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Phonon observations from 1ƒ noise measurements
Volume 104A, number 3
PHYSICS LETTERS
20 August 1984
PHONON OBSERVATIONS FROM lff NOISE MEASUREMENTS Mihai MIH~dLA R & D Center for Semiconductors (CCSITS). Str. Erou lancu Nicolae 32B, 72996 Bucharest, Romania Received 13 June 1984
From mobility fluctuation 1/f noise parameter measurements five phononic energies corresponding to LO, TO vibrational modes as well as TA + $2 or O, TO + TA, TO + O combined modes were identified. They stand for phonon replicas of nonradiative recombination processes. It is thus demonstrated that the carrier-phonon interaction is the source of 1/f noise in semiconductors.
A way to dispose of the recombination energy in semiconductors is to emit it as lattice vibrations [ 1,2]. Through carrier-phonon interactions [3] such a process could be a source of I / f noise. It was possible to verify this hypothesis by measuring the mobility fluctuation 1//'noise parameter for holes (ap) injected from base to emitter in bipolar transistors with, and for comparison, without, dislocated emitters, because Narayanamurti et al. [3] proved that dislocated p - n junctions show enhanced phonon emission. Extending Kleinpenning's mobility fluctuation theory [5] for a p - n junction to a bipolar transistor structure, van der Ziel [6] deduced the following expression for C~p: ap = (3SIB/IB ,
(1)
4-(TO • TA) "~ -~
v re"
,,, I,.-
10-4 8 6
1-LO
2-TO
LIJ n"~ -
3-( TA. 5 2 ) or0 [ ?
4
-~TO.O)
2
O..
¢A,k
1oo
z
6
~
4 @
where S I s is the noise spectral density o f the base current I B . The coefficient/3 depends on the electronic charge, the measuring frequency (in this case 10 Hz), and some injection and electrical characteristics of the devices. For the devices used in this experiment ~ 6.25 X 1010 A -1 Hz. All the measurements were performed at room temperature. During these measurements it was observed that for a given transistor batch the distribution of ap values versus base currents exhibits maxima (fig. 1), indicating that in some devices the scattering is resonant in character. Repeating the measurements on fifteen transistor batches, processed under different conditions and at intervals o f years, similar results were obtained. In search for an adequate explanation of these results, the
10-6
I
I
I
I
I
I
I
i
I
I
3
i.
5
6
7
8
9
10-7
2
3
BASE CURRENT, A Fig. 1. The distribution of the mobility fluctuation 1/f noise parameter for holes C~pversus base current I B for a batch of devices containing dislocations. For all devices the base currents were determined at a collector current of 10 uA. Notations: LO, longitudinal optical; TO, transversal optical; TA, transversal acoustical; O, optical phonons of zero-wave number; S2 , longitudinal acoustic phonons corresponding to scattering between valleys on different axes.
157
Volume 104A, number 3
PHYSICS LETTERS
20 August 1984
Table 1 Peak IB(A) number 1 2 3 4 5
3.3 4.1 6.2 1.3 1.95
× × × × ×
IR(A) 10-8 10-8 10 -8 10-7 10-7
4 × 4.1× 5.5× 7.2 × 2.1 ×
10 -11 10 -11 10 -11 10 -11 10-11
qV from 1If noise (10-3eV)
Ref. [10] (10-3eV)
Ref. [8] (10-3eV)
Assignment
52.3 57.8 61.3 a) 76.3 117.6 b)
53.7 57.8 64.4 76.0 120.7
54.3 57.6 65.4 78.6 121.0
LO TO TA+S2orO TO + TA TO+O
a) Palevsky et al. [15] reported 61.5 meV. b) Haynes et al. [16] reported 119 meV. qVvalues for each maximum were calculated from a Shockley-type formula [7]: 1B = 1R e x p ( A E g / k T ) [ e x p ( q V / k T ) - 1 ] ,
(2)
where 1R is the reverse current o f the e m i t t e r - b a s e junction, and AEg stands for the band-gap narrowing due to heavy doping effects in the emitter. Taking [7] AEg = 0.12 eV, the following sequence o f q V values was obtained: 52.3 meV, 57.8 meV, 61.3 meV, 76.3 meV and 117.6 meV. These energies correspond to fundamental LO and TO lattice vibration modes, and to TA + S 2 or O [11 ], TO + TA, and TO + O combined modes, respectively; $2(0.046 eV) and 0(0.063 +0.003 eV) are the energies corresponding to longitudinal acoustic-mode phonon scattering between the valleys on different axes [9] and to o p t i c ~ phonons of zero-wave number [ 10,15], respectively. Table 1 shows that the phononic energies determined from l / f noise measurements are in fairly good agreement with the data obtained from neutron scattering [ 10] or tunneling spectroscopy [8]. A zone ~ o f " f o r b i d d e n " currents was observed. A rough estimation o f f gave a value o f 0.0057 eV which is exactly the localization energy for excitons bound to neutral phosphorus donors in silicon * 1. The (TO + TA) and (TO + O) peaks always appeared, regardless whether the devices contained dislocations or not. The remaining peaks were mainly observed for devices conraining dislocations. These results give an indication that the sharp peaks located above ~ are due to exciton two-phonon replicas. Dean, Haynes and Flood [ 11 ] showed that the TO + O phonon replicas are due ,1 Dean et al. [ 11 ] showed that although the probability of a single O phonon-assisted transition is weak, such a possibility exists. 158
either to free exciton recombination in the pure silicon lattice or to bound exciton recombination at neutral donors while a TO + TA replica could be attributed to a transition o f free excitons involving two electrons in the vicinity o f neutral donors. We only mention that also phonons could be emitted in the two-phonon processes [8,12], a phenomenon which can be interpreted in the sense o f Handel's [ 13 ] theory of 1/f noise. Concluding, one can say that a large variety o f quantum phenomena are involved in the 1/f noise generation. Confirming Hooge's [ 14] mobility fluctuation hypothesis, these results, in total agreement with Hooge's and Vandamme's ones [3], definitely show that the c a r r i e r - p h o n o n interaction is the source o f 1/fnoise in semiconductors.
[1] Y. Toyozawa, Solid State Electron. 21 (1978) 1313. [2] C.H. Henry and D.V. Lang, Phys. Rev. B15 (1977) 989. [3] F.N. Hooge and L.K.J. Vandamme, Phys. Lett. 66A (1978) 315. [4] V. Narayanamurfi, R.A. Logan and M.A. Chin, Phys. Rev. Lett. 40 (1978) 63. [5] T.G.M. Kleinpenning, Physiea 98B (1980) 289. [6] A. van der Ziel, Solid State Electron. 25 (1982) 141. [7] R.P. Mertens, R.J. van Overstraeten and H.J. de Man, Adv. Electron. Electron Phys. 55 (1981) 77. [8] A.G. Chynoweth, R.A. Logan and D.E. Thomas, Phys. Rev. 125 (1962) 877. [9] W.P. Dumke, Phys. Rev. 118 (1960) 938. [10] B.N. Brockhouse, Phys. Rev. Lett. 2 (1959) 256. [11] P.J. Dean, J.R. Haynes and W.F. Flood, Phys. Rev. 161 (1967) 711. [12] J.R. Haynes, Phys. Rev. Lett. 17 (1966) 860. [13] P.H. Handel, Phys. Rev. Lett. 34 (1975) 1492. [ 14] F.N. Hooge, Physica 60 (1972) 130. [15] H. Palevsky, D.J. Hughes, W. Kley and E. Tunkelo, Phys. Rev. Lett. 2 (1958) 258. [16] J.R. Haynes, M. Lax and W.F. Flood, J. Phys. Chem. Solids 8 (1959) 392.
PHYSICS LETTERS
20 August 1984
PHONON OBSERVATIONS FROM lff NOISE MEASUREMENTS Mihai MIH~dLA R & D Center for Semiconductors (CCSITS). Str. Erou lancu Nicolae 32B, 72996 Bucharest, Romania Received 13 June 1984
From mobility fluctuation 1/f noise parameter measurements five phononic energies corresponding to LO, TO vibrational modes as well as TA + $2 or O, TO + TA, TO + O combined modes were identified. They stand for phonon replicas of nonradiative recombination processes. It is thus demonstrated that the carrier-phonon interaction is the source of 1/f noise in semiconductors.
A way to dispose of the recombination energy in semiconductors is to emit it as lattice vibrations [ 1,2]. Through carrier-phonon interactions [3] such a process could be a source of I / f noise. It was possible to verify this hypothesis by measuring the mobility fluctuation 1//'noise parameter for holes (ap) injected from base to emitter in bipolar transistors with, and for comparison, without, dislocated emitters, because Narayanamurti et al. [3] proved that dislocated p - n junctions show enhanced phonon emission. Extending Kleinpenning's mobility fluctuation theory [5] for a p - n junction to a bipolar transistor structure, van der Ziel [6] deduced the following expression for C~p: ap = (3SIB/IB ,
(1)
4-(TO • TA) "~ -~
v re"
,,, I,.-
10-4 8 6
1-LO
2-TO
LIJ n"~ -
3-( TA. 5 2 ) or0 [ ?
4
-~TO.O)
2
O..
¢A,k
1oo
z
6
~
4 @
where S I s is the noise spectral density o f the base current I B . The coefficient/3 depends on the electronic charge, the measuring frequency (in this case 10 Hz), and some injection and electrical characteristics of the devices. For the devices used in this experiment ~ 6.25 X 1010 A -1 Hz. All the measurements were performed at room temperature. During these measurements it was observed that for a given transistor batch the distribution of ap values versus base currents exhibits maxima (fig. 1), indicating that in some devices the scattering is resonant in character. Repeating the measurements on fifteen transistor batches, processed under different conditions and at intervals o f years, similar results were obtained. In search for an adequate explanation of these results, the
10-6
I
I
I
I
I
I
I
i
I
I
3
i.
5
6
7
8
9
10-7
2
3
BASE CURRENT, A Fig. 1. The distribution of the mobility fluctuation 1/f noise parameter for holes C~pversus base current I B for a batch of devices containing dislocations. For all devices the base currents were determined at a collector current of 10 uA. Notations: LO, longitudinal optical; TO, transversal optical; TA, transversal acoustical; O, optical phonons of zero-wave number; S2 , longitudinal acoustic phonons corresponding to scattering between valleys on different axes.
157
Volume 104A, number 3
PHYSICS LETTERS
20 August 1984
Table 1 Peak IB(A) number 1 2 3 4 5
3.3 4.1 6.2 1.3 1.95
× × × × ×
IR(A) 10-8 10-8 10 -8 10-7 10-7
4 × 4.1× 5.5× 7.2 × 2.1 ×
10 -11 10 -11 10 -11 10 -11 10-11
qV from 1If noise (10-3eV)
Ref. [10] (10-3eV)
Ref. [8] (10-3eV)
Assignment
52.3 57.8 61.3 a) 76.3 117.6 b)
53.7 57.8 64.4 76.0 120.7
54.3 57.6 65.4 78.6 121.0
LO TO TA+S2orO TO + TA TO+O
a) Palevsky et al. [15] reported 61.5 meV. b) Haynes et al. [16] reported 119 meV. qVvalues for each maximum were calculated from a Shockley-type formula [7]: 1B = 1R e x p ( A E g / k T ) [ e x p ( q V / k T ) - 1 ] ,
(2)
where 1R is the reverse current o f the e m i t t e r - b a s e junction, and AEg stands for the band-gap narrowing due to heavy doping effects in the emitter. Taking [7] AEg = 0.12 eV, the following sequence o f q V values was obtained: 52.3 meV, 57.8 meV, 61.3 meV, 76.3 meV and 117.6 meV. These energies correspond to fundamental LO and TO lattice vibration modes, and to TA + S 2 or O [11 ], TO + TA, and TO + O combined modes, respectively; $2(0.046 eV) and 0(0.063 +0.003 eV) are the energies corresponding to longitudinal acoustic-mode phonon scattering between the valleys on different axes [9] and to o p t i c ~ phonons of zero-wave number [ 10,15], respectively. Table 1 shows that the phononic energies determined from l / f noise measurements are in fairly good agreement with the data obtained from neutron scattering [ 10] or tunneling spectroscopy [8]. A zone ~ o f " f o r b i d d e n " currents was observed. A rough estimation o f f gave a value o f 0.0057 eV which is exactly the localization energy for excitons bound to neutral phosphorus donors in silicon * 1. The (TO + TA) and (TO + O) peaks always appeared, regardless whether the devices contained dislocations or not. The remaining peaks were mainly observed for devices conraining dislocations. These results give an indication that the sharp peaks located above ~ are due to exciton two-phonon replicas. Dean, Haynes and Flood [ 11 ] showed that the TO + O phonon replicas are due ,1 Dean et al. [ 11 ] showed that although the probability of a single O phonon-assisted transition is weak, such a possibility exists. 158
either to free exciton recombination in the pure silicon lattice or to bound exciton recombination at neutral donors while a TO + TA replica could be attributed to a transition o f free excitons involving two electrons in the vicinity o f neutral donors. We only mention that also phonons could be emitted in the two-phonon processes [8,12], a phenomenon which can be interpreted in the sense o f Handel's [ 13 ] theory of 1/f noise. Concluding, one can say that a large variety o f quantum phenomena are involved in the 1/f noise generation. Confirming Hooge's [ 14] mobility fluctuation hypothesis, these results, in total agreement with Hooge's and Vandamme's ones [3], definitely show that the c a r r i e r - p h o n o n interaction is the source o f 1/fnoise in semiconductors.
[1] Y. Toyozawa, Solid State Electron. 21 (1978) 1313. [2] C.H. Henry and D.V. Lang, Phys. Rev. B15 (1977) 989. [3] F.N. Hooge and L.K.J. Vandamme, Phys. Lett. 66A (1978) 315. [4] V. Narayanamurfi, R.A. Logan and M.A. Chin, Phys. Rev. Lett. 40 (1978) 63. [5] T.G.M. Kleinpenning, Physiea 98B (1980) 289. [6] A. van der Ziel, Solid State Electron. 25 (1982) 141. [7] R.P. Mertens, R.J. van Overstraeten and H.J. de Man, Adv. Electron. Electron Phys. 55 (1981) 77. [8] A.G. Chynoweth, R.A. Logan and D.E. Thomas, Phys. Rev. 125 (1962) 877. [9] W.P. Dumke, Phys. Rev. 118 (1960) 938. [10] B.N. Brockhouse, Phys. Rev. Lett. 2 (1959) 256. [11] P.J. Dean, J.R. Haynes and W.F. Flood, Phys. Rev. 161 (1967) 711. [12] J.R. Haynes, Phys. Rev. Lett. 17 (1966) 860. [13] P.H. Handel, Phys. Rev. Lett. 34 (1975) 1492. [ 14] F.N. Hooge, Physica 60 (1972) 130. [15] H. Palevsky, D.J. Hughes, W. Kley and E. Tunkelo, Phys. Rev. Lett. 2 (1958) 258. [16] J.R. Haynes, M. Lax and W.F. Flood, J. Phys. Chem. Solids 8 (1959) 392.