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PHYSICAL REVIEW B 68, 073307 2003

dc-electric-field-induced second-harmonic interferometry of the Si,, 111 ... - SiO2 interface in Cr- SiO2 - Si MOS capacitor
T. V. Dolgova, A. A. Fedyanin, and O. A. Aktsipetrov*
Department of Physics, Moscow State University, 119992 Moscow, Russia Received 11 October 2002; revised manuscript received 24 March 2003; published 28 August 2003 The Si( 111) -SiO2 interface is probed by the interferometry of dc-electric-field-induced second-harmonic EFISH generation in planar Cr-SiO2 -Si MOS structures. The phase shift between EFISH and dc-fieldindependent contributions to the second-harmonic field is extracted from the combination of intensity and phase bias dependences. This allows the complete separation of the complex EFISH contribution to the nonlinear response which is difficult to do by intensity measurements. The approach using EFISH generation as an internal homodyne for diagnostics of charge properties of MOS structure is proposed. DOI: 10.1103/PhysRevB.68.073307 PACS number s : 42.65. k, 73.20. r, 78.68. m

dc-electric-field-induced second-harmonic EFISH generation1,2 stands out among other interface-sensitive techniques based on second-harmonic generation SHG due to its information capability as a probe of charge properties of buried interfaces of centrosymmetric semiconductors such as silicon and germanium.3,4 EFISH generation and EFISH spectroscopy have been intensively used for characterization of Si-SiO2 interfaces in MOS capacitors with various silicon crystallographic orientations,5 in both normal and in-plane configurations of the field application.6 The low-frequency modulation EFISH probe has been developed.4,7 Recently, using the phase-sensitive SHG techniques of frequencydomain interferometry and external homodyne detection, the 180° -phase shift of the EFISH component at the flatband voltage was observed8 and the vector character of the inplane dc-electric field was probed.9 EFISH generation, modulated due to the charge transfer through Si-SiO2 interface induced by UV light, yields time-dependent SHG,10 which can be used as a probe of electron-hole dynamics at the Si-SiO2 interfaces.11 The EFISH component of the total second-harmonic SH field, called the EFISH field below, interferes with dc-fieldindependent SHG contributions. The phase shift between the EFISH and field-independent SH waves, which is essential for extraction of the EFISH signal, is varied strongly with the bias due to optical retardation in the space charge region of significant up to microns depth. In previous studies this shift was neglected5­7 or treated as a model parameter involved indirectly to intensity measurements.4 Since the EFISH generation is governed by the spatial distribution of the dc-electric field in the space charge region, both amplitude intensity and relative phase of the EFISH field are sensitive to properties of MOS structures, such as interface and oxide charges, interface traps, and doping concentration.4 Thus, development of diagnostic capabilities of EFISH generation requires the combination of direct measurements of the EFISH intensity and relative phase. From a basic viewpoint, the EFISH phenomenon manifests itself in both bias dependence of intensity and bias dependence of phase of the EFISH field. The latter has not been experimentally studied earlier. In this Brief Report, the nonlinear-optical response of the Si( 111) -SiO2 interface of planar Cr-SiO2 -Si MOS capacitors
0163-1829/2003/68 7 /073307 4 /$20.00

is studied by EFISH interferometry. Bias dependences of intensity and relative phase of the EFISH field, generated in the silicon space charge region, are extracted from the interference patterns. The EFISH contribution at the unbiased interface, which is related to initial band bending and directly governed by the oxide charge density of the MOS structure, is distinguished correctly from the total SHG signal using the internal homodyne scheme. The output of a Q-switched Nd:YAG-laser at 1064 nm with pulse duration of 15 ns and energy of approximately 5 mJ/pulse is used as the fundamental radiation. The SHG signal is selected by appropriate color and interference filters and detected by a photomultiplier tube and gated electronics. The MOS capacitor consists of a 3-nm-thick semitransparent chromium gate electrode, a 68-nm-thick silicon oxide layer, and a low-doped n silicon 111 ( 2.4 1016 cm 3 , P-doped wafer with a backside aluminum electrode. The bias voltage U is applied between the gate and backside electrodes. The bias interval is from 20 to 20 V and restricted by the leakage current flowing through the MOS capacitor at larger biases. This current produced by local oxide defects is due to the large electrodes area ( 2 cm2 ) . A small size of the laser spot ( 2 mm2 ) allows us to avoid the influence of the current on the bias homogeneity across the illuminated capacitor area. The MOS capacitor studied was independently characterized by the C -V measurements. The oxide charge density is found to be Q ox 6 1012 cm 2 leading to the flatband 18.9 V at the very boundary of the interval voltage U FB of available biases. For all experimental biases the dcelectric-field screening in the space charge region corresponds to the accumulation regime leaving out the 180° -shift of the EFISH-field phase at U FB due to changing the sign of the dc-electric field. The combination of the off-resonant infrared fundamental radiation and the specially designed MOS capacitor for the large flatband voltage allows us to associate the bias dependence of the EFISH-field phase entirely with effects of the optical retardation in the space charge region. The phase shift between interfering SH fields from the reference and the MOS sample is produced in the space between them due to air dispersion.12 The EFISH interference patterns are obtained for every bias value translating a 30©2003 The American Physical Society

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FIG. 1. EFISH interference patterns measured in reflection from the Si( 111) -SiO2 -Cr MOS capacitor for different bias values 15 V filled circles and 15 V open circles . Solid curves are the dependences given by Eq. 1 . The inset shows the schematic of EFISH interferometry: 1 the MOS capacitor, 2 the SHG reference sample, and 3 green filter.

nm-thick indium tin oxide film reference along the fundamental laser beam varying the distance l between the reference and the MOS sample inset in Fig. 1 . The SHG signals from the reference and the MOS capacitor are independently controlled by inserting the appropriate filters between the tot reference and the sample. The total SH intensity I 2 ( l , U ) is r produced by the coherent sum of the SH waves E2 and E2 from the reference and MOS sample, respectively, I
tot 2

l,U

c r E2 l 8 I
r 2

E2 U 2 I
r 2

2

I
rs

2

U

I

2

U cos 2 kl 1

FIG. 2. Bias dependences of the SH intensity top panel and relative phase of the SH wave bottom panel . The results of combine fit with the surface EFISH contribution dashed lines without it solid lines . Thin lines: fit of the SH intensity bias pendence and corresponding reconstructed bias dependence of relative phase.

the the and dethe

U,

where k 2 n / with n n 2 n describing air dispersion, rs is the bias-dependent phase difference between the reference and sample SH waves, and 1 is the phenomenological parameter accounting for both spatial and temporal coherences of the laser pulses. For the infrared output of r YAG laser with a small beam divergence, I 2 is position independent and the period of the SHG interferogram is the well-defined value k 1 130 mm. The adjustable parameters in Eq. 1 are I 2 ( U ), rs ( U ) , and . Figure 1 shows two EFISH interference patterns measured at 15 and 15 V in the maximum of the p-in,p-out tot rotational anisotropy. The total SH intensity I 2 oscillates strongly as a function of the distance between the reference and the MOS capacitor riding on a small positionindependent SHG background. The positions of the maximal SH intensity are almost the same for both biases, while their magnitudes are strongly different. The set of interference pat-

terns is fitted by Eq. 1 . The top panel in Fig. 2 shows I 2 as a function of the applied bias U. The bottom panel in Fig. 2 presents the bias dependence of the phase shift rs . The strong, almost two times increase of I 2 is observed, while rs demonstrates a gradual decrease with the U increase. The maximal variation of the phase is rs 8°. In silicon, SHG arises from the surface dipole S BQ (2), S : E E , and the bulk quadrupole P2 P2 2 (2),BQ i : E E k quadratic nonlinear polarizations. Here E and k are the amplitude and the wave vector of the fundamental radiation, respectively. In the presence of internal or external dc-electric field E0 , the silicon inversion symmetry is broken in the space charge region, and the dc-electric-field-induced bulk dipole polarization PBD (3),BD E E E0 is generated. The total SHG signal in the point of detection r0 is the sum of all nonlinear polarization terms integrated with the corresponding Green's functions:13

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z int 0 0 S G2 z z : P S 2

PHYSICAL REVIEW B 68, 073307 2003

E2 z

z dz
BD P2 z

G
0

2

z

0

BQ z : P2 z

dz , 2

where the z axis is directed inside the silicon, the dependence ( x, y) , is the plane wave, on the in-plane coordinates, E2 ( ) exp i( · k2 2 t ) , and k2 is the SH wave vector. Parameter z int is the characteristic thickness of the interface layer and is approximately two to three atomic layers S thick.13,14 The spatial distribution of P2 is associated with the inhomogeneity of the fundamental field and the dielectric BQ constants at the interface. The P2 ( z ) dependence is attributed to the optical absorption in silicon at the fundamental BD wavelength and the P2 ( z ) dependence is additionally governed by the spatial dc-electric-field distribution in the space charge region. For the off-resonant conditions, the nonlinear susceptibility tensors (2), S , (2),BQ, and (3),BD can be considered as real quantities. A phase shift between the fieldindependent bulk quadrupole and surface dipole and EFISH contributions gives rise due to the retardation of the optical fields in the space charge region taken into account in S BQ Eq. 2 by Green's functions. The SH fields E2 and E2 , S BQ generated by P2 and P2 , respectively, are mostly in phase, S BQ while P2 and P2 are initially shifted by /2 due to gradient nature of the bulk quadrupole term. The total SH field BD E2 is a coherent sum of the EFISH field E2 and the dcFI S BQ field-independent SH field E2 E2 E2 : E2 e
i FI E2 e i BD E2 e i .

3

The bias dependence of the SH intensity I 2 E2 2 does FI BD not allow the unambiguous separation of E2 and E2 due to . The EFISH contribution the uncontrolled phase shift can be extracted entirely from combined measurements of I 2 ( U ) and ( U ) dependences. The bias dependence of the relative phase rs r is associated with the bias dependence of . Bias dependences BD BD of E2 and are calculated by the convolution of P2 with Green's function G2 in the form of Eq. 2 . The spatial BD distribution of P2 in the space charge region is found from the spatial distribution of dc-electric field, which is calculated for every bias using the first integral of Poisson's equation with the carrier density in the form of the Fermi integral.4 The model bias dependences of the EFISH amplitude and phase calculated for parameters of the MOS strucBD ture studied are presented in Fig. 3. E2 has a fracture at U FB and increases monotonously with the bias as a function close to the square root within the bias region used in experiment. Transition from depletion to inversion screening reBD gimes produces the inflection of the E2 bias dependence near 23 V. The EFISH field phase has a 180° -drop at U FB and then decreases monotonously with the bias from approximately 65° to 30° in the used bias interval. The inset in Fig. 3 shows dependence of the zz element of the complex Green's function tensor G2 G1 i G2 , on the coordinate z

BD FIG. 3. Model bias dependences of E2 top panel and bottom panel . Arrows indicate the experimental bias interval. The dashed arrow emphasizes the flatband voltage. Inset: Distributions across the space charge region of the electrostatic potential thin line and the Green's function corrections G zz and G zz thick and 1 2 dashed lines, respectively calculated for U 0.

inside the space charge region. The EFISH field is generated in the region of approximately 100-nm depth. Due to oscillations in the real and imaginary parts of Green's function corrections, the interfering EFISH fields induced in different planes of the space charge region, z z , have different phases that results in the bias dependence of the total EFISH field. The dependences I 2 ( U ) and rs ( U ) are fitted by Eq. 3 FI with the amplitude E2 and the phases and r as adjustable parameters. The best fit to the data is shown in Fig. 2 FI BD 36° and E2 / E2 (0) 1.7. Here and and achieved for below the amplitude of the EFISH field at unbiased Si-SiO2 BD interface E2 (0) corresponding to the internal bias U FB , is taken as a reference value. The fit curve matches the rs ( U ) dependence quite well. A good agreement with the I 2 ( U ) dependence is achieved also for the most biases. Note, that the fit to the I 2 ( U ) dependence solely gives the better agreement with the data. However, the parameter valFI BD 75° and E2 / E2 (0) 2.6 are sufficiently differues ent from the values obtained within the combine fit, and the rs ( U ) dependence calculated with these parameters is quite far from the data. The indirect determination of the EFISH-

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field phase in intensity measurements gives rise significant errors and ambiguity in both amplitude and phase of the EFISH field. The quality of the combine fit can be improved in the vicinity of U FB if the surface EFISH field15 is taken into SE (3), S E E E0int is proportional to account. The term E2 the dc-electric field at the Si-SiO2 interface E 0int and to the effective surface cubic susceptibility (3), S . The difference of (3), S from (3),BD yields an additional contribution proportional to ( E 0int) 2 to the SH intensity.15 The results of the combine fit of I 2 ( U ) and rs ( U ) dependences by Eq. 3 SE with the surface EFISH term E2 exp(i ) are shown in Fig. SE and the bias2. The bias-dependent amplitude E2 independent phase are treated as adjustable parameters. 65° and The best fit to the data is achieved for BD FI BD SE 40° , E2 / E2 (0) 4.6 and E2 (0) / E2 (0) 2.0. The agreement between fit curves and data is quite well from 15 V until approximately 8 V, including biases around the flatband voltage. Deviations for larger biases could indicate that the relation between electrostatic potential and dcelectric-field strength becomes nonlocal for large band bending and the quantum-mechanical corrections are to be included into the E 0int( U ) dependence.4 Meanwhile, both fits with and without the surface EFISH term show that the bulk BD FI EFISH field E2 and field-independent SH field E2 are does not mostly in-phase, and the phase difference exceeds 35° . In contrast to the SHG homodyne detection,16 in which a weak signal of interest is visualized through the

interference with an external reference signal, the dc-fieldindependent SH field serves here as an internal homodyne for the EFISH field with matching spatial and temporal characteristics, providing the most efficient interference between these signals. Finally, to demonstrate the advances of the EFISH phase measurements for the studies of the charge parameters of MOS structures, combine and intensity fits of bias dependences are performed treating the oxide charge density as adjustable parameter. Intensity fit gives the low accuracy of the charge density determination: Q ox is varied almost at one order of magnitude from 1.5 1012 to 8 1012 cm 2 . The combined fit defines the Q ox value more precisely covering the interval from 5 1012 to 7 1012 cm 2 . The intervals are determined by the ranges of chi squared values which are less than double chi squared for the fit with the fixed Q ox . In conclusion, the dc-field-dependent SHG contribution of the buried Si( 111) -SiO2 interface in the planar MOS structures is isolated using the EFISH interferometry. The amplitude and phase of the EFISH field are extracted from the EFISH phase measurements with increased accuracy and unambiguity of isolation. The advances of the internal EFISH homodyne detection for diagnostics of charge parameters of buried Si-SiO2 interfaces in MOS capacitors are demonstrated. This work was supported by the Presidential Grant for Leading Russian Science Schools and INTAS Grant No. YSF-2001/1-160.

*Electronic address: aktsip@shg.ru URL:http://www.shg.ru
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