`N P
`‘|J3fhysics
`
`The electrical properties of polycrystalline silicon films
`John Y. W. Seto
`
`Citation: Journal of Applied Physics 46, 5247 (1975); doi: 10.1063/1.321593
`
`View on|ine: http://dx.doi.org/10.1063/1.321593
`
`View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/46/12?ver=pdfcov
`
`Published by the AIP Publishing
`
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`

`The electrical properties of polycrystalline silicon films
`
`John Y. W. Seto
`
`Electronics Department, GM Research Laboratories, Warren. Michigan 48090
`(Received 14 July 1975)
`
`Boron doses of l X 10" — 5 X 10" /cm’ were implanted at 60 keV into 1-um-thick polysilicon films. After
`annealing at 1l00"C for 30 min, Hall and resistivity measurements were made over a temperature range
`- 50-250°C. lt was found that as a function of doping concentration, the Hall mobility showed a minimum
`at about 2X10”/cm: doping. The electrical activation energy was found to be about half the energy gap
`value of single-crystalline silicon for lightly doped samples and decreased to less than 0.025 eV at a doping
`of I X 10”/cm3. The carrier concentration was very samll at doping levels below 5X10”/cm3 and increased
`rapidly as the doping concentration was increased. At 1>( 10”/cm} doping, the carrier concentration was
`about 90% of the doping concentration. A grain-boundary model including the trapping states was
`proposed. Carrier concentration and mobility as a function of doping concentration and the mobility and
`resistivity as a function of temperature were calculated from the model. The theoretical and experimental
`results were compared. It was found that the trapping state density at the grain bound was 3.34><10”/cm:
`located at 0.37 eV above the valence band edge.
`
`PACS numbers: 73.60.F, 73.20.H, 72.20.F
`
`in this study ranged from 0. 99 to 1.12 um. Boron doses
`ranging from 1X 10” to 5X 1015/cmz were implanted into
`the polysilicon films at 60 keV energy. The samples
`were then annealed at 1100°C for 30 min in a dry nitro-
`gen atmosphere. The annealing was intended to elimi-
`nate most of the damage produced by the implantation
`process and to create a uniform impurity distribution
`in the polysilicon films due to redistribution by diffu-
`sion. Hall measurements on successively anodized and
`stripped samples show that both carrier concentration
`and mobility were uniformly distributed. After anneal-
`ing, Hall bar samples were delineated photolithogra-
`phically. Aluminum was then electron-beam deposited
`and another photomask and etching was used to define
`the contacts. The contacts were alloyed at 500°C for 10
`
`I 020
`
`+ Experimental
`-—. Theoretical
`
`
`
`
`
`
`
`
`
`AverageCarrierConcentrationlcma
`
`INTRODUCTION
`
`The electrical properties of polycrystalline silicon
`(polysilicon) films prepared by thermal decomposition
`of silane and doped by diffusion or during growth have
`been reported by various researcher-s.1" In some of
`these experiments only the dopant-to— silicon atomic
`ratio in the gas phase was known. In others,
`the doping
`concentration was assumed to be the same as the carrier
`
`concentration of the epitaxial single-crystalline silicon
`prepared at the same time or under the same conditions.
`This appeared to be a reasonable assumption. However,
`there is still doubt as to what was the actual doping con-
`centration. When experimental results are to be com-
`pared with theory,
`it is important that the impurity con-
`centration be known precisely. In the present work,
`this is accomplished by using ion implantation. Hall
`measurements were reported by Kamins‘ and Cowher
`and Sedgwicks but their results were not in good agree-
`ment with each other. Neither Hall effect nor resistivity
`vs temperature have previously been measured or cal-
`culated for polysilicon films, although Munoz et al. 5
`performed such measurements on undoped bulk poly-
`silicon rods.
`
`Here we report the results of our electrical mea-
`surements on polysilicon films ion implanted with boron
`so that _the doping concentration could be precisely con-
`trolled. We made Hall and resistivity measurements
`over a wide range of temperatures on polysilicon films
`doped from 1X 10”’ to 5X 10”/cm”. A theoretical model
`is proposed and detailed calculations of the electrical
`transport properties of polysilicon are compared with
`experimental results.
`
`EXPERIMENT
`
`The polysilicon films were intentionally prepared un-
`doped by thermal decomposition of silane in argon onto
`a layer of approximately 3000 A of silicon dioxide which
`was thermally grown on 1)-type 10-82 cm (111)-oriented
`silicon wafers. All polysilicon depositions were done
`at 650°C in an infrared heated horizontal reactor. The
`details of the deposition procedure have been reported
`elsewhere. 3 The thickness of the polysilicon films used
`
`1015
`
`18
`
`101°
`10
`101° A10"
`Doping Concentration lcm3
`FIG. 1. Comparison of the calculated average carrier concen-
`tration vs doping concentration with the room-temperature
`Hall-measurement data. The solid line is the theoretical
`curve.
`
`102°
`
`1021
`
`5247
`
`Journal of Applied Physics, Vol. 46, No. 12, December {97s
`
`Copyright © 1975 American institute of Physics
`
`5247
`
`

`

`the carrier concentration remains very small
`creased,
`compared to the doping concentration and then increases
`very rapidly when the doping concentration reaches
`about 5>< 10”/cm”. For a doping concentration of 5>< 1013/
`cm3 the carrier concentration is approximately 28% of
`the doping. As the doping concentration is increased
`further,
`the carrier concentration approaches that of
`the doping concentration. Our result is quite similar
`to that obtained by Cowher and Sedgwick3 who doped
`their polysilicon films during growth.
`
`The hole mobility in polysilicon and in single—crystal-
`line silicon as a function of doping concentration are
`plotted in Fig. 2. The most prominent feature in Fig.
`2 is the mobility minimum at a doping concentration
`slightly above 1 X 10”/cm’. As the doping is increased
`above IX 1019/cm3 the mobility approaches that in single-
`crystalline silicon. For doping less than 1>< 101°/cm“,
`the mobility increases as the doping is decreased but
`the mobility is always much smaller than that in single-
`crystalline silicon. Our over—all result is very much
`like that of Cowher and Sedgwick. 3 However,
`the mo-
`bility of their lightly doped samples was much higher,
`while the mobility of the heavily doped samples was
`smaller than this work. Figure 3 is a plot of the room-
`temperature resistivity as a function of doping. The
`resistivity reached 10‘ $2 cm for lightly doped samples.
`Increasing the doping from about 1>< 10”/cm3 results in
`an abrupt resistivity drop of about five orders of mag-
`nitude for only a factor of 10 further increase in doping
`concentration. Beyond that range the resistivity de-
`creases almost linearly for further increase in doping.
`The abrupt decrease in resistivity is the result of the
`increase in carrier concentration and mobility as shown
`in Figs. 1 and 2.
`
`10 "
`
`L
`
`105
`
`+
`
`+ Experimental
`
`Theoretical
`
`+
`
`104'
`
`Resistivity52-cm
`
`15
`
`l6
`
`1017
`1018
`1019
`Doping Concentrations lcm3
`FIG. 3. Room-temperature resistivity vs doping concentra-
`tion. The experimental data is plotted with theoretical curve.
`
`1020
`
`1021
`
`1000
`
`\‘‘—~-- \
`
`\\
`
`\
`
`+ Experimental
`—— Theoretical
`
`—— Single Crystalline
`Silicon
`
`\
`
`§l00
`é(‘J
`
`EE2
`
`? EO22 E
`
`10
`
`Doping Concentration /cm
`
`3
`
`FIG. 2. Room—temperature hole Hall mobility vs doping con-
`centration. The experimental result is plotted together with
`the theoretical solid curve. The broken line is for single-
`crystalline silicon.
`
`min to make good Ohmic contacts. Hall measurements
`were made in magnetic inductions up to 1 T. Hall volt-
`ages were always found to be proportional to theapplied
`magnetic field and current through the samples. For
`each measurement the current polarity was reversed
`and the Hall voltages in both directions were averaged
`for calculating the carrier concentration and mobility.
`In samples doped with less than 5>< 1017/cm“ of boron,
`the resistance across the Hall bar was over 107 Q and
`could be as high as 10“ 9. For those samples,
`the cur-
`rent was supplied by a specially built polyethylene isolat-
`ed current supply. The Hall voltage was measured by a
`digital voltmeter buffered by a unity gain electrometer
`amplifier having an input
`impedance of 10”‘ S2. When
`measuring the Hall coefficient and resistivity vs tem-
`perature,
`the sample was mounted on an aluminum
`block which was enclosed in an aluminum container.
`The temperature was measured by a thermocouple in
`direct contact with the back of the polysilicon sample.
`The whole setup was placed in a temperature chamber.
`The temperature variation during a measurement was
`less than i O. 5°C.
`
`EXPERIM ENTAL RESULTS
`
`Figure l is a plot of the carrier concentration vs
`doping concentration. Since the carriers were found to
`be uniformly distributed in the film the doping concen-
`tration was obtained by dividing the total dose/cm“ by
`the thickness of the polysilicon film. At a doping con-
`centration of 101°/ems the carrier concentration is only
`about 1. 8X 1011/cm’. As the doping concentration is in-
`
`5243
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`J. Appl. Phys., Vol. 46, No. 12, December 1975
`
`John Y.W. Seto
`
`5248
`
`

`

`6160
`
`100
`
`60 40
`
`20
`
`0
`
`-20
`
`-40 —50° c
`
`Log(pm(1601))
`
`FIG. 4. Logarithm of resistivity vs 1/kT for samples with dif-
`ferent doping concentrations. The resistivity is normalized by
`the resistivity at 160°C.
`
`Figure 4 is a logarithmic plot of resistivity normalized
`by the resistivity at 160°C vs 1/kT. A linear dependence
`on 1/kT is observed for all samples doped from 1X 10”’
`to 1><1019/cm3. The slopes of the curves decrease as
`the doping was increased. The rate of decrease of the
`slope as a function of doping was highest at a doping
`concentration around 1>< 1013/cm”. As an example,
`the
`difference in slopes between samples doped at 1X 1015
`and 3X 10”/cm‘ is about 0.07 eV; the difference between
`5X 10” and 1>< 101°/cm” is about 0. 03 eV; but the differ-
`ence between 1x 10” and 5X10”/cms is 0.25 eV. The
`slopes of the lightly doped samples are approximately
`equal to the half-energy—gap value of single—crystalline
`silicon. Figure 5 shows hole Hall mobility as a function
`of 1/kT for four samples. For the samples doped 1><l0“‘
`and 5X 10”/cm3 the experimental data yield straight
`lines having slopes of O. 15 and 0.0335 eV, respectively.
`For samples doped 1X 10” and 5X 10”/cm’ the data de-
`viate from straight lines. The mobility of the 5><1O19/
`cm’ doped sample decreases as the temperature is
`raised, while all the other samples showed increased
`mobility with temperature.
`
`THEORY
`
`A polycrystalline material is composed of small crys-
`iallites joined together by grain boundaries. The angle
`between the orientations of the adjoining crystallites
`is often large. Inside each crystallite the atoms are
`arranged in a periodic manner so that it can be consi-
`dered as a small single crystal. The grain boundary is
`a complex structure, usually consisting of a few atomic
`layers of disordered atoms. Atoms in the grain bound-
`ary represent a transitional region between the differ-
`ent orientations of neighboring crystallites. There are
`two schools of thought concerning the effects of the grain
`boundary upon the electrical properties of doped poly-
`crystalline semiconductors. One school’ believes that
`the grain boundary acts as a sink for impurity atoms
`due to impurity segregation at the grain boundary. Con-
`sequently,
`the amount of impurity in the crystallite is
`reduced, which leads to a much smaller carrier con-
`centration than the uniformly distributed impurity con-
`
`5249
`
`J. Appl. Phys., Vol. 46, No. 12, December 1975
`
`centration. The carrier concentration does not approach
`that of the doping concentration until the grain boundary
`is saturated with impurity atoms. It was also suggested‘
`that segregation of impurity caused the grain interiors
`to have higher resistance than the grain boundaries.
`However,
`it has been shown’ that segregation of boron
`at the grain boundary is significant only at extremely
`heavily doped concentrations of silicon, e. g. , 1. 3 at. %
`of boron. No segregation was observed for doping as
`high as 1. 3><102°/cm3." If the reduction of carriers is
`the result of impurity segregation at the grain boundary,
`it is expected that the carrier concentration reduction
`would depend on the impurity element. It was observed‘
`that both boron and phosphorus behaved similarly in
`polysilicon. It is also difficult to explain how impurity
`segregation can lead to the mobility minimum seen in
`Fig. 2.
`
`The other school of thought“ reasons that since the
`atoms at the grain boundary are disordered, there are
`a large number of defects due to incomplete atomic
`bonding. This results in the formation of trapping states.
`These trapping states are capable of trapping carriers
`and thereby immobilizing them. This reduces the num-
`ber of free carriers available for electrical conduction.
`After trapping the mobile carriers the traps become
`electrically charged, creating a potential energy bar-
`rier which impedes the motion of carriers from one
`crystallite to another,
`thereby reducing their mobility.
`Based on this model, for the same amount of doping,
`the mobility and carrier concentration of a polycrystal-
`line semiconductor would be less than that of a single-
`crystalline material. Kamins‘ used this model to ex-
`plain some of the trends observed in his Hall-effect
`data. He attributed the decrease in mobility with de-
`creasing carrier concentration to the effect of the high-
`resistivity space- charge region surrounding the grain
`
`100
`
`HoleMobilityincmzlv-sec
`
`U18
`
`20
`
`25
`
`30
`
`35
`llKT ev
`
`40
`
`45
`
`FIG. 5. Hole Hall mobility vs 1/kT for samples with different
`doping concentrations.
`
`John
`
`Seto
`
`5249
`
`

`

`mation, Poisson’s equation becomes
`
`dzV qN
`dx =—€—,
`
`l<ixI<%L,
`
`(1)
`
`where E is the dielectric permittivity of polysilicon.
`Integrating Eq.
`(1) twice and applying the boundary con-
`ditions that V(x) is continuous and dV/dx is zero at x=l
`gives
`
`V(x) = (qN/2E)(x — Z)” + V,,0,
`
`z<|x|<%L,
`
`(2)
`
`where V,,0 is the potential of the valence band edge at the
`center of the crystallite. Throughout this calculation
`the intrinsic Fermi level is taken to be at zero energy
`and energy is positive towards the valence band (the
`energy band diagram for holes).
`
`For a given crystallite size, there exist two possible
`conditions depending on the doping concentration: (a)
`LN<Q,, and (b) Qt .< LN.
`
`We first consider the case for LN< Q,. Under this
`condition,
`the crystallite is completely depleted of car-
`riers and the traps are partially filled, so that Z: 0 and
`Eq.
`(2) becomes
`
`V(x) = Vvo + (qN/2e)xa,
`
`Ix i $51,.
`
`(3)
`
`The potential barrier height, VB, is the difference be-
`tween V(0) and V(%L),
`i. e.,
`
`Va =<ILaN/8€
`
`(4)
`
`showing that VB increases linearly with N, Using
`Boltzmann statistics,
`the mobile carrier concentration,
`p(x), becomes
`
`p(x) =Nv exp{'
`
`-
`
`where N, is the density of states and E, is the Fermi
`level. The average carrier concentration, P,,, is ob-
`tained by integrating Eq.
`(5) from —%L to %L and divid-
`ing by the gmn size. The result is
`
`_E n2<kT)1/2
`P“‘Lq( N
`
`exp
`
`(EB +155)
`kT
`
`515 N
`6” 2
`2<kT
`
`where
`
`Ea =qVa
`
`and
`
`n, = N” exp(— EE,/kT)
`
`1/2]
`
`’
`(6)
`
`(5')
`
`(6")
`
`is the intrinsic hole concentration of single-crystalline
`silicon (with band gap E,) at temperature T.
`
`the Fermi level is determined by equating
`(6),
`In Eq.
`the number of carriers trapped to the total number of
`trapping states occupied, given as
`
`LN =
`
`Qt
`2exp|(E,—E,)7kT +1
`The traps are considered to be identical; each trap is
`capable of trapping only one hole of either spin; and
`there is no interaction between traps. From Eq. (7),
`Fermi level is given as
`
`E,=E,— kT l.n[%(Q,/LN— 1)].
`
`7
`
`)
`
`(
`
`the
`
`(8)
`
`Grain Boundary \‘
`
` crystallite
`
`(a) Crystal Structure
`
`0 (
`
`b) Charge Distribution
`
`(cl Energy Band Structure
`
`(a) Model for the crystal structure of polyslllcon
`FIG. 6.
`lb) The charge distribution within the crystallite and at
`films.
`the grain boundary.
`(c) The energy band structure for polystli—
`con crystallites.
`
`boundary. Choudhury and Howerz used the same model
`and treated the potential energy barrier as a parameter
`to explain their measurements of resistivity vs doping
`concentration.
`
`We believe that the electrical transport properties
`of polysilicon films are governed by carrier trapping
`at the grain boundary. In a real polycrystalline material,
`the crystallites have a distribution of sizes and irre-
`gular shapes. To simplify the model we assume that
`polysilicon is composed of identical crystallites having
`a grain size of L cm. We also assume that there is only
`one type of impurity atom present,
`the impurity atoms
`are totally ionized, and uniformly distributed with a
`concentration of N/cm“. The single-crystalline silicon
`energy band structure is also assumed to be applicable
`inside the crystallites. We further assume that the
`grain boundary is of negligible thickness compared to
`L and contains Qt/cm” of traps located at energy E, with
`respect to the intrinsic Fermi level. The traps are as-
`sumed to be initially neutral and become charged by
`trapping a carrier. Using the above assumptions an
`abrupt depletion approximation is used to calculate the
`energy band diagram in the crystallites. In this approxi-
`mation, Fig. 6 shows that all the mobile carriers in a
`region of (-;-L — l) cm from the grain boundary are
`trapped by the trapping states, resulting in a depletion
`region. The mobile carriers in the depletion region are
`neglected in this calculation. Although polysilicon is
`a three-dimensional substance, for the purpose of cal-
`culating its transport properties, it is sufficient to treat
`the problem in one dimension. Using the above approxi-
`
`5250
`
`J. Appl. Phys., Vol. 46, No. 12, December 1975
`
`John Y.W. Seto
`
`5250
`
`

`

`carriers possessing high enough energy to surmount
`the potential barrier at the grain boundary. On the other
`hand,
`the tunneling current arises from carriers with
`energy less than the barrier height. These carriers go
`through the barrier by quantum- mechanical tunneling.
`
`the tunneling
`When the barrier is narrow and high,
`current can become comparable to or larger than the
`thermionic emission current. In polysilicon the poten-
`tial barrier is highest when the barrier width is the
`widest. The barrier height decreases rapidly to a small
`value for a highly doped polysilicon, therefore,
`the tun-
`neling current is always expected to be smaller than
`the thermionic emission current. Because of this,
`tun-
`neling current will be neglected in our calculation.
`Following Bethe, 9 the thermionic emission current den-
`sity, Jm, for an applied voltage, V,, across a grain
`boundary is
`
`— 1] ,
`
`(12)
`
`qV
`
`exp (—k—7,9-5 [exp
`
`V
`
`kT )1 /2
`Jth=‘IPa(
`2m*1r
`where m* is the effective mass of the carrier. Equation
`(12) was obtained by neglecting collisions within the de-
`pletion region and the carrier concentration in the crys-
`tallite was assumed to be independent of the current
`flow, so that it is applicable only if the number of car-
`riers taking part in the current transport is small com-
`pared to the total number of carriers in the crystallite.
`This condition restricts the barrier height to be larger
`than or comparable to kT. If V, is small, qV,<< kT, Eq.
`(12) can be expanded to give
`
`PotentialBarrierHeightinArbitrary
`
`Units
`
`0
`
`0
`
`UL
`Doping Concentration in Arbitrary Units
`
`FIG. 7. Functional dependence of the potential barrier height
`on doping concentration.
`
`the carrier concentration can be
`(6) and (8),
`With Eqs.
`calculated for a given N,
`if L, Q,, and E, are known.
`A method of obtaining these values will be discussed
`later.
`
`If LN >Q, only part of the crystallite is depleted of
`carriers and l > 0. The potential barrier height then
`becomes [from Eq. (2)]
`
`VB =qQf/8<N.
`
`(9)
`
`(4) and (9), a plot of V5 as a function of
`Using Eqs.
`doping concentration is shown in Fig. 7. It is noted that
`as the doping concentration is increased,
`the potential
`barrier at first increases linearly, reaching a maximum
`at LN=Q,,
`then decreases rapidly as 1/N. This beha-
`vior results from the dipole layer created when impurity
`atoms are first introduced and the traps are being filled.
`The strength of the dipole layer increases as more im-
`purity atoms are added. However, after all the traps
`are filled, the total charge in the dipole remains the
`same but the width of the dipole layer is decreased and
`the potential barrier decreases. The average carrier
`concentration, p,,,
`is obtained as before, by averaging
`over the crystallite. In the undepleted region,
`the car-
`rier concentration, 12,,
`is the same as that of a similar-
`ly doped single-crystalline silicon,
`
`12., =N., exp[— (Em, — E.)/kTi
`
`(10)
`
`for a nondegenerately doped sample. The carrier con-
`centration in the depletion region is given in Eq. (5).
`The average carrier concentration, 1),, can be shown
`to be
`
`Ju.= (12.94 (5,773
`
`1
`
`1 /2
`
`q V
`
`exp (-77 Va:
`
`(13)
`
`which is a linear current-voltage relationship. From
`Eq.
`(13) the conductivity of a polysilicon film with a
`grain size L cm is
`
`o=.Lq2pa
`
`1
`
`1 /2
`
`V
`
`exp (— -2%) .
`
`(14)
`
`Inserting Eqs.
`
`(6) and (11) into Eq.
`
`(14), we find that
`
`as exp[— (iE, — E.)/kri,
`
`ifNL<Q,,
`
`ooc 7''“ exp(— 12,, /kT),
`
`itNL>Q,.
`
`(15)
`
`(16)
`
`Plotting the logarithm of the resistance vs 1/kT should
`give a straight line with a slope equal to %E,— E, if LN
`< Q, and E, if LN > Q,. This interpretation will fail when
`E5 <<kT, which is likely for highly doped material.
`
`17¢=17» {(1 -5%) +qiL(2€fvTfl)
`
`1/2'
`
`erf(2sk1TN)
`
`1 /2
`
`Using the relationship
`
`0‘: (IP11
`
`(17)
`
`(11)
`
`together with Eq. (14), an effective mobility, um,
`given as
`
`is
`
`The resistance of a polycrystalline material consists of
`the contributions from the grain-boundary region and
`the bulk of the crystallite. If the conduction in the crys-
`tallite is much higher than that through the grain bound-
`ary, it is a good approximation to consider just the re-
`sistance of the grain-boundary region. There are two
`important contributions to the current across the grain
`boundary: thermionic emission and tunneling (field
`emission). Thermionic emission results from those
`
`“eff = 141
`
`1
`
`1/2 I
`
`EB
`
`EXP (- k—T)
`
`(18)
`
`Since the energy barrier, E3, exhibits a maximum as
`a function of doping, Eq. (18) shows that the mobility
`will have a minimum as a function of doping. The mini-
`mum occurs when LN =Q,. Furthermore, a plot of the
`logarithm of ti," vs 1/kT should yield a straight line
`with a negative slope of E,,,
`if E3 >kT.
`
`5251
`
`J. Appl. Phys., Vol. 46, No. 12, December 1975
`
`John Y.W. Seto
`
`5251
`
`

`

`+ Experimental
`—— Theoretical
`
`+ +* 5x10 /cm3
`
`I
`
`8
`
`
`
`HoleMobilityincmz/V-sec 8
`
`1/kT ev
`
`FIG. 8. The experimental hole mobility vs I/kT is compared
`with the theoretical curve for 5 X1019 and 1 X1019/cm3 doping
`using potential barrier heights of 0. 005 and 0. 022 eV,
`respectively.
`
`COMPARISON WITH EXPERIMENT
`
`The above results can be summarized as (a) the car-
`rier concentration of polysilicon is very small for LN
`< Q, and increases abruptly as LN approaches Qt,
`then
`for further increase in doping concentration the carrier
`concentration asymptotically approaches that of the car-
`rier concentration of a single-crystalline silicon with
`the same amount of doping; (b) the conductivity and mo-
`bility of polysilicon vary as exp(— EB /kT) for E3 >kT;
`(c) the mobility as a function of doping concentration
`exhibits a minimum when N:Q,/L.
`
`In this theory there are three parameters: the grain
`size, L; the grain boundary trapping state density, Q,;
`and the trapping state energy level, E,. The grain size
`can be observed directly using transmission electron
`microscopy and image analysis. Such experiments
`
`showed that the average grain size for our samples was
`about 200 A. Q, can be obtained from the mobility-vs-
`1/kT plot and Eqs.
`(9) and (18). From Fig. 5,
`the value
`of EB for the 5><10“’/cm" sample results directly from
`the slope of the curve.
`In the samples doped with IX 10”’
`and 5><1019/cm3 a fitting to Eq.
`(18) is used to obtain
`E5 . The values of EB that give the best fit to the experi-
`mental results are 0. 022. and 0. 005 eV, respectively.
`The result of the fitting is shown in Fig. 8. Table I
`lists the values of Q, for the three samples; they range
`from 2. 98X 1012 to 3. 64x10”/cmz. The average value
`of Q, 3. 34><1012/cmz, will be used in our calculation.
`This value is approximately equal to the value of the
`surface state density of a single-crystalline silicon.
`The grain boundary of a polysilicon can probably be
`considered as composed of two free silicon surfaces in
`contact. The number of trapping states is thus likely
`to be close to the surface state density of a free silicon
`surface. From Fig. 5, the slope of the 1X10”/cm”
`sample is 0. 15 eV. Since LN is less than Q, for this
`
`in
`sample, using Eq. (4), L is calculated to be 270 ii,
`good agreement with the average value of 200 .3. obtained
`from transmission electron microscope study. The
`trapping state energy, Et, can be obtained from Eqs.
`(6) and (8). It has been shown"9 that for a composite
`material such as polysilicon, Hall measurements give
`the carrier concentration within the crystallites if the
`conductivity of the bulk crystallite is much higher than
`that of the grain boundary. It has also been shown”
`that if the mobility in the crystallite is not a function
`of position then the carrier concentration obtained by
`the Hall measurement is the average value within the
`crystallite, as given in Eqs.
`(6) and (11). Therefore,
`Hall measurements give the average carrier concen-
`trations in the lightly and highly doped polysilicon films.
`For the intermediately doped film, where LN=Q,,
`the
`energy bands within the crystallite are very nonuniform
`and the carrier concentration obtained by the Hall mea-
`surement can be significantly different from the average
`value in the crystallite. To ensure the validity of the
`experimental data when computing E,, we use the ex-
`perimental value at a doping density of 1>< 101°/cma,
`the lowest doping used in our experiment. Using Eqs.
`(6) and (8) and the measured carrier concentration of
`1. 8>< 10“/cms the trapping state energy is found to be
`0.37 eV above the valence band edge. Dumin“ found a
`deep level in silicon on sapphire at 0. 3 eV above the
`valence band edge. It is possible that this level might
`be of the same origin as that in polysilicon films.
`
`Using these values of L, Q,, and E, the theoretical
`carrier concentration vs doping concentration is plotted
`as a solid line in Fig. 1. The experimental and theo-
`retical values are in good agreement. The deviation in
`the range between 5X 10” and 7X 10”’/cma is the result
`of the rapid rise in carrier concentration as a function
`of doping so that it is very sensitive to experimental
`error. Also, as discussed previously,
`the carrier con-
`centration derived from the Hall measurement can dif-
`fer significantly from that of the actual average carrier
`concentration. Figures 2 and 3 are the theoretical hole
`mobility and resistivity vs doping concentration plotted
`together with experimental data. In these plots a scaling
`factor of 0. 154 has been applied to Eq.
`(4) to obtain
`the theoretical curves. Andrews and Lepselter” cal-
`culated the effective Richardson’s constant for holes
`in silicon for metal silicide Schottky barriers to be
`about 0. 25 that of free electron. Our value of the effec-
`tive Richardson’s constant is found to be 0. 12. This
`supports our assumption that the hole transport in poly-
`silicon is dominated by thermionic emission.
`In Fig. 9,
`the theoretical and experimental values of the activation
`energy for samples with different doping densities are
`shown. The experimental activation energies are de-
`
`TABLE I. Trapping state density and energy barrier height for
`three samples with different doping concentrations.
`
`Doping
`Energy barrier,
`Trapping state
`
`concentration
`EB
`density, Q,
`5><10“*/cm3
`0.0335 eV
`2.9sx1o”/cm?
`1 X1019/cm3
`0.022 eV
`3.41 x10”/cm?
`5><10‘9/cm“
`0.005 eV
`3.64 ><1o”/cm?
`
`5252
`
`J. Appl. Phys., Vol. 46, No. 12, December 1975
`
`John Y.W. Seto
`
`5252
`
`

`

`+ Experimental
`—- Theoretical
`
`Activation
`
`EnergyeV
`
`15
`
`16
`
`1018
`1017
`Doping Concentration Icma
`
`1019
`
`1020
`
`FIG. 9. Comparison of the experimental and theoretical acti-
`vation energy as a function of doping concentration. The ex-
`perimental values are derived from Fig. 4.
`
`rived from the slopes of the resistivity-vs-1/kT plot
`in Fig. 4. The theoretical values are obtained from
`Eqs.
`(8),
`(9),
`(15), and (16). The energy gap, E“ in
`Eq.
`(15) is taken to be that of single-crystalline silicon.
`The experimental values of the activation energy is
`always larger than the theoretical values for lightly
`doped samples. This is because in our theory the trap-
`ping states are assumed to have a 5 function distribution,
`while in real polysilicon the trapping states are dis-
`tributed over an energy range.” The 6-function approxi-
`mation causes the Fermi energy to increase much more
`rapidly as dopants are added to the polysilicon film.
`This results in a lower calculated activation energy.
`Otherwise,
`the theoretical and experimental results
`are in good agreement.
`
`To compare our theory with previously reported ex-
`periments is complicated by the fact that most reports
`did not indicate the grain size of their samples. This
`in itself is not a problem because, at worst,
`the grain
`size can be treated as a parameter. It was reported
`that the grain size of polysilicon films changed as the
`doping concentration and deposition temperature were
`changed.“"15 If the grain size is neither known nor can
`be treated as a constant a comparison with theory can
`only provide an indication of the validity of the theory.
`We compared our theory with the experimental results
`reported by Kamins‘ and Cowher and Sedgwick3; a broad
`agreement between experiment and theory was obtained.
`
`DISCUSSION
`
`it is equal-
`theory has been applied to p-type polysilicon,
`ly applicable to n-type polysilicon. It has been shown”
`that in n-type silicon the grain boundary has an electron
`trapping level located between the intrinsic Fermi level
`and the conduction band edge. By performing the type
`of experiments reported here, a comparison between
`theory and experiment is possible and the trapping state
`density and energy can be found.
`We now discuss some of the limitations of the model
`
`and our calculations. We neglected the contribution to
`the resistivity by the bulk of the crystallites. This as-
`sumption fails if the resistance of the bulk is compara-
`ble to that of the barrier. Such a situation is possible
`if the grain size of the polysilicon film is large and the
`doping is high as is the case in Kamins’s polysilicon‘
`doped above 7>< 101°/cm3. For those samples it is neces-
`sary to take the bulk of the crystallites into account. It
`has been shown” that the surface states of a free sili-
`con surface are not fixed at a discrete energy but dis-
`tributed over an energy range. It is likely that the
`trapping states in the grain boundary of polysilicon are
`also distributed over an energy range. Such a distribu-
`tion will modify the calculations since we assumed a 6-
`function approximation. The effect on the activation
`energy was discussed in the above section. The effects
`on mobility and carrier concentration are to cause their
`changes as a function of doping concentration to be much
`slower when LN=Q,. Unless the distribution spreads
`to within a few kT of the valence band there should be
`
`no effect on the highly doped samples, 1. e. , LN >> (2,.
`
`In large grain polysilicon, such as the ones prepared
`in hydrogen at temperatures around 1000°C and bulk
`polysilicon rods,
`the free-carrier concentration in the
`"depletion layer” can be appreciable. Using the deple-
`tion approximation leads to inaccurate values of the
`barrier heights. The mobility is exponentially depen-
`dent on the barrier height, as shown in Eq. (18). Any
`inaccuracy in the calculated potential barrier height
`