188 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35, NO. 2, FEBRUARY 1988

An Analysis Performance

KAN M.

of the DC and Small-Signal AC of the Tunnel Emitter Transistor

Abstract-Based on a general model for tunneling in metal thin-in- sulator semiconductor structures, a model to describe the I-V charac- teristics of the tunnel emitter transistor (the TETRAN) is developed. This model is then used to compute typical magnitudes for the param- eters appearing in the small-signal hybrid-n equivalent circuit of this new device. From these it is predicted that the cutoff frequency for realistic TETRAN's based on AI/SiO,/n-Si structures is about 1 GHz. This is considerably less than the values recently predicted for a related device, the BICFET, with which the TETRAN might be confused.

I. INTRODUCTION NE OF THE INTERESTING properties of the metal 0 thin-insulator semiconductor structure is that it can

exhibit current gain. The phenomenon was first studied by Shewchun and coworkers [ 13 , [2], and later examined within the context of a general analytical model for the MIS tunnel junction by Tarr et al. [3]. More recently a detailed analysis of current gain has been carried out by Simmons and Taylor [4] for a MIS structure specifically designed to exhibit the effect. The structure has been la- beled a tunnel emitter transistor (TETRAN) and is shown in Fig. 1.

Application of a reverse bias voltage to the metal em- itter leads to depletion of the underlying semiconductor; see Fig. 2. Holes can be injected into the depletion region from the p+ contact, the source, thereby inverting the sur- face region of the semiconductor underneath the emitter. This increase in hole concentration leads to a redistribu- tion of the voltage drops across the emitter insulator and the depletion region; see Fig. 2(b). The increased field in the insulator paves the way for an increase in the electron tunnel current. There will be some tunneling of holes from the semiconductor to the metal, but if this current is less than the enhancement in electron current, the structure will exhibit current gain. Modest gains of around 120 have been measured in operational devices [ 5 ] .

In [5] the device is referred to as a bipolar inversion- channel field-effect transistor (BICFET). This could be confusing as the same name has been used by Taylor and Simmons to refer to a different device [6], [7]. In the BIC- FET described in [6] and [7] the thin insulating layer of the emitter is replaced by a thick wide-bandgap semicon-

Manuscript received May 18, 1987; revised September 8, 1987. The authors are with the Department of Electrical Engineering, Univer-

sity of British Columbia, Vancouver, British Columbia, V6T 1W5, Can- ada.

IEEE Log Number 8718083.

METALLIC EMITTER ULTRA-THIN INSULATOR

N-SUBSTRATE COLLECTOR

"CE

Fig. 1. The structure of a TETRAN.

(a) (b) Fig. 2. The effect of source current on the potential distribution and charge

flow in the MIS junction. (a) I , = 0. (b) Is > 0.

ductor, and current transport through this region is deemed to be by diffusion or thermionic emission, rather than by tunneling; see Fig. 3. One of the claims for this device is a value forfT of around 10 000 GHz [7]. Moravvej-Farshi and Green [5] suggest that, in a TETRAN, the transcon- ductance is lower and the input capacitance is higher than in a BICFET, and they hint that the intrinsic cutoff fre- quency for the TETRAN is about 600 GHz. This is still a sensational figure, one that has prompted us to perform the work reported in this paper. This, to our knowledge, is the first detailed analysis of the high-frequency capa- bilities of the TETRAN.

11. MODEL FORMULATION The basis for our model of the TETRAN is the analyt-

ical model for the MIS tunnel junction [3]. This model has been modified to accommodate a third electrode (the source) and to improve the characterization of the tunnel- ing process. The latter improvements are twofold: firstly, the two-band model for Si02 based on the Franz disper- sion relation has been replaced by a one-band model; sec- ondly, the restriction of the tunneling probability factor to a constant value [3] has been removed.

0018-9383/88/0200-0188$01.00 @ 1988 IEEE

CHU AND PULFREY: PERFORMANCE OF THE TUNNEL EMITTER TRANSISTOR 189

EMITTER Q

‘‘W DEPLETION REGION .-- ~. .~ ~,

. ~~. N-SUBSTRATE

d COLLECTOR

Fig. 3 . The structure of a BICFET [ 6 ] , [7]. Note that the wide-bandgap semiconductor is considerably thicker than the insulator employed in the TETRAN (Fig. 1 ) .

A. The One-Band Model The motivation for switching to a one-band model of

the oxide is the success achieved by O’Neill [8] in using it to explain the asymmetry in electron and hole tunnel currents in thin Si02 layers. In [8] the tunneling states of electrons and holes are deduced from the complex band structure of Si02. It is found that the evanescent states derived from the conduction band edge dominate the tun- neling for both electrons and holes. These states have a wave vector defined by the parabolic relationship

where m& is the scalar effective mass associated with the conduction band and E,-,(x) is the energy of the oxide conduction band edge.

The energy reference for E,, the component of energy of the tunneling particle in the direction toward and per- pendicular to the interface, is Eco for electrons and EVo for holes; see Fig. 4. Thus, the term ( E , - E , ( x ) ) for an electron in the semiconductor conduction band is smaller by the extent of the silicon bandgap energy than the corresponding term for a hole in the valence band. This difference in tunneling barriers can be expressed with reference to the hole and electron barrier heights by

A wide range of values for xe has been repqrted in the literature, e.g., from 0.25 to 3 .3 eV for a 25-A-thick ox- ide [9]. The barrier height also appears to depend upon oxide thickness, being smaller for thinner oxides [lo]. This barrier lowering effect is not fully understood at present and may be due to a number of factors, including image forces, surface effects, and the presence of amor- phous silicon oxide. For our purposes, xe is taken as an adjustable model parameter.

B. The Tunneling Probability

the electron tunnel current can be written as Using Harrison’s independent electron approach [ 1 13,

* exp [-ye( - E,)’’*] dE, ( 3 )

L; .......... ~~

I-,, ...~.. _....... ~. E /I d A’

Fig. 4. Symbolic energy band diagram for the TETRAN. Note that the lower portion of the energy band diagram does not represent the insulator valence band. It is, instead, a reflected version of the top part of the diagram, configured in such a way as to give the correct barrier shape for holes. In this one-band model, the holes interact with the oxide con- duction band and xh = xr + E,.

where

and fm, f, are the Fermi functions in the metal and at the semiconductor surface, respectively, mz is the electron effective mass transverse to the barrier in silicon, and d is the oxide thickness. Note that ET is the component of par- ticle energy that is transverse to the interface. E,, is the mean energy of the conduction band of the oxide. Its use here renders the tunneling barrier rectangular, rather than trapezoidal as shown in Fig. 4. The tunneling probability is given by [l I]

8 = exp ( -2 s Ikl,l (4)

where the integral is carried out over the thickness of the oxide. In our notation we have

If the band bending in the oxide is ignored, and if all the electrons tunneling from the semiconductor have the same energy, then 8 is a constant and the solution of (3) is greatly simplified. This approach, with e( = 0,) evalu- ated at E, = Eco, is often justifiable in tunneling studies; however, it is not valid in the case of the TETRAN. For example, in the case of electrons, the reverse bias oper- ation of the device results in ( EFM - E,) being in excess of 20 kT. Thus, if all the electrons available for tunneling are assigned an energy Eco, the tunneling current J c M will be greatly underestimated. It is necessary, therefore, to account for the energy dependence of 8,. We have chosen to do this by a complete numerical integration of (3).

An analogous expression to (3) holds for the hole cur- rent J V M , but, again, the assumption of a constant tunnel- ing probability is not justifiable. The injection of holes from the source contact can render the surface degenerate. We have found that practical values of Js result in (Evo - EFP) I 5 kT; see Fig. 4. In view of the relatively small

190

magnitude of this energy difference, it is not necessary to perform a complete numerical integration in order to ac- count for the energy dependence of the hole tunneling probability 8,. Instead JvM can be computed satisfactorily by representing 8, by the first three terms of a power se- ries approximation (see Appendix A), i.e.,

where

@,(E:) = exp [y - 4 ~ d (2mZI)' /* (E: - E&)'/'].

F,, is the Fermi-Dirac integral of order n , and m,* is the transverse effective mass for holes in silicon.

Note the use of m& and E: and E b in these equations. They highlight the fact that hole tunneling takes place via states derived from the oxide conduction band [8]. As ex- plained in the caption to Fig. 4, E: and are merely the reflected forms of E, and EL-, as required when consid- ering potential energy barriers for holes.

C. Computation of the Terminal Currents Any solution for the tunnel currents JcM and JvM using

the equations of the previous section must be consistent with the stipulations of Kirchhoff's laws. Regarding volt- ages, summation of the potential drops shown in Fig. 4 yields

IEEE TRANSACTIONS ON ELECTRON DEVICES. VOL. 35, NO. 2 , FEBRUARY 1988

where VcE is the collector emitter voltage and $I is the potential drop across the oxide given by

where in the semiconductor, is derived in Appendix B as

is the oxide permittivity and Q,, the total charge

EVO - EFP - no + N,F,/2 ( kT )

(9)

where no and po are the equilibrium concentrations of electrons and holes, respectively.

Considering now the need for continuity of charged

particle flows across the interface, we have, for the case of holes, neglecting recombination/generation in the de- pletion region [ 4 ] , impact ionization effects [ 121, surface state tunneling [ 131, and trap-assisted tunneling [ 141

where J D is the current due to the diffusion of holes from the source into the quasi-neutral region of the collector (see Fig. 4), and is given by

Equations (7) and (10) are two nonlinear equations that need to be solved simultaneously. By substituting (6) and (11 ) into (lo), and (8) and (9) into (7), (7) and (10) can be written in terms of two independent variables $$ and 4. Thus, for given values of Js , VcE, X h , and xe (see ( 2 ) ) , solutions for $$ and 4 can be obtained. We used a stan- dard iterative technique based on a generalized secant method for this purpose.

Once $, and 4 are known, the electron tunnel current JcM can be computed (see ( 3 ) ) , as well as the terminal currents

J E = JCM + JVM

Jc = J,-M - J D .

( 1 2 )

(13)

111. RESULTS AND DISCUSSION A. DC Characteristics

To test the capabilities of the TETRAN model, dc cur- rent-voltage characteristics were generated for a device structure resembling that used in the experimental work reported in [5]. The physica! parameters of the device were: oxide thickness of 16 A , collector doping density of 7 x 1014 cmP3, and collector thickness of 10 pm. The other parameters used in the simulation are listed in Table I. In the absence of detailed information on xm for metals on thin oxides, we use xm = xp.

Results for the case of xe = 1.1 eV are shown in Fig. 5 . At a collector current density of around 2 X lo3 A/cm3 the predicted current gain A J c / A Js is 100. This is in close agreement with the value of 120 measured by Moravvej- Farshi and Green [5] at similar collector current densities. As would be expected, the predicted current gain is sen- sitive to the value chosen for x e . For example, reducing xe to 1 .O eV leads to about a 30-percent increase in gain.

A unique feature of the TETRAN I-V characteristic is the reversal in polarity of the collector current at low col- lector-emitter voltages. The effect is clearly visible in Fig. 5 . The value of VcE at which the current reversal occurs is called the cut-in voltage. The predicted value of 0.4 V is close to the measured value of 0.6 V [5]. No doubt even better agreement could be achieved by adjusting the value of the hole lifetime used to compute Lp in the expression for J D (see (1 I ) ) , or by including in the model effects due to other currents, e.g., recombination/generation in the depletion region. In the present model the collector cur-

CHU AND PULFREY: PERFORMANCE OF THE TUNNEL EMITTER TRANSISTOR

J j lAcm'2J

3 . 0 vcc

Fig. 5 . Predicted I-V characteristics for the TETRAN described in [SI. The electron barrier height x, is 1.1 eV, and the other parameters are as in Table I .

TABLE I MODEL PARAMETER VALUES

T temperature 300 K

E silicon bandgap 1.12 eV

m& electron effective mass in oxide 0.5 m

m* electron transverse mass in Si 0.2 me

I$ hole transverse mass in Si 0.66 m

E permittivity of silicon

permittivity of Si0

v hole mobility

11.9 E

3.9 E

480 cm2V-ls-l

T hole life-time Bus

ni intrinsic carrier concentration 1.45 x IO"

NC conduction band density of states 2 . 8 x 1019

NV valence band density of states 1.04 x 1019 ~ r n - ~

rent at voltages below the cut-in voltage is due to the dominance of JD over J,.

Another interesting correlation of predicted and exper- imental data is the effect of the passage of high collector currents. In [5] irreversible reduction of current gain was observed in devices for which J c was taken above lo4 A/cm2. This effect was attributed to a generation of sur- face states at the oxide-semiconductor interface. The re- sults for our model suggest an alternative mechanism. Our calculations indicate that, at these current levels, the volt- age drop across the oxide is about 1 V. This corresponds to an oxide field strength of 6.25 x lo6 V/cm, which is about the breakdown field strength of thin oxides [ 151.

B. Small-Signal Analysis The common-emitter small-signal hybrid-a model of

the TETRAN is shown in Fig. 6. We define the parame- ters as follows:

Transconductance g , = -

Common-emitter input capacitance C,, = -

191

Fig. 6 . The common-emitter small-signal hybrid-* equivalent circuit for the TETRAN.

Collector-source capacitance c,, = I dVcE VSE

Input resistance r,, = - 2 lir Output resistance ro = - . d v c E l dJ, Js

The unity current gain cutoff frequency can be ex- pressed as

(14) g m

f T = 2aCse [ 1 + (2C,c/Cs,

*

1) Numerical Evaluation of fT: The hybrid-a parame- ters listed in Section 111-B were computed from the model described in Section I1 by examining the changes in ter- minal currents, terminal voltages, and stored charge in the semiconductor in response to small changes in either Jc, V,,, or V ~ E . The perturbations had a magnitude of 1 per- cent of the operative steady-state values.

The results for a range of operating conditions and two different values of electron barrier height X , are listed in Table 11.

With respect to the conditions used to obtain the first row of Table 11, we note that a reduction in either Js or VsE, or an increase in xe, leads to a reduction infr, prin- cipally via a decrease in transconductance. However, the changes are not great and f T remains in the neighborhood of 1-2 GHz. This is a far cry from the value offT = 600 GHz previously suggested [5] as being appropriate for a TETRAN of the type under discussion.

Comparing the structure of the BICFET and the TE- TRAN, Figs. 3 and 1, it is clear that the thin insulator employed in the TETRAN will cause it to have a larger input capacitance than the BICFET. Also, the effective electron barrier height x, is likely to be much larger for a semiconductor-insulator interface than for a semiconduc- tor-semiconductor interface. Thus, gm for the BICFET should exceed that for the TETRAN. The input capaci- tance C,, usually exceeds Csc, certainly in the case of the TETRAN (see Table 11), and, therefore, (14) can be re- duced to

It is quite clear from this equation that the aforemen- tioned differences in g , and C,, will cause fT in the case of the TETRAN to be inferior to that of the BICFET. The

192 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35, NO. 2, FEBRUARY 1988

TABLE I1 SIMULATION RESULTS FOR THE SMALL-SIGNAL HYBRID-* PARAMETERS

VCE = 5v

x, = 1.0 eV

Js = 3 2 A ~ r n - ~

VCE = 5v

x, = 1.0 eV

Js - 8 Acm-’

VCE = 2v

xe - 1.0 eV

Js - 32Acrn-’

VCE = 5v

xe = 1.1 eV

Js - 32Acrn-’

2.7x10’

.9x10’

1.8x10’

1.5~10’

r 8e

: h 2 )

-

!x10-7

5x10-;

8x10-7

x10-7

K

( h 2 )

1.9x10-4

1.8x10-4

1.9x10-‘

3.3x10-‘

fT

GHz )

2.3

. 7

1.8

1.4

results presented in this section indicate the large extent of this difference in high-frequency capability.

2) Analytical Evaluation of fT: Confirmation of the es- timate of fT resulting from the numerical analysis can be obtained by carrying out an approximate analytical eval- uation offT via (15). This is demonstrated below.

To obtain an estimate for g,, we neglect the contribu- tion of the diffusion current to Jc (see (13)) and seek an expression for JcM that can be readily differentiated. Such an equation appears as [4, eq. (A.32)]. Taking the dom- inant term in this equation and ignoring the voltage de- pendence of pre-exponential factors, we have in our no- tation

JCM = K exp [ -ye ( X, - q t ) ” 2 ] . (16)

V. Substituting these values into (17) gives

g, = 3.3 J~ = 1 . 1 x lo8 Q2-’/m2.

As regards the input capacitance, this can be taken as being approximately equal to the capacitance of the ultra- thin emitter oxide, i.e.

€1

d’ c,, = -

F o r d = 16 A and lop2 F/m2.

yields f T = 0.8 GHz.

numerical analysis given in Table 11.

= 3.9 eo, we have C,, = 2.2 X

Using thesl; approximate values of g, and C,, in (15)

This figure is in good agreement with the results of the

J c M the insulator, is the main contributor to VsE; thus

JC as noted above, and &, the potential drop across IV. CONCLUSION There are two conclusions to be drawn from this work.

Firstly, a one-band representation of the thin insulator, when incorporated in a general tunneling model for the metal thin-insulator semiconductor structure, allows an accurate prediction of the dc characteristics of a tunnel emitter transistor (the TETRAN) to be made. Secondly, this new tunneling model also allows the high-frequency capability of the TETRAN to be examined. It has been found that the realistic figure for the intrinsic cutoff fre- quency is about 1 GHz.

4Ye a c &CM- 1 /2 J c M .

- g r n = - = - vSE d$’I

( 1 7 ) Taking X, = 1 . 1 eV, d = 16 A , VcE = 5 V, and Js =

3.2 X lo5 A/m2 (Le., as per row 4 of Table 11), we find from the model that Jc = 3.8 x lo7 A/m2 and = 0.68

CHU AND PULFREY. PERFORMANCE OF THE TUNNEL EMITTER TRANSISTOR 193

APPENDIX A fore, (A3) becomes

4rm$k2T2 OD A POWER SERIES EXPANSION FOR THE HOLE TUNNEL

The hole current equation equivalent to (3) is CURRENT JvM = h3 "=0,1,2 c (kT)" W E v o )

EVO . [Fn+l [Evok -EFpJ - .+I[ Evo kT - EFM 11. 4rm$ JVM = 9 7 -,

SE,:, (A4)

This is (6) of the text. Computer simulation indicates that a sum using the first three terms of this series approxi- mates the exact integral within an error of 1 percent if

1 * [ s o w [ I + exp [ ( E F ~ + ET - E : ) / k T ]

1 , - I 1 dET) (EVO - E F P ) / k T 5kT*

1 + exp [ (EFM + ET - E : ) / k T ] APPENDIX B

THE TOTAL SEMICONDUCTOR CHARGE Q, ('41) In the depletion region of the semiconductor, the elec-

tric field E is given by Poisson's equation

We can express e,( E:) as a Taylor series expanded about E: = Evo, i.e.,

Multiplying by E ( = - d $ / a k ) gives

€,E dE = q E ( p - n ) du + gN, d$. (B2)

where

The current transport equations can be expressed in the form

dn J,, = gpnnE t qD,- du

From (B3) and (B4) and using the Einstein relation Substituting (A2) into (Al), the hole tunnel current can

kT be written as DP - = - - Dn - - P p P n 9

where q ( p - n ) E = (: - ;) ak

Combining with (B2), we get

e,EdE = (G - &) du + ( a d p P P + P n Pp P n

and Z . is the same with EFM in place of EFp. Zpj can be + @" d$ + k T ( d p - dn) . (B6) 'I" simplified by changing the order of - integration of the dou- ble integral and assuming ( E , , ~ - E ; , ) / ~ T is very large. The result, in terms of the Fermi-Dirac function F is

Integrating (B6) between the semiconductor surface and the edge Of depletion region gives

Zpj = ( k T ) ' + 2 e i ( E v o ) F,+I

Again, Zmj is the same with EFM in place of EFp. There- 037)

194 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35, NO. 2 , FEBRUARY 1988

Neglecting the integral, for it is usually small (see [4, eq. B.61, we have

Q,’ = (GS?

(B8) The electron and hole concentrations at the surface n, and p s can be expressed as

EVO - EFP P s = N,F,/2 ( kT )

Therefore, the total charge in the semiconductor is

REFERENCES [I] M. A. Green and J. Shewchun, “Current multiplication in metal-in-

sulator-semiconductor (MIS) tunnel diodes,” Solid-State Electron.,

[2] R. A. Clarke and J. Shewchun, “Non-equilibrium effects on metal- oxide semiconductor tunnel currents,” Solid-State Electron., vol. 14, pp. 957-973, 1971.

[3] N . G. Tarr, D. L. Pulfrey, and D. S. Carnporese, “An analytic model for the MIS tunnel junction,” IEEE Trans. Electron Devices, vol.

[4] J. G. Simmons and G. W. Taylor, “Concepts of gain at an oxide- semiconductor interface and their application to the TETRAN-A tunnel emitter transistor-and to the MIS switching device,” Solid- State Electron., vol. 29, pp. 287-303, 1986.

[5] M. K. Moravvej-Farshi and M. A. Green, “Operational silicon bi- polar inversion-channel field-effect transistor (BICFET),” IEEE Electron Device Lett., vol. EDL-7, pp. 513-515, 1986.

[6] G. W. Taylor and J. G. Simmons, “The bipolar inversion channel field-effect transistor (B1CFET)-A new field-effect solid-state de- vice: Theory and structures,” IEEE Trans. Electron Devices, vol.

[7] -, “Small-signal model and high-frequency performance of the BICFET,” IEEE Trans. Electron Devices, vol. ED-32, pp. 2368- 2377, 1985.

VOI. 17, 349-365, 1974.

ED-30, pp. 1760-1770, 1983.

ED-32, pp. 2345-2367, 1985.

[E] A. G. O’Neill, “An explanation of the asymmetry in electron and hole tunnel currents through ultra-thin SiOz films,” Solid-State Elec- tron., vol. 29, pp. 305-310, 1986.

[9] P. V. Dressendorfer and R . C. Barker, “Photoemission measure- ments of interface barrier energies for tunnel oxides on silicon,” Appl. Phys. Lett., VOI. 36, pp. 933-935, 1980.

[ lo] L. A. Kasprzak, R . B. Laibowitz, and M. Ohring, “Dependence of the Si-Si02 barrier height on SiOz thickness in MOS tunnel struc- tures,”J. Appl. Phys. , vol. 48, pp. 4281-4286, 1977.

[ l I ] W. A. Harrison, “Tunneling from an independent-particle point of view,” Phys. Rev. , vol. 123, pp. 85-89, 1961.

[12] E. R. Fossum and R. C. Barker, “Measurement of hole leakage and impact ionization currents in bistable metal-tunnel oxide-semiconduc- torjunctions,” IEEE Trans. Electron Devices, vol. ED-31, pp. 1168- 1174, 1984.

[I31 S . Jain and W. E. Dahlke, “Measurement and characterization of interface state tunneling in metal-insulator-semiconductor struc- tures,” Solid-State Electron., vol. 29, pp. 597-606, 1986.

[14] F. Campabadal, V. Milian, and X. Ayrnerich-Humet, “Trap-assisted tunneling in MIS and Schotty structures, Phys. Status Solidi. ( a ) , vol. 79, pp. 223-236, 1983.

[15] K. Yamabe and K. Taniguchi, “Time-dependent dielectric break- down of thin thermally grown SiOz films,” IEEE J . Solid-State Cir- cuits, VOI. SC-20, pp. 343-348, 1985.

*

David L. Pulfrey (M’73) is a Professor in the Electric Engineering Department at the University of Bntish Columbia, Vancouver, B.C., Canada. His research interests are in the fields of semicon- ductor device physics and integrated-circuit de- sign. He has worked on the topics of electrical breakdown in thin dielectrics, the preparation and properties of plasma-anodized thin-oxide films, and the analysis and fabrication of solar cell struc- tures suited to large-area terrestrial applications His present work at the University of British Co-

lumbia is in the areas of high-gain polysilicon emitter transistors, the char- acterization and applications of MIS tunnel junctions, and the algorithmic generation of IC marcocells.

Kan M. Chu was born in Hong Kong on May 16, 1962. He received the B.Eng (Honors E.E.) de- gree from McGill University, Montreal, Canada, in 1984 and the M.A.Sc. (E.E.) degree from the University of Bnttsh Columbia, Vancouver, B.C., Canada, in 1986. He is presently working toward the Ph.D. degree in electrical engineering.

His research interests are in CMOS-integrated circuit design and semiconductor device model- ing.