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Material and device characterization using a correlation spectrum analyzer
Materials Science in Semiconductor Processing 4 (2001) 133–136
Material and device characterization using a correlation spectrum analyzer G. Ferrari, M. Sampietro* Dipartimento di Elettronica e Informazione, Politecnico di Milano, P.za L.da Vinci 32, 20133 Milano, Italy
Abstract The paper presents the possibilities offered by the Correlation Spectrum Analyzer in the characterisation of semiconductor materials and microelectronic devices. The instrument performs noise analysis in a frequency range from p p a few mHz to 1 MHz with an extraordinary sensitivity of 1fA/ Hz in current noise measurements and of 20 pV/ Hz in voltage noise measurements. Noise spectra taken in these conditions can be used as a non-destructive-sensitive probe to investigate physical properties of semiconductor materials as well as quantify the noise produced by new devices. As an example of these applications, the text reports on the extraction of noise parameters from a MOSFET operated in strong sub-threshold regime to be inserted in noise models for circuit simulation and on the determination of carrier mobility in single-crystal cadmium telluride (CdTe) samples. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Noise measurement; Spectrum analyzer; Device characterization; Subthreshold MOSFET; CdTe
1. Introduction The importance of noise measurements in the characterisation of semiconductor material or devices is manifold. Noise measurements can be (i) directly used to quantify the noise contribution of a new device (ii) indirectly used to investigate the statistical properties of the carrier transport and (iii) indirectly used to measure other physical properties of the samples, such as device bandwidth, carriers time of flight, carriers mobility and others [1,2]. Nowadays particular experimental conditions occur in which the noise power density of interest is very low, well below the sensitivity threshold of the best available commercial instruments. To cope with such extreme measuring situations, a Correlation Spectrum Analyzer should be used. An instrument using this technique is *Corresponding author. Tel.: +39-0223996188; fax: +39022367604. E-mail address: [email protected] (M. Sampietro).
based on the processing of signals from two independent channels operated in parallel and takes advantage of the uncorrelated properties of the noises of the two input stages. The instrument is therefore made of two separate, independent input amplifiers in parallel properly connected to the same device under test (DUT) and can be provided with special input stages that perform direct measurements of the voltage noise across the DUT (see Fig. 1(a) for a schematic diagram of this configuration) or of the current noise flowing in the DUT independently biased at any desired voltage by the instrument itself (see Fig. 1(b)). A detailed description of the instrument is given in Ref. [3]. The instrument operates in a frequency range from a few mHz to 1 MHz p and has a sensitivity of 1 fA/ Hz in current noise p measurements and of 20 pV/ Hz in voltage noise measurements. The possibility to perform noise measurements with a sensitivity not available before, opens new perspectives in testing advanced devices and in measuring physical parameters of new semiconductor materials.
1369-8001/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 9 - 8 0 0 1 ( 0 0 ) 0 0 1 3 8 - 4
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G. Ferrari, M. Sampietro / Materials Science in Semiconductor Processing 4 (2001) 133–136
Fig. 1. Block diagram of the Correlation Spectrum Analyzer in the configuration for voltage measurements (a) and for direct current measurements (b).
Fig. 2. (a) Noise current spectra of a 10 1.2 mm2 n-channel MOSFET in saturation region at various bias conditions; (b) 1=f noise power density taken at 10 Hz vs. the drain current.
2. Parameters extraction on sub-threshold operated MOSFETS The trend of low-power circuits and systems solicits the operation of MOSFET devices in sub-threshold regime, in order to reduce current flow while maintaining the highest possible transconductance. A precise modeling of the device noise parameters in these operating conditions is very important, in particular when the device noise performance directly affects the functionality of the full circuit, as it is the case, for example, with the phase noise in low-power oscillators introduced by the 1=f noise components of the used device [4]. Despite the very low value of standing current (as low as 320 pA), the direct measurement of the current noise spectrum of a MOSFET operated in strong subthreshold can be very precisely performed with the Correlation Spectrum Analyzer. Fig. 2(a) shows the spectra of 1.2 mm nMOSFET at various bias conditions, showing the possibility to easily investigate currents of the order of few nA, as given by strong sub-threshold operation. The 1=f noise power density taken at 10 Hz is plotted in Fig. 2(b) as a function of the standing current clearly
showing at about 1 mA the delimiting current between subthreshold and inversion region of operation. From these measurements one can extract the coefficients for device noise models of any complexity to be used in circuit simulation programs. For example, the standard SPICE noise model of the MOSFET, SId ¼ 4kT
KF I AF 1 2 gm þ 2 d ; 3 Leff Cox f
would result in the following coefficients: AF ¼ 1:9 and KF ¼ 2:1 1022 when in strong subthreshold and AF ¼ 1:05 and KF ¼ 4:8 1027 when in inversion. The high precision of the noise measurement, owing also to the possibility to bias the MOSFET directly with the instrument input ports without adding additional components, reflects in very accurate parameters and, ultimately, in a better circuit design.
3. Shot noise reduction in quantum devices A striking application of the suppression of instrument noise by using correlation techniques has been done by Saminadayar and co-workers in the
G. Ferrari, M. Sampietro / Materials Science in Semiconductor Processing 4 (2001) 133–136
135
Fig. 3. (a) Schematic of the single-crystal CdTe detector. (b) High-frequency section of CdTe current noise spectra at different bias voltages. (c) Carriers mobility in a CdTe crystal as a function of the biasing voltage applied across the device.
experimental observation of fractionally charged Laughlin quasiparticles [5] and on the precise evaluation of the quantum suppression of shot noise in mesoscopic conductors [6]. The low standing currents and consequently the very low-noise spectral densities to be p measured (of about 0.4 nV/ Hz), lower than the level set by the full shot noise, are at the real limit of sensitivity for a standard instrument [7] and have driven the authors to the choice of a two-channel crosscorrelation spectrum analysis method to ensure ultralow noise detection with 10 mK noise temperature resolution.
4. Carrier mobility evaluation on single-crystal semiconductors As an example of indirect extraction of semiconductor physical properties from high-sensitivity noise measurements, we present the experimental calculation of carrier mobility of a single-crystal CdTe (see Fig. 3(a)) based on the consideration that the maximum possible extension of the shot noise is limited by the transit time of the
carriers in the device [8]. Fig. 3(b) shows the current noise spectra taken at various device operating conditions. The spectrum is flat only until a given transition frequency f0 , after which it decreases neatly. In order to better estimate the transition frequency, a fitting (dotted line) has been made on the experimental data by using a single-pole function Zð f Þ ¼ Z0
1 1 þ ð f =f0 Þ2
in which Z0 is the best fit of the flat white noise section. The values of the frequency f0 delimiting the flat noise spectrum set the inverse of the transit time ttr of the carriers within the active part of the device. In the case of our CdTe sample, having a length L¼ 2 mm, an average carrier mobility can be obtained as m¼
L cm2 : ffi 21 sV ttr ðVext =LÞ
Fig. 3c shows the mobility as a function of the bias voltage as obtained from the experimental noise spectra. The small diminishing of the mobility at high fields is analogous to the same typical behavior in silicon devices
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G. Ferrari, M. Sampietro / Materials Science in Semiconductor Processing 4 (2001) 133–136
although at higher electric fields [9]. The most important feature made available by the Correlation Spectrum Analyzer and not available with other techniques is that the carrier mobility can be calculated directly on the real device biased in its operating conditions, by using a configuration as given in Fig. 1(b).
References [1] Landauer R. Nature 1998;392:658. [2] Jones BK. IEEE Trans Electron Devices 1994;41:2188.
[3] Sampietro M, Fasoli L, Ferrari G. Rev Sci Instr 1999;70:2520. [4] Chang J, Abidi AA, Viswanathan CR. IEEE Trans Electron Devices 1994;41:1965. [5] Saminadayar L, Glattli DC, Jin Y, Etienne B. Phys Rev Lett 1997;79:2526. [6] Kumar A, Saminadayar L, Glattli DC, Jin Y, Etienne B. Phys Rev Lett 1996;76:2778. [7] de Picciotto R, Reznikov M, Heiblum M, Umansky V, Bunin G, Mahalu D. Nature 1997;389:162. [8] Buckingham MJ, Noise in electronic devices and systems New York: Wiley, 1983. p. 34. [9] Smith P, Inoue M, Frey J. Appl Phys Lett 1980;37:797.
Material and device characterization using a correlation spectrum analyzer G. Ferrari, M. Sampietro* Dipartimento di Elettronica e Informazione, Politecnico di Milano, P.za L.da Vinci 32, 20133 Milano, Italy
Abstract The paper presents the possibilities offered by the Correlation Spectrum Analyzer in the characterisation of semiconductor materials and microelectronic devices. The instrument performs noise analysis in a frequency range from p p a few mHz to 1 MHz with an extraordinary sensitivity of 1fA/ Hz in current noise measurements and of 20 pV/ Hz in voltage noise measurements. Noise spectra taken in these conditions can be used as a non-destructive-sensitive probe to investigate physical properties of semiconductor materials as well as quantify the noise produced by new devices. As an example of these applications, the text reports on the extraction of noise parameters from a MOSFET operated in strong sub-threshold regime to be inserted in noise models for circuit simulation and on the determination of carrier mobility in single-crystal cadmium telluride (CdTe) samples. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Noise measurement; Spectrum analyzer; Device characterization; Subthreshold MOSFET; CdTe
1. Introduction The importance of noise measurements in the characterisation of semiconductor material or devices is manifold. Noise measurements can be (i) directly used to quantify the noise contribution of a new device (ii) indirectly used to investigate the statistical properties of the carrier transport and (iii) indirectly used to measure other physical properties of the samples, such as device bandwidth, carriers time of flight, carriers mobility and others [1,2]. Nowadays particular experimental conditions occur in which the noise power density of interest is very low, well below the sensitivity threshold of the best available commercial instruments. To cope with such extreme measuring situations, a Correlation Spectrum Analyzer should be used. An instrument using this technique is *Corresponding author. Tel.: +39-0223996188; fax: +39022367604. E-mail address: [email protected] (M. Sampietro).
based on the processing of signals from two independent channels operated in parallel and takes advantage of the uncorrelated properties of the noises of the two input stages. The instrument is therefore made of two separate, independent input amplifiers in parallel properly connected to the same device under test (DUT) and can be provided with special input stages that perform direct measurements of the voltage noise across the DUT (see Fig. 1(a) for a schematic diagram of this configuration) or of the current noise flowing in the DUT independently biased at any desired voltage by the instrument itself (see Fig. 1(b)). A detailed description of the instrument is given in Ref. [3]. The instrument operates in a frequency range from a few mHz to 1 MHz p and has a sensitivity of 1 fA/ Hz in current noise p measurements and of 20 pV/ Hz in voltage noise measurements. The possibility to perform noise measurements with a sensitivity not available before, opens new perspectives in testing advanced devices and in measuring physical parameters of new semiconductor materials.
1369-8001/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 9 - 8 0 0 1 ( 0 0 ) 0 0 1 3 8 - 4
134
G. Ferrari, M. Sampietro / Materials Science in Semiconductor Processing 4 (2001) 133–136
Fig. 1. Block diagram of the Correlation Spectrum Analyzer in the configuration for voltage measurements (a) and for direct current measurements (b).
Fig. 2. (a) Noise current spectra of a 10 1.2 mm2 n-channel MOSFET in saturation region at various bias conditions; (b) 1=f noise power density taken at 10 Hz vs. the drain current.
2. Parameters extraction on sub-threshold operated MOSFETS The trend of low-power circuits and systems solicits the operation of MOSFET devices in sub-threshold regime, in order to reduce current flow while maintaining the highest possible transconductance. A precise modeling of the device noise parameters in these operating conditions is very important, in particular when the device noise performance directly affects the functionality of the full circuit, as it is the case, for example, with the phase noise in low-power oscillators introduced by the 1=f noise components of the used device [4]. Despite the very low value of standing current (as low as 320 pA), the direct measurement of the current noise spectrum of a MOSFET operated in strong subthreshold can be very precisely performed with the Correlation Spectrum Analyzer. Fig. 2(a) shows the spectra of 1.2 mm nMOSFET at various bias conditions, showing the possibility to easily investigate currents of the order of few nA, as given by strong sub-threshold operation. The 1=f noise power density taken at 10 Hz is plotted in Fig. 2(b) as a function of the standing current clearly
showing at about 1 mA the delimiting current between subthreshold and inversion region of operation. From these measurements one can extract the coefficients for device noise models of any complexity to be used in circuit simulation programs. For example, the standard SPICE noise model of the MOSFET, SId ¼ 4kT
KF I AF 1 2 gm þ 2 d ; 3 Leff Cox f
would result in the following coefficients: AF ¼ 1:9 and KF ¼ 2:1 1022 when in strong subthreshold and AF ¼ 1:05 and KF ¼ 4:8 1027 when in inversion. The high precision of the noise measurement, owing also to the possibility to bias the MOSFET directly with the instrument input ports without adding additional components, reflects in very accurate parameters and, ultimately, in a better circuit design.
3. Shot noise reduction in quantum devices A striking application of the suppression of instrument noise by using correlation techniques has been done by Saminadayar and co-workers in the
G. Ferrari, M. Sampietro / Materials Science in Semiconductor Processing 4 (2001) 133–136
135
Fig. 3. (a) Schematic of the single-crystal CdTe detector. (b) High-frequency section of CdTe current noise spectra at different bias voltages. (c) Carriers mobility in a CdTe crystal as a function of the biasing voltage applied across the device.
experimental observation of fractionally charged Laughlin quasiparticles [5] and on the precise evaluation of the quantum suppression of shot noise in mesoscopic conductors [6]. The low standing currents and consequently the very low-noise spectral densities to be p measured (of about 0.4 nV/ Hz), lower than the level set by the full shot noise, are at the real limit of sensitivity for a standard instrument [7] and have driven the authors to the choice of a two-channel crosscorrelation spectrum analysis method to ensure ultralow noise detection with 10 mK noise temperature resolution.
4. Carrier mobility evaluation on single-crystal semiconductors As an example of indirect extraction of semiconductor physical properties from high-sensitivity noise measurements, we present the experimental calculation of carrier mobility of a single-crystal CdTe (see Fig. 3(a)) based on the consideration that the maximum possible extension of the shot noise is limited by the transit time of the
carriers in the device [8]. Fig. 3(b) shows the current noise spectra taken at various device operating conditions. The spectrum is flat only until a given transition frequency f0 , after which it decreases neatly. In order to better estimate the transition frequency, a fitting (dotted line) has been made on the experimental data by using a single-pole function Zð f Þ ¼ Z0
1 1 þ ð f =f0 Þ2
in which Z0 is the best fit of the flat white noise section. The values of the frequency f0 delimiting the flat noise spectrum set the inverse of the transit time ttr of the carriers within the active part of the device. In the case of our CdTe sample, having a length L¼ 2 mm, an average carrier mobility can be obtained as m¼
L cm2 : ffi 21 sV ttr ðVext =LÞ
Fig. 3c shows the mobility as a function of the bias voltage as obtained from the experimental noise spectra. The small diminishing of the mobility at high fields is analogous to the same typical behavior in silicon devices
136
G. Ferrari, M. Sampietro / Materials Science in Semiconductor Processing 4 (2001) 133–136
although at higher electric fields [9]. The most important feature made available by the Correlation Spectrum Analyzer and not available with other techniques is that the carrier mobility can be calculated directly on the real device biased in its operating conditions, by using a configuration as given in Fig. 1(b).
References [1] Landauer R. Nature 1998;392:658. [2] Jones BK. IEEE Trans Electron Devices 1994;41:2188.
[3] Sampietro M, Fasoli L, Ferrari G. Rev Sci Instr 1999;70:2520. [4] Chang J, Abidi AA, Viswanathan CR. IEEE Trans Electron Devices 1994;41:1965. [5] Saminadayar L, Glattli DC, Jin Y, Etienne B. Phys Rev Lett 1997;79:2526. [6] Kumar A, Saminadayar L, Glattli DC, Jin Y, Etienne B. Phys Rev Lett 1996;76:2778. [7] de Picciotto R, Reznikov M, Heiblum M, Umansky V, Bunin G, Mahalu D. Nature 1997;389:162. [8] Buckingham MJ, Noise in electronic devices and systems New York: Wiley, 1983. p. 34. [9] Smith P, Inoue M, Frey J. Appl Phys Lett 1980;37:797.