Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 1063-1074 |
| Journal | IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control |
| Volume | 61 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 2014 |
| MoE publication type | A1 Journal article-refereed |
Fingerprint
Cite this
}
Determination of doping and temperature-dependent elastic constants of degenerately doped silicon from MEMS resonators. / Jaakkola, Antti; Prunnila, Mika; Pensala, Tuomas; Dekker, James R; Pekko, Panu.
In: IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 61, No. 7, 2014, p. 1063-1074.Research output: Contribution to journal › Article › Scientific › peer-review
TY - JOUR
T1 - Determination of doping and temperature-dependent elastic constants of degenerately doped silicon from MEMS resonators
AU - Jaakkola, Antti
AU - Prunnila, Mika
AU - Pensala, Tuomas
AU - Dekker, James R
AU - Pekko, Panu
PY - 2014
Y1 - 2014
N2 - Elastic constants c11, c12, and c44 of degenerately doped silicon are studied experimentally as a function of the doping level and temperature. First-and second-order temperature coefficients of the elastic constants are extracted from measured resonance frequencies of a set of MEMS resonators fabricated on seven different wafers doped with phosphorus (carrier concentrations 4.1, 4.7, and 7.5 x 1019 cm -3), arsenic (1.7 and 2.5 x 1019 cm-3), or boron (0.6 and 3 * 1019 cm-3). Measurements cover a temperature range from-40°C to +85°C. It is found that the linear temperature coefficient of the shear elastic parameter c11- c>sub>12 is zero at n-type doping level of n ~ 2 x 1019 cm -3, and that it increases to more than 40 ppm/K with increasing doping. This observation implies that the frequency of many types of resonance modes, including extensional bulk modes and flexural modes, can be temperature compensated to first order. The second-order temperature coefficient of c 11-c12 is found to decrease by 40% in magnitude when n-type doping is increased from 4.1 to 7.5 * 1019 cm -3. Results of this study enable calculation of the frequency drift of an arbitrary silicon resonator design with an accuracy of ±25 ppm between the calculated and real(ized) values over T =-40°C to +85°C at the doping levels covered in this work. Absolute frequency can be estimated with an accuracy of ±1000 ppm
AB - Elastic constants c11, c12, and c44 of degenerately doped silicon are studied experimentally as a function of the doping level and temperature. First-and second-order temperature coefficients of the elastic constants are extracted from measured resonance frequencies of a set of MEMS resonators fabricated on seven different wafers doped with phosphorus (carrier concentrations 4.1, 4.7, and 7.5 x 1019 cm -3), arsenic (1.7 and 2.5 x 1019 cm-3), or boron (0.6 and 3 * 1019 cm-3). Measurements cover a temperature range from-40°C to +85°C. It is found that the linear temperature coefficient of the shear elastic parameter c11- c>sub>12 is zero at n-type doping level of n ~ 2 x 1019 cm -3, and that it increases to more than 40 ppm/K with increasing doping. This observation implies that the frequency of many types of resonance modes, including extensional bulk modes and flexural modes, can be temperature compensated to first order. The second-order temperature coefficient of c 11-c12 is found to decrease by 40% in magnitude when n-type doping is increased from 4.1 to 7.5 * 1019 cm -3. Results of this study enable calculation of the frequency drift of an arbitrary silicon resonator design with an accuracy of ±25 ppm between the calculated and real(ized) values over T =-40°C to +85°C at the doping levels covered in this work. Absolute frequency can be estimated with an accuracy of ±1000 ppm
U2 - 10.1109/TUFFC.2014.3007
DO - 10.1109/TUFFC.2014.3007
M3 - Article
VL - 61
SP - 1063
EP - 1074
JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
SN - 0885-3010
IS - 7
ER -