Silicon whiskers for mechanical sensors

Sensors and Actuators

A, 30 (1992)

27

21-33

Silicon whiskers for mechanical sensors V Voronm, Polytechmcal

I Maryamova,

lnstttute,

Department

Y Zaganyach,

of Semtcondwtor

E Karetmkova

Electronrcs, Mwa Str

and A Kutrakov

12, Lvov 290646 (Ukrame)

Abstract Some problems related to creating mechamcal plezoreslstlve sensors based on s~hcon whiskers are considered Physlcochemlcal aspects of semlconductor whisker technology usmg the chemical vapour deposltlon (CVD) method are dlscussed Theoretical and expenmental mvestrgatlons of the longltudmal plezoreslstance m p-type SI (B) whiskers with lmpunty concentrations of I x IO”-3 x 10’9cn-’ have been carned out m ddferent temperature ranges It 1s shown that stram gauges based on p-S1 whiskers have extremely high mechamcal strength and a wide operating temperature range from cryogenic temperatures to +400 “C Several types of pressure sensors for vanous apphcatlons, containing an ongmal umversal stram umt with SI whiskers, are described Their advantages are small size and weight, high resonance frequency and the posslbdity of operating m temperature ranges from -269- $20 “C to -6O- + 350 “C under unfavourable condltlons Different kinds of sensors for medical mvestlgatlons are also presented

1. Introduction Today s&on IS a maJor material for sensor manufacture due to its technological posslbhtles, stability, mechamcal propertles and low cost [ 1,2] Furthermore, slhcon sensors can operate wlthm an extended temperature range Parallel v&h the widely used IC technology to produce silicon mechamcal sensors, some other technologres are used to manufacture sensors for special apphcatlons We have chosen semlconductor whiskers (SW) as active sensor elements because these crystals have various advantages (1) extremely high mechanical strength because of the structural perfection of the grown whiskers, (2) SW, due to their size, geometry and crystallographic onentatlon, can be used directly to manufacture some kinds of sensors (strain gauges) without any technolo@cal operations, the only operation needed 1s to create ohmic contacts and to connect lead wres, (3) the whiskers may be doped dunng their growth to obtain crystals with the required electncal parameters, (4) the sensor manufactunng technology based on SW differs from other technologies m its slmphaty, lack of complicated technologcal operations and mmlmal waste of semiconductor material 0924-4247/92/U 00

In our opmlon, SW grown from the vapour phase are very promising for sensor construction because of their extremely high mechanical strength, mmlature size, posslblhty of impurity doping during the growth process and relative slmphclty of production technology In order to elaborate semiconductor whisker growth technology, the details of the physical and chemical aspects of this process need to be mvestlgated It 1s well known that crystal growth condltlons, doping level and other technological factors have an influence on sensor charactenstlcs That IS why a full cycle of mvestlgatlons was carried out from a fundamental study of the physlcochemlcal aspects of semiconductor crystal growth by chemical vapour deposltlon (CVD) technology to the creation of mechanical sensors

2. Physicochemical aspects of SW technology Chemical vapour deposition (CVD) technology 1s a complex process because of the mutual influence of the parameters It is Just relative to fundamental thermodynamic constants of the most important chemical systems used for semiconductor compounds crystalllzatlon by CVD method Data on the coefficients of mutual diffusion components m the @ 1992 ~- Elsewer Sequoia All nghts reserved

28

vapour phase are limited, and there 1s practically no mformatlon about the and there IS practically no mforrnatlon about the kmetlc parameters of surface processes and the connection between processes on the atomic and molecular levels, so the physical properties of the deposited material have not been sufficiently studied This also refers to the macroprocess responsible for vapour phase composltlon (evaporation, chemical reactions) as well as to the dehvery of components to the deposition zone Thus, the msufficlent level of studies on CVD processes slows down the working out of the sclentlfic fundamentals of this method Quantitative methods for CVD processes of semiconductors, especially Sl, were developed by mvestlgatlons of the heterogeneous equlhbrla and kinetic characterlstlcs of halogen-hydride processes m the dlffuslon zone Theoretical and experimental mvestlgatlons of the physlcochemlcal regularltles based on the synthesis and crystalhzatlon of the above-mentioned compounds m closed and flowing systems were carried out We suggested a systematic approach to the analysis of complex chemical equlhbrla based on both homologous systems and a mathematical model based on established mterrelatlons of heterogeneous equlhbrla with the thermodynamic and kinetic characteristics of CVD There are a number of ways to describe quaslequlhbnum heterogeneous systems, but there 1s no unified methodological approach to their study at present To use complex methods of systematic analysis for the systems bemg mvestlgated, it 1s necessary to consider topological representations of complex physlcochemlcal equlhbna, matnx methods of calculation and computer slmulatlon It should be mentioned that while studying eqmhbrla m complex chemical systems, one encounters some dlfficultles connected with the stolchlometrlc equations of the reactions This difficulty can be overcome if a real process of physlcochemlcal mteractlon 1s carried out by means of a structural-topological model (STM), stolchlometrlc matrices bemg created on its basis and only hnear Independent reactions bemg defined At this stolchlometrlc matnx the STM 1s transformed into a triangle (trapezoidal) mattlx by elementary conversions (addltlon, subtraction and multlphcatlon of lines and rearrangement of columns)

The suggested procedure of transformmg stolchlometrlc matrices constructed by means of the STM of chemical equlhbrlum allows a basis to be chosen, which includes composite substances that take part m the majority of chemical reactions These mltlal substances introduce into the system then- standard thermodynamic charactenstlcs, which have reliable values The method includes the followmg stages (1) a hypothesis about the eqmhbrmm composltlon of the investigated system usmg mformatlon about its physlcochemlcal properties 1s put forward, (2) the direct eqmhbrmm problem 1s solved usmg equations worked out on the basis of the mass action law, (3) expenmental results of heterogeneous eqmhbrmm mvestlgatlons by the tenslmetrlc method are used to dlscrlmmate the physlcochemlcal model, (4) the thermodynamic characterlstlcs of the composite substances and the parameters of the whole process are the result of a mutual solution of the direct and reverse problems Apphcatlon of this method to the deposltlon of semiconductor compounds from the vapour phase was considered m detail m ref 3 The study of CVD process kmetlcs 1s most mterestmg In this connection the main task of modelhng such processes 1s forecasting the speeds of substance deposltlon and the optlmlzatlon of deposition condltlons by controlling the technologlcal factors To obtam an adequate model, all analysed stages of the process should be taken mto account However, m most cases the productlvlty of a process 1s defined by the hmltmg stage velocity In our condltlons such a stage 1s the diffusive mass transport m vapour phase In this connection a sufficiently general mathematical model of dlffuslve mass transport during vapour phase crystalhzatlon was worked out on the basis of the equlhbrmm thermodynamics and hydrodynamics of ideal gas processes This model mcludes molecular dlffuslon and Stefan’s flow as well as thermodlffuslon The gas dynamics m flowing systems are analysed by a numerlcal computer solution of combined Navler-Stokes equations with suitable boundary condltlons CVD modelhng allowed the technological process parameters that control the doping level to be

29

optimized and materials with previously determined properties to be obtained This mvestlgatlon combined with a study of the technological factors mfluencmg crystal morphology allows the growth of whiskers suitable for sensor manufacture The influence of such technological factors as the temperature of the crystalhzatlon zone, the temperature gradient, and the type and quantity of doping lmpurlties on the morphology and structure of S1 whiskers grown by the CVD method m halide systems was investigated In an h-Au-Br system at crystalhzatlon temx 850-900 “C, slhcon whiskers are peratures formed as hexagonal prisms with a [ 1111 growth direction and {211} faces The influence of halogen concentration and the length of the growth process on crystal size and reslstlvlty while undergomg complex doping have been studied P-type Sl whiskers grown usmg complex doping by Au, Pt and B,O, have a [I 111 growth dlrectlon and are formed as hexagonal pnsms with faces l-30 pm m width The reslstlvlty of these Sl whiskers can be varied by doping from 0 001 to 0 1 R cm

3. Mechanical and piezoresistive properties of Si whiskers The mechanical and electrical properties of ptype slhcon whiskers with different diameters and dopant densltles were investigated The structural perfection of these crystals gives them high mechanical strength Sl whiskers with 20-40 pm dlameter had an ultimate strength m the range (10-24) x 10’ Pa, whereas thm crystals with d 2: 10 pm achieved 30 x lo* Pa or higher Theoretical and experimental mvestlgatlons of lon@tudmal plezoreslstance m p-type Sl (B) whiskers with 1 x lo”-3 x 10” cm-3 impurity concentration were carried out m different temperature ranges chmatlc [4], 77-300 K [ 51 and at 4 2 K [ 61 The longltudmal [ 1111 crystallographic axes of these whiskers correspond to the maximal plezoreststance m p-S1 In accordance with a published method [7], the kinetic coefficients m semiconductors with warped energy surfaces m the presence of external mechanical stress were determined from the kinetic equation and strain was introduced mto the valence-band energy Thus the relaxation time tensor was determined by solving

the kinetic equation and this method allows the plezoreslstance caused by the strain of constantenergy surfaces to be taken into account If we take into account only the ‘large’ plezoresistance due to the redlstnbutlon of carriers between heavy- and light-hole bands, then the piezoreslstance constant nn44IS given by

-J52M4*Mo)l

(1)

where q IS the positive charge of a hole, C, IS the elastic constant, d IS the deformation potential of the SI valence band, k IS the Boltzmann constant, p. the average reslstlvlty of a crystal, L, and L2 are constants, I, (p*) and Z2(p*) are kinetic integrals dependmg on the Fermi energy F = kTp* m the form oc Z&t*) =

s

( -@J~~x),.x”~ dx

b

where x = E/kT, E IS the hole energy, f. the Fermi-Dn-ac function and u,(O) the hole moblhty m an unstressed crystal IndIces 1 and 2 m eqn (1) correspond to light and heavy holes, respectively Equation (1) shows the temperature and concentration dependences of the longltudmal [ 1111 plezoreslstance The mam factors which determlnate these dependences are the integrals Z&*), moblhtles u,(O) and reslstlvlty p. As a result of the deformation of constantenergy surfaces, the density of states and hole moblhtles agamst strain dependence in sphttmg valence band appear Such mechanisms are smaller than the first one described by eqn (1) but the ptezoreslstance 1s also affected by them A ‘large’ plezoreslstance m p-type Sl for some impurity concentrations within the range 1 x lo”-3 x lO”~rn-~ was evaluated m the temperature range 77-300 K Hole moblhtles were determined by takmg mto conslderatlon mainly the ionized lmpunty scattering Delomzatlon of the doping lmpurltles m moderately and heavily doped p-S1 [S] was also taken into account The resulting energy-averaged moblhtles were corrected by the temperature-dependent factor /?,,,,,[9] caused by hole-hole scattering Contrlbutlons of ‘small’ effects were also estlmated, especially connected with the valence-band density of states as a function of strain As expected, these contrlbutlons were more important

for relatively lightly doped Sl crystals and may be neglected for heavily doped ones In order to mvestlgate plezoreslstance at liquid helium temperatures, it 1s necessary to mention other mechanisms of reslstlvlty change with external stress m mtermedlately doped semlconductors near the metal-insulator transition at the msulatmg side of it [IO] Strain affects the localized state wave functions and, therefore, the overlap mtegrals of these wave functions It results m a strong dependence on the impurity conduction, bemg mainly a percolatlve process In this case the gauge factor of mtermedlately doped p-S1 at 4 2 K IS approximately two orders higher than for tradltional plezoresistance Expenmental mvestlgatlons of longtudmal plezoreslstance of p-S1 whiskers with [ 11I] onentatlon were carried out for dopant densities of 1 x lo”-3 x lOi cmm3 in different temperature ranges The normalized whisker resistance AR/R0 as a function of external strain E was studied for strain values E = f 1 2 x 10e3 rel units and E = ( - 1 0- +O 8)% at different temperatures The gauge factor G = AR/(Roe) and its temperature dependence G =f(T) were determmed for dlfferent dopant levels

4. Strain gauges It was shown that p-type Sl whiskers with boron density N = (1-5) x 10” cmP3 (pO= 0 Ol0 02 Q cm) have optimal characteristics for creatmg a strain gauge which can operate at chmatlc temperatures At 300 K these whiskers have a gauge factor G = 100-140 and a temperature coefficient of resistance (TCR) of (0 8-O 12)%/K [4] Sensors developed for mechamcal parameter measurements are based on the plezoreslstlve effect m semiconductors SW, with their various advantages, are unique crystals for strain gauge production and for creating other plezoreslstlve sensors for mechanical parameter measurements Strain gauges on the basis of p-S1 whiskers have extremely high mechanical strength without breakage they permit extending strain up to 1% and are able to operate at more than lo7 load cycles of alternating strain with an amphtude E = + 1 x lo3 pm/m (1 x 10m3) and a frequency from 50 Hz to 1 kHz This property, combined with their small size (thickness 20-30 ,um, active

Fig I Output of half-bridge 4 2, 77 and 300 K

contammg

two sd~con stram gauges at

base from 1 to 3 mm) and mass, allows them to be used for dynamic strain measurements as well as at a high velocity of increasing strain Strain gauges based on s&on whiskers have a wide operating temperature range from hquld hehum temperature [ 1I] to +400 “C [ 121 Investigations have shown that heavily doped p-type slhcon crystals with a reslstlvlty p0 = 0 005 Q cm are the most suitable for creating sensors for mechamcal value measurements at cryogenic temperatures Strain gauges based on these crystals can operate at 4 2 K and m strong magnetic fields up to 5 T [ 121 A typical output of two SW stram gauges connected m a half-bndge versus strain at 4 2, 77 and 300 K 1s presented m Fig 1 Special doping of p-type Sl whiskers allows strain gauges with a uniquely high gauge factor to be manufactured At 4 2 K, K = IO OOO20 000, whereas then resistance 1s of the same order as at room temperature It 1s possible to create highly sensitive low-pressure sensors for cryogemc media measurements on the basis of these strain gauges It 1s known that the hneanty of a mechanical sensor’s output 1s defined by the linearity of the strain gauge, which m turn depends on the strain that 1s Incorporated mto a ‘SW-spring element’ structure as a result of the difference m thermal expansion coefficients of SW and the spring element (SE) This difference also causes a

31

temperature dependence of the gauge factor Thus by varying this incorporated strain (called the ‘apparent strain’), It 1s possible to optlmlze the output of a strain gauge The apparent strain of an Sl stram gauge at temperature T can be estimated from T

E(T) =

s

(as,(f)- 40) dt

(3)

TO

where as,(t) and a(t) are the Sl and SE temperature expansion coefficients, and To 1s the temperature of the bmdmg agent (adhesive) hardening (polymerization) Varying a(T) and To by choice of SE material and bmdmg agent, one can change the E value wlthm the operating temperature range PC Pascal apphcatlon software has been used to carry out an optlmlzmg evaluation The results can be presented m numerical and graphtcal form The apparent strain versus temperature dependence of an Sl strain gauge mounted on mvar by a cold polymerlzatlon adhesive (To = 300 K) 1s presented m Fig 2 A second programme 1s intended to reevaluate the AR/(&e) =S(E) dependences at different temperatures when an mltlal deformation of the Sl strain gauge exists

5. Pressure sensors Sensors to measure pressure and differential pressure utlhzmg Sl SW were deslgned on the basis

Fig 2 Calculated temperature dependence of apparent swam gauge mounted on mvar

stram of SI

of an original universal strain unit a spring-senntlve element containing a cantilever beam wth slhcon strain gauges [ 131 The pressure of the medium to be measured acts on a diaphragm rigidly connected to the cantilever beam Its deflectlon causes the deformation of strain gauges connected in a full Wheatstone bridge configuration The strain unit 1s designed m such a way that Its mstallatlon m a sensor case 1s very simple and its connection with other elements 1s carried out by laser welding This provides a ngld sensor construction and high resonance frequency For special apphcatlons, the strain unit itself can be the sensor case [ 151 The construction design 1s umversal because the same type of strain unit 1s used m sensors for different pressure ranges and only the size of the diaphragm 1s varied Pressure sensors to operate m different temperature ranges were developed using certain alloys for the sensor spring units and agents for strain gauge mounting The strain unit and all the construction elements for high-temperature sensors were produced from Fe-Nl-Co alloy (29% Ni, 17% Co) with a = 4 6-5 5 deg-’ SI strain gauge mounting was carried out by glass-to-metal fusion [12] As a result the unit covar alloy-slhconglass with approximately equal thermal expansion coefficients of all components was created Using mvar alloys to manufacture the spring unit and polymeric adhesives to mount the Sl strain gauges, it 1s possible to extend the sensor’s operating temperature range to cryogenic temperatures [ 121 High-temperature sensors for liquid and gas media to control the parameters of technological processes [ 141, high-frequency sensors for hlghspeed mvestlgatlons, pressure sensors for cryogenic temperature measurements [ 111, plane sensors to measure stress or pressure m different constructions [ 151, sensors for medical and blologlcal research, etc , have now been designed and fabricated Different types are shown m Fig 3 Some modlficatlons of miniature sensors for variable pressure measurements m liquids and gases m the ranges O-2 5 x lo2 kPa to 0- lo2 MPd have been designed The sensor diaphragm dlameter IS no more than 4 mm and its weight 1s less than 5 g The operating temperature range 1s - 60- + 350 “C The sensors have linear static cahbratlon charactenstlcs, the full-scale output wlthout amphficatlon 1s 40-60 mV The resonance

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Fig 3 Different types of pressure and force sensors based on s~hcon whiskers

TABLE I Performance

of s~hcon pressure sensors

Parameter Pressure ranges (Pa) Temperature ranges (“C) Full-scale output wcthout amphficatlon for 2 V d c excltatlon (mV) Resonance fequency (Hz) Mountmg sze diameter (mm) hetght (mm) Weight (g)

Value O-105, -1 x 105-+2 5 x 105, O-IO’. o-4 x 10’ -6O-+350, -269-+20

N-60 10 000-40 000 9-14 2- 10, 30 (for cryogemc sensor) I-20

frequency equals lo-40 kHz for different sensor modlficatlons and measurement pressure ranges The mam parameters of the developed sensors are presented m Table 1 Their advantages are small size and weight (from 1 to 20 g), high resonance frequency ( 2 10 kHz), and the posslblhty of operating m wide temperture ranges from -6O- -1-350 “C or - 269- + 20 “C under unfavourable condltlons (aggressive media, overloadmg, vlbratlons, etc )

6. Sensors for medical and biological investigations Plane sensors wth 10 mm diameter, height 2 mm and weight 3 g for medical and blological mvestigations, m particular for cerebral trauma diagnostics, have been deslgned (Fig 4) The measured pressure range IS O-4 x lo4 Pa (O-300 mm Hg) The designed sensor IS able to measure intracranial pressure directly m different

Rg

4 Pressure sensor for cerebral trauma dlagnostlcs

sections of the brain with further pressure reglstratlon m analog or digital form A diagnostic dynamometer based on s&con strain gauges to measure forces in extremities was designed m order to reveal a section of brain damage when the cerebral trauma occurs The dynamometer 1s able to measure force wlthm two ranges O-30 N and O-300 N with 1 N and 10 N resolution, respectively Output registration is made by a digital device which permits measurements to be made manually or with computer assistance The measuring range choice IS carned out automatically A device for mterbone pressure measurement m order to carry out disease diagnostics and medical treatment has also been designed The measured pressure range IS O-300 mm Hz0 with pressure resolution of - 5 mm HZ0 The device IS supphed with a scale indicator A special probe including two pressure sensors and a pH-meter for diagnosis of gastro-intestinal diseases has been developed This probe allows the mtracavlty pressure to be measured, which mdlrectly reflects the motor activity of gastrointestinal organs The construction included a dlaphragm to convert the measured pressure mto displacement and transmit it to an intermediate displacement transducer (strain unit with strain gauges secured on it) Pressure sensors for gastroenterological investigations contain a rectangular polymeric diaphragm 4 mm x 10 mm m size connected with the cantilever beam of the strain unit by means of a strut wire Strain gauges based on slhcon whiskers are used m the sensor and Its parameters are given m Table 2 The strain unit

33

TABLE 2 Parameters mvestlgations

of pressure sensor for gastro-enterologlcal

Measurmg pressure range (mm Hg) Output signal without amphficatlon at 2 v supply (mV) Dimensions (mm3) Weight (g) Whole probe diameter (mm) Resolution (mm HzO)

O-300 60 5x10~12
References I J C Greenwood, Slhcon m mechamcal sensors, J fhys E Scl Instrum , 4 (1983) 669-678 2 S Middelhoek, Integrated sdlcon sensors, Proc 12th Ann School Sentrcondwrrons Lasers, Mtcrowaw IC and SateIhte Televtston, Mtcroelectromc Sensors, Sozopol, Bulgarm, May I989 3 V A Voronm, V A Prochorov

4

itself forms the sensor’s housmg The sensor height IS 1 2 mm, and it IS mounted m a s&unless steel capsule The capsule mth mounted pressure sensor IS connected with a catheter The sensor output IS regstered by a multichannel recorder All sensors for medical and blologlcal mvestlgatlons have passed chmcal tests

7. Conclusions Sthcon whiskers are a good material for modelhng and study of longltudmal plezoreslstance Due to then structural perfection, high mechamcal strength, morphology, SEX and geometry, these crystals are an excellent material for mechanical sensors such as strain gauges, pressure sensors and dynamometers Sensors based on silicon whiskers can operate wlthm a wide temperature range and under extreme condltlons, they have small size and weight, high resonance frequency and high senslt1v1ty

Sensors based on silicon SW are used m several branches of industry and science m machmebuilding, the aircraft Industry, 011,coal and chemlcal mdustnes, cryogenic techniques, and also medlcme and saentlfic research

5

6

7

and S K Chuchmarev, Topology of heterogeneous eqmhbrmm and thermodynanucs of CVD processes, Proc 5th European Con/ on Chetmcal Vapour DeposrIron, Up&a, Sweden, June 17-20, 1985, p 123 I I Maryamova, Yu I Zaganyach, Yu S Jatzuk et al, Whiskers for new techmque, Proc III Sower Conf on Whrskers for New Techniques, Vorenege, ClS S R , 1979, pp 119- 124 I I Maryamova, E N Karetmkova and Yu S Jatzuk, Investigation of piezoreslstance m p-type SI at low temperatures, Phys Electronrcs, No 26 Lvou, 1983, pp 28-32 I I Maryamova, E N Karetmkova and Yu S Jatzuk, Slhcon stram gauges charactenstics mvestlgatlon at cryogenic temperatures, Phys Electromcs, No 36, Loov, 1988, pp 106-108 Ya S BudJak and E N Karetmkova, Tensors of physlcal properties of crystals wth arbitrary energy low, Phys Electrontcs No

24, Lwv, 1982, pp 3-7 8 S S LI, The dopant densrty and temperature

dependence of hole mobdlty and reslstlvlty m boron doped sihcon, Sohd-State Elec-

tron, 21 (1978) 1109-1117 9 D A TJapkm, T I Tosic and M M Jevtrc, Mobdlty of holes m p-type sdlcon determmed by the self-umnstent method SohdState Electron, 27 (1984) 667-673 IO B I Shklovsky and A L Efros, Electromc fropertres of Doped Semrconductors, Spnnger, Berhn, 1984

II I I Maryamova, E N Karetmkova, Yu S Jatzuk and A A Demldova, Sensors on the basis of silicon whiskers for cryogemc temperatures, Prtb Syst Upra, (1) (1989) 27 12 1 I Maryamova, Yu I Zaganyach, Yu S Jatzuk and T M Ivashuk, On operating temperature range extendmg of sennconductor strain gauges and sensors on their bans, Prrb Syst Upra , (3) (1981) 25-26 13 Yu I Zaganyach, V A Gdka, I I Maryamova et al, Pressure transducer, Author’s certtfcate 883680 USSR, Bull of InventIon, No 43, 1981 I4 Yu I Zaganyach, I I Maryamova, T M Ivashuk et al, Semiconductor sensor with universal stram utut for low pressure measurements, Prlb Syst Upra, (3) (1984) 31-32 15 Yu Zaganyach, A Kutrakov and M Tychan, Pressure sensor, Author’s certtfcatron 1281940 USSR Bull of Invention, No 1, 1987