Showing papers on "Responsivity published in 1996"
TL;DR: In this article, a transition-edge superconducting bolometer for detecting infrared and millimeter waves is presented, which operates on the Tc∼95 mK transition of a tungsten film with a thermal conductance of G∼1.2×10−9 W/K.
Abstract: We present a theoretical analysis and experimental evaluation of a transition‐edge superconducting bolometer for detecting infrared and millimeter waves. The superconducting film is voltage biased and the current is read by a superconducting quantum interference device ammeter. Strong electrothermal feedback maintains the sensor temperature within the transition, gives a current responsivity that is simply the inverse of the bias voltage, and reduces the response time by several orders of magnitude below the intrinsic time constant C/G. We evaluated a voltage‐biased bolometer that operates on the Tc∼95 mK transition of a tungsten film with a thermal conductance of G∼1.2×10−9 W/K. As expected, the electrical noise equivalent power of 3.3×10−17/W√Hz is close to the thermal fluctuation noise limit and is lower than that of other technologies for these values of G and temperature. The measured time constant of 10 μs is ∼100 times faster than the intrinsic time constant.
217 citations
TL;DR: In this article, the spectral responsivity of the GaN detector at 360 nm is about 1 A/W biased at 8 V at room temperature, and the carrier lifetime derived from the voltage-dependent responsivity is 0.13−0.36 ms.
Abstract: AlxGa1−xN (0≤x≤0.50) ultraviolet photoconductors with a minimum cutoff wavelength shorter than 260 nm have been fabricated and characterized. The AlGaN active layers were grown on (00⋅1) sapphire substrates by metalorganic chemical vapor deposition (MOCVD). The spectral responsivity of the GaN detector at 360 nm is about 1 A/W biased at 8 V at room temperature. The carrier lifetime derived from the voltage‐dependent responsivity is 0.13–0.36 ms.
176 citations
TL;DR: In this article, the InAs/Ga1−xInxSb strained-layer superlattice (SLS) holds promise as an alternative III-V semiconductor system for long wavelength infrared detectors.
Abstract: The InAs/Ga1−xInxSb strained‐layer superlattice (SLS) holds promise as an alternative III–V semiconductor system for long wavelength infrared detectors. In this article, we present the first investigation, to the best of our knowledge, of heterojunction photodiodes using this new material. The devices were grown by molecular beam epitaxy on GaSb substrates, and are comprised of a 38 A InAs/16 A Ga0.64In0.36Sb SLS used in double heterojunctions with GaSb contact layers. The structures were designed to optimize the quantum efficiency while minimizing transport barriers at the heterointerfaces. The photodiodes are assessed through the correlation of their performance with the SLS material quality and the detector design. X‐ray diffraction, absorption, and Hall measurements are used to determine the SLS material properties. The electrical and optical properties of the photodiodes are determined using current–voltage and spectral responsivity measurements. At 78 K, these devices exhibit rectifying electrical behavior and photoresponse out to a wavelength of 10.6 μm corresponding to the SLS energy gap. The responsivity and resistance in these thin‐layered (0.75 μm), unpassivated photodiodes result in a detectivity of 1×1010 cm √Hz/W at 8.8 μm and 78 K. Based upon the performance of these devices, we conclude that high‐sensitivity operation of long‐wavelength photovoltaic detectors at temperatures well in excess of conventional III–V band gap‐engineered systems, and potentially in excess of HgCdTe, is feasible using this material system.
165 citations
TL;DR: In this paper, the authors presented a new model for the simulation of quantum well infrared photodetectors (QWIPs) both in dark conditions and under illumination.
Abstract: We present the results of a new model for the simulation of quantum well infrared photodetectors (QWIPs) both in dark conditions and under illumination. This model takes into account the elementary mechanisms involved in the detection process (injection at the contacts, balance between capture and emission in each well) in a self‐consistent way. The main feature emerging from the model is the redistribution of the electric field along the structure in order to maintain current conservation. The calculated dark current, electrical noise, responsivity, and detectivity of different QWIP structures are compared with experimental measurements and the agreement is found to be fairly good. This model may be considered as a step toward more powerful simulation tools for QWIPs.
116 citations
TL;DR: In this article, a novel silicon photodetector suitable for high-speed, low-voltage operation at 780- to 850-nm wavelengths is reported, which consists of an interdigitated p-i-n detector fabricated on a silicon-on-insulator (SOI) substrate by using a standard bipolar process.
Abstract: A novel silicon photodetector suitable for high-speed, low-voltage operation at 780- to 850-nm wavelengths is reported. It consists of an interdigitated p-i-n detector fabricated on a silicon-on-insulator (SOI) substrate by using a standard bipolar process. Biased at 3.5 V, this device attains a -3-dB bandwidth in excess of 1 GHz at /spl lambda/=840 nm. The dc responsivity measured at /spl lambda/=840 nm on nonoptimized structures ranges from 0.05 to 0.09 A/W, depending on the finger shadowing factor. A new approach for improving the responsivity is proposed and quantitatively analyzed. The fabricated devices exhibit extremely low dark currents, small capacitance, large dynamic range, and no evidence of low-frequency gain. The overall performance and process compatibility of these photodetectors make them viable candidates for the fabrication of silicon monolithic receivers for fiber-optic data links.
96 citations
TL;DR: In this article, a model of the optical characteristics of HEMTs, which takes into account carrier transport as well as the quantum mechanical nature of the two-dimensional (2D) electron gas channel, is presented.
Abstract: The use of microwave high-electron mobility transistors (HEMTs) as photodetectors or optically controlled circuit elements have attracted interest. A model of the optical characteristics of HEMTs, which takes into account carrier transport as well as the quantum mechanical nature of the two-dimensional (2-D) electron gas channel, is presented. It is shown that the effect of illumination is equivalent to a shift in the gate to source bias voltage, referred to as the internal photovoltaic effect. The theoretical model is supported by experimental results that demonstrate that the HEMT photoresponse is a nonlinear function of light intensity with very high responsivity at low optical power levels.
94 citations
TL;DR: In this paper, a dual-function InGaAsP waveguide modulator and photodetector was used for high-frequency, high-linear dynamic range (HLSDR) transmission.
Abstract: A Franz-Keldysh effect InGaAsP electroabsorption waveguide device is utilized as a high-frequency, high-linear dynamic range modulator and photodetector. The dual-function modulator/photodetector can be useful in compact transmit/receive front end antenna architectures. Adjusting the electrical bias to the reverse-biased p-i-n diode, either efficient optical modulation or detection is demonstrated. As an electroabsorption modulator, a fiber optic link with a -17.4-dB RF loss and a 124-dB-Hz/sup 4/5/ suboctave spurious-free dynamic range is obtained with electrical biases in the 2 to 3 V range. As a waveguide photodetector, a 0.45-A/W fiber coupled responsivity, photocurrents up to 20 mA, and an output second-order intercept of +34.5 dBm are achieved at 7-V electrical bias.
68 citations
01 Jan 1996
TL;DR: In this paper, a dual-function modulator/photodetector was used as a high-frequency, high-linear dynamic range modulator and photodetector.
Abstract: A Franz-Keldysh effect InGaAsP electroabsorp- tion waveguide device is utilized as a high-frequency, high- linear dynamic range modulator and photodetector. The dual- function modulator/photodetector can be useful in compact trans- miffreceive front end antenna architectures. Adjusting the electri- cal bias to the reverse-biased p-i-n diode, either efficient optical modulation or detection is demonstrated. As an electroabsorption modulator, a fiber-optic link with a -17.4-dB RF loss and a 124- dB-Hz4/5 suboctave spurious-free dynamic range is obtained with electrical biases in the 2 to 3 V range. As a waveguide photode- tector, a 0.45-ANV fiber coupled responsivity, photocurrents up to 20 mA, and an output second-order intercept of +34.5 dBm are achieved at 7-V electrical bias.
61 citations
TL;DR: InGaAs as discussed by the authors exhibit 150 mA continuous photocurrent at 2 W power dissipation with a responsivity of 0.97 A/W at 1319 nm with greater than 60% external quantum efficiency from 920 to 1650 mm.
Abstract: We present novel (InGa)As photodetectors which exhibit 150 mA continuous photocurrent at 2 W power dissipation. A responsivity of 0.97 A/W at 1319 nm is achieved with greater than 60% external quantum efficiency from 920 to 1650 mm. Measured dark currents are below 1 nA and bandwidths of 295 MHz are achieved. These low dark-current devices have utility to applications requiring large output current and large dynamic range.
60 citations
TL;DR: In this paper, a thin film inverted metal-semiconductor-metal (I-MSM) photodetector is reported for the first time, which is separated from the growth substrate, has fingers on the bottom of the device, and is bonded to a silicon host substrate.
Abstract: To improve the external quantum efficiency and maintain the high speed of metal-semiconductor-metal (MSM) photodetectors, a thin film inverted MSM (I-MSM), which is separated from the growth substrate, has fingers on the bottom of the device, and is bonded to a silicon host substrate, is reported for the first time. This device optimizes the tradeoff between speed and responsivity, demonstrating the improvement in responsivity that can be achieved using an I-MSM. The photodetector time domain response at /spl lambda/=1.3 /spl mu/m is 50 ps FWHM, with a 34 ps rise time and a 85 ps fall time.
60 citations
TL;DR: In this article, a pseudomorphic p-type Si0.64Ge0.36/Si quantum well infrared photodetector is presented, which exhibits a photoresponse between 3 and 8 μm with a peak responsivity of Rp=76 mA/W, at a peak wavelength of λp=5 μm, resulting in a detectivity as high as Dλ*=2×1010 cm√Hz/W at a temperature of T=77 K.
Abstract: The detector characteristics of a pseudomorphic p‐type Si0.64Ge0.36/Si quantum well infrared photodetector are reported. The device exhibits a photoresponse between 3 and 8 μm with a peak responsivity of Rp=76 mA/W, at a peak wavelength of λp=5 μm, resulting in a detectivity as high as Dλ*=2×1010 cm√Hz/W at a temperature of T=77 K. Background limited infrared performance is achieved up to T=85 K. Investigation of the polarization dependence shows that in‐plane polarized radiation produces the largest photoresponse, thus making normal‐incidence detection feasible. The relevant optical transitions are analyzed on the basis of a self‐consistent 6‐band Luttinger–Kohn calculation including the in‐plane dispersion.
TL;DR: In this article, the frequency response and quantum efficiency of silicon-on-insulator (SOI) metal-semiconductor-metal photodetectors in the near-infrared (∼800 nm) are greatly enhanced with a simple reactive ion etching to form electrodes inside the interdigitated trenches.
Abstract: The frequency response and quantum efficiency (QE) of silicon‐on‐insulator (SOI) metal‐semiconductor‐metal photodetectors in the near‐infrared (∼800 nm) are greatly enhanced with a simple reactive ion etching to form electrodes inside the interdigitated trenches. Detectors with 1.25 μm trench spacing were fabricated on a SOI substrate with a 6‐μm‐thick silicon top layer. The unique device structure isolates carriers generated deep inside the semiconductor substrate and at the same time provides a highly uniform electric field throughout the active region of the detector, resulting in an instrumentation limited response time of 23 ps at 5 V bias and a −3 dB bandwidth of 2.3 GHz as measured at 790 nm. The dc responsivity is 0.12 A/W, corresponding to an external QE of 18.7% and an internal QE of 88.5%. The large bandwidth and good responsivity at the wavelength of interest, combined with their low operating voltages, make these detectors attractive for use in short‐distance optical communication systems.
TL;DR: In this article, a monolithic integrated infrared sensor system consisting of a thermopile, a sensor measuring the chip temperature and an amplifier stage fabricated in a CMOS process on SIMOX (separation by implanted oxygen) wafers is presented.
Abstract: We report on a monolithic integrated infrared sensor system consisting of a thermopile, a sensor measuring the chip temperature and an amplifier stage fabricated in a CMOS process on SIMOX (separation by implanted oxygen) wafers. A responsivity of 209 V W−1 and a normalized detectivity D ∗ of 1.3 × 108 cm Hz 1 2 W−1 are found for thermopiles with single-crystalline p-Si/n-polysilicon thermocouples on silicon oxide/silicon nitride membranes. A first analysis of the thermal influence of the power consumed by the circuitry on the thermopile voltage indicates that the sensor performance is not deteriorated by the integrated electronic circuitry.
TL;DR: In this article, a waveguide integrated photodiodes were fabricated on InP. The device design is intended to provide ultrafast photoresponse together with a high responsivity.
Abstract: Evanescently coupled, waveguide integrated photodiodes were fabricated on InP. The device design is intended to provide ultrafast photoresponse together with a high responsivity. A 3 dB bandwidth of 45 GHz and 90% internal quantum efficiency is achieved at 1.55 /spl mu/m wavelength. High-speed operation with linear power response is obtained at power levels as high as 5 mW.
TL;DR: In this article, the authors presented a microwave detector which utilises the nonlinear properties of 2D electronic fluid in a high electron mobility transistor (HEMT), operating between 8 and 18 GHz.
Abstract: The authors present a microwave detector which utilises the nonlinear properties of 2D electronic fluid in a high electron mobility transistor (HEMT). The detector operates between 8 and 18 GHz and the measured responsivity is in good agreement with the recent theory of 2D electronic fluids.
TL;DR: An InAlAs/InGaAs/INP metal-semiconductor-metal photodetector with engineered Schottky barrier heights has been fabricated in this paper, which exhibits a dark current density of 20.0 fA/μm2 at an applied bias of 5 V.
Abstract: An InAlAs/InGaAs/InP metal‐semiconductor‐metal photodetector with engineered Schottky barrier heights has been fabricated. A significant decrease in dark current with no change in the responsivity or the bandwidth was obtained by independently engineering the Schottky barrier heights at the anode and cathode. These photodiodes with an electrode width and spacing of 2 μm exhibited a dark current density of 20.0 fA/μm2 at an applied bias of 5 V. This dark current density is ∼6 times lower than the previously reported minimum.
TL;DR: In this article, a high-speed silicon metal-semiconductor-metal photodetector with novel structure is presented. But the structure of the diode is not described.
Abstract: We report on fabrication and characterization of a high-speed silicon metal-semiconductor-metal photodetector with novel structure. Metal contacts on the sidewalls of the interdigitated trenches are used to generate a highly uniform electric field well below the detector surface so that carriers deep within the semiconductor bulk can easily attain their saturation velocities. The detector, with 9-/spl mu/m-deep interdigitated trenches and a trench spacing of 1 /spl mu/m, has a pulse width of 28.2 ps and a -3-dB bandwidth of 2.2 GHz at 5 V. The responsivity measured at 790 nm is 0.14 A/W, corresponding to an external quantum efficiency of 22.1%. Our results also show that a bias as low as 2 V is sufficient for this diode to operate at high-speed without reducing responsivity.
TL;DR: In this article, thermally evaporated polycrystalline lead selenide was used to make detector arrays on high-resistivity Si substrates, for use as infrared photodetectors in the range.
Abstract: Thermally evaporated polycrystalline lead selenide was used to make detector arrays on high-resistivity Si substrates, for use as infrared photodetectors in the range. The arrays were made using standard photolithographic methods and a process fully compatible with the technologies used in the microelectronics industry. After activation at high temperature in an atmosphere, excellent uniformity and room-temperature peak detectivities up were obtained. The spectral response at 273 K of the detectors went up to , with peak responsivity of at . These arrays have been used to develop compact gas sensors with the addition of integrated bandpass multilayer optical filters.
01 Feb 1996
TL;DR: Ion-implanted GaAs MESFETs with transparent indium oxide (ITO) gate electrodes have been fabricated using both sputtered and evaporated ITO gates.
Abstract: Ion-implanted GaAs MESFETs with transparent indium oxide (ITO) gate electrodes have been fabricated using both sputtered and evaporated ITO gates. High-quality ITO films with transparency greater than 90% and low sheet resistance of 8/spl Omega///spl square/ have been used in the fabrication of RF sputtered transparent gates. Transparent-gate FETs have also been fabricated using thermally evaporated ITO which have shown excellent electrical device performance comparable to the conventional GaAs MESFET. The optical responsivity of these devices is about 4.5 A/W for a radiation wavelength of 6328 /spl Aring/. Fabrication details are also discussed for optoelectronic devices with transparent electrodes where the fine-structure processing are not compatible with standard lithography techniques.
TL;DR: In this article, a simplified quantum well infrared photodetector (SQWIP) has been designed and demonstrated which shows very high performance, and it produces a built-in potential in the structure for a photovoltaic (PV) effect.
Abstract: A simplified quantum well infrared photodetector (S‐QWIP) has been designed and demonstrated which shows very high performance. The S‐QWIP is designed to have only three quantum wells with detection peak wavelengths at 7.3, 8.3, and 10 μm, for the first, second, and third well, respectively. The two barriers between the three wells are graded to block the dark current effectively when reverse bias is applied. It also produces a built‐in potential in the structure for a photovoltaic (PV) effect. The two end barriers are designed with different widths so that the electron transport can be compared when the bias directions are changed. The responsivity of the S‐QWIP shows three photoreponse peaks at zero bias (PV effect) and migrates to one wide peak when the bias increases. The device is BLIP at 85 K within the operable reverse bias range. The responsivity is greatly enhanced at higher temperature and small bias. The conversion efficiency of photon absorption to photocurrent calculated conservatively at a b...
12 May 1996
TL;DR: In this article, six phototransistor configurations easily produced in CMOS technology and compared their experimental performance are discussed and compared with the experimental performance of a standard CMOS fingerprint identification system.
Abstract: Development of a standard CMOS fingerprint identification system has necessitated the search for a photodetector with the optimum performance of responsivity, crosstalk, dynamic range, and matching parameters. Pixel resolution is also important in order that fingerprint features on the order of 80 /spl mu/m may be detected. This paper discusses six phototransistor configurations easily produced in CMOS technology and compares their experimental performance.
TL;DR: In this paper, the intersubband infrared photodetector performance is theoretically analyzed for various stages of interdiffusion in AlGaAs/GaAs quantum well, and the absorption strength and responsivity are enhanced for certain extents of inter-diffusion and the peak detection wavelength red shifts continuously with a large tunable range from 7 to 38.4 μm.
Abstract: The intersubband infrared photodetector performance is theoretically analyzed for various stages of interdiffusion in AlGaAs/GaAs quantum well. The absorption strength and responsivity are enhanced for certain extents of interdiffusion and the peak detection wavelength red shifts continuously with a large tunable range from 7 to 38.4 μm. The dark current is at an acceptable value for small diffusion extent.
TL;DR: In this paper, the authors have fabricated 0.5×0.5mm3 Ge:Ga photoconductors for the [OI] 63-µm line channel of the Far-Infrared Line Mapper (FILM) on the Infrared Telescope in Space (IRTS).
Abstract: We have fabricated 0.5×0.5×0.5-mm3 Ge:Ga photoconductors for the [OI] 63-µm line channel of the Far-Infrared Line Mapper (FILM) on the Infrared Telescope in Space (IRTS). These photoconductors have a high responsivity of 10–20 A/W (ηG of 0.13–0.25) and a good noise equivalent power (NEP) of about 2×10-17 W/√ Hz for step change in photon influx at a bias field of 1.8 V/cm and operational temperature of 2 K under a low background photon influx of 1.1 to 2.2×106 photons/s. The photoconductors show slow transient response with a time constant of about 10 s at low temperature under low background conditions, but they have almost no hook response. The responsivity to chopped light decreases as the chopping frequency increases from 7.5 to 210 Hz. We infer that this is due to what we call the "moderately fast response". Two time constants, τ a~10 s and τ m~0.23 s, derived from the two-region model of a Ge:Ga photoconductor, correspond to the slow transient response and the "moderately fast response", respectively.
TL;DR: In this paper, a two-section amplifier-modulator-detector semiconductor optical amplifier (AMD-SOA) is presented, which is used as transparent add-drop node in photonic packet-switched optical ring networks.
Abstract: The multifunctional characterization of a two-section amplifier-modulator-detector semiconductor optical amplifier (AMD-SOA) is presented. Detectivity is analyzed in terms of bandwidth and responsivity while modulation properties are characterized by temporal response and extinction ratio. Receiver sensitivities of -26 dBm at 155 Mb/s and -19.5 dBm at 622 Mb/s and error-free signal modulation/transmission with simultaneous 10 dB amplification at 622 Mb/s with a 2/sup 23/-1 PRBS signal are reported. This device could find application as transparent add-drop node in photonic packet-switched optical ring networks.
TL;DR: In this article, the authors demonstrate a technique for decreasing the dark current in GaAs and AlGaAs-GaAs photodetectors without compromising the responsivity or the bandwidth.
Abstract: We demonstrate a novel technique for decreasing the dark current in GaAs and AlGaAs-GaAs metal-semiconductor-metal (MSM) photodetectors without compromising the responsivity or the bandwidth This technique involves the placement of the electrode tips and the contact pads on top of an insulating layer of silicon nitride to eliminate parasitic leakage paths and high electric field regions near the tips of the electrodes For GaAs devices biased at 5 V with a 50/spl times/50-/spl mu/m/sup 2/ active area and 3-/spl mu/m electrode spacing and width, the dark current was reduced from 488 to 249 nA and the noise equivalent power was reduced from 119 to 269 nW For similar AlGaAsGaAs devices, the dark current was reduced from 16 to 03 nA and the noise equivalent power was reduced from 192 to 812 nW
TL;DR: In this paper, a SiGe/Si multiquantum well device grown on a bonded silicon-on-insulator substrate reflector was used for the detection of long wavelength infrared radiation.
Abstract: Resonant‐enhanced detection of long wavelength infrared radiation using a SiGe/Si multiquantum well device grown on a bonded silicon‐on‐insulator substrate reflector is reported. A low refractive index in the wavelength region below the 9.2 μm absorption peak in SiO2 gives high Si/SiO2 reflectivities between 7 and 9 μm. Comparison with a control device grown on a p+‐Si substrate shows a fivefold enhancement in the peak responsivity at 7.2 μm, which is the resonant wavelength of the cavity formed between the buried Si/SiO2 and the Si/air interfaces.
TL;DR: In this paper, the performance of metal-semiconductor-metal photodetectors on Si substrates was investigated, and the devices were fabricated by standard technology employing metalorganic vapor-phase epitaxy growth on unpatterned exactly [001]-oriented Si substrate and conventional photolithography.
Abstract: The performance of In/sub 0.53/Ga/sub 0.47/As metal-semiconductor-metal photodetectors on Si substrates was investigated. The devices were fabricated by standard technology employing metalorganic vapor-phase epitaxy growth on unpatterned exactly [001]-oriented Si substrates and conventional photolithography. At a bias voltage of 5 V the devices exhibit low dark currents of 10/sup -6/-10/sup -7/ A, a high responsivity of 0.26 A/W at 1.3 /spl mu/m, and a cutoff frequency of 1.5 GHz. A further improvement could be achieved by increasing the bias voltage.
TL;DR: In this article, the transient response after bias switching depends on the trapped charge in the device, the transients after switching-on the light is strongly influenced by the generation profile.
Abstract: Bandgap and defect engineered amorphous silicon based nipin photo diodes can be used as color detectors. Changing the applied voltage from -1.5 V to -0.6 V and 1.0 V shifts the responsivity from red, to green, to blue, respectively. Wavelength dependent voltage switching and switching-on the illumination experiments are carried out to investigate the transient behavior and to determine the frame rate for color detection. While the transient response after bias switching depends on the trapped charge in the device, the transients after switching-on the light is strongly influenced by the generation profile.
TL;DR: In this paper, a longwavelength InTlSb photodetector operating at room temperature was reported, and the photo detectors were grown on (100) semi-insulating GaAs substrates by low-pressure metalorganic chemical vapor deposition.
Abstract: Long‐wavelength InTlSb photodetectors operating at room temperature are reported. The photo‐ detectors were grown on (100) semi‐insulating GaAs substrates by low‐pressure metalorganic chemical vapor deposition. Photoresponse of InTlSb photodetectors is observed up to 11 μm at room temperature. The maximum responsivity of an In0.96Tl0.04Sb photodetector is about 6.64 V/W at 77 K, corresponding to a detectivity of about 7.64×108 cm Hz1/2/W. The carrier lifetime in InTlSb photodetectors derived from the stationary photoconductivity is 10–50 ns at 77 K.
TL;DR: In this paper, a dual-band, monolithically integrated InGaAs/InP photodetectors (QWIPs) were constructed on an InP substrate by gas source molecular beam epitaxy.
Abstract: Lattice‐matched InGaAs/InP quantum well intersubband photodetectors (QWIPs) have been grown on an InP substrate by gas source molecular beam epitaxy. Detection at 4.55 μm was observed for a narrow well p‐type InGaAs QWIP which, when complimented by a high responsivity 8.93 μm n‐type InGaAs/InP QWIP, demonstrates the possibility of dual band, monolithically integrated QWIPs on the same InP substrate. Theoretical calculations of the photocurrent spectra are in excellent agreement with the experimental data.