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Βιογραφικό Σημείωμα

Ανάπτυξη | Σύμπτυξη

Δημήτριος Τάσσης

Επίκουρος Καθηγητής, Τμήμα Φυσικής

Προσωπικά Στοιχεία

- 2310998086
dtassis@auth.gr
Scopus ID6603597934
Γνωστικό Αντικείμενο:
ΗΛΕΚΤΡΟΝΙΚΕΣ ΙΔΙΟΤΗΤΕΣ ΗΜΙΑΓΩΓΩΝ ΚΑΙ ΗΜΙΑΓΩΓΙΚΕΣ ΔΙΑΤΑΞΕΙΣ
Επιστημονική Ειδίκευση: Φυσική

Εκπαίδευση

Προπτυχιακές Σπουδές

1990	Πτυχίο, BSc Τμήμα Φυσικής / Φυσικομαθηματική Σχολή Ιωαννίνων Ελλάδα

Μεταπτυχιακές Σπουδές

1993	MEng School of Electronic and Electrical Engineering / Faculty of Engineering University of Leeds Μεγάλη Βρετανία Radio Communications and High Frequency Engineering

Διδακτορικό Δίπλωμα

2000	PhD Τμήμα Φυσικής / Σχολή Θετικών Επιστημών Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης Ελλάδα

Επίβλεψη Εργασιών

Εργασίες Φοιτητών εντός ΑΠΘ

Σε εξέλιξη

Λουρης Ευαγγελος. "Κατασκευή και βελτιστοποίηση οργανικών ενδύσιμων ηλεκτρονικών διατάξεων και κυκλωμάτων σε υποστρώματα υφασμάτων με διαφορετικές δομές"
Στεφανακης Διονυσιος. "Ανάπτυξη νανομετρικών τρανζίστορ εγκαρσίου πεδίου από καρβίδιο του πυριτίου (SiC)", Εξειδίκευση σε: "Ανάπτυξη μικρομετρικών τρανζίστορ εγκαρσίου πεδίου από καρβίδιο του πυριτίου (SiC)"

2017–2018

Αλεπιδης Μιλτιαδης. "Μελέτη των UTBB FD-SOI MOSFET τρανζίστορ με μεθόδους προσομοίωσης TCAD"

2015–2016

Οπρογλιδης Θεοδωρος. "Βελτιστοποίηση νανο-τρανζίστορ πολλαπλής πύλης χωρίς ετεροεπαφές (Junctionless FinFETs) και σύγκριση με συμβατικά FinFET με την βοήθεια προσμοιώσεων"
Τσιαρα Αρτεμισια. "Simulation of nanoscale triple gate FinFETs, with TCAD tools - A comparative study"

2013–2014

Καρατσορη Θεανω. Ανάλυση - Πρόβλεψη της Μεταβλητότητας Τρανζιστορ FinFET Νανοκλίμακας
Σιδηροπουλου Παναγιωτα. Μελέτη των παρασιτικών χωρητικοτήτων σε τρανζίστορ FinFET τριών πυλών χωρίς προσμίξεις ή χαμηλής συγκέντρωσης προσμίξεων

Ερευνητικά Έργα

2013–2014

ΔΡΑΣΗ Β: Ενίσχυση νέων ερευνητών στη βαθμίδα του επίκουρου καθηγητή:Βελτιστοποίηση της δομής "γεφυρωμένων κρυσταλλιτών (Bridged Grain:BG)" σε τρανζίστορ λεπτών υμενίων πολυκρυσταλλικού πυριτίου πύλης (DG-MOSFET)

Δημοσιεύσεις

2014

Άρθρο σε Περιοδικό

Fasarakis N, Karatsori T.A, Tassis Dimitrios, Theodorou Georgios, Andrieu F, Faynot O, Ghibaudo G, Dimitriadis Charalampos (2014). Analytical modeling of threshold voltage and interface ideality factor of nanoscale ultrathin body and buried oxide SOI MOSFETs with back gate control. IEEE Transactions on Electron Devices.
Fasarakis N, Karatsori T.A, Tsormpatzoglou A, Tassis Dimitrios, Papathanasiou Konstantinos, Bucher M, Ghibaudo G, Dimitriadis Charalampos (2014). Compact modeling of nanoscale trapezoidal finFETs. IEEE Transactions on Electron Devices.

Άρθρο σε Πρακτικά Συνεδρίου

Tassis Dimitrios, Messaris I, Fasarakis N, Nikolaidis Spyridon, Ghibaudo G, Dimitriadis Charalampos (2014). Variability analysis-Prediction method for nanoscale triple gate FinFETs. 29th International Conference on Microelectronics, MIEL 2014.

2013

Άρθρο σε Πρακτικά Συνεδρίου

Fasarakis N, Tassis Dimitrios, Tsormpatzoglou A, Papathanasiou Konstantinos, Dimitriadis Charalampos, Ghibaudo G (2013). Compact modeling of nano-scale trapezoidal cross-sectional FinFETs. 2013 IEEE International Semiconductor Conference Dresden - Grenoble.
Tassis Dimitrios, Fasarakis N, Dimitriadis Charalampos, Ghibaudo G (2013). Variability analysis - Prediction method for nanoscale triple gate FinFETs. 2013 IEEE International Semiconductor Conference Dresden - Grenoble.

2012

Άρθρο σε Περιοδικό

Fasarakis N, Tsormpatzoglou A, Tassis D. H, Pappas I, Papathanasiou K, Bucher M, Ghibaudo G, Dimitriadis C. A (2012). Compact model of drain current in short-channel triple-gate FinFETs. Ieee Transactions on Electron Devices. τόμ.59 αρ.7 σ.1891-1898.
Fasarakis Nikolaos, Tsormpatzoglou Andreas, Tassis Dimitrios, Pappas Ilias, Papathanasiou Konstantinos, Bucher M, Ghibaudo G, Dimitriadis Charalampos (2012). Compact Capacitance Model of Undoped or Lightly Doped Ultra-Scaled Triple-Gate FinFETs. Ieee Transactions on Electron Devices. τόμ.59 αρ.12 σ.3306-3312.
Papathanasiou K, Theodorou C. G, Tsormpatzoglou A, Tassis D. H, Dimitriadis C. A, Bucher M, Ghibaudo G (2012). Symmetrical unified compact model of short-channel double-gate MOSFETs. Solid-State Electronics. τόμ.69 σ.55-61.
Tsormpatzoglou A, Pappas I, Tassis D. H, Dimitriadis C. A, Ghibaudo G (2012). Analytical threshold voltage model for short-channel asymmetrical dual-gate material double-gate MOSFETs. Microelectronic Engineering. τόμ.90 σ.9-11.
Tsormpatzoglou A, Papathanasiou K, Fasarakis N, Tassis D. H, Ghibaudo G, Dimitriadis C. A (2012). A Lambert-Function Charge-Based Methodology for Extracting Electrical Parameters of Nanoscale FinFETs. Ieee Transactions on Electron Devices. τόμ.59 αρ.12 σ.3299-3305.

Άρθρο σε Πρακτικά Συνεδρίου

Fasarakis N, Tsormpatzoglou A, Tassis D. H, Pappas I, Papathanasiou K, Dimitriadis C. A (2012). Analytical compact modeling of nanoscale triple-gate FinFETs. σ.72-75.

2011

Άρθρο σε Περιοδικό

Fasarakis N, Tsormpatzoglou A, Tassis D. H, Dimitriadis C. A, Papathanasiou K, Jomaah J, Ghibaudo G (2011). Analytical unified threshold voltage model of short-channel FinFETs and implementation. Solid-State Electronics.
Ioannidis Eleftherios G, Tsormpatzoglou A, Tassis D. H, Dimitriadis Charalampos, Ghibaudo G, Jomaah J (2011). Effect of localized interface charge on the threshold voltage of short-channel undoped symmetrical double-gate MOSFETs. Ieee Transactions on Electron Devices. τόμ.58 αρ.2 σ.433-440.
Tsormpatzoglou A, Tassis D. H, Dimitriadis C. A, Ghibaudo G, Collaert N, Pananakakis G (2011). Analytical threshold voltage model for lightly doped short-channel tri-gate MOSFETs. Solid-State Electronics. τόμ.57 αρ.1 σ.31-34.

2010

Άρθρο σε Περιοδικό

Ioannidis Elefhterios G, Tsormpatzoglou A, Tassis D. H, Dimitriadis Charalampos, Templier F, Kamarinos G (2010). Characterization of traps in the gate dielectric of amorphous and nanocrystalline silicon thin-film transistors by 1/f noise. Journal of Applied Physics. τόμ.108 αρ.10.
Ioannidis Eleftherios G, Theodorou C. G, Tsormpatzoglou A, Tassis D. H, Papathanasiou K, Dimitriadis Charalampos, Jomaah J, Ghibaudo G (2010). Analytical low-frequency noise model in the linear region of lightly doped nanoscale double-gate metal-oxide-semiconductor field-effect transistors. Journal of Applied Physics. τόμ.108 αρ.6.
Tassis D. H, Tsormpatzoglou A, Dimitriadis C. A, Ghibaudo G, Pananakakis G, Collaert N (2010). Source/drain optimization of underlapped lightly doped nanoscale double-gate MOSFETs. Microelectronic Engineering. τόμ.87 αρ.11 σ.2353-2357.
Tsormpatzoglou A, Tassis D. H, Dimitriadis C. A, Ghibaudo G, Pananakakis G, Collaert N (2010). Analytical modelling for the current-voltage characteristics of undoped or lightly-doped symmetric double-gate MOSFETs. Microelectronic Engineering. τόμ.87 αρ.9 σ.1764-1768.

Άρθρο σε Πρακτικά Συνεδρίου

Pappas I, Tassis D, Siskos S, Dimitriadis C. A (2010). Characteristics of double-gate polycrystalline silicon thin-film transistors for AMOLED pixel design. International Conference on Electronics, Circuits, and Systems. Athens, Greece. σ.301-304.

2009

Άρθρο σε Περιοδικό

Tsormpatzoglou A, Tassis D. H, Dimitriadis C. A, Mouis M, Ghibaudo G, Collaert N (2009). Electrical characterization and design optimization of FinFETs with a TiN/HfO2 gate stack. Semiconductor Science and Technology. τόμ.24 αρ.12.
Tsormpatzoglou A, Tassis D. H, Dimitriadis C. A, Ghibaudo G, Pananakakis G, Clerc R (2009). A compact drain current model of short-channel cylindrical gate-all-around MOSFETs. Semiconductor Science and Technology. τόμ.24 αρ.7.

2008

Άρθρο σε Περιοδικό

Arpatzanis N, Hatzopoulos A. T, Tassis D. H, Dimitriadis C. A, Templier F, Oudwan M, Kamarinos G (2008). Degradation of n-channel a-Si:H/nc-Si:H bilayer thin-film transistors under DC electrical stress. Microelectronics Reliability. τόμ.48 αρ.4 σ.531-536.
Hatzopoulos A. T, Tassis D. H, Arpatzanis N, Dimitriadis C. A, Templier F, Oudwan M, Kamarinos G (2008). Stability of n -channel a-Si:Hnc-Si:H bilayer thin-film transistors under dynamic stress. Journal of Applied Physics. τόμ.103 αρ.8.

2007

Άρθρο σε Περιοδικό

Arpatzanis N, Tassis D. H, Dimitriadis C. A, Charitidis C, Song J. D, Choi W. J, Lee J. I (2007). Current-voltage and noise characteristics of reverse-biased Au/n-GaAs Schottky diodes with embedded InAs quantum dots. Semiconductor Science and Technology. τόμ.22 αρ.10 σ.1086-1091.
Hatzopoulos A. T, Arpatzanis N, Tassis D. H, Dimitriadis C. A, Templier F, Oudwan M, Kamarinos G (2007). Stability of amorphous-silicon and nanocrystalline silicon thin-film transistors under DC and AC stress. IEEE Electron Device Letters. τόμ.28 αρ.9 σ.803-805.
Hatzopoulos A. T, Arpatzanis N, Tassis D. H, Dimitriadis C. A, Templier F, Oudwan M, Kamarinos G (2007). Effect of channel width on the electrical characteristics of amorphous/ nanocrystalline silicon bilayer thin-film transistors. Ieee Transactions on Electron Devices. τόμ.54 αρ.5 σ.1265-1269.
Hatzopoulos A. T, Arpatzanis N, Tassis D. H, Dimitriadis C. A, Templier F, Oudwan M, Kamarinos G (2007). 1/f noise characterization of amorphous/nanocrystalline silicon bilayer thin-film transistors. Solid-State Electronics. τόμ.51 αρ.5 σ.726-731.
Hatzopoulos A. T, Arpatzanis N, Tassis D. H, Dimitriadis C. A, Oudwan M, Templier F, Kamarinos G (2007). Study of the drain leakage current in bottom-gated nanocrystalline silicon thin-film transistors by conduction and low-frequency noise measurements. Ieee Transactions on Electron Devices. τόμ.54 αρ.5 σ.1076-1082.

2006

Άρθρο σε Περιοδικό

Arpatzanis N, Tassis D. H, Dimitriadis C. A, Zekentes K, Camara N (2006). Experimental investigation of noise in 4H-SiC p+-n-n+ junctions. Semiconductor Science and Technology. τόμ.21 αρ.5 σ.591-593.
Hatzopoulos A. T, Tassis D. H, Arpatzanis N, Dimitriadis C. A, Kamarinos G (2006). Effects of hot carriers in offset gated polysilicon thin-film transistors. Microelectronics Reliability. τόμ.46 αρ.2-4 σ.311-316.
Hatzopoulos A. T, Pappas I, Tassis D. H, Arpatzanis N, Dimitriadis C. A, Templier F, Oudwan M (2006). Analytical current-voltage model for nanocrystalline silicon thin-film transistors. Applied Physics Letters. τόμ.89 αρ.19.
Hatzopoulos A. T, Arpatzanis N, Tassis D. H, Dimitriadis C. A, Templier F, Oudwan M, Kamarinos G (2006). Electrical and noise characterization of bottom-gated nanocrystalline silicon thin-film transistors. Journal of Applied Physics. τόμ.100 αρ.11.
Pappas I, Hatzopoulos A. T, Tassis D. H, Arpatzanis N, Siskos S, Dimitriadis C. A, Kamarinos G (2006). A simple and continuous polycrystalline silicon thin-film transistor model for SPICE implementation. Journal of Applied Physics. τόμ.100 αρ.6.
Tassis D. H, , Arpatzanis N, Dimitriadis C. A, Kamarinos G (2006). Dynamic hot-carrier induced degradation in n-channel polysilicon thin-film transistors. Microelectronics Reliability. τόμ.46 αρ.12 σ.2032-2037.
Tsormpatzoglou A, Tassis D. H, Dimitriadis C. A, Kamarinos G, Frigeri P, Franchi S, Gombia E, Mosca R (2006). Noise spectroscopy of localized states in Au/n-GaAs Schottky diodes containing InAs quantum dots. Solid-State Electronics. τόμ.50 αρ.3 σ.340-344.
Tsormpatzoglou A, Tassis D. H, Dimitriadis C. A, Frigeri P, Franchi S, Gombia E, Mosca R (2006). Stress-induced local trap levels in Au/n-GaAs Schottky diodes with embedded InAs quantum dots. IEEE Electron Device Letters. τόμ.27 αρ.5 σ.320-322.
Tsormpatzoglou A, Tassis D. H, Dimitriadis C. A, Dózsa L, Galkin N. G, Goroshko D. L, Polyarnyi V. O, Chusovitin E. A (2006). Deep levels in silicon Schottky junctions with embedded arrays of Β-FeSi2 nanocrystallites. Journal of Applied Physics. τόμ.100 αρ.7.

Άρθρο σε Πρακτικά Συνεδρίου

Arpatzanis N, Hatzopoulos A. T, Tassis D. H, Dimitriadis C. A, Kamarinos G (2006). Hot carrier effects in self-aligned and offset-gated polysilicon thin-film transistors. τόμ.888 σ.353-358.
Pappas I, Hatzopoulos A. T, Tassis D. H, Arpatzanis N, Siskos S, Chatzopoulos Alkiviadis, Dimitriadis Charalampos, Kamarinos G (2006). A simple polysilicon thin-film transistor SPICE model. 25th International Conference on Microelectronics (MIEL 2006). Belgrade, Serbia. σ.513-516.

2005

Άρθρο σε Περιοδικό

Hatzopoulos A. T, Tassis D. H, Hastas N. A, Dimitriadis C. A, Kamarinos G (2005). On-state drain current modeling of large-grain poly-si TFTs based on carrier transport through latitudinal and longitudinal grain boundaries. Ieee Transactions on Electron Devices. τόμ.52 αρ.8 σ.1727-1733.
Hatzopoulos A. T, Tassis D. H, Hastas N. A, Dimitriadis C. A, Kamarinos G (2005). An analytical hot-carrier induced degradation model in polysilicon TFTs. Ieee Transactions on Electron Devices. τόμ.52 αρ.10 σ.2182-2186.
Hatzopoulos A. T, Tassis D. H, Dimitriadis C. A, Kamarinos G (2005). Analytical on-state current model of polycrystalline silicon thin-film transistors including the kink effect. Applied Physics Letters. τόμ.87 αρ.6.
Hatzopoulos A. T, Tassis D. H, Hastas N. A, Dimitriadis Charalampos, Siskos S, Hatzopoulos A. A (2005). A simple and continuous on-state current model of polysilicon thin-film transistors for circuit simulation. Journal of Physics: Conference Series. τόμ.10 αρ.1 σ.27-30.
Koutsouras D. A, Hastas N. A, Tassis D. H, Dimitriadis C. A, Frigeri P, Franchi S, Gombia E, Mosca R (2005). Depth distribution of traps in Aun-GaAs Schottky diodes with embedded InAs quantum dots. Journal of Applied Physics. τόμ.97 αρ.6 σ.1-6.
Tassis D. H, Hastas N. A, Dimitriadis C. A, Kamarinos G (2005). Improved analysis of low frequency noise in polycrystalline silicon thin-film transistors. Solid-State Electronics. τόμ.49 αρ.3 σ.513-515.
Tsormpatzoglou A, Hastas N. A, Tassis D. H, Dimitriadis C. A, Kamarinos G, Frigeri P, Franchi S, Gombia E, Mosca R (2005). Low-frequency noise spectroscopy in Au/n-GaAs Schottky diodes with InAs quantum dots. Applied Physics Letters. τόμ.87 αρ.16 σ.1-3.

2004

Άρθρο σε Περιοδικό

Hastas N. A, Tassis D. H, Dimitriadis C. A, Dozsa L, Franchi, Frigeri P (2004). Electrical transport and low frequency noise characteristics of Au/n-GaAs Schottky diodes containing InAs quantum dots. Semiconductor Science and Technology. τόμ.19 αρ.3 σ.461-467.

2003

Άρθρο σε Περιοδικό

Hastas N. A, Tassis D. H, Dimitriadis C. A, Kamarinos G (2003). Determination of interface and bulk traps in the subthreshold region of polycrystalline silicon thin-film transistors. Ieee Transactions on Electron Devices. τόμ.50 αρ.9 σ.1991-1994.
Hastas N. A, Tassis D. H, Dimitriadis C. A, Brini J, Kamarinos G (2003). Stability of hydrogenated in pure hydrogen plasma p-channel polycrystalline silicon thin-film transistors. Solid-State Electronics. τόμ.47 αρ.1 σ.25-31.

2002

Άρθρο σε Περιοδικό

Hastas N. A, Dimitriadis C. A, Panayiotatos Y, Tassis D. H, Logothetidis S, Papadimitriou D, Roupakas G, Adamopoulos G (2002). High-field transport and noise properties of sputter-deposited amorphous carbon-silicon heterojunctions. Semiconductor Science and Technology. τόμ.17 αρ.7 σ.662-667.

2001

Άρθρο σε Περιοδικό

Hastas N. A, Dimitriadis C. A, Tassis D. H, Panayiotatos Y, Logothetidis S, Papadimitriou D (2001). Electrical properties of magnetron sputtered amorphous carbon films with sequential sp(3)-rich/sp(2)-rich layered structure. Applied Physics Letters. τόμ.79 αρ.20 σ.3269-3271.
Hastas N. A, Dimitriadis C. A, Tassis D. H, Logothetidis S (2001). Electrical characterization of nanocrystalline carbon-silicon heterojunctions. Applied Physics Letters. τόμ.79 αρ.5 σ.638-640.
Hastas N. A, Dimitriadis C. A, Patsalas P, Panayiotatos Y, Tassis D. H, Logothetidis S (2001). Structural, electrical, and low-frequency-noise properties of amorphous-carbon-silicon heterojunctions. Journal of Applied Physics. τόμ.89 αρ.5 σ.2832-2838.

2000

Άρθρο σε Περιοδικό

Hastas N. A, Dimitriadis C. A, Panayiotatos Y, Tassis D. H, Patsalas P, Logothetidis S (2000). Noise characterization of sputtered amorphous carbon films. Journal of Applied Physics. τόμ.88 αρ.9 σ.5482-5484.

1999

Άρθρο σε Περιοδικό

Dimitriadis C. A, Lee J. I, Patsalas P, Logothetidis S, Tassis D. H, Brini J, Kamarinos G (1999). Characteristics of TiNx/n-Si Schottky diodes deposited by reactive magnetron sputtering. Journal of Applied Physics. τόμ.85 αρ.8 I σ.4238-4242.
Tassis D. H, Dimitriadis C. A, Polychroniadis E. K, Brini J, Kamarinos G (1999). Structural and trap properties of polycrystalline semiconducting FeSi2 thin films. Semiconductor Science and Technology. τόμ.14 αρ.11 σ.967-974.
Tassis D. H, Dimitriadis C. A, Brini J, Kamarinos G, Birbas A (1999). Low-frequency noise in polycrystalline semiconducting FeSi2 thin films. Journal of Applied Physics. τόμ.85 αρ.8 I σ.4091-4095.

1998

Άρθρο σε Περιοδικό

Tassis D. H, Dimitriadis C. A, Valassiades O (1998). The Meyer-Neldel rule in the conductivity of polycrystalline semiconducting FeSi2 films. Journal of Applied Physics. τόμ.84 αρ.5 σ.2960-2962.
Tassis D. H, Dimitriadis C. A, Brini J, Kamarinos G, Angelakeris M, Flevaris N (1998). Low frequency noise in β-FeSi2/n-Si heterojunctions. Applied Physics Letters. τόμ.72 αρ.6 σ.713-715.

1997

Άρθρο σε Περιοδικό

Tassis D. H, Dimitriadis C. A, Boultadakis S, Arvanitidis J, Ves S, Kokkou S, Logothetidis S, Valassiades O, Poulopoulos P, Flevaris N. K (1997). Influence of conventional furnace and rapid thermal annealing on the quality of polycrystalline β-FeSi2 thin films grown from vapor-deposited Fe/Si multilayers. Thin Solid Films. τόμ.310 αρ.1-2 σ.115-122.

1996

Άρθρο σε Περιοδικό

Dimitriadis C. A, Tassis D. H (1996). On the threshold voltage and channel conductance of polycrystalline silicon thin-film transistors. Journal of Applied Physics. τόμ.79 αρ.8 σ.4431-4437.
Tassis D. H, Mitsas C. L, Zorba T. T, Dimitriadis C. A, Valassiades O, Siapkas D. I, Angelakeris M, Poulopoulos P, Flevaris N. K, Kiriakidis G (1996). Infrared spectroscopic and electronic transport properties of polycrystalline semiconducting FeSi 2 thin films. Journal of Applied Physics. τόμ.80 αρ.2 σ.962-968.
Tassis D. H, Mitsas C. L, Zorba T. T, Angelakeris M, Dimitriadis C. A, Valassiades O, Siapkas D. I, Kiriakidis G (1996). Optical and electrical characterization of high quality β-FeSi2 thin films grown by solid phase epitaxy. Applied Surface Science. τόμ.102 σ.178-183.

1995

Άρθρο σε Περιοδικό

Dimitriadis C. A, Tassis D. H (1995). Output characteristics of short-channel polycrystalline silicon thin-film transistors. Journal of Applied Physics. τόμ.77 αρ.5 σ.2177-2183.

1994

Άρθρο σε Περιοδικό

Dimitriadis C. A, Tassis D. H, Economou N. A, Giakoumakis G (1994). Influence of deposition pressure on the bulk and interface states in low pressure chemical vapor deposited polycrystalline silicon thin-film transistors. Applied Physics Letters. τόμ.64 αρ.20 σ.2709-2711.

1993

Άρθρο σε Περιοδικό

Dimitriadis C. A, Tassis D. H, Economou N. A, Lowe A. J (1993). Determination of bulk states and interface states distributions in polycrystalline silicon thin-film transistors. Journal of Applied Physics. τόμ.74 αρ.4 σ.2919-2924.

Ενημερώθηκε: 2018-09-21