Contactless optical probe for use in semiconductor processing metrology

A method and/or device (285) for determining first and second band offsets (100, 110) at a semiconductor/dielectric heterointerface (115), which includes the semiconductor/dielectric heterointerface (115) exposed to incident photons (205) from a light source (200); a detector (275, 280) for generating a signal by detecting emitted photons (260, 265) from the semiconductor/dielectric heterointerface (115); and an element (310) for changing the energy of incident photons (205) to monitor the first and second band offsets (100, 110).

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to semiconductor processing technology, and, more particularly, to a device and method for contactless metrology.

2. Description of the Related Art

The physical characteristics, and, in particular, the electronic characteristics of the silicon/silicon dioxide (Si/SiO2) interface have played a major role in establishing the dominance of Si in semiconductor technology. As the physical dimensions and critical dimensions (CD) of semiconductor devices such as Complementary Metal Oxide Semiconductor (CMOS) transistors, and the like, continue to shrink, it is becoming increasingly important to understand how thin oxide films influence the charge carrier dynamics at buried Si/SiO2interfaces. Examples of such influences include charge breakdown and hot carrier injection.

Valence band-offset (Δvb) may be defined as the difference between the top of the valence band100in Si and the top of the valence band105in SiO2(see FIG.1). Similarly, conduction band-offset (Δcb) may be defined as the difference between the bottom of the conduction band110in Si and the bottom of the conduction band115in SiO2(see FIG.1). The band-offsets Δvband Δcbat the Si/SiO2interface are important parameters that help determine whether thin oxide films will exert influences such as charge breakdown and hot carrier injection over the charge carrier dynamics. The band-offsets Δvband Δcbat the Si/SiO2interface represent barrier heights for carrier injection or quantum mechanical tunneling processes, for example. Bandgap Δbgin Si is about 1.1 eV and bandgap Δbgin SiO2is about 9 eV (see FIG.1).

Several techniques have traditionally been used to measure one or more of the band-offsets Δvband Δcbat semiconductor heterointerfaces (interfaces between different types of materials) such as the Si/SiO2heterointerface. For example, X-ray photoelectron spectroscopy (XPS) has been employed for measuring valence band-offsets (Δvb). Although this technique allows contactless Δvbmeasurements, it utilizes X-ray photons of several tens of eVs and is therefore limited in energy resolution to a few hundred meV (a few percent of the X-ray photon energy). Internal photoemission spectroscopy, which can be used for measuring both, the Δvband conduction band-offsets (Δcb), on the other hand, requires electrical contacts on the device under test to measure the photo-generated current in an external circuit. This becomes increasingly difficult, as gate oxide thicknesses shrink below 40 Å. In addition, for using internal photoemission, the semiconductor has to be doped p-type or n-type to measure Δvbor Δcb, respectively.

SUMMARY OF THE INVENTION

In one aspect of the present invention, a method is provided for determining first and second band-offsets at a semiconductor/dielectric heterointerface, the method comprising exposing the semiconductor/dielectric heterointerface to incident photons and generating a signal by detecting emitted photons that have interacted with the semiconductor/dielectric heterointerface. The method also comprises changing the energy of the incident photons and monitoring the signal to determine a first threshold energy for injection of first carriers into the dielectric of the semiconductor/dielectric heterointerface, the first threshold energy corresponding to the first band-offset. The method further comprises changing the energy of the incident photons beyond the first threshold energy and monitoring the signal to determine a second threshold energy for injection of second carriers into the dielectric of the semiconductor/dielectric heterointerface, the second threshold energy corresponding to the second band-offset.

In another aspect of the present invention, a device is provided to determine first and second band-offsets at a semiconductor/dielectric heterointerface, the device comprising a source of incident photons exposing the semiconductor/dielectric heterointerface to the incident photons and a detector generating a signal by detecting, emitted photons that have interacted with the semiconductor/dielectric heterointerface. The device also comprises having the energy of the incident photons be changeable and the signal be monitorable to determine a first threshold energy for injection of first carriers into the dielectric of the semiconductor/dielectric heterointerface, the first threshold energy corresponding to the first band-offset. The method further comprises having the energy of the incident photons be changeable beyond the first threshold energy and the signal be monitorable to determine a second threshold energy for injection of second carriers into the dielectric of the semiconductor/dielectric heterointerface, the second threshold energy corresponding to the second band-offset.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

The present invention permits band-offset measurements at semiconductor/dielectric, semiconductor/semiconductor, metal/semiconductor, and metal/dielectric heterointerfaces. As will be understood, any metal, dielectric and semiconductor, amorphous, monocrystalline or polycrystalline, possessing a cubic structure with the [100] direction (x axis) normal to the heterointerface is suitable for practice of the invention. For purposes of description and illustration, band-offset measurements at an Si/SiO2heterointerface will be described, having particular applications in the testing of MOSFET transistors used in microelectronics. Applicants' present invention, however, is not so limited, and may find applications in a variety of heterointerfaces within a variety of semiconductor devices. For example, the present invention may find applications to band-offset measurements at a plurality of heterointerfaces, as in quantum wells and/or quantum well superlattices. The present invention may also find applications to band-offset measurements at heterointerfaces between two different semiconductors having different bandgaps and/or between a metal and a semiconductor and/or between a metal and a dielectric, for example.

Illustrative embodiments of a new optical technique in accordance with the present invention allow precise measurements (with energy resolutions of approximately 10 meV) of band-offsets at semiconductor/dielectric heterointerfaces. An optical signal is generated by a laser beam, either in reflection or in transmission from the structure under test (see FIGS.2and3). The optical signal is sensitive to the space charge field E(t) in the semiconductor at the buried heterointerface. In addition, in alternative illustrative embodiments of the present invention, the optical signal may be sensitive to external electric and/or external magnetic fields in the semiconductor at the buried heterointerface. In other alternative illustrative embodiments of the present invention, we also believe that the optical signal may be sensitive to piezoelectric stress and/or piezoelectric strain fields in the semiconductor at the buried heterointerface. Depending on the crystal structure of the semiconductor substrate, two different optical effects may be employed to monitor the space charge field E(t): (1) second-order non-linear optical effects and (2) the Pockels effect.

For centrosymmetric semiconductors, such as Ge and Si, the Pockels-effect vanishes because of the centrosymmetric crystal structure. In this case, a higher-order nonlinear optical effect is utilized for monitoring the space charge field E(t). A quasi-static electric field breaks the inversion symmetry of a centrosymmetric medium, which allows a bulk dipolar second-harmonic response. This method will be called electric field-induced second-harmonic generation (EFISHG). The electric field-induced second-harmonic generation (EFISHG) technique can therefore be used for monitoring a space charge field E(t) at the surface and/or interface and/or heterointerface of centrosymmetric semiconductors.

As shown inFIG. 2, a source200of substantially monochromatic electromagnetic radiation may produce a stream of incident photons205. The incident photons205may be reflected from a mirror210and may pass through a filter215, a first polarizer220and a lens or lens system225. The incident photons205interact with the space charge field E(t) of the Si/SiO2heterointerface sample230on sample stand235. Emitted photons240that have interacted with the space charge field E(t) of the Si/SiO2heterointerface may pass through a lens or lens system245and a second polarizer250and enter a prism255. The emitted photons240may be separated by the prism255into photons260with an energy ho or hν (first-harmonic photons) and photons265with an energy 2hω or 2hν (second-harmonic photons). The photons260and265may be reflected from a mirror270. The photons260are stopped by a discriminator (slit)275that selects the second-harmonic photons265. The second-harmonic photons265may pass through a filter280and enter a photomultiplier tube/photon counter285that counts the second-harmonic photons265. In alternative embodiments (not shown), the emitted photons240that have interacted with the space charge field E(t) of the Si/SiO2heterointerface may pass transmissively through the sample230rather than being reflected thereby.

The Pockels effect may be utilized in non-centrosymmetric semiconductors, for example III-V and II-VI compound semiconductors. In this case, the space charge field E(t) couples to the optical field via the Pockels effect in the semiconductor. For a linear polarized excitation beam, for example, this internal, linear electro-optic effect will generate an elliptically polarized signal, which is directly proportional to the space charge field E(t) at the buried heterointerface. These techniques will be called reflective electro-optical sampling (RE-OS) and transmissive electro-optical sampling (TE-OS), respectively.

As shown inFIG. 3, a source300of substantially monochromatic electromagnetic radiation may produce a stream of linearly-polarized incident photons305. The incident photons305interact with the space charge field E(t) of a Si/SiO2heterointerface sample310. For reflective electro-optical sampling (RE-OS), reflectively-emitted photons315A that have interacted with the space charge field E(t) of the Si/SiO2heterointerface may be reflected from a mirror320and may pass through a beam-splitting polarizer325A. Beam-split, reflectively-emitted photons330A having a polarization state substantially perpendicular to the plane of the beam-splitting may be detected by a detector335A. The detector335A may send a signal340A to one input of an amplifier345A. Beam-split, reflectively-emitted photons350A having a polarization state substantially in the plane of the beam-splitting may be detected by a detector355A. The detector355A may send a signal360A to the other input of the amplifier345A.

The signals340A and360A correspond to the two components of the elliptical polarization generated by the internal, linear electro-optic Pockels effect on the linearly-polarized incident photons305. The degree of elliptical polarization of the linearly-polarized excitation beam is directly proportional to the space charge field E(t) at the buried Si/SiO2heterointerface.

For transmissive electro-optical sampling (TE-OS), transmissively-emitted photons315B that have interacted with the space charge field E(t) of the Si/SiO2heterointerface may pass through a beam-splitting polarizer325B. Beam-split, transmissively-emitted photons330B having a polarization state substantially perpendicular to the plane of the beam-splining may be detected by a detector335B. The detector335B may send a signal340B to one input of an amplifier345B. Beam-split, reflectively-emitted photons350B having a polarization state substantially in the plane of the beam-splitting may be detected by a detector355B. The detector355B may send a signal360B to the other input of the amplifier345B.

The signals340B and360B also correspond to the two components of the elliptical polarization generated by the internal, linear electro-optic Pockels effect on the linearly-polarized incident photons305. The degree of elliptical polarization of the linearly-polarized excitation beam is directly proportional to the space charge field E(t) at the buried Si/SiO2heterointerface.

As described above, a semiconductor/dielectric heterointerface exhibits two band-offsets (seeFIG. 1) associated with the conduction bands (Δcb) and the valence bands (Δvb). In general, these two band discontinuities, Δcband Δvb, are different. This enables photo-injection of only one type of carrier, either electrons or holes, by increasing the photon energy hω (hν) above the lowest band-offset. In this case, a charge separation will be induced across the buried heterointerface, which will change the space charge field E(t) in the semiconductor at the buried heterointerface. The resulting field-enhancement may be monitored, using a monitor laser beam, and/or a plurality of monitor laser beams, either by electric field-induced second-harmonic generation (EFISHG) techniques or by reflective electro-optical sampling (RE-OS) and/or transmissive electro-optical sampling (TE-OS) techniques.

These optical techniques may be utilized for monitoring the threshold for carrier injection that is determined by the band-offset at the heterointerface. In various illustrative embodiments, ultraviolet light from an ultraviolet lamp, and the like, and/or monochromatic light, for example, from a tungsten or mercury lamp, and the like, and/or one or more tunable and/or pulsed lasers, including free electron lasers, and the like, may be utilized as a pump beam for carrier injection, providing an energy resolution of a few meV for the band-offset. In various alternative illustrative embodiments, one or more tunable and/or pulsed lasers may be used both as a pump beam and as a monitoring beam, as a source for the photons used in the electric field-induced second-harmonic generation (EFISHG) techniques and/or the reflective electro-optical sampling (RE-OS) and/or transmissive electro-optical sampling (TE-OS) techniques.

For example, in various illustrative embodiments, as shown inFIG. 4, when the energy hω (hν) of the incident photons (from an ultraviolet light source, for example) exceeds approximately 4.08 eV (corresponding to an approximate wavelength λ=3040 Å), electrons (e) from the Si valence band100may be excited into the SiO2conduction band115. When electrons (e) are excited from the Si valence band100into the SiO2conduction band115and become trapped, primarily on an SiO2outer surface420in an oxygen (O2) ambient, a charge separation occurs. This charge separation alters the space charge field E(t) in the Si at the buried Si/SiO2heterointerface. The resulting alteration in the space charge field E(t) may be monitored, using one or more monitor laser beams, either by electric field-induced second-harmonic generation (EFISHG) techniques (seeFIG. 2) or by reflective electro-optical sampling (RE-OS) and/or transmissive electro-optical sampling (TE-OS) techniques (see FIG.3).

The second band-offset may be determined by increasing the photon energy hω (hν) of the pump beam until it passes the threshold for photo-injection of the second type of carriers. The injection of carriers complementary to the ones associated with the lowest band-offset will reduce the charge separation across the heterointerface, and, hence, reduce the space charge field E(t) and the optical signal as well. The photon energy hω (hν) at which this process begins corresponds to the second band-offset.

For example, in these various illustrative embodiments, as shown inFIG. 5, when the energy hω (hν) of the incident photons (from an ultraviolet light source, for example) exceeds approximately 6.08 eV (corresponding to an approximate wavelength λ=2040 Å), holes (h) may be excited in the SiO2valence band105, or, equivalently, holes (h) may be excited from the Si conduction band110into the SiO2valence band105.

The injection of holes into the SiO2valence band105will reduce the charge separation across the buried Si/SiO2heterointerface, and, hence, reduce the space charge field E(t) in the Si at the buried Si/SiO2heterointerface and affect the optical signal as well. The resulting reduction in the space charge field E(t) may be monitored, using one or more monitor laser beams, either by electric field-induced second-harmonic generation (EFISHG) techniques (seeFIG. 2) or by reflective electro-optical sampling (RE-OS) and/or transmissive electro-optical sampling (TE-OS) techniques (see FIG.3).

In various alternative illustrative embodiments, as shown inFIG. 6, for example, when the energy hω (hν) of the incident photons (from a pulsed laser source, for example) exceeds approximately 1.36 eV (corresponding to an approximate wavelength λ=9120 Å), three-photon processes, including cascaded one-photon and two-photon processes, and/or direct three-photon processes, may occur. In particular, three incident photons with energies hω (hν) of approximately 1.36 eV each (approximately 4.08 eV total) may excite an electron (e) from the Si valence band100into the SiO2conduction band115. Indeed, it is believed that the trapping rate for photo-injected electrons, which is proportional to the reciprocal time-dependent second-harmonic generation (TDSHG) rise time, follows approximately an (Iω)3dependence, measured by using a fundamental, incident beam (with an intensity Iω) having 110 femtosecond (fs) pulses at an approximate wavelength λ=7700 Å.

When electrons are excited from the Si valence band100into the SiO2conduction band115and become trapped, primarily on an SiO2outer surface420in an oxygen (O2) ambient, a charge separation occurs. This charge separation alters the space charge field E(t) in the Si at the buried Si/SiO2heterointerface. The resulting alteration in the space charge field E(t) may be monitored, using one or more monitor laser beams, either by electric field-induced second-harmonic generation (EFISHG) techniques (seeFIG. 2) or by reflective electro-optical sampling (RE-OS) and/or transmissive electro-optical sampling (TE-OS) techniques (see FIG.3).

The second band-offset may be determined by increasing the photon energy hω (hν) of the pump beam until it passes the threshold for photo-injection of the second type of carriers. The injection of carriers complementary to the ones associated with the lowest band-offset will reduce the charge separation across the heterointerface, and, hence, reduce the space charge field E(t) and the optical signal as well. The photon energy hω (hν) at which this process begins corresponds to the second band-offset.

For example, in these various alternative illustrative embodiments, as shown inFIG. 7, when the energy hω (hν) of the incident photons (from a pulsed laser source, for example) exceeds approximately 1.52 eV (corresponding to an approximate wavelength λ−8160 Å), four-photon processes, including cascaded one-photon, two-photon and three-photon processes, and/or direct four-photon processes, may occur. In particular, four incident photons with energies hω (hν) of approximately 1.52 eV each (approximately 6.08 eV total) may create a hole (h) in the SiO2valence band105(or equivalently, may excite a hole h from the Si conduction band110into the SiO2valence band105).

The injection of holes into the SiO2valence band105will reduce the charge separation across the buried Si/SiO2heterointerface, and, hence, reduce the space charge field E(t) in the Si at the buried Si/SiO2heterointerface and affect the optical signal as well. The resulting reduction in the space charge field E(t) may be monitored, using one or more monitor laser beams, either by electric field-induced second-harmonic generation (EFISHG) techniques (seeFIG. 2) or by reflective electro-optical sampling (RE-OS) and/or transmissive electro-optical sampling (TE-OS) techniques (see FIG.3).

FIG. 8illustrates schematically a determination of a threshold for multiphoton photo-injection of holes at a heterointerface. In particular,FIG. 8illustrates schematically that the second band-offset may be determined by increasing the photon energy of the pump beam until it passes the threshold for photo-injection of holes (h) into the SiO2valence band105.

In one illustrative embodiment, such measurements may be made using optical second-harmonic generation (SHG) techniques (see FIG.2). The source200of substantially monochromatic electromagnetic radiation may be a titanium:sapphire (Ti:sapphire) laser that provides approximately 150 femtosecond (fs) pulses of photons205with a wavelength λ in a range tunable from approximately 7000 to 9200 Å (corresponding to photon205energies hν in a range of approximately 1.35-1.77 eV) and an average power of approximately 300 mW at a repetition rate of approximately 80 MHz. The photon205beam may be focused to approximately 10 microns (μm) in diameter on the Si/SiO2heterointerface sample230on the sample stand235, and the reflectively emitted second-harmonic photons265that have interacted with the space charge field E(t) of the Si/SiO2heterointerface sample230may be measured with approximately 0.5 second temporal resolution by the photomultiplier tube/photon counter285.

For thermal SiO2grown on lightly boron-doped (approximately 1015 cm−3) Si(001) wafers to thermal SiO2thicknesses of approximately 40, 50 and 65 Å, and also for thermal SiO2grown on lightly boron-doped Si(001) wafers to a thickness of approximately 40 Å that is subsequently etched-back in a dilute hydrogen fluoride (HF) solution to a thickness of approximately 10 Å, a rapid increase in the second-harmonic generation (SHG) signal may be observed for the first few hundred seconds of irradiation. The second-harmonic generation (SHG) signal may then gradually reach a saturation level defined as Δ1. The energy dependence of the saturation level Δ1is illustrated schematically inFIG. 8by the upper set of data points800, plotted as a function of the incident photon205energy.

The time-dependent second-harmonic generation (TDSHG) generated from the Si/SiO2heterointerface sample230may be described by I2ω(t)=|χ(2)+χ(3)E(t)|2(Iω)2, where Iωis the intensity of the incident beam of photons205, I2ω(t) is the intensity of the emitted second-harmonic photons265that have interacted with the space charge field E(t) of the Si/SiO2heterointerface sample230, χ(3)is the third-order nonlinear susceptibility of Si and χ(2)is the effective SHG susceptibility from all other sources. The space charge field E(t) is a quasistatic electric field in the Si space charge region at the Si/SiO2heterointerface of the sample230.

The space charge field E(t) may arise from a charge separation at the Si/SiO2heterointerface of the sample230, the charge separation causing a field substantially perpendicular to at the Si/SiO2heterointerface of the sample230. Consequently, the time-dependent second-harmonic generation (TDSHG) techniques of various embodiments of the present invention provide a direct contactless method of probing electric fields at heterointerfaces, such as the Si/SiO2heterointerface of the sample230. As described above, when electrons (e) are excited from the Si valence band100into the SiO2conduction band115and become trapped, primarily on the SiO2outer surface420in an oxygen (O2) ambient, a charge separation occurs. This charge separation alters the space charge field E(t) in the Si at the buried Si/SiO2heterointerface. The resulting alteration in the space charge field E(t) may be monitored, using one or more monitor laser beams, either by electric field-induced second-harmonic generation (EFISHG) techniques (seeFIG. 2) or by reflective electro-optical sampling (RE-OS) and/or transmissive electro-optical sampling (TE-OS) techniques (see FIG.3).

For thermal SiO2grown on lightly boron-doped (approximately 1015cm3) Si(001) wafers to thicknesses of at least approximately 40 Å, we have observed a new and scientifically revealing phenomenon that involves a pronounced increase in the time-dependent second-harmonic generation (TDSHG) signal after the excitation beam generated by the source200of substantially monochromatic electromagnetic radiation, for example, the Ti:sapphire laser having a wavelength λ of approximately 7900 Å (corresponding to photon205energies hν of approximately 1.57 eV), has been blocked for several seconds and then unblocked. For example, after about 600 seconds of irradiation, the excitation beam may be blocked (or, alternatively, and equivalently, switched off) for about 100 seconds and then the excitation beam may be unblocked (or, alternatively, and equivalently, switched on). Surprisingly, the initial reading of the time-dependent second-harmonic generation (TDSHG) signal may be observed to be higher than before the excitation beam was blocked (or, alternatively, and equivalently, switched off). The enhanced time-dependent second-harmonic generation (TDSHG) signal may be observed to then decrease in a few tens of seconds to the former saturation level A1and follow the saturation trend thereafter, until a subsequent blockage of the excitation beam, in which case the beam-off, dark field enhancement may again be observed.

The magnitude of this beam-off, dark field enhancement may be defined as Δ2. The energy dependence of the beam-off, dark field enhancement Δ2is illustrated schematically inFIG. 8by the lower set of data points810, plotted as a function of the incident photon205energy. Note that the lower set of data points810indicates that the beam-off, dark field enhancement Δ2does not occur substantially until the incident photon205energy has exceeded a photon energy threshold of approximately 1.52 eV.

By way of contrast, for the thermal SiO2grown on lightly boron-doped Si(001) wafers to a thickness of approximately 40 Å that is subsequently etched-back in a dilute hydrogen fluoride (HF) solution to a thickness of approximately 10 Å, the beam-off, the time-dependent second-harmonic generation (TDSHG) response shows that the dark field enhancement Δ2does not occur. In fact, in this case, the beam-off, dark field may be drastically lowered in magnitude. Consequently, we conclude that as a general feature the newly observed dark field enhancement Δ2is pronounced for SiO2films that exceed a thickness of approximately 30-40 Å. For thinner SiO2films, the hole-related effect (seeFIGS. 7 and 9) is less apparent due to fast electron (e) detrapping (from the SiO2film outer surface420in the O2ambient) that neutralizes the holes (h) trapped in the SiO2film and at the Si/SiO2heterointerface.

As shown inFIG. 8, the saturation level Δ1decreases with increasing incident photon205energy. By way of contrast, the dark field enhancement Δ2increases with increasing incident photon205energy, at least when the incident photon205energy has exceeded the photon energy threshold of approximately 1.52 eV. In addition, the sum of the saturation level Δ1and the dark field enhancement Δ2remains substantially constant, after the incident photon205energy has exceeded the photon energy threshold of approximately 1.52 eV, consistent with charge conservation and our hole-injection model, as described in more detail below. Moreover, below the photon energy threshold of approximately 1.52 eV, the saturation level Δ1, which we believe may be attributed substantially to electron-injection behavior (see FIG.4), is substantially maximized.

We believe that the above observations may be interpreted consistently as follows. As shown inFIGS. 1,6and7, the Si/SiO2heterointerface of the sample230exhibits two band-offsets associated with the conduction bands (Δcb) and the valence bands (Δvb). These two band discontinuities, Δcband Δvb, are different, with the band-offset Δcbbeing approximately 2.98 eV and with the band-offset Δvbbeing approximately 4.98 eV. These values may be determined as follows. As shown inFIG. 4, three incident photons205with energies hω (hν) of approximately 1.36 eV each (approximately 4.08 eV total) may excite an electron (e) from the Si valence band100into the SiO2conduction band115. Since the bandgap Δbgin Si is about 1.1 eV, and the sum of the bandgap Δbgin Si and the band-offset Δcbis approximately 4.08 eV, the band-offset Δcbis approximately 2.98 eV. Similarly, as shown inFIG. 5, four incident photons205with energies ho (hν) of approximately 1.52 eV each (approximately 6.08 eV total) may excite a hole (h) from the Si conduction band110into the SiO2valence band105. Since the bandgap Δbgin Si is about 1.1 eV, and the sum of the bandgap Δbgin Si and the band-offset Δvbis approximately 6.08 eV, the band-offset Δvbis approximately 4.98 eV.

This enables photo-injection of only electrons (e) by increasing the incident photon205energy hω above approximately 1.36 eV (one-third of the sum of the bandgap Δbgin Si and the lowest band-offset Δcb), while keeping the incident photon205energy hω below approximately 1.52 eV (one-quarter of the sum of the bandgap Δbgin Si and the highest band-offset Δvb). Because of the significant difference in transition probabilities between a three-photon process (seeFIG. 4) and a four-photon process (see FIG.5), the photo-excitation of electrons (e) is strongly favored. Consequently, the initial feature of the time-dependent second-harmonic generation (TDSHG) signal is dominated by photo-injection of hot electrons (e), even though there may be some holes (h) that are photo-excited into the SiO2as well, and even though there may be some recombination of photo-injected electrons (e) with photo-injected holes (h).

However, when the incident photon205energy hω is below approximately 1.52 eV (one-quarter of the sum of the bandgap Δbgin Si and the highest band-offset Δvb), hot holes (h) generally are not photo-injected into the SiO2and the dynamical behavior is determined substantially by the hot electrons (e) photo-injected into the SiO2. This may explain why, when the incident photon205energy hω (hν) is above approximately 1.52 eV (one-quarter of the sum of the bandgap Δbgin Si and the highest band-offset Δvb), the saturation level Δ1decreases with increasing incident photon205energy since the total space charge field E(t) at the Si/SiO2heterointerface is lessened due to the photo-injection of hot holes (h) into the SiO2.

During the photo-injection of hot electrons (e) and hot holes (h) into SiO2, several things may happen. The density of electron traps, particularly in thermally grown bulk SiO2, may be quite small, so that considerably less than about 1% of the hot electrons (e) photo-injected at room temperature will therefore be trapped in the insulating SiO2. Since electrons (e) have a normal mobility of about 0.002 m2Ns, the hot electrons (e) photo-injected at room temperature will leave the bulk SiO2, very fast (within picoseconds) either to the Si or to the SiO2outer surface420. Due to the O2ambient at the SiO2outer surface420, some of the photo-injected hot electrons (e) may eventually travel to the SiO2outer surface420and become trapped. For thick SiO2(with a thickness at least about 30-40 Å), the trapped photo-injected hot electrons (e) may remain on the SiO2/O2ambient interface at the SiO2outer surface420after the incident excitation photon205beam has been switched off and/or blocked.

For SiO2below a critical thickness at most about 30-40 Å, the trapped photo-injected hot electrons (e) may quantum mechanically tunnel back from the SiO2/O2ambient interface at the SiO2outer surface420to the Si, and combine with holes (h) in the Si, after the incident excitation photon205beam has been switched off and/or blocked. Consequently, the charge separation and the corresponding time-dependent second-harmonic generation (TDSHG) signal behave very differently, depending on the thickness of the SiO2, following the switching off and on (and/or blocking and unblocking) of the incident excitation photon205beam.

In contrast to the photo-injected hot electrons (e), the hot holes (h) photo-injected into the SiO2behave quite differently. Hole transport is highly variable, with a very low apparent mobility of about 10−10m2/Vs. Models explaining this type of hole (h) transport assume a large density of shallow hole traps. The holes (h) are assumed to move either by quantum mechanically tunneling between localized states (hole traps) or by becoming trapped and then reemitted into the valence band100of the Si with a large time constant dispersion due to the distribution in hole trap depths. Hole traps are believed to be more abundant in thermally grown bulk SiO2than electron traps, and since the hole traps also have larger cross-sections, a substantial fraction of the hot holes (h) photo-injected into the SiO2may be captured. It is believed that as many as about 10% of the hot holes (h) photo-injected into the SiO2at room temperature may become trapped in the SiO2close to the Si/SiO2heterointerface.

As a result of these considerations, we suggest that in the presence of the incident photon205beam with photon energies hω (hν) of at least approximately 1.52 eV, a substantial proportion of the hot holes (h) photo-injected into the SiO2, having surmounted both the bandgap Δbgin Si (approximately 1.1 eV) and the band-offset Δvb(approximately 4.98 eV) and crossed into the SiO2, may remain close to the Si/SiO2heterointerface. Consequently, these photo-injected hot holes (h) may readily move back to the Si when the incident photon205beam (with photon energies hω or hν of at least approximately 1.52 eV) is switched off and/or blocked, as shown inFIG. 7, for example.FIG. 7illustrates schematically the photo-injected hot holes (h) crossing the Si/SiO2heterointerface back into the Si under dark conditions (the incident photon205beam switched off and/or blocked), leading to the enhancement of the space charge field E(t), as monitored, using one or more monitor laser beams, by time-dependent second-harmonic generation (TDSHG) and the dark field enhancement Δ2, for example, arising from the increased charge separation at the Si/SiO2heterointerface.

After again switching on and/or unblocking the incident photon205beam (with photon energies hω or hν of at least approximately 1.52 eV), hot holes (h) may again be photo-injected across the Si/SiO2heterointerface back into the SiO2. On the other hand, relatively few hot electrons (e) may be photo-injected across the Si/SiO2heterointerface into the SiO2, after again switching on and/or unblocking the incident photon205beam (with photon energies hω or hν of at least approximately 1.52 eV), because any newly photo-injected hot electrons (e) would have to drift against an already strong space charge field E(t) created by the trapped photo-injected hot electrons (e) that may remain on the SiO2outer surface420at the SiO2/O2ambient interface. Consequently, there are more hot holes (h) than hot electrons (e) moving from the Si into the SiO2after the incident photon205beam (with photon energies hω or hν of at least approximately 1.52 eV) is again switched on and/or unblocked. This reduces the charge separation. Therefore, the space charge field E(t) and the time-dependent second-harmonic generation (TDSHG) signal may decrease to near the previous saturation level Δ1when the incident photon205beam (with photon energies hω or hν of at least approximately 1.52 eV) is again switched on and/or unblocked.

The new optical techniques of various illustrative embodiments of the present invention allow contactless measurements of valence and conduction band-offsets at semiconductor/dielectric heterointerfaces and monitor changes of the space charge field E(t) in the semiconductor region at the buried heterointerface caused by photo-injection of carriers into the dielectric. This may be accomplished by utilizing either the linear electro-optical (e.g., the Pockels effect) or higher-order nonlinear-optical response (e.g., second-harmonic generation or SHG) of the semiconductor material. In contrast to synchrotron and X-ray photoemission spectroscopy, which employ photons with energies of the order of several tens of eV, the new optical techniques of various embodiments of the present invention use light with photon energies of a few eV. This allows the determination of band-offsets with an accuracy of a few meV, an improvement of at least one order of magnitude compared to previous uncertainties. Furthermore, the new optical techniques of various illustrative embodiments of the present invention may be employed for measuring the conduction band-offset, which is not possible with single-photon photoemission spectroscopy, where electrons are ejected into the vacuum and not into the conduction band.

Internal photoemission spectroscopy, which can be used for measuring both valence and conduction band-offsets, on the other hand, requires electrical contacts on the device under test to measure the photo-generated current in an external circuit. In addition, for using internal photoemission the semiconductor has to be doped p-type or n-type to measure the valence or conduction band-offset, respectively. This is not required for the new optical techniques of various illustrative embodiments of the present invention. Since these purely optical techniques are contactless, non-invasive, and have very fast response times (of the order of microseconds), they may be used as an efficient in-situ control for the growth of ultrathin dielectric layers on semiconductors, e.g., in CMOS processing. For example, ultrathin dielectric layers, with thicknesses ranging from a few Angstroms (Å) to hundreds of Å, may be measured in-situ, and controlled, while growing on semiconductors.

Embodiments of the present invention allow contactless measurements of the band-offsets at the heterointerface of an ultrathin dielectric on a wide variety of semiconductors, including Si, Ge, GaAs and InP. The energy resolution of illustrative embodiments is a few meV. Dielectrics with thicknesses ranging from a few Angstroms (Å) to hundreds of Å may be measured.