Patent Application: US-9876405-A

Abstract:
a polarization modulation photoreflectance technique has been developed for optical characterization of semiconductor electronic interfaces . by using a laser source in conjunction with polarization state modulation , a polarization modulation spectroscopy technique may be used to characterize the optical response of semiconductor materials and structures . disclosed methods and instruments are suitable for characterization of optical signatures of electronic interfaces , including characterization of electric fields at semiconductor interfaces .

Description:
the following discusses use of the polarization modulation photoreflectance ( pmpr ) technique for characterization of electronic interfaces . it is understood that the pmpr technique of the present drawings and descriptions may be used to analyze any semiconductor material , the discussion of electronic interfaces considered to be exemplary only and in no way limiting in scope . turning now descriptively to the drawings , in which similar reference characters denote similar elements throughout the several views , fig1 contains , in an exaggerated view , an exemplary electronic interface test structure that may be characterized using the polarization modulation photo - reflectance technique of the present disclosure . the electronic interface test structure , which may be grown using molecular beam epitaxy , comprises a negatively doped gallium arsenide ( gaas ) semiconductor substrate upon which is grown a negatively doped aluminum gallium arsenide ( algaas ) “ spacer ” layer of ˜ 94 . 5 nanometer thickness . an undoped barrier layer comprising algaas is grown on the spacer layer . then a multiple quantum well section comprising a number of periods of gaas quantum wells and algaas barrier layers is grown on the first barrier layer . in an exemplary embodiment , individual quantum wells may comprise a thickness of approximately 7 . 4 nanometers , and barriers may comprise a thickness of approximately 7 . 4 nanometers . a second confinement layer is grown on the multiple quantum well section . the electronic interface test structure further comprises an additional algaas spacer layer of approximately 94 . 5 nanometer thickness , followed by a thin gaas capping layer . in accordance with the arrangement of the present disclosure as shown in fig2 , polarization modulation photo - reflectance may be used to measure the reflected spectra from an electronic interface test structure in order to characterize the properties of the electronic interface , and importantly , establish the energy of optical transitions in the electronic interface , and establish the profile of the dielectric function in the vicinity of such transitions . by introducing the laser beam at a non - zero angle of incidence with respect to the electronic interface layers , a component of polarization perpendicular to the plane of the layers is realized . for polarization in the plane of the electronic interface , acceleration of free carriers may occur , whereas for components perpendicular to the interface layers , no acceleration is possible . as shown in fig2 , the polarization modulation photo - reflectance arrangement comprises a tunable diode laser , a laser controller , a beamsplitter , a phase modulator with a function generator , a polarizer , a polarizing beamsplitter , an optical system , a sample , a photoreceiver , a lock - in amplifier , and a computer with measurement and system control software . in certain embodiments the laser diode is an external cavity tunable laser diode with center wavelength of approximately 844 nm and tunable range of approximately 20 nanometers . laser embodiments include external cavity tunable diode lasers emitting in the uv - nir wavelength range ( 200 - 1700 nm ). the laser power is approximately 15 mw . however , laser embodiments include lasers operating at powers of approximately 0 . 5 mw or above . the laser controller is a programmable power source compatible with the laser diode and may be controlled by the computer . the laser beam is directed to a beamsplitter , where the beam is separated into a pump and a probe arm . the pump arm is directed through the phase modulator where its polarization state is modulated . in an exemplary embodiment the phase modulator is an electro - optic modulator based on the pockel &# 39 ; s effect with resonant frequency of approximately 20 mhz driven by an external function generator . embodiments also include broadband phase modulation , dc bias operation , and photo - elastic modulation . the pump beam is then passed through a polarizer , which produces an amplitude modulation . the pump and probe arms are then made collinear through the use of a polarizing beamsplitter . this yields a single beam wherein the amplitude modulated pump has linear polarization with direction perpendicular to the probe polarization . the beam is then focused onto the sample surface at an angle of incidence of approximately 65 °. the optical system comprises various optical elements including focusing and collimation lenses , and mirrors . all optical elements are matched to the laser source wavelength . fig3 shows the polarization state of the laser beam as it passes through the optical system . the pump polarization is aligned either parallel or perpendicular to the plane of incidence . in either alignment , the pump polarization state remains linearly polarized after reflection from the sample , allowing the pump light to be effectively eliminated from the beam with the use of a calcite polarizer . once the beam is reflected from the sample surface , it has sources of amplitude modulation from the amplitude modulated pump “ channel ,” and on the probe channel from any induced change in the semiconductor optical response . the calcite polarizer is oriented to minimize the transmission of the pump beam . this also provides maximal transmission of the probe beam , which contains the photoreflectance signal . any residual pump light produces a constant or sloping background which may be removed . as an exemplary mode of operation , the amplitude modulated pump beam is directed onto the sample with polarization parallel to the plane of incidence , also known as “ p ” polarization . the “ p ” orientation of the pump allows the reflected pump intensity to be minimized by placing the pump angle of incidence near the brewster angle . the probe beam then has polarization perpendicular to the plane of incidence , known as “ s ” polarization . the intensity of the “ s ” polarized probe light may be written : i s = i probe r s + i probe δr s ( ω ). alternatively , the amplitude modulated pump beam may be directed onto the sample with “ s ” polarization . in this case , as shown in fig4 ., the pump polarization is entirely in the plane of the electronic interface , producing a sharp optical response due to the acceleration of carriers in the interfacial plane . the intensity of the “ p ” polarized probe light then may be written : i p = i probe r p + i probe δr p ( ω ). in either arrangement , the δr terms contained in the probe beam are induced by changes in the semiconductor optical response ( aspnes , 1980 ; shay , 1970 ). the reflected beam is collected and focused onto the photodiode . the lock - in amplifier divides photodiode ac output at the phase modulation frequency by the dc signal . the computer controls the laser wavelength and intensity and records the measurement photocurrents . any linear reflectivity contribution to the ac signal is removed by a fit to the slowly varying linear reflectivity background . thus δr / r is recorded as a function of laser wavelength and intensity . fig5 . contains a block diagram of the electronic signals of the polarization modulation photo - reflectance apparatus . embodiments include alterations to the arrangement which do not alter the fundamental polarization modulation photo - reflectance signal . embodiments also include any configurations where the photoreceiver ac signal contains a photo - reflectance signal due to changes in sample semiconductor optical response induced by the change in pump beam polarization state . the underlying principle of the polarization modulation photo - reflectivity technique is to characterize the photo - reflectance spectra associated with semiconductor electronic interfaces , and to derive critical point parameters associated with electronic interfaces such as excitonic resonance energies and spectral widths . critical point parameters generally characterize the “ active ” electronic properties of electronic interfaces . excitonic features are also enhanced in the presence of electronic confinement and characterize the splitting of the valence band . as is well known , the photoreflectance spectrum is proportional to a derivative of the dielectric function . the dielectric function of critical point and excitonic resonance features may be written : ε ( e , γ )= aexp { i φ }/( e - eg + i γ ) n , where e is the photon energy , a is the oscillator amplitude , φ is the phase projection , eg is the oscillator energy , γ is the broadening , and n is an exponent which characterizes the dimensionality of the resonance ( aspnes , 1980 ). due to the dependence of electronic interface optical response on input polarization , amplitude analysis may be used to quantify anisotropies in the polarization modulation photo - reflectivity technique . however , the oscillator energy , eg , and the spectral width , γ , are the primary parameters of interest . both eg and γ may be determined simply from the lineshape of δr / r itself ( aspnes , 1980 ). the amplitude , broadening , and position of excitonic absorptions are strongly influenced by internal fields generated by photo - excited carriers . fig6 . illustrates photo - reflectance data from an electronic interface test structure exposed to a series of wavelength scans at laser powers of 3 mw , 6 mw , 9 mw , and 12 mw . the data is scaled with increasing laser power and curves are included to guide the eye . in these scans , the pmpr spectrum exhibits sharp derivative - like structures at interband transition energies . these nearby features indicate the valence band split into “ heavy - hole ” and “ light - hole ” bands , i . e . the degeneracy of the valence band is lifted . the ability to resolve such features is also important for the characterization of strain , since a primary effect of uniaxial stress is to split the valence bands . it is also seen that the relative amplitude of the lower energy transition increases with laser power , indicating a transfer of oscillator strength from the light hole to the heavy hole . each curve is analyzed using the lineshape of δr / r ( aspnes , 1980 ), which reveals a redshift of the transition energies as laser intensity is increased . transition energies derived from this data are shown in fig7 . the transition widths are essentially independent of laser intensity . the total redshift for either the light hole or the heavy hole transition is approximately 5 mev . for electronic interface test structure , redshifts due to space - charge separation of photo - excited carriers of approximately 1 mev per 6 kv / cm internal electric field are expected . thus , the observed shifts are indicative of internal electric fields approximately 30 kv / cm in magnitude . such fields can also be directly measured by photo - reflectance using the above bandgap franz - keldysh oscillations ( gray , 2001 ; seraphin , 1965 ). however , the polarization modulation photoreflectivity technique provides a means to determine interfacial electric fields from line - shape analysis . in order to further teach the polarization modulation technique , fig8 contains , in an exaggerated view , an exemplary silicon electronic interface test structure that may be characterized using the polarization modulation photo - reflectance technique of the present disclosure . the electronic interface test structure comprises a silicon semiconductor substrate upon which is grown a silicon dioxide “ insulator ” layer of ˜ 87 . 1 nanometer thickness . an epitaxial silicon layer is bonded with the spacer layer , cleaved and re - grown to a thickness of approximately 25 nm . then a silicon dioxide or high - k dielectric capping film of approximately 2 nanometer is grown . in accordance with the arrangement of the present disclosure as shown in fig9 , polarization modulation photo - reflectance may be used to measure the reflected spectra from the electronic interface test structure in order to characterize the properties of the electronic interface and to establish the form of the dielectric function in the vicinity of critical points of silicon semiconductor material . as shown in fig9 , a preferred polarization modulation photo - reflectance arrangement comprises a pump diode laser , a laser controller , a polarizer , a phase modulator driven by an external function generator , a sample , an analyzer , a probe light source , a polarizing beamsplitter , a compensator , a pump wavelength filter , pump and probe optical systems , photodiodes , a lock - in amplifier , and a computer with measurement and system control software . the pump source is preferably a diode laser with center wavelength of approximately 844 nm . preferred laser embodiments include diode lasers emitting in the uv - nir wavelength range ( 200 - 1700 nm ). the laser power is approximately 15 mw . however , laser embodiments may also include lasers operating at powers of approximately 0 . 5 mw or above . the laser controller is a programmable power source compatible with the laser diode and may be controlled by the computer . the pump beam is directed through a polarizer to the phase modulator where its polarization state is modulated . in an exemplary embodiment the phase modulator has a resonant frequency of approximately 20 mhz and is driven by an external function generator . preferred embodiments also include broadband phase modulation , including dc bias operation , and photo - elastic modulation . the probe light source is a diode laser with center wavelength of approximately 375 nm . this wavelength is at or very near the strong silicon “ e1 ” direct interband transition . the pump and probe are made coincident of the sample . the optical system comprises various optical elements including focusing and collimation lenses , and mirrors . the beam containing the polarization modulated pump is focused onto the sample surface at an angle of incidence of approximately 65 °. once the pump beam is reflected from the sample surface , it has sources of amplitude modulation from the differential reflectivity of the “ s ” and “ p ” polarizations , and from any induced change in the semiconductor optical response . the pump beam is configured as an ellipsometer with a polarization analyzer placed in the path of the reflected beam ( jellison , 2001 ). fig1 shows the polarization state of the pump beam as it passes through the pump optical system . in an exemplary embodiment , the first polarizer is set to 45 ° degrees with respect to the plane of incidence , φ p = 45 °, the azimuthal angle of the phase modulator is aligned with the plane of incidence , and the polarization analyzer is set to 45 ° with respect to the angle of incidence , φ a = 45 °. the intensity of the polarized pump then is : i = i 0 r / 4 ×{ 1 + s × sin [ asin ( ω t )]+ c × cos [ asin ( ω t )]}, where the amplitudes s and c are the isotropic mueller matrix elements related to the ellipsometric parameters ψ and δ through the relation : thus , the ellipsometer is configured to be sensitive to the ellipsometric parameter δ irrespective of its value . this is important for the characterization of ultra - thin films , since , for such films , the optical thickness is proportional to the parameter δ . fig1 shows a block diagram of the electronic signals associated with the pump / ellipsometer system . the pump laser beam is directed through the phase modulator to generate polarization state modulation , onto the sample , and to an analyzer which converts the signal to amplitude modulation . the optical system supplies an amplitude modulated light beam to the photoreceiver . the photoreceiver generates a photocurrent proportional to the intensity . this signal and the reference signal from the phase modulator are input to the lock - in amplifier . the lock - in amplifier divides photodiode ac output at the phase modulation frequency by the dc signal . the computer controls the pump laser intensity and records the measurement photocurrents . thus the ellipsometric parameters ψ and δ may be recorded as a function of pump wavelength and intensity . as an exemplary mode of operation a normally incident probe laser source can be spatially overlapped with the pump beam at the sample . fig1 shows the polarization state of the probe beam as it passes through the probe optical system . the normally incident probe beam passes through a polarization beamsplitter and quarter wave plate to the sample , and returns through the wave plate to the beamsplitter with a 90 ° polarization rotation about the optical axis . the beamsplitter directs this rotated polarization light to a photodiode . any light from the pump may also be eliminated with a wavelength filter . in other embodiments , the probe beam is separated from the pump through the use of a dichroic beamsplitter and / or a wavelength filter . fig1 shows the polarization state of the pump and the probe beams through an optical system with such a collinear beam arrangement . the linearly polarized probe may be transmitted to the photodiode without polarization elements . the probe light source may also be unpolarized . the probe beam has amplitude modulation only from pump induced changes in the semiconductor optical response ( aspnes , 1980 ; shay , 1970 ). the reflected beam is collected and focused onto the photodiode . fig1 contains a block diagram of the electronic signals associated with the probe system . the pump laser beam is directed through the phase modulator to induce modulation of the sample optical response . the probe beam contains the modulated reflectivity of the sample . the optical system supplies the amplitude modulated probe light beam to the photoreceiver . the photoreceiver generates a photocurrent proportional to the intensity . this signal and the reference signal from the phase modulator are input to the lock - in amplifier . the lock - in amplifier divides photodiode ac output at the phase modulation frequency by the dc signal . the computer controls the laser intensity and records the measurement photocurrents . thus δr / r is recorded as a function of probe wavelength and pump intensity . preferred embodiments include alterations to the arrangement which do not alter the fundamental polarization modulation photo - reflectance signal . certain embodiments also include any configurations where the photoreceiver ac signal contains a photo - reflectance signal due to changes in sample semiconductor optical response induced by the change in pump beam polarization state . as discussed , the underlying principle of the polarization modulation photo - reflectivity technique is to characterize the photo - reflectance spectra associated with semiconductor electronic interfaces , and to derive critical point parameters associated with electronic interfaces such as interband transition energies . critical point parameters generally characterize the “ active ” electronic properties of electronic interfaces . absorption features near critical points are enhanced in the presence of an electric field . the optical absorption at energies just below the critical point energy depends on the electric field amplitude and direction and may be written : where c and k are constants which depend on the “ zero field ” absorption , the effective electronic mass , and difference in photon energy from the strong absorption feature . the “ zero field ” absorption is the optical absorption of the material wherein no electric field is applied , and may be anisotropic . the effective mass is the mass along the direction of the applied field and also may be anisotropic . the expression above describes the redshifting of an optical absorption edge in the presence of a strong electric field ( keldysh , 1958 ). the change in absorption induces a simultaneous change in refractive index . these are manifest in the photoreflectance data though the relation : where δε 1 and δε 2 , are the change in real and imaginary parts of the dielectric function , and α and β are the seraphin coefficients ( xiang , 1988 , seraphin , 1965 ). due to the dependence of interfacial electric fields on input polarization , amplitude analysis may be used to quantify the electric field ( pollack , 1994 , aspnes , 1980 ). fig1 . illustrates photo - reflectance data from an electronic interface test structure exposed to a power scan of the pump laser from 3 mw to 12 mw . the data shows the natural logarithm of the probe photoreflectance signal at 375 nanometer wavelength with increasing pump laser power . the amplitude of the photoreflectance signal increases from approximately 1 . 13 × 10 − 6 , to approximately 5 . 83 × 10 − 3 , over this power interval . analysis of the amplitude according to the keldysh expression indicates internal electric fields in the range of 15 - 30 kv / cm . thus , the polarization modulation photoreflectance technique provides a means to determine interfacial electric fields from amplitude analysis . thus , this disclosure is suitable for the characterization of polarization modulated photo - reflectance as a function of pump intensity and probe wavelength . a diode laser focused onto the semiconductor material provides the optical intensity needed to induce changes in the optical response of semiconductor electronic interfaces due to space - charge separation of electrons and holes . the laser controller provides intensity control for the laser and , in the case of a tunable laser , the controller also provides wavelength control . the computer may program power and wavelength scans via interface to the laser controller . the phase modulator modulates the polarization state of the pump beam . an external function generator is used to provide ac drive current to the modulator . the probe light source may consist of a single wavelength laser , a tunable laser , or a lamp based source . the pump and probe beams are then spatially overlapped at a focal spot on the sample and reflected light is collected by the optical system . the probe beam is directed to a photoreceiver which generates an electrical current proportional to the input intensity . the photoreceiver output comprises the ac signal at the modulation frequency and the dc photocurrent . the ac signal is divided by the dc signal , which provides normalization of the probe light intensity . the ac signal is then proportional to the differential change in reflectivity . a lock - in amplifier with reference frequency from the phase modulator then conditions the photoreceiver signal . the computer records experimental photocurrents from the lock - in amp . thus photoreflectance information related to the optical response of electronic interfaces is acquired . the ellipsometric information contained in the reflected pump beam may also be analyzed . after reflection from the sample , the polarization modulated pump beam is passed through a polarizer and directed to a photoreceiver which generates an electrical current proportional to the input intensity . the photoreceiver output comprises the ac signal at the modulation frequency and the dc photocurrent . the ac signal is a sum of odd and even harmonics of the phase modulation frequency . the amplitude of these harmonics contain the ellipsometric parameters ψ and δ . the ac signal is divided by the dc signal , which provides normalization of the pump intensity . a lock - in amplifier with reference frequency from the phase modulator then conditions the photoreceiver signal . the computer records experimental photocurrents from the lock - in amp . thus ellipsometric information related to the optical response of semiconductor materials is acquired . as to a further discussion of the manner of usage and operation of the present disclosure , the same should be apparent from the above description . accordingly , no further discussion relating to the manner of usage and operation will be provided . with respect to the above description then , it is to be realized that the optimum dimensional relationships for the parts of the disclosure , to include variations in size , materials , shape , form , function and manner of operation , assembly and use , are deemed readily apparent and obvious to one skilled in the art , and all equivalent relationships to those illustrated in the drawings and described in the specification are intended to be encompassed by the present disclosure . therefore , the foregoing is considered as illustrative only of the principles of the disclosure . further , since numerous modifications and changes will readily occur to those skilled in the art , it is not desired to limit the disclosure to the exact construction and operation shown and described , and accordingly , all suitable modifications and equivalents may be resorted to , falling within the scope of the disclosure . 6 , 195 , 166 february 2001 gray 356 / 477 4 , 931 , 132 june 1990 aspnes 156 / 601 3 , 982 , 207 march 1975 dingle 331 / 94 . 5 “ physics of optical metrology of silicon - 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