Strained Pt Schottky diodes on n-type Si and Ge
M. H. LiaoDepartment of Electrical Engineering and Graduate Institute of Electro-Optical Engineering, National Taiwan University, Taipei, Taiwan, Republic of China
P.-S. Kuo and S.-R. Jan
Department of Electrical Engineering and Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, Taiwan, Republic of China
S. T. Chang
Department of Electrical Engineering, National Chung Hsing University, Taichung, Taiwan, Republic of China
C. W. Liua兲
Department of Electrical Engineering, Graduate Institute of Electro-Optical Engineering, and Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, Taiwan, Republic of China
共Received 7 November 2005; accepted 16 February 2006; published online 5 April 2006兲
The variation of electron barrier height and built-in voltage of Pt Schottky diodes on the mechanically strained n-type Si and Ge is investigated experimentally and theoretically. The mechanical strain is measured by Raman spectroscopy and analyzed by the finite element method. The built-in voltage and barrier height measured by capacitance-voltage and current-voltage methods, respectively, decrease with increasing external tensile strain. The reduction of the built-in voltage and barrier height originates mainly from the conduction band lowering with strain. The extracted value of conduction band lowering is consistent with the theoretical calculations using the “stress-free” boundary condition. © 2006 American Institute of Physics.关DOI:10.1063/1.2191831兴
Strained Si and Schottky barrier source/drain technolo-gies have received considerable attention recently and can be used for high performance metal oxide semiconductor field effect transistors共MOSFETs兲1,2The substrate strain technol-ogy using the lattice misfit between Si and SiGe yields glo-bal biaxial strain and changes the conduction band and the valence band structure of Si. The carrier effective mass and the intervalley scattering are reduced, and thus the mobility is enhanced. Process and package induced strains can also produce sufficient strain for mobility enhancement at low cost.3,4 Schottky barriers improve the short channel effect due to the shallow junction.2 The previous study of the Schottky barrier height on the Pt/ p-strained Si Schottky di-ode was reported.5 The external biaxial strain to reduce the Schottky barrier height and to increase complementary MOSFET drive current was also calculated by another group.6 In this Letter, the effect of externally mechanical strain on n-type Schottky barrier diodes on Si and Ge is presented experimentally and theoretically, and the shifts of the conduction band edge with mechanical strain are also studied.
The n-Si共100兲 and n-Ge 共100兲 wafers used in this study were cleaned by dipping in dilute HF to remove the native oxide layer just before loading in the deposition chamber. Pt was deposited through a shadow mask with an area of 5⫻10−3cm2 by electron beam evaporation at a pressure of 2⫻10−6mbar to form the Schottky diodes. The Ohmic con-tact was made by thermal evaporation of Al on the back side of the wafer. The experimental setup to apply external me-chanical strain to Schottky barrier diodes is similar to that
described in Refs. 7 and 8. Two external strain conditions are applied in this work: 共1兲 uniaxial tensile strain along the 具110典 directions on 共001兲 substrate and 共2兲 biaxial tensile strain on共001兲 substrate. The level of strain is determined by the four screws on the sides of the washer. The strain of the Si and Ge under mechanical strain is simulated by finite element method共ANSYS兲 and measured by Raman
spectros-copy. Raman spectra were excited by an Ar laser 共wave-length of 514 nm兲. The Ge–Ge peak in the Raman spectra 共Fig. 1兲 shifts towards the negative axis under mechanical tensile strain. The Raman shifts of 0.91 and 1.32 cm−1under uniaxial and biaxial tensile strains, respectively, were ex-tracted from the curve fitting using a Lorentzian profile. The strain is obtained by9
⌬= 1 20
关pzz+ q共xx+yy兲兴. 共1兲
For biaxial tensile strain,
a兲Author to whom correspondence should be addressed; electronic mail:
FIG. 1. Raman spectra of the mechanically strained Ge. The position of Ge–Ge peak of strained Ge indicates 0.32% for the biaxial tensile strain and 0.45% for the uniaxial tensile strain.
APPLIED PHYSICS LETTERS 88, 143509共2006兲
0003-6951/2006/88共14兲/143509/3/$23.00 88, 143509-1 © 2006 American Institute of Physics
zz= −共2C12兲/共C11兲xx, xx=yy. 共2兲
For uniaxial tensile strain,
xx= 0.5T共S11+ S12兲 + 0.25TS44, 共3兲 yy= 0.5T共S11+ S12兲 − 0.25TS44, 共4兲
zz= TS12, 共5兲
where0 is the longitudinal phonon frequency at the zone center of reciprocal space, p and q are phenomenological potentials to calculate the frequency shift as the function of external strain in Raman spectra,xx, yy,zz are the strain
along the具110典, 具11¯0典, 具001典 directions on 共100兲 wafer, T is the stress, and S11, S12, S44, C11, and C12 are elastic coeffi-cients. The material parameters used in the calculation are given in Table I.9,10In Table I, the⌶d+共1/3兲⌶uis the
defor-mation potential constant to calculate the conduction band shift of Si and Ge as a function of external strain. Using the Raman shift of the Ge–Ge phonon peak in Fig. 1, the strain in Ge is estimated to be 0.32% for biaxial strain and 0.45% for uniaxial strain. Similarly, the strain in Si can also be estimated to be 0.13% for biaxial strain and 0.35% for uniaxial strain.7The strain level obtained from Raman shift agrees well with the finite element simulation using ANSYS
software.
Figure 2 shows the current-voltage共I-V兲 characteristic of Pt/ n-Si and Pt/ n-Ge Schottky barrier diodes under biaxial tensile and uniaxial tensile mechanical strains. The barrier height and ideality factor共n兲 can be calculated from the for-ward I-V curves. The ideality factors of n = 1.07 and
n = 1.13 for Si and Ge are observed, respectively, indicating
that the current is mainly due to the thermionic emission.11 The barrier height changes of the Pt/ n-Ge sample are found to be −9 and −27 meV for uniaxial strain 共⬃0.45%兲 and biaxial strain共⬃0.32%兲, respectively. For Pt/n-Si diode, the changes are −8 and −13 meV for uniaxial strain共⬃0.35%兲 and biaxial strain共⬃0.13%兲, respectively. The Schottky bar-rier height decreases with increase of external mechanical
tensile strain. Neglecting the effect of surface dipole, the barrier height change of a Schottky junction under mechani-cal strain can be written as
⌬bn共兲 = ⌬m共兲 − ⌬共兲, 共6兲
wherebn,m, and represent barrier height, metal work
function, and electron affinity of the semiconductor, respec-tively. The change of metal work functionm共兲 for single
crystalline Pt is within⬃4 meV under our mechanical strain conditions based on the derivation in Ref. 12.
EF,strain EF,unstrain=
冉
Vunstrain Vstrain冊
2/3 , 共7兲where V is the volume of metal and EFis the Fermi energy.
Since the Pt in our sample is polycrystalline, the exact strain in the polygrains can be even smaller, and the change of the work function can be neglected. Therefore, the change of the Schottky barrier height under mechanical strain is mainly due to the change of the conduction band edge of the semiconductor.
Capacitance-voltage共C-V兲 characteristics of Pt/n-Si and Pt/ n-Ge samples under the biaxial tensile or uniaxial tensile strain are shown in Fig. 3. The doping concentrations obtained from the Si and Ge devices at reverse bias are ⬃1⫻1015 and ⬃1⫻1016cm−3, respectively. The barrier height variation can be determined from11
⌬bn共兲 = ⌬Vbi共兲 + ⌬共EC− EF兲共兲, 共8兲
where Vbi共兲 is the built-in voltage measured from the volt-age intercept of C-V, and 共EC− EF兲共兲 is the depth of the
Fermi level below the conduction band, which can be com-puted when the doping concentration is known,
⌬共EC− EF兲共兲 = − KT ln
冋
n Nc共兲
册
, 共9兲
where Nc共兲 is the electron effective density of state as a
function of strain in Si and Ge, respectively.13 Based on
C-V measurement, the barrier height also decreases with
ex-ternal tensile strain.
TABLE I. The numerical value of parameters used in the calculation. C11 共GPa兲 C12 共GPa兲 C44 共GPa兲 S11 共GPa兲 S12 共GPa兲 S44 共GPa兲 p 共1027s−2兲 q 共1027s−2兲 ⌶ d+共1/3兲⌶u 共eV兲 Si共⌬兲 167 65 79 770 −214 126 −14.3 −18.9 4.18 Ge共L兲 131 49 66 960 −261 151 −4.7 −6.17 −6.84
FIG. 2. Experimental forward I-V characteristics of Pt/ n-Si and Pt/ n-Ge Schottky diodes with and without mechanical strain.
FIG. 3. C-V characteristic of Pt/ n-Si and Pt/ n-Ge Schottky diodes with and without mechanical strain.
143509-2 Liao et al. Appl. Phys. Lett. 88, 143509共2006兲
The theoretical calculation and experimental data of the conduction band shift in Si and Ge as a function of external strain along具110典 are shown in Fig. 4. Using the parameters in Refs. 10 and 14, and the formulas in Refs. 14 and 15, the shift of conduction band edge due to external tensile strain along 具110典 is calculated under the stress-free condition. “Stress-free” means no stress along the in-plane direction perpendicular to the uniaxial strain axis 具110典, i.e., 具11¯0典 direction. The downshifts of −23 共−22兲 meV/% for the uniaxial strain and −100共−84兲 meV/% for the biaxial strain are obtained for the Si共Ge兲 devices from I-V measurement. In summary, the reduction of the Schottky barrier height for the n-type semiconductor under external mechanical strain is observed. This reduction is shown to originate from the reduction of the conduction band edge. Using the stress-free boundary condition, a reasonable agreement between ex-perimental data and theoretical calculation is obtained.
Raman measurements by Professor Chih-Ta Chia at the National Taiwan Normal University is highly appreciated. This work is supported by the National Science Council of ROC under Contract Nos. E-002-040 and 94-2215-E-002-041, and the Asian Office of Aerospace Research and Development共AOARD兲, US Air Force.
1C. W. Liu, S. Maikap, and C.-Y. Yu, IEEE Circuits Devices Mag. 21, 21
共2005兲.
2M. Fritze, C. L. Chen, S. Calawa, D. Yost, B. Wheeler, P. Wyatt, C. L.
Keast, J. Snyder, and J. Larson, IEEE Electron Device Lett. 25, 220 共2004兲.
3F. Yuan, C.-F. Huang, M.-H. Yu, and C. W. Liu, IEEE Trans. Electron
Devices 53, 724共2006兲.
4M. H. Liao, S. T. Chang, M. H. Lee, S. Maikap, and C. W. Liu, J. Appl.
Phys. 98, 066104共2005兲.
5S. Chattopadhyay, L. K. Bera, S. K. Ray, and C. K. Maiti, Appl. Phys.
Lett. 71, 942共1997兲.
6A. Yagishita, T.-J. King, and J. Bokor, Jpn. J. Appl. Phys., Part 1 43, 1713
共2004兲.
7M. H. Liao, M.-J. Chen, T. C. Chen, P.-L. Wang, and C. W. Liu, Appl.
Phys. Lett. 86, 223502共2005兲.
8M. H. Liao, C.-Y. Yu, C.-F. Huang, C.-H. Lin, C.-J. Lee, M.-H. Yu, S. T.
Chang, C.Y. Lee, T.H. Guo, C.C. Chang, and C. W. Liu, Tech. Dig. -Int. Electron Devices Meet. 1023共2006兲.
9Y. Hida, T. Tamagawa, H. Ueba, and C. Tatsuyama, J. Appl. Phys. 67,
7274共1990兲.
10Properties of Crystalline Silicon, EMIS Data Reviews Series No. 20,
edited by R. Hull共INSPEC, London, 1999兲.
11S. M. Sze, Physics of Semiconductor Devices共Wiley, New York, 1981兲. 12N. W. Ashcroft and N. D. Mermin, Solid State Physics共Harcourt Brace
Jovanovitch, San Diego, 1975兲, pp. 32–38.
13M. V. Fischetti and S. E. Laux, J. Appl. Phys. 80, 2234共1996兲. 14C. Ohler, C. Daniels, A. Forster, and H. Luth, Phys. Rev. B 58, 7864
共1998兲.
15J.-S. Lim, S. E. Thompson, and J. G. Fossum, IEEE Electron Device Lett. 25, 731共2004兲.
FIG. 4. Theoretical calculation and the experimental data of the shift of conduction band of Si and Ge under the external mechanical strain.
143509-3 Liao et al. Appl. Phys. Lett. 88, 143509共2006兲
