI process is that it leads to injection of one type of charge carrier, possibly at only one interface, which makes it very similar to IPE. However, neither the optical excitation nor the transport of the excited carrier is relevant to the electron states of the emitter. For this reason this process was denoted in Section 1.6 as pseudo-IPE. As one can see from the scheme of this photoinjection process in Fig. 1.9, optical excitation in this case occurs entirely inside the collector material, leading to a greatly enhanced effective carrier escape cone (close to 2π at all the excitation

Internal Photoemission Spectroscopy Methods

151

energies) compared with the narrow and energy-dependent electron escape cone in the Fowler model of photoemission given by Eq. (3.5) and illustrated in Fig. 3.2. In addition, the energy of the excited state in the PI process is still smaller than the collector bandgap width, which means that the only mechanism of its relaxation in energy is interaction with phonons. The latter is much less efficient than the inelastic electron
electron scattering in IPE from metals or narrow-gap semiconductors. Thus, the lifetime of the excited state in the process of PI, including the pseudoIPE excitations, will probably greatly exceed the lifetime of excited charge carriers in IPE from an emitter. These two features, the larger escape cone and the longer lifetime of the excited state, make the escape of a carrier from the excited state of the PI in the collector much more probable than that from the state optically excited inside the emitter. For this reason the quantum yield of the pseudo-IPE may be large even if the density of the contributing initial states in the bandgap of the collector remains far lower than the density of occupied electron states in the emitter in the same energy range (cf. processes B and A in Fig. 1.9). In some cases the photocurrent originating from the pseudo-IPE may bury the real IPE signal entirely. There are two crucial questions about the pseudo-IPE photocurrent. First, how can this signal be separated from the conventional IPE; in other words, how do we identify the source of the photocurrent observed? Second, what kind of physical information can possibly be extracted from the pseudo-IPE current spectra? A simple way to address the first question is to check the correlation between the observed photocurrent and the variations of DOS in the emitter electrode. In IPE the current is directly correlated with the density of initial states whereas PI/pseudo-IPE current will be sensitive to the density of initial gap states in the collector. A good example of such an approach is given by identification of the photon-stimulated tunnelling (PST) current in Si/SiO2 structures (Afanas’ev and Stesmans, 1997b,c), in which the signal was traced as a function of the electron density in the CB of Si varied through intentional doping with phosphorous donors. From the data obtained on the sample with just one donor concentration (Fig. 4.37), it appears that the current at different photon energies and fields can be well described if assuming the rate-limiting step to be the electron tunnelling from some optically excited state. By using the model of electron tunnelling from the Si CB into SiO2 (Weinberg 1977, 1982), one can fit the data as indicated by lines in panel (a) and determine the energy of initial electron state and the density of electron in this state as functions of the electric field (panel (b)). What is unusual in the latter plot is that the density of electrons contributing to the photoexcitation and subsequent tunnelling from the excited state into the oxide has the field onset at about 2 MV/cm, which is inconsistent with assumption that photoexcitation occurs inside the silicon emitter. The most straightforward way to resolve this discrepancy is to change the Si doping level and then trace the PST current with the current of conventional IPE of electrons from the silicon CB which can be observed at somewhat higher photon energy, as shown in Fig. 4.26. The results for crystals with different concentrations of electrons in the CB of the semiconductor are summarized in Fig. 4.38, which compares behaviour of the quantum yield of IPE and PST. In IPE, the linear

152

Internal Photoemission Spectroscopy

Fig. 4.37 (A) Relative yield of PST at the (111)Si/SiO2 interface as a function photon energy at different strengths of the electric field in the oxide, denoted in megavolts per centimetre. The lines represent fitting results. (B) Binding energy EB of the initial state of the PST transition (cf. insert) and the pre-exponential factor A as functions of the electric field obtained from the data fitting. Curves are guides to the eye.

Yield/(Field)2 (relative units)

(A) F (MV/cm): 2.7 3.1 3.4 3.8 4.2 4.6 5.0 5.4 5.7 6.5

102

101

100

10–1 2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

3

150

2

100

EB (eV)

(B)

EB

1

50

A (relative units)

Photon energy (eV)

hν

0

0 0

1

2

3

4

5

6

Field (MV/cm)

relation between the yield and the electron density is evident. However, no correlation between the PST transition rate and the electron density in the Si CB is seen. The latter result clearly indicates a different source of electrons in the PST process than the CB of silicon. The data shown in Fig. 4.38 may also be used to illustrate another approach to identification of the initial electron state (Afanas’ev and Stesmans, 1997c). If the same collector material (SiO2) is applied to different emitter materials (Si or different polytypes of SiC), the variation of the supposed initial state energy (the bottom of the semiconductor CB) will directly affect the energy derived from the PST analysis. The energy positions of the CB for several emitter crystals measured with respect to the collector CB (which represents the final electron state in PST) are indicated in Fig. 4.38 by arrows (Afanas’ev et al., 1996a). The symbols show the energy of initial state EB in the PST transitions observed at the relevant interfaces as determined from the PST current analysis. It is clearly seen that the energy of this initial state is uncorrelated with the band structure of the semiconductor, which would mean that it belongs to a SiO2 collector rather than to an emitter

Internal Photoemission Spectroscopy Methods

101

IPE

3.2 Energy (eV)

n,p–(100)Si 100 3.0

(0001)6H-SiC 10–1

2.8

PST

Yield (relative units)

n+–(100)Si

153

(0001)4H-SiC 10–2 2.6 1014 1015 1016 1017 1018 1019 1020 1021 1022 Conduction electron concentration (cm–3)

Fig. 4.38 Energy EB of the initial state of PST transitions measured relative the CB of SiO2 at the interfaces with (100)Si (x), (111)Si (&), (0001) 6H-SiC (Δ) and (0001) 4H-SiC (r) for different nominal concentrations of electrons in the substrate. The solid arrows indicate the CB offsets at the corresponding interfaces as determined from IPE spectroscopy. The relative yield of PST (red circles) and IPE (green squares) at the interfaces of SiO2 with (100)Si are also shown. Lines are guides to the eye.

(Afanas’ev and Stesmans, 1997c). The latter conclusion has found independent support from the observation that the method of SiO2 fabrication (thermal oxidation of Si, chemical vapour deposition, implantation of O1 ions) has a marked impact on the PST quantum yield while the electron band structures of the Si crystal and the oxide itself remain largely unaffected (Afanas’ev and Stesmans, 1997d,e). One may further refine the model of the process by observing PI of the same state when the strength of field in SiO2 is kept above the 2 MV/cm onset value needed to provide electrons to the oxide gap states, as revealed by PST analysis. These PI results are shown in Fig. 4.39 for several field strength values rewardingly yielding the same energy of the initial electron state as the PST current data analysis. The scheme of the corresponding electron transition is shown in the insert, indicating the two-step process of the pseudo-IPE in which the PI of the oxide gap states represents the rate-limiting step. From the results discussed earlier, one may sketch two approaches to the identification of the photocurrent generation mechanism. First, one might attempt to trace the sensitivity of the photocurrent spectra to the known features of electron DOS in the emitter. In addition to the variation of the carrier concentration and the energy of the bands (by varying the emitter material), it is also possible to associate the optical singularities and onsets of electron scattering processes with the IPE from the states excited inside the emitter material. One can see, for instance, that the optical singularities of a Si crystal at points E1  3.4 eV and E2  4.4 eV are universally observed in the IPE spectra from this semiconductor into different

154

Internal Photoemission Spectroscopy

Yield (relative units)

1.5

δ (h ν) = 0.05 eV

1.0

5.7 MV/cm hν

0.5

2.3 MV/cm

0.0 2.8

IPE yield (relative units)

Fig. 4.39 Quantum yield of defects PI at the Si(111)/SiO2 interface as a function of photon energy for strengths of the electric field increasing from 2.3 to 5.7 MV/cm. The insert shows the schematics of the observed pseudo-IPE electron transitions. The arrows indicate the energy width of the monochromator slit.

3.0 3.2 Photon energy (eV)

Si(100)/SiOx/ZrO2 F = 3 MV/cm 1.0

500°C × 60 min

650°C × 30 min as-deposited

0.5 800°C × 10 min 0.0

2.4

3.4

Fig. 4.40 IPE yield as a function of photon energy for n-Si/7.4 nm ZrO2/ Au MOS structures in as-deposited state and after supplementary oxidation at the indicated thermal budgets. The measurements are done with an applied field strength in the ZrO2 layer of 3 MV/cm, the metal biased positively. The error in the yield determination is smaller than the symbol size.

2.6 2.8 Photon energy (eV)

collector materials (cf. Fig. 2.7, Figs 4.6, 4.7, 4.8, 4.11 and 4.14), provided the IPE threshold energy is lower than that of the optical feature. Second, it is also possible to affect the properties of the near-interface layer of the collector to track possible pseudo-IPE excitations. The marginal sensitivity of the spectral thresholds to the type of interlayer would in this case indicate the IPE from the emitter: One may see that at the interfaces of Si with HfO2 the chemical composition of the interlayer (SiON or O-free Si3N4) has only a little influence on the spectral curves (cf. Fig. 4.7). Analysis of the low-energy of photocurrent spectra for the Si(100)/ZrO2 interface delivers the opposite result: The photocurrent yield is seen in Fig. 4.40 to decrease dramatically after oxidation of the sample in O2 at 650 C. This treatment results in the growth of a SiOx-like interlayer, which apparently affects the electron occupancy of gap states in zirconia leading to the photocurrent; this excitation can be identified as the pseudo-IPE process. Now one may address the second question about the kind of physical information that can be extracted from analysis of the pseudo-IPE photocurrents.

Internal Photoemission Spectroscopy Methods

155

The threshold of the PI transition is determined by the barrier between the uppermost occupied electron state in the collector and the lowest unoccupied energy band. (One may, in a similar way, define the barrier for the case of hole photoexcitation.) Although the band edge energy remains the fundamental property of the collector, the energy distribution of electrons in states within the collector bandgap will be determined by two factors: the energy distribution of the available levels and their electron occupancy function. The latter, in turn, is determined by the Fermi energy in the nearby electrode as well as by the distribution of electrostatic potential across the interface. If one were to consider an ensemble of states with identical atomic structure, the levels of these states might also be expected to be close in energy. Therefore, their PI will occur with the spectral threshold corresponding to this energy provided the electrons can be supplied from an electrode. As a result, the pseudo-IPE threshold, if observed, is expected to be marginally sensitive to the electron structure of the “emitter”, which serves only as the source of electrons needed to re-fill the gap states. Another possibility concerns the quasi-continuous energy spectrum of gap states or a wide trap distribution in energy, which is expected to occur in strongly disordered systems and is frequently encountered in deposited oxide insulators (Wang et al., 2009, 2012); see, e.g., the results for Al2O3 in Fig. 4.36. In the presence of a wide trap level distribution, the upper edge of the occupied states will probably be determined by the Fermi level of the nearby (semi)conducting electrode. In addition, it might also be affected by the variation of the electrostatic potential across the depth of electron exchange between this electrode and the collector gap states. In this case, one may expect a certain sensitivity of the pseudo-IPE threshold to the Fermi energy of the “emitter” accompanied by a strong sensitivity of this threshold to the applied electron field. The latter is related to the tunnelling mechanism of electron exchange between the gap state and the electrode which supplies the carriers to traps located at a larger depth in the collector away from the interface with increasing strength of electric field. This is most difficult to analyse because the pseudo-IPE photocurrent behaviour closely resembles that of the conventional IPE. One may attempt to “decouple” the trap-assisted photocurrent from the true IPE using a variety of approaches, for example by tracing the dependence of the photocurrent on the density of charge carriers available for photoexcitation in the emitter (Afanas’ev and Stesmans, 1998b) or on the intensity of photoexcitation (Fereiro et al., 2013). It seems, however, that the controlled modification of the collector material DOS ensuring significant variation of the Fermi level represents the most reliable way to distinguish between true IPE and the trap-assisted transitions (Afanas’ev, 2013). Some of the problems outlined in the identification of the dominant photocurrent excitation mechanism are exemplified by the electron IPE spectra from different metallic conductors, as shown in Fig. 4.41 using the Fowler co-ordinates for two insulating collector materials: (a) a chemical vapour deposited (CVD) SiO2 and (b) a spin-on deposited porous methyl-silesesquioxane (p-MSQ) (Shamuilia et al., 2006). In the former case, the thresholds of IPE from the same metal into thermal SiO2 on Si are shown by an arrow for comparison. One may notice two effects: First, the

156

Internal Photoemission Spectroscopy

9

(A)

Ta

CVD SiO2

8 7 6 Ox

5

-

Φ

Al TaNx Au

~1 eV

Me TaNx

4 Thermal SiO2

Yield1/2 (relative units)

3 2

Al

TaNx

Al Au

Au

1 0 (B)

p-MSQ (κ = 2.3)

6

Au Al TaNx

5 4 3

ΔΦ = 0.2 eV

2 1 0 2.5

3.0

3.5

4.0

4.5

5.0

Fig. 4.41 (A) Fowler plots of the electron IPE yield at interfaces of 100-nm thick CVD SiO2 with Ta (x), TaNx (&), Al (W) and Au (e) electrodes measured at the same bias of 210 V on the metal. Lines illustrate the determination of the spectral threshold. The spectral thresholds of IPE from these metals into thermally grown SiO2 on Si are indicated by bold arrows for comparison. The insert shows the metal/insulator interface band diagram in the ideal case (solid lines) and in the presence of a negative polarization layer (dashed curve). (B) Fowler plots of electron IPE yield at interfaces of 190 nm thick p-MSQ with Au (V), Al (¢) and TaNx (’) layers compared with the interfaces of Al(W) and Au(e) with the deposited SiO2.

5.5

Photon energy (eV)

thresholds of photoexcitation are considerably higher for the deposited oxide; second, the sensitivity to the metal type nearly disappears (cf. data for Al and Au). This insensitivity to the Fermi energy of the conducting electrode suggests the dominance of the pseudo-IPE process involving some states with a well-defined energy level. The fact that these states are observed at close energies in both CVD SiO2 and p-MSQ matrices suggests that they do not constitute an element of the collector material network but, more likely, are related to some extrinsic species, for instance adsorbate (e.g., water) molecules. As an additional complication to the picture, one might notice the spectral threshold variation in the interface of Ta and TaNx with CVD SiO2, which appears in correlation with the application of a plasma-assisted interface formation process. The latter is likely to affect the charge density in the nearinterface collector layer, changing the electrostatic potential variation shown in the insert in Fig. 4.41(a).

References Adachi, S., 1988. Model dielectric constants of Si and Ge. Phys. Rev. B. 38, 12966
12976. Adamchuk, V.K., Afanas’ev, V.V., 1984. Determination of the band gap of a thermal oxide on silicon. Sov. Phys.: Solid State. 26, 1519
1520.

Internal Photoemission Spectroscopy Methods

157

Adamchuk, V.K., Afanas’ev, V.V., 1985. Barrier energy determination at the semiconductor
insulator interface. Sov. J. Phys. Chem. Mech. Surf. 4 (10), 42
47 (in Russian). Adamchuk, V.K., Afanas’ev, V.V., 1992a. Internal photoemission spectroscopy of semiconductor
insulator interfaces. Prog. Surf. Sci. 41, 111
211. Adamchuk, V.K., Afanas’ev, V.V., 1992b. Photocharging technique for barrier determination on semiconductor
insulator interface. Phys. Status Solidi (a). 132, 371
379. Adamchuk, V.K., Afanas’ev, V.V., Akulov, A.P.H., 1988. Disordering of silicon surface during thermal oxidation. Sov. J. Phys. Chem. Mech. Surf. 7 (12), 106
111 (in Russian). Afanas’ev, V.V., 1991. Electron scattering in the image force potential well during photoemission into insulator. Sov. J. Phys. Chem. Mech. Surf. 10 (7), 75
81 (in Russian). Afanas’ev, V.V., 2013. Comment on “A model for internal photoemission at high-κ oxide/ silicon energy barriers”. [J. Appl. Phys. 112 (064115) (2012)]. J. Appl. Phys. 113 (166101). Afanas’ev, V.V., Stesmans, A., 1997a. H-complexed oxygen vacancy in SiO2: energy level of a negatively charged state. Appl. Phys. Lett. 71, 3844
3846. Afanas’ev, V.V., Stesmans, A., 1997b. Photon stimulated tunnelling of electrons in SiO2: evidence for a defect assisted process. J. Phys.: Condens. Matter. 9, L55
L60. Afanas’ev, V.V., Stesmans, A., 1997c. Interfacial defects in SiO2 revealed by photon stimulated tunnelling of electrons. Phys. Rev. Lett. 78, 2437
2440. Afanas’ev, V.V., Stesmans, A., 1997d. Electrical conduction of buried SiO2 layers analyzed by photon stimulated electron tunnelling. Appl. Phys. Lett. 70, 1260
1262. Afanas’ev, V.V., Stesmans, A., 1997e. Analysis of near-interfacial SiO2 traps using photon stimulated electron tunnelling. Microelectron. Eng. 36, 149
152. Afanas’ev, V.V., Stesmans, A., 1998a. Positive charging of thermal SiO2/Si(100) interface by hydrogen annealing. Appl. Phys. Lett. 72, 79
81. Afanas’ev, V.V., Stesmans, A., 1998b. Hydrogen-induced valence alternation state at SiO2 interfaces. Phys. Rev. Lett. 80, 5176
5179. Afanas’ev, V.V., Stesmans, A., 1999a. Trapping of H1 and Li1 ions at the Si/SiO2 interface. Phys. Rev. B. 60, 5506
5512. Afanas’ev, V.V., Stesmans, A., 1999b. Photoionization of silicon particles in SiO2. Phys. Rev. B. 59, 2025
2034. Afanas’ev, V.V., Stesmans, A., 2000. Valence band offset and hole injection at the 4H-, 6H-SiC/SiO2 interfaces. Appl. Phys. Lett. 77, 2024
2026. Afanas’ev, V.V., Stesmans, A., 2003. Polytype determination at the SiC
SiO2 interface by internal electron photoemission scattering spectroscopy. Mater. Sci. Eng., B. 102, 308
312. Afanas’ev, V.V., Stesmans, A., 2004. Band alignment at the interfaces of Si and metals with high-permittivity insulating oxides. In: Houssa, M. (Ed.), High-κ Gate Dielectrics. Institute of Physics Publishing, Bristol, pp. 217
250. ISBN 0-7503-0906-7. Afanas’ev, V.V., Stesmans, A., 2006. Spectroscopy of electron states at interfaces of (100) Ge with high-κ insulators. Mater. Sci. Semicond. Process. 9, 764
771. Afanas’ev, V.V., Stesmans, A., 2007. Applied physics review: internal photoemission at interfaces of high-κ insulators with semiconductors and metals. J. Appl. Phys. 102 (081301). Afanas’ev, V.V., Novikov, S.V., Sokolov, N.S., Yakovlev, N.L., 1991. MBE-grown (Ca,Sr) F2 layers on Si(111) and GaAs(111): electronic structure of interfaces. Microelectron. Eng. 15, 139
142. Afanas’ev, V.V., Mizerov, N.S., Novikov, S.V., Sokolov, N.S., 1992a. MBE-grown heterostructures fluoride/GaAs(111)B: control of interfacial barrier by Eu and Sm insulator doping. Appl. Surf. Sci. 60/61, 637
642.

158

Internal Photoemission Spectroscopy

Afanas’ev, V.V., Akulov, A.P.H., Gorid, E.M., Petrov, V.V., Prosolovich, V.S., 1992b. Dumping of electron heating effects in thermal oxides on Ge-doped silicon. Microelectron. Eng. 19, 481
484. Afanas’ev, V.V., Bassler, M., Pensl, G., Schulz, M., Stein von Kamienski, E., 1996a. Band offsets and electronic structure of SiC/SiO2 interfaces. J. Appl. Phys. 79, 3108
3114. Afanas’ev, V.V., Stesmans, A., Andersson, M.O., 1996b. Electron states and microstructure of thin a-C:H layers. Phys. Rev. B. 54, 10820
10826. Afanas’ev, V.V., Stesmans, A., Bassler, M., Pensl, G., Schulz, M., Harris, C.I., 1996c. Elimination of SiC/SiO2 interface states by preoxidation ultraviolet-ozone cleaning. Appl. Phys. Lett. 68, 2141
2143. Afanas’ev, V.V., Bassler, M., Pensl, G., Schulz, M., 1997. Intrinsic SiC/SiO2 interface states. Phys. Status Solidi (a). 162, 321
337. Afanas’ev, V.V., Stesmans, A., Chen, F., Shi, X., Campbell, S.A., 2002a. Internal photoemission of electrons and holes from (100)Si into HfO2. Appl. Phys. Lett. 81, 1053
1055. Afanas’ev, V.V., Ciobanu, F., Dimitrijev, S., Pensl, G., Stesmans, A., 2004. Band alignment and defect states at SiC/oxide interfaces. J. Phys.: Condens. Matter. 16, S1839
S1856. Allen, F.G., Gobeli, G.W., 1966. Energy structure in photoelectric emission from Cs-covered silicon and germanium. Phys. Rev. 144, 558
575. An, Y.Q., Price, J., Lei, M., Downer, M.C., 2013. Role of photo-assisted tunneling in timedependent second-harmonic generation from Si surfaces with ultrathin oxides. Appl. Phys. Lett. 102 (051602). Aspnes, D.E., Studna, A.A., 1983. Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV. Phys. Rev. B. 27, 985
1009. Berglund, C.N., Powell, R.J., 1971. Photoinjection into SiO2: electron scattering in the image force potential well. J. Appl. Phys. 42, 573
579. Berglund, C.N., Spicer, W.E., 1964. Photoemission studies of copper 1 silver
theory. Phys. Rev. 136, A1030
A1043. Bortz, M.L., French, R.H., 1989. Optical reflectivity measurements using a laser plasma light source. Appl. Phys. Lett. 55, 1955
1957. Cardona, M., Pollak, F.H., 1966. Energy band structure of germanium and silicon
k-p method. Phys. Rev. 142, 530
541. Choyke, W.J., 1990. Optical and electronic properties of SiC. In: Freer, R. (Ed.), The Physics and Chemistry of Carbides, Nitrides, and Borides. NATO ASI Series vol. 185. Kluwer, Dordrecht, pp. 563
588. DeKeersmaecker, R.F., DiMaria, D.J., 1980. Electron trapping and detrapping characteristics of arsenic-implanted SiO2 layers. J. Appl. Phys. 51, 1085
1101. DiMaria, D.J., DeKeersmaecker, R.F., Young, D.R., 1978. Light-activated storage device (LASD). J. Appl. Phys. 49, 4655
4659. DiStefano, T.H., Eastman, D.E., 1971. The band edge of amorphous SiO2 by photoinjection and photoconductivity measurements. Solid State Commun. 9, 2259
2261. DiStefano, T.H., Lewis, J.E., 1974. Influence of sodium on Si
SiO2 interface. J. Vac. Sci. Technol. 11, 1020
1024. Engelbrecht, F., Helbig, R., 1993. Effect of crystal anisotropy on infrared reflectivity of 6H-SiC. Phys. Rev. B. 48, 15698
15707. Fereiro, J.A., McCreery, R.L., Bergren, A.J., 2013. Direct optical determination of interfacial barriers in molecular tunnel junctions. J. Am. Chem. Soc. 135, 9584
9587. Fitting, H.J., Boyde, J., 1983. Monte-Carlo calculation of electron attenuation in SiO2. Phys. Status Solidi (a). 75, 137
142.

Internal Photoemission Spectroscopy Methods

159

Fitting, H.J., Friemann, J.U., 1982. Monte-Carlo studies of the electron mobility in SiO2. Phys. Status Solidi (a). 69, 349
358. French, R.H., 1990. Electronic band structure of Al2O3, with comparison to AlON and AlN. J. Am. Ceram. Soc. 73, 477
489. Goodman, A.M., 1966a. Photoemission of electrons from n-type degenerate silicon into silicon dioxide. Phys. Rev. 152, 785
787. Goodman, A.M., 1966b. Photoemission of holes from silicon into silicon dioxide. Phys. Rev. 152, 780
784. Houssa, M., Naili, M., Zhao, C., Bender, H., Heyns, M.M., Stesmans, A., 2001. Effect of O2 post-deposition anneals on the properties of ultra-thin SiOx/ZrO2 gate dielectric stacks. Semicond. Sci. Technol. 16, 31
38. Im, C., Engenhardt, K.M., Gregory, S., 1999. Light-induced transient currents from molecular films in a tunnelling microscope junction. Phys. Rev. B. 59, 3153
3159. Jacobs, E.P., Dorda, G., 1977a. Charge storage by irradiation with UV light of non-biased MNOS structures. Solid State Electron. 20, 361
665. Jacobs, E.P., Dorda, G., 1977b. Optically induced charge storage in ion-implanted SiO2. Solid State Electron. 20, 367
672. Jan, G.J., Pollak, F.H., Tsu, R., 1982. Optical properties of disordered silicon in the range 1
10 eV. Sol. Energy Mater. 8, 241
248. Kapoor, V.J., Feigl, F.J., Butler, S.R., 1977a. Energy and spatial distribution of an electron trapping center in the MOS insulator. J. Appl. Phys. 48, 739
749. Kapoor, V.J., Feigl, F.J., Butler, S.R., 1977b. Low-temperature photocurrent spectroscopy of localized states in SiO2 films. Phys. Rev. Lett. 39, 1219
1222. Landsberg, P.T., 1991. Recombination in Semiconductors. Cambridge University Press, Cambridge, ISBN 0-521-36122-2. Lee, C.H., Lambrecht, W.R.L., Segall, B., Kelires, P.C., Frauenheim, T.H., Stephan, U., 1994. Electronic structure of dense amorphous carbon. Phys. Rev. B. 49, 11448
11451. Lei, M., Yum, J.H., Price, J., Hudnall, T.W., Bielawski, C.W., Banerjee, S.K., et al., 2012a. Spectroscopic evaluation of band alignment of atomic layer deposited BeO on Si(100). Appl. Phys. Lett. 100 (122906). Lei, M., Yum, J.H., Banerjee, S.K., Bersuker, G., Downer, M.C., 2012b. Band offsets of atomic layer deposited Al2O3 and HfO2 on Si measured by linear and nonlinear internal photoemission. Phys. Status Solidi (b). 249, 1160
1165. Lucovsky, G., 1965. On the photoionization of deep impurity centers in semiconductors. Solid State Commun. 3, 299
302. Manger, D., Kaczer, B., Menou, N., Clima, S., Wouters, D.J., Afanas’ev, V.V., et al., 2009. Comprehensive investigation of trap-assisted conduction in ultra-thin SrTiO3 layers. Microelectron. Eng. 86, 1815
1817. Marka, Z., Pasternak, R., Rashkeev, S.N., Jiang, Y., Pantelides, S.T., Tolk, N.H., et al., 2003. Band offsets measured by internal photoemission-induced second-harmonic generation. Phys. Rev. B. 67 (045302). Mehta, D.A., Butler, S.R., Feigl, F.J., 1972. Electronic charge trapping in chemical vapourdeposited thin films of Al2O3 on silicon. J. Appl. Phys. 43, 4631
4638. Pankove, J.I., 1975. Optical Processes in Semiconductors. Dover, New York, NY, ISBN 0-486-60275-3. Philipp, H.R., 1971. Optical properties of non-crystalline Si, SiO, SiOx, and SiO2. J. Phys. Chem. Solids. 32, 1935
1943. Pollak, F.H., Rubloff, G.W., 1972. Piezo-optical evidence for lambda optical transitions at 3.4-eV optical structure of silicon. Phys. Rev. Lett. 29, 789
792.

160

Internal Photoemission Spectroscopy

Powell, R.J., 1969. Photoinjection into SiO2: use of optical interference to determine electron and hole contributions. J. Appl. Phys. 40, 5093
5101. Powell, R.J., 1970. Interface barrier energy determination from voltage dependence of photoinjected currents. J. Appl. Phys. 41, 2424
2432. Przewlocki, H.M., Brzezinska, D., Engstrom, O., 2012. Photoemission field and the electron escape depth determination in metal
oxide
semiconductor structures on N1-type and P1-type silicon substrates. J. Appl. Phys. 111 (114510). Shamuilia, S., Afanas’ev, V.V., Somers, P., Stesmans, A., Li, Y.-L., To¨kei, Z.S., et al., 2006. Internal photoemission of electrons at interfaces of metals with low-κ insulators. Appl. Phys. Lett. 89 (202909). Siegrist, K., Ballarotto, V.W., Breban, M., Yongsunthon, R., Williams, E.D., 2004. Imaging buried structures with photoelectron emission microscopy. Appl. Phys. Lett. 84, 1419
1421. Sze, S.M., 1981. Physics of Semiconductor Devices. second ed. Wiley, New York, NY, ISBN 0-471-05661-8. Thomas III, J.H., Feigl, F.J., 1970. Spectrally resolved photo depopulation of electron trapping defects in amorphous silica films. Solid State Commun. 8, 1669
1672. Vanbel, M.K., Afanas’ev, V.V., Adelmann, C., Caymax, M., Valev, V.K., Verbiest, T., 2013. Tunneling of holes is observed by second-harmonic generation. Appl. Phys. Lett. 102 (082104). Wang, W.C., Badylevich, M., Afanas’ev, V.V., Stesmans, A., Adelmann, C., Van Elshocht, S., et al., 2009. Band alignment and electron traps in Y2O3 layers on (100)Si. Appl. Phys. Lett. 95 (132903). Wang, W.C., Badylevich, M., Adelmann, C., Swets, J., Kittl, J.A., Afanas’ev, V.V., 2012. Electron trap energy distribution in ALD Al2O3, LaAl4Ox, and GdyAl22yO3 layers on silicon. IOP Conf. Ser.
Mater. Sci. Eng. 41 (012008). Weinberg, Z.A., 1977. Tunnelling of electrons from Si into thermally grown SiO2. Solid State Electron. 20, 11
18. Weinberg, Z.A., 1982. On tunnelling in metal
oxide
silicon structures. J. Appl. Phys. 53, 5052
5056. Wilk, G.D., Wallace, R.M., Anthony, J.M., 2001. High-κ gate dielectrics: current status and material considerations. J. Appl. Phys. 89, 5243
5275. Williams, R., 1965. Photoemission of electrons from silicon into silicon dioxide. Phys. Rev. 140, A569
A575. Yan, R.S., Zhang, Q., Li, W., Calizo, I., Shen, T., Richter, C.A., et al., 2012. Determination of graphene work function and graphene
insulator
semiconductor band alignment by internal photoemission spectroscopy. Appl. Phys. Lett. 101 (022105). Yan, R.S., Zhang, Q., Kirillov, O.A., Li, W., Basham, J., Boosalis, A., et al., 2013. Graphene as transparent electrode for direct observation of hole photoemission from silicon to oxide. Appl. Phys. Lett. 102 (123106). Zahid, M.B., Aguado, D.R., Degraeve, R., Wang, W.C., Govoreanu, B., Toledano-Luque, M., et al., 2010. Applying complementary trap characterization technique to crystalline γ-phase Al2O3 for improved understanding of non-volatile memory operation and reliability. IEEE Trans. Electron Devices. 57, 2907
2916.