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A new analytical approach to amorphous silicon thin film transistors
Journal of Non-Crystalline Solids 59 & 60 (1983) 1171-1174 North-Holland Publishing Company
1171
A NEW ANALYTICAL APPROACH TO AMORPHOUSSILICON THIN FILM TRANSISTORS M. Shur and M. Hack+ Dept. of Electrical Engineering, U. of Minnesota, Minneapolis, MN U.S.A. Energy Conversion Devices, Inc., 1675 W. Maple Rd., Troy, MI U.S.A. Using both analytical and computer models the I-V characteristics of amorphous silicon (a-Si) thin f i l m transistors are related to the basic material parameters. The characteristic energies of the density of states variations are related to the slope of the current-voltage characteristics in the subthreshold regime. For the acceptor-like states between the Fermi level and 0.15 eV below the conduction band edge we deduce the characteristic energy Eca= 80-I00 mV for devices fabricated by various researchers, in good agreement with photoconductivlty measurements and other experimental data. Based on the transfer characteristics at voltages above threshold, we determine the temperature dependence of the electron mobility the characteristic energy of the t a l l states and the contact resistance. Our theory of a-Si thin f i l m transistors predicts how device characteristics scale with gate length, oxide thickness, channel doplng, temperature, and material properties. This theory may be used to optimize the design of a-Si thln f i l m transistors. I.
INTRODUCTION In this paper we propose a new physical mechanism describing the a-Si
f i e l d effect transistor (FET) operation and develop i t into an analytical theory describing t h e i r operation.
We check the v a l i d i t y of our analytical
approach using a computer simulation based on the solution of the complete set of transport equations for an a-Si FET. We distinguish between two basic modes of device operation.
At low gate
voltages, in the subthreshold regime nearly all the charge induced into the a-Si channel goes into the localized states in the energy gap.
This shifts
the Fermi level in the channel c l o s e r to the conduction band thus increasing the concentration of mobile electrons in the channel. assumed t h a t a t high gate voltages v i r t u a l l y the conduction band as mobile electrons 1.
I t has p r e v i o u s l y been
a l l the induced charge goes i n t o However, the analysis given in
t h i s paper demonstrates t h a t t h i s may only happen at u n r e a l i s t i c a l l y high gate voltages, as f o r t h i s s i t u a t i o n to occur the Fermi l e v e l in the conducting channel would have to be very close t o the conduction band edge.
Never-
theless, a dramatic change in the device I-V c h a r a c t e r i s t i c s , corresponding t o the "above threshold regime", does indeed occur at moderate gate voltages.
As
discussed below t h t s may be explained by considering the important r o l e played by the t a i l
states tn determining the charge d i s t r i b u t i o n in a-St FET's.
0022-3093/83/0000-0000/$03.00 © 1983 North-Holland/Physical Society of Japan
M. Shut, M. Hack /Amorphous silicon thin film transistors
1172
Photoconductlvlty and f i e l d effect data show that the acceptor localized states (which are important f o r the n-channel device operation) may be crudely divided into two groups:
deep localized states and t a i l states with a t r a n s i -
tion around 0.15 eV below the bottom of the conduction band (see Fig. I ) .
For
the t a i l states, the characteristic energy of the density of states variation, TI, is about 300 K and f o r the deep states, T2, is I000 K. According to the mechanism proposed In thls paper the transition from the "below threshold" to the "above threshold" regime occurs when the Fermi level enters the acceptor-like t a i l states. 2.
DISCUSSION The induced charge Is divided between the 1ocallzed states and the mobile
carriers.
We have calculated the induced charge a n a l y t i c a l l y by integrating
the density of states spectrum using Fermi-Oirac s t a t i s t i c s .
Our more
accurate computer simulation Is based on a numerical integration and takes Into account the occupancy of the localized states as predicted by the Shockley-Read-Hall s t a t i s t i c s . Figure 2 shows the calculated relatlonshlp between the s h i f t in the Fermi level AEF and the gate voltage. Figure 2 clearly shows two d i s t i n c t regimes divided by the Fermi level entering the t a i l states (at ~ 0.14 eV below the conduction band).
In the "subthreshold" regime only a very small
fraction of the charge goes into the extended states whereas in the "above" threshold regime a substantial fraction of the induced charge goes into the conduction
band.
07 O.E
l
l
l
l
l
l
l
l
l
~,o~,
o.s
==
~0.4 oJ
~,d9
i
o ). i-
0,3
0.2
aa
Q
0.1
I ~ S l I I I -0.3-Q2-~I 0 ~
I I I 0.2 ~ 3
ENERGY~V)
Fi~.l
I I ~4 ~5
~6 ~
0
I
2o
--3o
GATE VOLTAGE(V)
B©
Densi~ of state spectrum for amorphous silicon.
I
lo
Fig.2
Fermi level s h i f t in channel as a function of gate voltage.
M. Shur, M, llack / Amorphous silicon thin film transistors
10 "~
i
i
°...
.,.°."
• ,o-,""
10'
1()
1173
"
I 10 `3.5 (CJm 2) CHARGE
Fig.3
I 10 ~ - CHARGE
10 '5
(Flat - Band)
Computer simulated l-V characteristics for Vds << VgI.
This difference arises because in the "above-threshold" regime TI is less than or equal to 300 K and v l r t u a i l y a l l of the charge is actually located above the Fermi level close to the conduction band whereas in the below threshold regime most of the locallzed charge lles below the Fermi level. When Tl is less than or equal to T, the product of the density of states and the Fermi-Olrac function increases with increasing energy. We have used the gradual channel approximation to calculate analytically the f l e l d , potential and carrier distributions along the channel and the device current voltage characteristics. In agreementwith ref. 3 our theory predicts that Ids ~ (CoxVgl)¥ for Vds << VgI where Cox is the oxide capacitance, and VgI = Vgs - Ids Rs - VFB, where Vgs is the gate-to-source voltage, Rs Is the source series resistance, VFB is the effective f l a t band voltage, ¥ = 2 x T2/T where T is temperature.
We have
deduced values of T2 ranging from gO0 K to 1200 K from the experimental Ids-Vg curves measured by different researchers (see for example ref. 4-5).
Figure 3 shows Ids vs. gate voltage Vg for Vds << VgI computed using our complete computer model of a FET whlch is similar to our solar c e l l model6,
The characteristic slope Of the density of states as deduced from
the Ids - Vg characteristics of Fig. 3 using the above theory ts 82 meV, in good agreeementwith the value of 86 meV which was used In the model.
114.Shur, M. Hack/Amorphous silicon ttlin film transistors
1174
In the above threshold regime the r a t i o PFET/PBAND, where UFET is the f i e l d effect mobility and PBAND is the band mobility, is a complicated analytical function of the material parameters, device temperature and the charge Q = Cox Vg2 induced in the channel where Vg2 = VgI - Vt . Vt is the threshold voltage and is defined as the gate voltage required to s h i f t the Fermi level into the t a i l states. The calculated current-voltage characteristics in the above threshold regime are shown in Figure 4.
As can be seen from the figure, the general
shape of the I-V curves and the values of the current are in good agreement with experimental results, see f o r example reference 4.
Our results may be
also used f o r the device characterization which w i l l allow an accurate comparison wlth the experimental data.
The complete equations describing the
above threshold regime characteristics include t h e i r dependence on the position of the equilibrium Fermi level, and hence the effects of doping can be studied.
4C
i
t o x = 0.251~m W=200prn L=lOpm
.
...... "................ ! 5 y g ' "
2
.+ 12
10 1C
8 .... :
5 i 5
i
10
J 15
20
Vds (V) Fi~.4
Calculated l-V c h a r a c t e r i s t i c s in above threshold regime.
REFERENCES 1.
S. Lee and [ . Chen, Appl. Phys. L e t t . 41, 549 (1982).
2.
M. Shur and M. Hack, to be published.
3.
S. Kishida, e t a l . ,
Tech. Report of Elect. Dev. Soc. of IECE of Japan,
ED82-7 (1982). 4.
M. 3. Thompson, N. N. 3ohnson, M. O. Moyer and R. LuJan, IEEE Trans. Electron Dev., ED-29, 1643 (1982).
5.
Y. Nara and M. Matsumura, IEEE Trans. Elect. Dev. EO-29, 1646 (1982).
6.
M. Hack and M. Shur, IEEE Elect. Dev. L e t t . , EDL-4, 5, 140 (1983).
1171
A NEW ANALYTICAL APPROACH TO AMORPHOUSSILICON THIN FILM TRANSISTORS M. Shur and M. Hack+ Dept. of Electrical Engineering, U. of Minnesota, Minneapolis, MN U.S.A. Energy Conversion Devices, Inc., 1675 W. Maple Rd., Troy, MI U.S.A. Using both analytical and computer models the I-V characteristics of amorphous silicon (a-Si) thin f i l m transistors are related to the basic material parameters. The characteristic energies of the density of states variations are related to the slope of the current-voltage characteristics in the subthreshold regime. For the acceptor-like states between the Fermi level and 0.15 eV below the conduction band edge we deduce the characteristic energy Eca= 80-I00 mV for devices fabricated by various researchers, in good agreement with photoconductivlty measurements and other experimental data. Based on the transfer characteristics at voltages above threshold, we determine the temperature dependence of the electron mobility the characteristic energy of the t a l l states and the contact resistance. Our theory of a-Si thin f i l m transistors predicts how device characteristics scale with gate length, oxide thickness, channel doplng, temperature, and material properties. This theory may be used to optimize the design of a-Si thln f i l m transistors. I.
INTRODUCTION In this paper we propose a new physical mechanism describing the a-Si
f i e l d effect transistor (FET) operation and develop i t into an analytical theory describing t h e i r operation.
We check the v a l i d i t y of our analytical
approach using a computer simulation based on the solution of the complete set of transport equations for an a-Si FET. We distinguish between two basic modes of device operation.
At low gate
voltages, in the subthreshold regime nearly all the charge induced into the a-Si channel goes into the localized states in the energy gap.
This shifts
the Fermi level in the channel c l o s e r to the conduction band thus increasing the concentration of mobile electrons in the channel. assumed t h a t a t high gate voltages v i r t u a l l y the conduction band as mobile electrons 1.
I t has p r e v i o u s l y been
a l l the induced charge goes i n t o However, the analysis given in
t h i s paper demonstrates t h a t t h i s may only happen at u n r e a l i s t i c a l l y high gate voltages, as f o r t h i s s i t u a t i o n to occur the Fermi l e v e l in the conducting channel would have to be very close t o the conduction band edge.
Never-
theless, a dramatic change in the device I-V c h a r a c t e r i s t i c s , corresponding t o the "above threshold regime", does indeed occur at moderate gate voltages.
As
discussed below t h t s may be explained by considering the important r o l e played by the t a i l
states tn determining the charge d i s t r i b u t i o n in a-St FET's.
0022-3093/83/0000-0000/$03.00 © 1983 North-Holland/Physical Society of Japan
M. Shut, M. Hack /Amorphous silicon thin film transistors
1172
Photoconductlvlty and f i e l d effect data show that the acceptor localized states (which are important f o r the n-channel device operation) may be crudely divided into two groups:
deep localized states and t a i l states with a t r a n s i -
tion around 0.15 eV below the bottom of the conduction band (see Fig. I ) .
For
the t a i l states, the characteristic energy of the density of states variation, TI, is about 300 K and f o r the deep states, T2, is I000 K. According to the mechanism proposed In thls paper the transition from the "below threshold" to the "above threshold" regime occurs when the Fermi level enters the acceptor-like t a i l states. 2.
DISCUSSION The induced charge Is divided between the 1ocallzed states and the mobile
carriers.
We have calculated the induced charge a n a l y t i c a l l y by integrating
the density of states spectrum using Fermi-Oirac s t a t i s t i c s .
Our more
accurate computer simulation Is based on a numerical integration and takes Into account the occupancy of the localized states as predicted by the Shockley-Read-Hall s t a t i s t i c s . Figure 2 shows the calculated relatlonshlp between the s h i f t in the Fermi level AEF and the gate voltage. Figure 2 clearly shows two d i s t i n c t regimes divided by the Fermi level entering the t a i l states (at ~ 0.14 eV below the conduction band).
In the "subthreshold" regime only a very small
fraction of the charge goes into the extended states whereas in the "above" threshold regime a substantial fraction of the induced charge goes into the conduction
band.
07 O.E
l
l
l
l
l
l
l
l
l
~,o~,
o.s
==
~0.4 oJ
~,d9
i
o ). i-
0,3
0.2
aa
Q
0.1
I ~ S l I I I -0.3-Q2-~I 0 ~
I I I 0.2 ~ 3
ENERGY~V)
Fi~.l
I I ~4 ~5
~6 ~
0
I
2o
--3o
GATE VOLTAGE(V)
B©
Densi~ of state spectrum for amorphous silicon.
I
lo
Fig.2
Fermi level s h i f t in channel as a function of gate voltage.
M. Shur, M, llack / Amorphous silicon thin film transistors
10 "~
i
i
°...
.,.°."
• ,o-,""
10'
1()
1173
"
I 10 `3.5 (CJm 2) CHARGE
Fig.3
I 10 ~ - CHARGE
10 '5
(Flat - Band)
Computer simulated l-V characteristics for Vds << VgI.
This difference arises because in the "above-threshold" regime TI is less than or equal to 300 K and v l r t u a i l y a l l of the charge is actually located above the Fermi level close to the conduction band whereas in the below threshold regime most of the locallzed charge lles below the Fermi level. When Tl is less than or equal to T, the product of the density of states and the Fermi-Olrac function increases with increasing energy. We have used the gradual channel approximation to calculate analytically the f l e l d , potential and carrier distributions along the channel and the device current voltage characteristics. In agreementwith ref. 3 our theory predicts that Ids ~ (CoxVgl)¥ for Vds << VgI where Cox is the oxide capacitance, and VgI = Vgs - Ids Rs - VFB, where Vgs is the gate-to-source voltage, Rs Is the source series resistance, VFB is the effective f l a t band voltage, ¥ = 2 x T2/T where T is temperature.
We have
deduced values of T2 ranging from gO0 K to 1200 K from the experimental Ids-Vg curves measured by different researchers (see for example ref. 4-5).
Figure 3 shows Ids vs. gate voltage Vg for Vds << VgI computed using our complete computer model of a FET whlch is similar to our solar c e l l model6,
The characteristic slope Of the density of states as deduced from
the Ids - Vg characteristics of Fig. 3 using the above theory ts 82 meV, in good agreeementwith the value of 86 meV which was used In the model.
114.Shur, M. Hack/Amorphous silicon ttlin film transistors
1174
In the above threshold regime the r a t i o PFET/PBAND, where UFET is the f i e l d effect mobility and PBAND is the band mobility, is a complicated analytical function of the material parameters, device temperature and the charge Q = Cox Vg2 induced in the channel where Vg2 = VgI - Vt . Vt is the threshold voltage and is defined as the gate voltage required to s h i f t the Fermi level into the t a i l states. The calculated current-voltage characteristics in the above threshold regime are shown in Figure 4.
As can be seen from the figure, the general
shape of the I-V curves and the values of the current are in good agreement with experimental results, see f o r example reference 4.
Our results may be
also used f o r the device characterization which w i l l allow an accurate comparison wlth the experimental data.
The complete equations describing the
above threshold regime characteristics include t h e i r dependence on the position of the equilibrium Fermi level, and hence the effects of doping can be studied.
4C
i
t o x = 0.251~m W=200prn L=lOpm
.
...... "................ ! 5 y g ' "
2
.+ 12
10 1C
8 .... :
5 i 5
i
10
J 15
20
Vds (V) Fi~.4
Calculated l-V c h a r a c t e r i s t i c s in above threshold regime.
REFERENCES 1.
S. Lee and [ . Chen, Appl. Phys. L e t t . 41, 549 (1982).
2.
M. Shur and M. Hack, to be published.
3.
S. Kishida, e t a l . ,
Tech. Report of Elect. Dev. Soc. of IECE of Japan,
ED82-7 (1982). 4.
M. 3. Thompson, N. N. 3ohnson, M. O. Moyer and R. LuJan, IEEE Trans. Electron Dev., ED-29, 1643 (1982).
5.
Y. Nara and M. Matsumura, IEEE Trans. Elect. Dev. EO-29, 1646 (1982).
6.
M. Hack and M. Shur, IEEE Elect. Dev. L e t t . , EDL-4, 5, 140 (1983).