Vol. 31, No. 3 Journal of Semiconductors March 2010

Tunnelling piezoresistive effect of grain boundary in polysilicon nano-films

Chuai Rongyan(揣荣岩)1; Ž, Liu Bin(刘斌)1, Liu Xiaowei(刘晓为)2, Sun Xianlong(孙显龙)1, Shi Changzhi(施长治)2, and Yang Lijian(杨理践)1

(1 Information Science and Engineering School, Shenyang University of Technology, Shenyang 110023, China) (2 Department of Microelectronics, Harbin Institute of Technology, Harbin 150001, China)

Abstract: The experiment results indicate that the gauge factor of highly boron doped polysilicon nanofilm is bigger than that of monocrystalline silicon with the same doping concentration, and increases with the grain size decreasing. To apply the unique properties reasonably in the fabrication of piezoresistive devices, it was expounded based on the analysis of energy band structure that the properties were caused by the tunnel current which varies with the strain change forming a tunnelling piezoresistive effect. Finally, a calculation method of piezoresistance coefficients around grain boundaries was presented, and then the experiment results of polysilicon nanofilms were explained theoretically.

Key words: polysilicon nanofilm; tunnelling piezoresistive effect; gauge factor; piezoresistance coefficient DOI: 10.1088/1674-4926/31/3/032002 PACC: 7220F; 7360F; 7340G

1. Introduction was based on the test results of polysilicon films thicker than 200 nm, but opposite to the actual experiment results of polysil- icon nanofilms. The polysilicon nanofilms exhibit excellent The discoveryŒ1in 1974 that the polysilicon thin films have piezoresistive properties, which show potential for the fabrica- piezoresistive properties generated considerable research into tion and development of high performance piezoresistive sen- an increasing number of applications in piezoresistive sensors. sors. In this paper, in order to analyze the piezoresistive prop- Therefore, the investigations into their piezoresistive mecha- erties of polysilicon nanofilms, we prepared the 80-nm-thick nism have attracted great attention. The existing piezoresistive polysilicon films with different doping concentrations and a models of polysilicon were established during 1980s–1990s, series of polysilicon films with various thicknesses. By analyz- which were widely applied in the design and optimization ing the energy band structure and transport current components of polysilicon pressure sensorsŒ2. In the 1980’s, French and through grain boundaries, the relationship between piezoresis- Evans considered both thermionic emission and diffusion as tance coefficients of grain neutral regions and composite grain conducting mechanisms of polysilicon and their sensitivity to boundaries was obtained and the tunnelling piezoresistive ef- strain, and then presented a model valid over a wide range fect of polysilicon nanofilms differing from common polysili- of doping concentrationsŒ3 5. In their theory, the piezoresis- con films was presented and analyzed. Finally, the experimen- tance coefficient of grain boundaries was much lower than that tal results of polysilicon nanofilms were explained theoreti- of grains, resulting in the fall of gauge factor at high dop- cally. ing concentrations. Thus, the conclusion was drawn that larger Additionally, the piezoresistive effect derived from the grain sizes and low trap densities yielded a higher gauge factor. tunnelling current—tunnelling piezoresistive effect—was not Meanwhile, Schubert took the influences of depletion regions mentioned before. Although the view that the tunnelling cur- and grain boundaries into consideration and proposed a the- rent could generate a piezoresistive effect was accepted by oretical model for calculating the longitudinal and transversal Kleimann et al.Œ7, the regularity of tunnelling piezoresistive ef- gauge factorsŒ6. Also, the maximum gauge factor was obtained fect and its influence on the piezoresistive properties of polysil- in polysilicon films with large grain sizes. In view of the above icon have not been revealed, as a result of the complexity of conclusions, at present, the thickness of polysilicon films used tunnelling current formulas. in piezoresistive devices is mostly over 200 nm, and even larger than 1 m in some cases. Few polysilicon nanofilms (around or 2. Basic experimental phenomenon less than 100 nm in thickness) are adopted for sensing applica- tions, due to their extremely fine grain sizes and deficient crys- For the first group samples, the 80-nm-thick polysilicon tallization. In these existing piezoresistive models, it is con- films were prepared on 111 -orientated thermally oxidized sil- h i sidered that the piezoresistive effect of grain neutral regions icon substrates by LPCVD at 620ı. After the boron implanta- is stronger than that of grain boundaries. Therefore, when the tion, the annealing step was performed at 1080ı for 30 min, and grain size is fine, the proportion of the latter becomes large rel- the boron doping concentration was ranged from 8.1 1018 to 20 3  atively, and the piezoresistive effect should be weakened ac- 7.1 10 cm . Another group of polysilicon films (30–250 cordingly. nm in thickness) were deposited on thermally oxidized silicon However, the above deduction from the existing models substrates using the same process and temperature. After boron

* Project supported by the National Natural Science Foundation of China (No. 60776049), the Science and Technology Foundation of Liaoning Province of China (No. 20072036), and the Fund of Liaoning Province Education Department of China (No. 2007T130). Ž Corresponding author. Email: me [email protected] Received 30 July 2009, revised manuscript received 30 September 2009 c 2010 Chinese Institute of Electronics

032002-1 J. Semicond. 2010, 31(3) Chuai Rongyan et al.

Fig. 3. Energy band diagrams near a grain boundary under thermal equilibrium.

Fig. 1. Test results of the relationship between the gauge factor Gp and the doping concentration at room temperature (film thickness: 80 these phenomena can not be explained by the existing piezore- nm). sistive models of polysilicon. The reason is that the piezore- sistive effect of the grain boundary is underestimated in the existing models. 3. Energy band diagram and equivalent circuit of polysilicon The polysilicon could be regarded as being composed of small crystallites joined together by grain boundaries. In or- der to analyze the influence of tunnelling effect on the con- duction properties of polysilicon, the grain boundary is viewed as a disordered amorphous material, and the forbidden band width is much larger than that of monocrystalline silicon and Œ10 12 approaches that of amorphous silicon (1.5–1.6 eV ) , and the Fermi level is pinned near the midgap at grain boundaries. As a result, a heterojunction is formed at the interface between the crystallites and the grain boundary. For the sake of simpli- fication, a one dimensional ideal conduction model for polysil- icon was used. In this model, it is assumed that the distribution Fig. 2. Relationship between the longitudinal gauge factor G of pl of grain boundaries is homogeneous, and the grains serve as a polysilicon and the film thickness at room temperature (doping con- centration: 2.3 1020 cm 3/. series of cubes (the length of side is L) arranged in the one-  dimensional mode. Based on the above assumption, the energy band diagram diffusion, the doping concentration of the second group was es- around the grain boundaries was given in Fig. 3, where W timated to be 2.3 1020 cm 3. is the depletion region width, ı is the grain boundary width,  By the characterization of film microstructure, it was found q is the height of grain boundary barrier, and qVb is the that the apparent grain sizes of the first group were approx- height of depletion region barrier. For the holes traversing grain imately 32 nm and the grain sizes of the second group de- boundaries, when the kinetic energy Ex is less than qVb, they creased gradually from 60 to 15 nm with the film thickness can traverse the depletion regions and boundary barrier region Œ8 varying from 250 to 30 nm . To measure piezoresistive pa- only by tunneling, forming the field emission current J1; when rameters, these samples were processed to obtain cantilever qVb < Ex < q, they cross the depletion regions by ther- beamsŒ9, and then the test results of the gauge factor were mal emission and penetrate the boundary barrier region by tun- shown in Figs. 1 and 2 respectively. Seen from Fig. 1, when neling, forming the composite current J2; when Ex > q, 20 3 the doping concentration exceeded 10 cm , the gauge fac- they traverse the depletion regions and boundary barrier region tor Gp ascended again with the doping concentration increas- completely by thermal emission, forming the thermal emission ing. However, it is accepted commonly in the existing piezore- current J3. sistive model that the gauge factor of polysilicon films reaches Sequentially, by synthesizing the above three current the maximum when the doping concentration is elevated to 2 modes, the equivalent circuit of polysilicon is presented in 19 3  10 cm approximately, and then it decreases monotonously Fig. 4(a), where Rg is the resistance of grain neutral regions, Œ2; 3 with the doping concentration increasing . The test results RF and RT are the resistances determined by the currents J1 shown in Fig. 2 indicated that the gauge factor increased re- and J3, respectively. For the current J2, the composite current markably when the film thickness reduced from 150 to 90 nm, path was equated with two series resistances. One is the equiv- in despite of the distinct decrease of grain size. Obviously, alent emission resistance Rd of depletion regions determined

032002-2 J. Semicond. 2010, 31(3) Chuai Rongyan et al.

Fig. 5. Energy band diagram near a grain boundary without regard to depletion region barriers.

Fig. 4. Equivalent circuit of tunnel piezoresistive model. (a) The gen- ary related to the resistance Rı under the voltage drop Vı . Us- eral form. (b) The simplified form at a moderate temperature. ing Fermi–Dirac statistics, the number of holes having energy within the range dEx incident from left to right on the grain by thermal emission; the other is the equivalent tunnelling re- boundary barrier per unit time per unit area isŒ14 sistance Rı of grain boundary determined by tunnelling. Al- though these three current modes coexist in polysilicon, the 4mdkT N.T; ; Ex/dEx 3 current J2 is dominated for the samples with high doping con- D h centration at room temperature. Hence, the equivalent circuit Â Ä .Ex /à can be simplified into the form given in Fig. 4(b). ln 1 exp C dEx; (4) According to Fig. 4(b), the expression of gauge factor for  C kT polysilicon is given by where md is the effective mass of holes for state density,  D EF EV, is the difference of Fermi level and valence band Rg Rb Gp Gg Gb; (1) edge, h is Planck’s constant, k is Boltzmann’s constant, and T D Rg Rb C Rg Rb C C is the absolute temperature. where Gg and Gb are the gauge factors of the resistances Rg The grain boundary width in polysilicon is very small and Rb, respectively; Rb is the resistance of composite grain (around 1nm in general), and the number of holes with high boundary comprised of grain boundary and depletion regions, energies around q is few. Hence, when calculating the cur- and Rb Rd Rı . rent density, the oblique distribution of energy band at the top InsideD eachC grain, atoms are arranged in a monocrystallite of grain boundary barrier in Fig. 5 can be substituted by the mode, and the gauge factor of grain neutral regions is depen- horizontal line approximately. So, the probability of carriers 1 dent on the piezoresistance coefficient  of monocrystalline with the energy Ex (0 6 Ex 6 q qVı / tunnelling the g 2 silicon. The gauge factor Gb is dependent on the piezoresis- grain boundary barrier is given by tance coefficients of equivalent resistances Rd and Rı . For the 4ı equivalent resistance Rd, using the dependence of the thermal  1=2  D.Ex/ exp Œ2mi.a Ex/ ; (5) emission current on strain, the relational expressions of the lon- D h gitudinal and transversal piezoresistance coefficients dl and Œ13 dt in [111] orientation are given by 1 a q qVı ; (6) D 2 dl 0:525gl; (2) D where mi is the effective mass of holes in the tunnelling di- rection. In Fig. 5, the left valence band edge EVL is taken to dt 0:616gt; (3) D be the zero point of energy. Therefore, by deducing from Eqs. where gl and gt are the longitudinal and transversal piezore- (4)–(6), the hole-flux density tunnelling grain boundary barrier sistance coefficients of p-type monocrystalline silicon in 111 from left to right is orientation, respectively. The resistance ratio in Eq. (1) canh bei a figured out by the corresponding voltage drop ratio. Neverthe- Z SLR N.T; ; Ex/D.Ex/dEx: (7) less, calculating Gp requires determining the piezoresistance D 0 coefficient ı of the equivalent tunnel resistance Rı . It is obvious that the holes with energies less than EVL could not 4. Piezoresistive properties of grain boundary tunnel the barrier from right to left. Thus, the hole-flux density tunneling grain boundary barrier from right to left is written as Before analyzing piezoresistive properties of composite a grain boundary, the volt-ampere characteristics of the resis- Z SRL N.T; 0;Ex/D.Ex/dEx; (8) tance Rı should be determined. The resistance Rı is defined D 0 as the grain boundary resistance without regard to depletion re- gions. Figure 5 is the energy band diagram around grain bound- 0  qVı : (9) D C

032002-3 J. Semicond. 2010, 31(3) Chuai Rongyan et al. In the nondegenerate condition ( kT ), the logarithmic function term in Eq. (1) can be simplified into the exponential form, and then Equation (7) can be expressed as

a 4mdkT Z Ä .Ex / SLR 3 exp C D.Ex/dEx: (10) D h 0 kT

Owing to the fact that the holes gather mostly near the valence band edge, when solving the integration in Eq. (10), the square root term is expended by the Taylor’s series as follows: Fig. 6. Split off of valence bands subjected to a uniaxial stress. 1=2 Ex .a Ex/ pa : (11) D 2pa C


Considering the hole concentration formula in nondegenerate Œ15 After Equation (11) is substituted into Eq. (5), the yielded semiconductor : D.Ex/ expression is substituted into Eq. (10). By integration, 3 2 it results in   à Â2mdkT à ÂEV EF à p NV exp 2 exp ; D kT D h2 kT 2 2 4mdk T Ä Â 2ı a  à (18) SLR 3 exp p2mia C D h c1 h kT and then Equation (17) can be rewritten as

pq kT 1=2 a  4ı  Ã  à h  Á i exp p2mia ; (12) Jı exp c2 exp .2c2/ ; h kT D c1 2md kT qVı where pJı0: kT D 2ı r2mi (19) c1 kT 1: (13) D h a The valence band edge EV of silicon consists of two degen- In like manner, it can yield erate energy bands. Therefore, the tunnelling current of travers- ing grain boundary is comprised of the corresponding hole tun- 2 2 nelling current Jı1 and Jı2, and can be expressed by 4mdk T Ä Â 2ı a 0 à SRL 3 exp p2mia C D h c1 h kT 2

Jı X Jı Jı1 Jı2; (20) D j D C  4ı 0 à j 1 exp p2mia : (14) D h kT Jıj pj .Jı0/j ; (21) From Eqs. (12) and (13), the current density of tunnelling D where J is the tunnelling current component of degenerate boundary barrier region can be given by ıj energy band, pj is the corresponding hole concentration, j 1; 2; corresponds to two sorts of holes. D Jı q.SLR SRL/ D 4.1. Piezoresistance coefficient of equivalent tunnel resis- tance 2 2 4md k T   à q 3 exp The grain neutral region has the nature of monocrystalline D h c1 kT silicon, and its piezoresistive properties are considered as a result of the split off of two degenerate bands subjected to a Ä a  a qVı à exp c2 Á exp c2 C stressŒ16; 17. One of the two bands, E , is shifted upward; the  kT kT V1 other band, EV2, is shifted downward. The band shift "0 is de- fined as the strain additional energy, as shown in Fig. 6.  qVı à exp .2c2/ exp 2c2 ; (15) When subjected to a uniaxial stress, the isoenergetic sur- C kT faces of two split-off bands in the k space become the rotation where ellipsoid surfaces, the symmetry axis of which is in the stress 2ı direction. For simplification, the case that a uniaxial stress is c2 p2mia: (16) D h applied along 111 orientation is analyzed. According to the h i On the condition of low voltage bias (qV kT ), the expo- result of the cyclotron resonance experiment by Hensel and Fe- ı Œ18 nential terms in Eq. (15) can be expanded by using the Taylor’s her , the effective mass of holes under a strong stress is ob- series. After taking the first order approximation, it yields tained in Table 1, where mlj and mtj are the longitudinal and transversal effective mass of holes at the band EVj, respec- 2 tively. 4q mdkT  p à Jı 3 exp When the crystal is applied by a stress, two valence band D h c1 kT edges are split off and become EV " and EV " , respec- a C 0 0 hexp c2 Á exp .2c2/i Vı : (17) tively. For the nondegenerate p-type silicon, it is assumed that  kT

032002-4 J. Semicond. 2010, 31(3) Chuai Rongyan et al.

Table 1. Hole effective mass in highly stressed silicon (unit: free- to be 1 nm and the grain boundary barrier height q is about 0.6 eV. Usually, qVı q, and from Eq. (6), it can be obtained electron mass m0/.  Parameter Value that a q. Hence, using the data in Table 1 and Eq. (27), it results in ml1 0.870 mt1 0.170 3=2 2 m 0.293 m sml1m d1  d1 à t1 1:180; (28) ml2 0.135 2 md2 D ml2mt2 D mt2 0.369 md2 0.264 .Jı0/1 2 1:22 10 : (29) .Jı0/2 D  the Fermi level is constant for stress. After differentiating Eq. Using Eqs. (24), (26)–(29), the longitudinal piezoresistance co- (18) and substituting dEV by the strain additional energy "0, the efficient of the resistance Rı along 111 orientation is concentration changes of two sorts of holes are, respectively: h i  0:972 1 E E " ı 1  V F à 0 ıl DuC44 : (30) p1 Nv1 exp ; (22) D ı  D 3 k0T D kT kT N Similarly, the transversal piezoresistance coefficient along ÂEV EF à "0 p2 Nv2 exp : (23) 111 orientation is D kT kT h i

When the uniaxial stress is , the additional energy of band ı 0:684 1 1 Œ18; 19 N ıt DuC44 : (31) split-off is D ı  D 3 k0T N 1 1 "0 DuC ; (24) D 3 44 N Under the uniaxial stress  applied along 111 orientation, the longitudinal and transversalN piezoresistanceh i coefficients (for where D is deformation potential constant, C is the corre- u 44 grain neutral regions) of p-type monocrystalline silicon can be sponding elastic stiffness constant. expressed as follows, respectivelyŒ13: Due to the different effective mass of two sorts of holes, the change of the corresponding hole concentrations consequen- 0:695 1 1 tially results in the change in the current Jı , thereby leading gl DuC44 ; (32) D 3 k0T the resistance Rı to change accordingly—it is the mechanism of tunnelling piezoresistive effect. The relative change of re- 0:435 1 1 sistivity for tunnelling piezoresistive effect is gt DuC44 : (33) D 3 k0T

ı Jı p1.Jı0/1 p2.Jı0/2 C : (25) Comparing Eqs. (30) and (31) with (32) and (33) accordingly, ı D Jı D p1.Jı0/1 p2.Jı0/2 it yields C ı 1:4gl; (34) By combining Eqs. (18), (22), (23) and (25), it yields l D

ı 1:6gt: (35) m 3=2 .J / t D 1  d1 à ı0 1  m .J / " The above derivation is performed for a nondegenerate ı d2 ı0 2 0 : (26)  D 3=2 kT semiconductor. As to the degenerate semiconductor, the differ- ı Âmd1 à .Jı0/1 1 ence of the calculating formulas of carrier concentration could C m .J / d2 ı0 2 result in the change of piezoresistive coefficients. However, According to Eqs. (19)–(21), it results in the influences of this change on the resistance Rg and the resis- tance Rı are identical. Therefore, in the degenerate case, the ra-  a  tio of piezoresistance coefficients ı and g is invariable, still .c1/2 exp h.c2/1 i exp Œ2 .c2/1 .Jı0/1 kT determined by Eqs. (34) and (35). That is, no matter the de- ; generate or nondegenerate semiconductor, the piezoresistance .Jı0/2 D  a  .c1/1 exp h.c2/2 i exp Œ2 .c2/2 coefficients  and  always keep a uniform proportional rela- kT ı g (27) tionship. Moreover, the piezoresistance coefficient ı is larger than  remarkably. where (c1/j and (c2/j are a couple of constants for calculating g the tunnelling current component of holes at the band EVj and 4.2. Piezoresistance coefficient of composite grain bound- determined by Eqs. (13) and (16), respectively. For the longi- ary tudinal piezoresistive effect along 111 orientation, using the h i longitudinal effect mass ml1 in Table 1, (c1/1 and (c2/1 are The resistances Rd and Rı in Fig. 4(b) are two abstract calculated to be 0:84 and 3:72, respectively; using the lon- equivalent resistances. Although they appear to be in series, gitudinal effect mass ml2,(c1/2 and (c2/2 are equal to 0:94 they belong to the same physical space within the film actually, and –1.46, respectively. Referring to the experimental data pro- resulting in the resistivity of the composite grain boundary be- vided by MandurahŒ10 during the analysis of the conduction ing equal to the resistivity sum of two equivalent resistances, properties of polysilicon, the grain boundary width ı is taken b d ı . Thus, when the geometrical piezoresistive effect D C

032002-5 J. Semicond. 2010, 31(3) Chuai Rongyan et al.

Fig. 7. Normalized distribution of voltage drop applied to grain bound- Fig. 8. Shear piezoresistance coefficient 44 data points and fitting aries as a function of doping concentration. curve of p-type monocrystalline silicon with different doping concen- trations. is neglected, the piezoresistance coefficient of composite grain boundary b can be expressed as where NA is the boron doping concentration, Nt is the trap den- sity at grain boundary, "s and "0 are the relative dielectric con- b d d ı ı b stant of silicon and vacuum dielectric constant, respectively. D b D b d C b ı  N N N Using Eqs. (37)–(41), the relationship between VL, VR and R R d ı Vı can be resolved. Figure 7 provides the distribution of the d ı : (36) D Rb C Rb voltage Vı normalized to the voltage V0 as a function of NA, where the dashed line denotes the distribution curve of com- If the potential drops across depletion regions on the left mon polysilicon film with biggish film thickness, and the trap and right hand sides of the grain boundary are denoted by VL 12 2 density Nt is taken to be the value of 1.9 10 cm pro- and VR, respectively, then the potential drops on the resistance vided by LuŒ22; the solid line denotes the distribution curve of Rd and Rı are VL VR and Vı , respectively. Therefore, Equa- C the first group samples, the trap density Nt is taken to be 1.0 tion (36) can be expressed as follows: 13 2  10 cm . By substituting the relational expressions of longitudinal VL VR Vı b C d ı ; (37) piezoresistance coefficients in Eqs. (2), (3), (34) and (35) into D V C V 0 0 Eq. (36), the relationship between longitudinal piezoresistance

V0 Vı VL VR: (38) coefficients of composite grain boundary (bl/ and grain neu- D C C tral region (gl/ is where V0 is the potential drop over the complete grain bound- ary region. Thus, it can be seen that determining the propor-  Vı à Vı bl 0:525 1 gl 1:40 gl: (43) tional relationship between VL VR and Vı is the key to figure C D V0 C V0 out the piezoresistance coefficient b. As a piezoresistive material, the polysilicon films usually Using Eq. (43) and the relational curve in Fig. 7, the de- work under low current and low voltage bias, so the condi- pendence of the piezoresistance coefficient bl on NA can be tion of VL VR < 4Vb can be always satisfied. With this un- obtained. However, the piezoresistance coefficient gl along derstanding,C MandurahŒ10 colligated the theories presented by 111 orientation must be known first. For p-type monocrys- Œ20 Œ21 h i Œ23 Baccarani and Fonash , and gained the relationship of VL, talline silicon, 11 212 244, so yields : C  VR, Vb and Vı as follows: gl 244=3: (44) 1=2 1=2 1=2 D 2Vb .Vb VR/ .Vb VL/ ; (39) D C C Here, according to the experiment results presented by Tufte Œ24 Œ25 qN 1=2 & Stelzer and Sugiyama , the fitting curve of the shear  A à h 1=2 1=2i Vı ı .Vb VR/ .Vb VL/ : (40) piezoresistance coefficient 44 of monocrystalline silicon on D 2"s"0 C NA is provided in Fig. 8. The fitting relationship between 44 According to the approximation of depletion region, it yields and NA is

2 21 qNAW 44 307:44 exp. 7:41 10 NA/ 311:03 Vb ; (41) D  C D 2"s"0 20 exp. 2:02 10 NA/ Nt   W ; (42) 19 178:65 exp. 2:74 10 NA/ 452:45: (45) D 2NA C  C

032002-6 J. Semicond. 2010, 31(3) Chuai Rongyan et al. 5.2. Analysis on test results of samples with different film thickness

According to the results observed from SEM images and XRD patterns of the second group samplesŒ7, the dependence of gauge factor on film thickness shown in Fig. 2 indicates that: (a) When the film thickness is reduced from 250 to 150 nm, the average grain size is always around 60 nm and almost does not change, and there is a faint decrease for the measured gauge factor and the value is 22 approximately. In this case, the grain orientation of samples changes gradually from a faint 110 preferred orientation to a randomly oriented grain distribution.h i Referring to the calculating results provided by SchubertŒ6, the gauge factor ratio of the 110 preferred orientation and the random orientation is abouth 10/8.3.i Consequently, the phe- nomenon that the gauge factor decreases faintly with the film Fig. 9. Piezoresistance coefficients gl and bl as a function of doping thickness reducing is due to the change in grain orientation. (b) concentration. After the film thickness is reduced to 120 nm, the grain size begins to decrease remarkably with the film thickness decreas- ing, whereas the gauge factor increases notably; when the film Consequently, using Eqs. (42) and (44) and the relational thickness decreases to 90 nm, the grain size descends to 32 nm curve in Fig. 7, the dependence of the piezoresistance coeffi- approximately, and the gauge factor reaches 33; then, the film cient bl in polysilicon nanofilms on NA is shown in Fig. 9. thickness is further reduced to 60 nm, but the grain size does It can be seen from Fig. 9 that the change regularity of the not change foundationally, and the gauge factor almost does not change as well. (c) When the film thickness is reduced to piezoresistance coefficient bl with NA is complicated, but the change amplitude is smaller than that of the monocrystal grain. 40 nm, the grain size decreases to around 25 and the gauge factor descends to 27 accordingly; when the film thickness is Moreover, the piezoresistance coefficient bl is larger than that of the monocrystal grain at a high doping concentration, which reduced to 30 nm, the grain size becomes smaller and about 15 is the ultimate origin that polysilicon nanofilms possess a fairly nm, but the gauge factor increases a little. large piezoresistance coefficient at a high doping concentra- It could be seen from the experiment results (a) and (b) that tion. as long as the grain size does not change, the gauge factor will not change with film thickness. Hence, the change in gauge factor is not due to the nano size effect of film thickness but is 5. Comparison between theory and experiments actually caused by the change in grain size. For the samples in this paper, the grain size is smaller than the film thickness. The 5.1. Gauge factor versus doping concentration grain size becomes the major factor determining the piezore- sistive effect, thus the film thickness just indirectly influences From the test results in Fig. 1, it illustrates that the gauge the piezoresistive effect by the change of grain size. Therefore, factor increases again with NAincreasing, after NA reaches 2 when the tunnelling piezoresistive effect is discussed, the in- 20 3  10 cm . The phenomenon only exists in the polysilicon fluence of the film thickness is not taken into consideration. films with fine grains. If the grain size is large, the resistance of Also, the experiment results (a) and (b) indicate that the gauge grain boundaries Rb will be much lower than that of grain neu- factor increases with grain size reducing at high doping con- tral regions Rg. In this case, although the tunnelling piezoresis- centration. This conclusion has been explained reasonably by tive effect is strong, its influence on the piezoresistive proper- the tunnelling piezoresistive model—because the piezoresis- ties of polysilicon can be ignored. For the first group samples, tance coefficient b is larger than g at high doping concen- the film thickness was 80 nm, the apparent grain sizes were tration, the reduction of grain size consequentially results in 32 approximately. By comparison between the measured film the increase of grain boundary component, thereby leading the resistivity and monocrystalline silicon resistivity at the same gauge factor to increase. doping level, it is considered that the resistances Rg and Rb The experiment results (c) indicated that when the film 20 3 are at the same level when NA reached 10 cm . Here, the thickness decreases to 40 nm, the grain size becomes smaller resistance Rg decreases linearly with NA increasing, while the and the gauge factor also decreases. The fact appeared to be op- change in the resistance Rb is much gentler. It results from posite to the conclusions from the results (a) and (b); however, this that the width of depletion regions could be neglected at it is due to other reasons. In this case, the films are very thin, high doping concentrations, and the width of composite grain and the grain growth is not sufficient, causing the increase of boundaries approaches that of grain boundaries and no longer trap density at grain boundaries. This increases the weight of decreases with NA increasing. Therefore, with NA increasing, equivalent emission resistance so that the piezoresistance coef- the piezoresistance coefficient of polysilicon is obviously close ficient b decreases, resulting in the decrease of gauge factor. to that of composite grain boundaries, thereby resulting in the Additionally, as can be seen from the results (c), when the film piezoresistance coefficient of polysilicon increasing with NA thickness is reduced to 30 nm, the grain size becomes much increasing. smaller, but the gauge factor increases a little. It should be due

032002-7 J. Semicond. 2010, 31(3) Chuai Rongyan et al. to the change in film nature. On this condition, the apparent [7] Kleimann P, Semmache B, Le Berre M, et al. Stress-dependent grain size is about 15 nm. In view of smaller grains in the deep hole effective masses and piezo- resistive properties of p-type level of films, it could be considered that the films begin to monocrystalline and polycrystalline silicon. Phys Rev B, 1998, transfer toward nanocrystalline silicon. The nanocrystalline sil- 57: 8966 icon has a higher gauge factorŒ26. However, due to the imma- [8] Liu Xiaowei, Wu Yajing, Chuai Rongyan, et al. Temperature char- ture preparation technologies, its piezoresistive properties have acteristics of polysilicon piezoresistive nanofilm depending on film structure. Proceedings of the 2nd IEEE International Nano- not been applied practically for the moment. electronics Conference, Shanghai, China, 2008: 1660 [9] Chuai Rongyan, Liu Xiaowei, Huo Mingxue, et al. Influence of 6. Conclusions doping level on the gauge factor of polysilicon nanofilm. Chinese Journal of Semiconductors, 2006, 27(7): 1230 For polysilicon nanofilms, it was found that the tunnelling [10] Mandurah M M, Saraswat K C, Kamins T I. A model for conduc- piezoresistive effect was quite remarkable. Thus, when the tion in polycrystalline silicon – Part I: theory. IEEE Trans Elec- 20 3 tron Devices, 1981, ED-28: 1163 doping concentration exceeds 10 cm , the piezoresistance coefficient of composite grain boundaries is larger than that of [11] Kamins T I. Hall mobility in chemically deposited polycrystalline silicon. J Appl Phys, 1971, 42: 4357 the grain neutral regions. By comparison between the theory [12] Taniguchi M, Hirose M, Osaka Y. Substitutional doping of chem- and the experiments, the conclusions were drawn as follows: ically vapor-deposited amorphous silicon. J Cryst Growth, 1978, At high doping concentrations, polysilicon nanofilms have 45: 126 larger gauge factors than common ones. For the polysilicon [13] Liu Xiaowei, Huo Mingxue, Chen Weiping, et al. Theoretical re- nanofilms whose apparent grain size is about 32 nm, when search on piezoresistive coefficients of polysilicon films. Chinese 19 3 the doping concentration is approximately 4 10 cm , the Journal of Semiconductors, 2004, 25: 292 gauge factor has a maximum; after the doping concentration [14] Murphy E L, Good R H. Thermionic emission, field emission and 20 3 the transition region. Phys Rev, 1956, 102: 1464 reaches 10 cm , the gauge factor increases again with the doping concentration increasing. When the doping concentra- [15] Liu Enke, Zhu Bingsheng, Luo Jinsheng. Semiconductor physics. 20 3 Beijing: Publishing House of Electronics Industry, 2003 tion reaches 3 10 cm , the gauge factor is about 34. The influence of the film thickness on the gauge factor is [16] Adams E N. Elastoresistance in p-type Ge and Si. Phys Rev, 1954, 96: 803 quite large, which is only the indirect reason causing the change [17] Pikus G E, Bir G L. Cyclotron and paramagnetic resonance in in gauge factor and it is actually due to the change in grain strained crystals. Phys Rev Lett, 1961, 6: 103 size and grain boundary state. When the grain boundary states [18] Hensel J C, Feher G. Cyclotron resonance experiments in uniax- (trap density, grain boundary width, and grain boundary barrier ially stressed silicon: valence band inverse mass parameters and height and so on) are invariable, the gauge factor of polysilicon deformation potentials. Phys Rev, 1963, 129: 1041 nanofilms with high doping concentrations increases with the [19] Hasegawa H. Theory of cyclotron resonance in strained crystal. grain size decreasing. Phys Rev, 1963, 129: 1029 [20] Baccarani G, Impronta M, Ricco B, et al. I –V characteristics of References polycrystalline silicon resistors. Rev Phys Appl, 1978, 13: 777 [21] Fonash S J. 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