77 Kumar SSE 143 Cr Si O2 Tunnel diode

SoWStote

Electronics, 1977, Vol. 20, pp. 143-152. Pergamon Press.

Printed in Great Britain

CHARACTERISTICS OF Cr-SiOz-nSi TUNNEL DIODE% VIKRAM KUMAR and WALTER E. DAHLKE Department of Electrical Engineering, Lehigh University, Bethlehem, PA 18015,U.S.A. (Received 18 March 1976; in revised form 3 July 1976)

Abstract-The admittance of Cr-SiO,-nSi tunnel diodes was measured at 195 and 295K, from which the surface potential &( V.) and the energy distribution of the surface states N,, which communicate with the silicon were determined. By employing these data, the I( V,,) characteristics measured at 77, 195 and 295K are interpreted as tunneling current consisting of two components. The tirst is a net electron tunnel current from the Si-conduction band throughtheoxideintothemetalwhichdominatesatroomtemperatureforfonvardbias V, greaterthan0.4 V.Introducing a simple model of a trapezoidal SiOZbarrier allows us to calculate the band to band current, resulting in typical values of the barrier height no = 0.24eV and barrier width do = 24 A. The second component is a net recombination current of electrons from the Si-conduction band into surface states which then tunnel through the oxide into the metal; this component dominates for reverse bias and for small forward bias, especially at low temperatures. It is a current via surface states N,, which are at the Si-SiO, interface but rapidly communicate with the metal, and it is therefore recombination controlled.Together,these componentsexplainthe measuredbias and temperaturedependenceof the d.c. current. 1. INTRODUCTION Since details of the band structure of a few atomic Tunneling in metal-insulator-semiconductor structures is layers of SiO, or other components such as SiO, are increasingly employed in memories as MNOS devices [ 11, unknown, a simple phenomenological barrier model is in energy conversion as radiation detectors[2] and solar proposed assuming a parabolic energy-momentum relacells [2,3]. In these applications accurate modelling of tion in the oxide band gap and a trapezoidal barrier shape. MIS tunnel devices especially at low d.c. bias voltage is The calculated tunneling current agrees with the experimental data over eight decades when the experimentally important. Surface potential and surface state distribution in MOS tunnel diodes were determined by Kar and determined surface potential versus bias &( V,) and experimental device parameters, such as barrier height Dahlke[4] adapting the known low frequency capacitance [5] and conductance [6] techniques. Studies of and thickness, are employed. Sample preparation and the current-voltage characteristics of Al-SiO,-nSi tunnel measurements are discussed in Section 2, the barrier diodes by Clarke and Shewchun[7] showed agreement model and band to band current in Section 3, excess between theory and experiment for an oxide barrier current and its interpretation as tunneling current via height, Q = 3 eV, and width, d, = 13A, using arbitrarily surface states in Section 4, and conclusions in Section 5. assumed (i.e. not measured) values of oxide charge and surface states. Investigations of tunneling in Au-SiO*-nSi 2. SAhfPLES AND MEASUREMENTS tunnel diodes by Card and Rhoderick[& 91 indicated, on the other hand, a strongly decreasing barrier height with 2.1 Sample preparation decreasing oxide thickness from 26 to 8 A, but the authors Two types of samples were investigated, cf. inserts of neglected the bias dependence of the barrier. Maserjian et Fig. 1. Both were fabricated on phosphorus doped n-type al. [ 10,111 and Lewicki[ 12,131 investigated the currentSi substrates of (111) orientation, 1 ohm cm resistivity, voltage-thickness characteristics of Cr-SiO,-p+Si juncabout 1.25mm thick. Type A samples were essentially the tions with oxide thickness ranging from 20 to 400 A. They same as those used by Kar and Dahlke[4] which were observe elastic tunneling into the direct Si-conduction prepared as follows. After chemical cleaning, two thick band and the SiO,-conduction band when the oxide oxides were successively grown and etched off, followed voltage is larger than 3.4 V, and conclude that the normal by the final oxidation performed at about 900°C. All band model of MOS capacitors is appropriate for oxides oxidations were carried out in steam under 15OOVbias thicker than 65 A. But the Si-SiO, barrier decreases with using an rf-induction heated furnace. Circular chromium decreasing oxide thickness at a rate of IO-‘eV/A[12]. front metal contacts, 0.127 mm diameter, were deposited Inelastic tunneling into surface states and into the indirect in a high vacuum ion pump system at about 10m6 torr Si-conduction band occurs at oxide voltages lower than through an etched molybdenum mask. After removing the 3.4V. Its dependence on bias has not been discussed in back oxide, an aluminum back contact was deposited in detail, since little is known concerning the rules governing the same vacuum system. inelastic tunneling with a large mismatch in transverse Type B samples were oxidized in a resistance heated momentum. This introduces a large unknown factor on furnace. After chemical cleaning, a 4OOOAoxide was the order of lo-’ in the voltage dependence of the grown in wet oxygen at 113O”C,etched off, and a seccurrent [ lo]. Modelling of the current-voltage characterisond 4OOOAoxide grown similarly. Circular windows tics in this lower bias range is the subject of this paper. of 127pm diameter were etched in the oxide using negative photoresist. After phororesist removal and tWork supported by a grant from the National Science a slight oxide etch to remove any possible contamination, Foundation. the final oxide was grown in the same furnace at 910°C in 143

144

V. KUMARand W. E. DAHLKE

dry oxygen. Geometry of the evaporated chromium front contact was defined by photolithography to provide a gate on the thin oxide, a guard ring, and another gate on the thick oxide. Then, the back oxide was removed and an aluminum back contact deposited. After dicing the wafer by a diamond scriber, the chips were mounted on a TO 5 header using silver conducting paint. The front contacts were made by ultrasonic bonding of 25.4 pm Al-% wires. Contact to the thin oxide metal gate was accomplished at the metalization on the 400 A thick oxide. The die-bonding had negligible effect on the device admittance. The investigated samples, their type, oxide thickness and measuring temperature, etc. are listed in Table 1, further details will be discussed in Section 4.3. 2.2 Determination

of surfacepotential,

(195 K) and liquid nitrogen (77 K) temperatures were taken by immersing the samples in the coolant. The observed capacitance, C( V,, f), and conductance, G( V,, f), of the Cr-SiO,-nSi samples showed a frequency dispersion which indicated surface states in quasiequilibrium with the Si-conduction band [ 141at the Si-SiO, interface. Surface potential & (V,) and surface state density N,, were determined by low frequency capacitance[5] and conductance techniques [6], as reported and discussed by Kar and Dahlke[4]. Figure 1 presents the surface Fermi potentials, V, = @, - 4, defined in Fig. 2, of sample 3, type A, and sample 5, type B, at room and dry ice temperatures. The bulk Fermi potential Qp,was calculated from the silicon doping obtained from the slope of C-’ (V,, 1 MHz) under reverse bias. The surface Fermi potential of the type A sample is temperature independent in deep depletion, V, < -0.4V, but shifts in accumulation with decreasing temperature upward be-

surface states and

d.c. current

The admittance of the samples was measured with a Boonton capacitance bridge. Measurements at dry ice

I -0.8

1

I

1

-0.4

T

I

I

I

0 v, (volt)

0.4

0.8

I 2

Fig. 1. Experimental surface Fermi potential V, as function of applied bias V,. The inserts show the device structures, type A and type B. I Sample 3, type A at 295 K. A Sample 3, type A at 195 K. 0 Sample 5, type B al.295K. 0 Sample 5, type B at 195 K. Table 1. Sample parameters 1 Sample No.

2

3

4

5

6

7

8

9

10

Type

t,,/A

TI”K

K./amp

AI.&

s,/V”*A

7,/V

do/ii

A

1 2 3

A A A

4

B

5

B

6

B

27.0 27.0 26.8 26.8 34.4 34.4 35.4 35.4 35.4 33.8

295 295 295 195 295 195 295 195 77 295

3.0 2.0 2.1 2.1 1.5 1.5 1.8 1.9 1.9 1.5

0.32 0.24 0.25 0.25 0.21 0.21 0.23 0.24 0.24 0.21

23 24 24 24 22 22 23 23 23 22

0.0 0.0 0.0 0.0 0.3 0.3 0.3 0.3 0.3 0.3

A,, = 1.27 x 10m4cm*;

2.2 x 8.8X 7.5 x 9.0 x 8.0 x 4.5 x 1.2 x 3.8 x 7.0 x 6.0 x

to, = 3.82 E~/C_.

lo-’ lo-‘ 1om4 lo-’ IO-’ 10-f lO-4 10-j lomh 1O-5

1x 5x 3x 1x 4x 5x 6x 4x 5x 3x

1om6 lo-’ lo-” 1o-6 lo-’ 10-7 lo-’ lo-’ lo-’ lo-’

11

12 g,, /cm* continuum single level at 0.1 V 0) and I_( V, < 0), are presented in Fig. 4 as dots. They show a similarity to I-V characteristics of Schottky barriers but are modified by the thin oxide film between metal and silicon. The theory of the I-V characteristics will be discussed in Section 3. 3. BAIWEE MODEL AND BAND TO BAND CURRENT

Assuming a trapezoidal barrier shape of effective height n( V,) and width d( V,), the barrier parameters for flat bands in the oxide no and do (Fig. 5a), are determined from the measured surface potential & (V.) and current-

2

Fig. 4. Comparison of measured (. .) current I( V.) and calculated (-_) tunnel current I=,,,(V,,),eqn (4) of sample 2, see Table 1.

r-n

(0)

(b)

Fig. 5. Bias dependence of oxide barrier. (a) V, = 0. The oxide barrier is rectangular for flat oxide bands; height no. width do. (b) qV,,, > TV. The electrons tunnel from the semiconductor conduction band through the triangular barrier into the oxide conduction band.

voltage characteristics Z( V.) as described in the following sections. Assuming for simplicity (i) conservation of energy and transverse momentum of tunneling electrons, (ii) a parabolic energy momentum relationship in the oxide band gap, (iii) a maximum contribution to the current by electrons of transverse energy close to the Si-conduction band edge, and employing a WKB approximation, the net electron tunnel current from the conduction band of silicon in (100) orientation across the oxide into the metal [ 161is: Z,, = 4?rqm,h-’ A

m TnbW_fs -fm)E I0

dE,

(1)

where the lower integral limit corresponds to EC, = 0 as reference energy (see Fig. 2). m, is the silicon transverse electron mass, A the cross section of the tunneling area, and 6 and f, the occupancies of the semiconductor and of the metal. The tunneling transmission probability, e.g. for a rectangular barrier height n and width d, is -04

-0.8 E”

0 EC

E WI

Fig. 3. Measured surface state distribution N,,(E) type A and sample 5, type B.

r, = exp { - 2(2m */h*)“‘,rl“*d} = exp (- n “*d), (2)

of sample 3.

where the approximation is valid if the effective mass in

146

V.

KUMAR and W. E.

the oxide equals the free electron mass, m* = m, and if n is in eV and d in A. The integrand of eqn (1) is sharply peaked at energy E = E,, for F,,, E,,. Therefore, T, is evaluated at this energy and taken out of the integral. A rectangular oxide barrier of height q0 and width do corresponding to oxide flat bands occurs according to Figs. 2 and 5(a) at V,,,= V, + V, = & - X~= -0.06 V [ 173,i.e. when the metal Fermi level is approximately aligned with the Si-conduction band edge. Application of a progressively more positive bias V, changes the barrier shape from rectangular to trapezoidal and finally to triangular[l8] (see Fig. 5b). Approximating the barrier by a rectangular barrier of the same width and equal average height results in the bias dependent tunneling transmission

I

(1-qlV,1/2nJ’* m

lnVn)=--qo”% q0,vjqv

for for

41V,I~nlo qV, > vO.

(3) The final expression for the band to band tunnel current is given by L =%r,(V,)[F,(-

v,Irr)-F,(-

V,n/~,)l,

(4)

where the prefactor, K, = ARAT’,

(5)

and A, = 4qm,qk*h-’ = 1.9 x 10’amp mm*K-* is the Richardson constant with respect to the transverse electron mass in silicon; A is the tunneling area, T the absolute temperature, T, the tunneling transmission probability, eqn (3), and vr = kT/q the thermal equivalent voltage. V,=@“-&=-F,/q,

V,=V,+@,-&=-F,,,/q

(6)

DAHLKE

silicon surface by tunneling to the metal. The silicon quasi Fermi levels split, most of the applied voltage drops across the silicon, and deep depletion occurs at the silicon surface. The metal Fermi level becomes pinned with respect to the Si-conduction band, i.e. V,,, +const. Then, the tunneling barrier is independent of bias, and the reverse current saturates. This is the characteristic behavior of the devices we are discussing in this paper. Second, if the oxide is thicker than 35 A, the silicon is in equilibrium[22]. An inversion layer builds up at reverse bias, V, < 0, the silicon quasi Fermilevels do not split, most of the applied voltage drops across the oxide, and the current for V, < 0 shows no saturation, as discussed by Ma and Baker [23],Hunter, Eaton and Sah [24] and others [25]. 3.1 Band-to-band funnel parameters The band-to-band tunnel current eqn (4) depends on the surface Fermi potentials V, and V, which according to Fig. 1 and eqn (6) are experimentally determined functions of the applied bias V,. The device parameters, area A, barrier height nO, and width do, will now be determined by fitting the theoretical and the experimental current-voltage characteristics. We select for demonstration the sample 2, type A, which almost ideally exhibits very little excess current via surface states. The measured forward and reverse currents, I+( V, > 0) and I_( V, < 0) presented in Fig. 4 as dots, and the surface Fermi potentials, V, and V, obtained from the measured surface potential I,!I~( V,) via eqn (6), are used to calculate the barrier function U( V,) = In (%T,) from eqn (4). Figure 6 presents such values of U as functions of V,,-’ and V,,, for sample 2. The slopes, eqn (3), Is,/ = ~~‘*do/Q2 = 2.0 eV”* A of U( V,,..‘) at large V, and s2= d,,/4q0”2= 11.6eV_“’ A of U( V,) at small V,, and the difference of their intercepts with the ordinate, s? = no”* do = 12.0eV”* A are indicated

are the semiconductor and the metal surface Fermi potentials (see Fig. 2). The Fermi-Dirac integralLl91, x dx l+exp(x-a)’

(7)

is tabulated and can be approximated by F,(a) = ey for a 0, V, > 0. Then the current, I,, = A,AT*T”(V,,,) e~“~“r[e”~“T- 11,

(8)

approaches that of a Schottky barrier at zero oxide thickness, where the barrier becomes transparent, T. + 1, and the height of the Schottky barrier, qV,, bias independent, T. decreases exponentially when the oxide thickness increases, while V, becomes a function of voltage. Two cases are of special interest: First, if the oxide is less than 35 A thick, the silicon is not in equilibrium [20,21]. Application of increasing reverse bias, V, < 0, drains the minority carriers away from the

I

I

I

0

0.4 v,

0.8 (volt)

Fig. 6. Comparison of experimental (. .) and calculated barrier functions U( V,,,) and U(l/ V,,,)of sample 2.

(-)

Characteristics

Fig. 6. They allow us to calculate from eqn (3) a pair of barrier parameters no and do, for each combination of s,, sl, etc. These data entered in Table 2 differ less than 25% from their averages, n0=0.24eV and do = 24A. The prefactor K, = 8.8 X 10e5amp is found from the intercept in Fig. 6. The solid curves Z( V,) in Fig. 4 and U( V,,,) in Fig. 6, calculated from the barrier parameters K., Q, do and eqns (3) and (4), fit the measured data over the entire bias range. The matching of the data is appreciably affected by a variation of do by more than 1 A and of no by more than 0.01 eV. If we follow Clarke and Shewchun[7] by assuming no = 3 eV and an effective width derr= 0.5t,, = 13 A, the calculated and measured currents can only be matched in a small bias range, e.g. from V, = 0.81.2 V. But the calculated current at smaller forward and reverse bias becomes up to four orders of magnitude larger than the measured data, since the transmission eqn (3) is practically bias independent for qlV,l G no. The obtained tunneling thickness, in

d, = 0.9 t,,,

(9)

is close to the average oxide thickness t,, from capacitance measurements. Theoretically, a thickness do < t,,, is expected, since the effective mass in the oxide is probably smaller than the free electron mass[lO], and since tunneling occurs preferentially across the thinnest part of the oxide[26]. But it is doubtful whether the dielectric constant or the thickness of the oxide are known to 10% because of compositional uncertainty[27,28]. Our effective barrier height no= 0.24eV is much smaller than the barrier height n,, 2 3 eV of thick oxide structures. This confirms a result of Card and Rhoderick[8] that the barrier height of oxide films, no, increases monotonically with oxide thickness and that the transmission coefficients of thin films are very much larger than those predicted from the band structure of bulk SiOz. This is illustrated in Fig. 7, where we plotted as circles their values s, = qo”*d,,versus the average oxide thickness t,,, and as triangles the values of two of our almost ideal samples 1 and 2. The points can be approximated by a straight line of slope 2. Its equation through the measuring point of sample 2 is d,=20.s,“4

(10)

where do is in A and s, in eVj”A. Our barrier height, no = 0.24 eV, seems to be at variance with results of Maserjian et al.[lO-131; however, it is possible that the different operating condition has a large influence on the measured effective barrier height. Their samples exhibit essentially tunneling of metal electrons into the direct Table 2. Oxide barrier parameters*

% vow dotd )

Using s1, s3

Using $2, $3

Using $1, s2

Average

0.235 24.1

0.253 23.6

0.245 23.0

0.244 23.8

*See Figs. Sa and 6.

147

of Cr-SiO,-nSi tunnel diodes 20

Fig. 7. Experimental barrier parameter s1 = Q”~ d, vs average oxide thickness f,, reported by Card and Rhoderick[8] (, ,), and

our samplesI and2(AA). conduction band of silicon which is in equilibrium, while our diodes show predominantly tunneling of electrons from the indirect conduction band of silicon which is not in equilibrium into the metal. Finally, we can estimate the tunneling area A from eqn (5) and the measured prefactor K. = 8.8 x lo-‘amp. The obtainedvalueA = 8 x lo-” cm*^- 5 x 10~‘Aoisonlyavery small fraction of the gate area A,. This discrepency is mainly caused by two different effects. First, the tunneling area is only a fraction lo-* to lo-’ of the gate area because of the inhomogeneity of the oxide thickness[29]. This result is supported by our own noise measurements at low frequencies[30]. Second, our assumption of transverse momentum conservation is an over-idealization that can introduce another factor of lo-’ in the tunneling current[lO, 311. 4. EXCESS CURRENT

Several of the Cr-SiOz-nSi tunnel diodes exhibited currents in excess of the calculated band-to-band tunneling, especially at reverse and at low forward bias. To determine themagnitudeandphysicaloriginoftheexcesscurrent,low temperature measurements of d.c. current and admittance characteristics were performed. They are discussed in the following sections. 4.1 Type A samples The barrier functions of sample 3, type A measured at room and dry ice temperatures are presented in Fig. 8. They show behavior and slope s, similar to Fig. 6 for V, > 0.3 V, but rise faster with decreasing V,,, < 0.3 V, especially at low temperature. Although the parameters s2 and sj cannot be directly extracted from Fig. 8, the barrier height no and width do are easily calculated from eqn (10) and the measured slope s, = 2.1 eV3j2b in Fig. 8. With the data, do = 24A and n,,= 0.26eV, the barrier functions U(l/ V,) and U( V,), calculated from eqns (3) and (4), are plotted as solid lines in Fig. 8. A comparison of the

148

V. KUMARand W. E. DAHLKE

1 -10

u -14

do = 21 A is plotted as dashed line in Fig. 8. The excess current dominates for V,,, < 0.3 V. 4.2 Current via surface states The bias and temperature dependent excess current in Fig. 9 can be interpreted as recombination controlled current via surface states. According to Freeman and Dahlke [ 141, the current density of electrons recombining from the Si-conduction band into single energy level states at the Si-SiOz interface and then tunneling through the oxide into the metal is iY= sN&L

- fm)l(rR + T,),

(11)

with Nrr[cmmZ] the total surface state density at energy E, = I$, -q@‘., f,,, and fi,, the occupancies at E, of the metal and the semiconductor, 7R the recombination time constant of surface states, and 7, the tunneling time constant. Equation (11) contains two limiting cases. For 7, % TV,the current via surface states,

-18

-22 0

j, -L

08

v,

= @I%&‘--~~)/T~

(12)

(volt)

Fig. 8. Comparison of barrier functions