potential and limitations of schottky-barrier barritt devices

Solid-State Electronics Vol. 27, No. 5, pp. 433 440, 1984 0038 1101/84 $3.00 + .00 Printed in Great Britain. Pergamon Press Ltd.

POTENTIAL AND LIMITATIONS OF SCHOTTKY-BARRIER BARITT DEVICESt

M. EI-GAaALY~ Department of Electrical Engineering, Kuwait University, Kuwait

and

J. AI-ZINKY Kuwait Institute for Applied Technology, Kuwait

(Received 28 June 1983; in revised form 20 September 1983)

Abstract--Computer simulation of various Schottky-barrier structures is carried out to investigate the large-signal properties of these devices. Comparison between Schottky-barrier devices and their p-n junction counterparts are also made to evaluate the potential and limitations of these devices and to explain the difference in performance between them. It is shown that among various Schottky-barrier structures, the M-n-i-p + structure is the most powerful one and the M-n-p-p + device is the most efficient one. Furthermore, Schottky-barrier devices with low barrier heights for minority carriers (less than 0.2 eV) are capable of producing power levels close to the generated power ofp-n junction devices. Investigation of the temperature dependence of the large-signal performance of these devices shows that Schottky barriers are more sensitive and exhibit their optimum performance close to room temperature value. At low temperature, the output power is limited by the low minority carrier injection, whereas at high temperature the limitation is due to the velocity-modulation losses in the injection and low-field regions of the device.

I. INTRODUCTION

Punch-through injection and transit-time devices are being utilized in microwave systems as oscillators, low-power amplifiers, mixers and detectors[I-7]. These devices are made o f p - n junctions or Schottky- barrier metal-semiconductor contacts. At present, p-n junction devices are shown experimentally to be more powerful and less sensitive to temperature variations than their Schottky-barrier counterparts[2]. As a result, p-n junction devices are exten- sively studied and their microwave performance is optimized [8-13].

Schottky-barrier BARITT (SBB) devices are inex- pensive and are easy to fabricate using available microelectronics technology. It is, therefore, expected that these devices will be implemented in microwave systems where low power and low noise are required at low cost. Before implementing these devices in real systems, however, their potential and limitations must be identified correctly.

The main difference between SBB devices and their semiconductor counterparts is the forward-biased injection contact. Minority carrier injection at this contact differs substantially from that which occurs across a p-n junction. Since the mobile carriers and

tPartially supported by Kuwait University Research Council under Grant No. EE008.

++Present address: Department of Electrical and Computer Engineering, The University of Michigan, Ann Arbor, MI 48109, U.S.A.

electric field distributions are closely related to their values at the forward-biased injection contact, an investigation of the carrier injection at this contact explains the difference in performance between the two devices. Also, improvement of the device performance can be achieved through the proper choice of the metal-semiconductor system and the doping profile of the active semiconductor region.

In a recent study on the boundary conditions of SBB silicon devices, it was shown that the density of injected holes depends on the net conduction current flow across the device[14]. At high current densities, the density of injected holes is reduced significantly and thus the microwave power output is greatly degraded.

The purpose of the present study is to gain a better understanding of the large-signal capabilities and limitations of Schottky-barrier BARITT devices and to compare the performance of these devices with their p-n junction counterparts. To achieve these objectives, an accurate large-signal computer simulation study is carried out and the results are presented and discussed. Various silicon structures, which differ in doping profile and semiconductor width, are investigated for the purpose of optimizing the microwave power and efficiency of the structure.

A theoretical large-signal model which considers the charge transport across the metal-semiconductor contacts and a realistic dependence of carrier velocity upon electric field and doping concentration is used in the simulation. This model provides a powerful

433

434 M. EL-GABALY and J. AL-ZINKY

tool in evaluating the microwave power and efficiency of the device and helps in establishing its design criteria.

At the present time, Schottky-barrier devices are rarely used in microwave systems because of their low r.f. power outputs and efficiencies. However, the microwave power of the structure can be improved significantly by proper choice of the metal type and the doping profile of the structure. To optimize the device performance, the minority carrier barrier height of the forward-biased injection contact must be as small as possible to enhance carrier injection at this contact. Also, double-layer structures (e.g. M - n - i - p ' and M - n - p - p ~ ) exhibit higher power output than uniformly doped ones. These structures will allow the use of higher doping levels in the n-layer and consequently higher r.f. voltage[13]. Detailed investigations of these effects are carried out and are presented in the following sections.

Available experimental data[2,15] show that Schottky-barrier devices are more sensitive to temperature variations than are p-n junction devices. While Schottky-barrier structures fail to produce any r.f. power at temperatures below 300 K, p-n junctions exhibit optimum performance at temperatures close to 100K. The main reason why Schottky-barrier punch-through injection devices are not active at low temperatures is due to the extremely low carrier injection at the forward-biased contact. The temperature dependence of the r.f. power output and efficiency for Schottky-barrier devices are evaluated and graphically described and discussed.

Finally, to identify the potential capability and limitations of BARITT devices with Schottky-barrier injection contacts, their microwave large-signal performance is compared with the performance of their p-n junction counterparts.

in the following section, the large-signal model of Schottky-barrier BARITT devices is described and the r.f. output power and conversion efficiency of a typical uniformly doped structure is graphically presented and discussed. The effects of the device physical parameters such as doping profile and semi-

conductor width are presented in Section 3. Com- parison between Schottky-barrier devices and their p-n junction counterparts, together with temperature effects, are discussed in Sections 4 and 5.

2. LARGE-SIGNAL ANALYSIS OF SCHOTTKY-BARRIER DEV1CES

An accurate large-signal analysis for Schottky- barrier punch-through injection devices can be obtained by computer simulation. This simulation uti- lizes the solution of Poisson's equation, the continuity equation for minority carriers, and the conduction current equation. Since the forward- biased metal-semiconductor contact can only be made on n-type silicon, the unipolar charge transport for holes is considered. The one-dimensional form of the above equations can thus be written as[16]

~E(x, l ) q - [ N i ) ( x ) - - N~(x) +p(x, t)] , (1 )

?p (x, t ) 1 8Jp(x, t )

?t q ?x

and

.l~,(_v, t) = qpp( E) P(.v, t) E(x, t) - q D p - - ~P(x , t)

?x

(2)

(3)

These equations are solved subject to the boundary conditions given by Ref.[14]:

PH[Jp(t)] Pe,,[l 7 - ( 1 - - ~ Jp(-xb' t ) ] 27 J, j , (4)

where Pu is the density of mobile holes at either boundary, Pe,, is the corresponding thermal equilibrium value, ~ is a numerical factor less than unity which is related to the net flux of holes entering the active semiconductor region, and J, is the junction saturation current. The minus (plus) sign applies to the forward (reverse) biased contact. Equation (4) is derived from the investigation of the hole flux at the metal-semiconductor interfaces of both contacts.

Table 1. Summary of structure parameters (layer width and doping concentrations) used for the computer simulation

Device ~,,~i:~th (~m, Dopin}~ Density (cm -~ ]

DevJ ce Strucsure Wn ~ i w N D N i 7;A

+ 1 ~,!-n-~, 7.9 - 1.2 x I015 -

+ 2 M-n-i-I~ 7.5 !.[! P.q x 1015 1.8 x iC I~ -

+ ~i-n-l,-~ ~.~ - 5.5 2.~) x LO Is - i x 1(314

M-n-I<-!, + 3.5 - 5.~ 2.5 x I<: 'Is - [ x I0 I~

+ [; M-n-!-p ].5 - 5.5 ~.~{ x IC ,15 - I x \C I~

( b~-:<-[ '+ 5 - 2 X if; 'I~ - -

+ + 7 Y' -n-I:, 5 - 2 x IC ,15 -

S r+-m-i-P + 3.5 5.[ 2.~ x iO Is 1.8 x IC ,~° -

Potential and limitations of Schottky-barrier BARITT devices

Equations (1) through (4) form the mathematical model of Schottky-barrier devices and with proper adjustments of Pno, • and J,, the model can describe p-n junct ion devices. For accurate analysis, it is important to include the dependence of the drift velocity of injected carriers with electric field and doping concentration. In this study the following mobility expression is used:

~" = 1 + ~ + (5) \ P c / ( N / S ) q.- N r F + ( E / A ) B '

where/~t is the low-field mobility for holes, N is the doping concentration of the active semiconductor layer, and E is the electric field strength. Other parameters are empirical constants which are deter- mined from experimental data[17].

The mathematical model described here is used to evaluate the microwave performance of various structures which differ in doping profile and semiconductor widths. The numerical methods used here are similar to those described in Refs. [18] and [19]. The d.c. solution is obtained by solving the differential equations directly[18], while the large-signal solution is furnished by using a finite-difference technique[19]. The purpose of these simulations is to gain a better understanding of the properties of Schottky-barrier devices and to determine their potential and limitations. The computed results are extremely useful for optimizing the device performance. Various structures investigated in the present study are labeled and their physical parameters are summarized in Table 1. Other parameters used for the room temperature computer simulation of Schottky-barrier devices are the barrier height for holes ~bsp=0.25eV,

ddc = 4 0 A /cm 2

3 0

~E 25

tL 20

o ~5

3 5

J I I I I I 0 2 4 6 8 I0 12 14

RF VOLTAGE, V

Fig. l. R. f. power output vs r. f. voltage amplitude for Device 1 at different frequencies.

435

3 5

3 0 ddc = 4 0 A lcm 2

f = 6 GHz

Z 5 5

a: ta 2 0 o_

>_- z w o 1 5

t.d

I 0

O 5

J I I ] I I 0 2 4 6 8 I0 12 14

RF VOLTAGE, V

Fig. 2. Conversion efficiency vs r. f. voltage amplitude for Device 1 at different frequencies.

Jr = 200 A/cm 2, ~ = 0.54 and Pso = 6.4 × 10 ~4 cm 3 In the remaining part of this section, the microwave large-signal performance of a uniformly doped M - n - p + structure (Device 1 of Table 1)is described.

The large-signal power and efficiency of SBB devices depend upon the d.c. current density, operating frequency, and r.f. voltage amplitude. The variation of power and efficiency with r.f. voltage for various operating frequencies at the opt imum d.c. current density are shown in Figs. 1 and 2, respectively. For a given d.c. current and frequency, the output power and efficiency first increase with an increase in r.f. voltage amplitude until a maximum value is reached. This is similar to the behavior o fp -n junct ion devices in a qualitative sense. As is shown later, the maximum power occurs at a lower r.f. voltage and d.c. current in comparison with p-n junct ion performance. A numerical search for the set of parameters Jd.c., f, and Vr.r. at which opt imum performance occurs is performed for this structure and the results are summarized in Table 2. As indicated in this table, for T = 300 K the opt imum power output occurs at Jdc. = 45 A/cm 2, f = 7 GHz, and Vr.f. = 11 V. The op- t imum efficiency occurs at Jd.c = 10 A/cm 2, which is much lower than the value for opt imum power. It is also indicated that opt imum power occurs at an operating frequency and current density close to those at which maximum negative small-signal con- ductance occurs.

3 . E F F E C T S O F D I F F E R E N T S T R U C T U R E S

BARITT devices with uniform doping are com- monly used because they are simple to make. How- ever, as shown in the previous section, the power output and efficiency of these structures are quite low. This is attributed to the low r.f. voltage handling capability and the relatively low d.c. current density.

436 M. EL-(]ABALY and J. At.-ZINKY

Table 2. Optimum microwave performance for Device 1

3ma 1 i-Si{;r '~ i

I ' [ , F F O F ~ L tY, C£

' = ( : ~ : l . : , c : : 7

"~t : ' = "i' ' ] ] : : '

J C . c , : • : ' c : r ,

= I ~. " m i n

[ = ) f, , : : r , 2 < : . c .

I , a P ~ , - F ~ L R ] [ e r f ' , * ~ ' t l t % L / t '

. ~ -IT r] -- .+ s-< l

, i < t : . l u - - .L, ,~ , ~ q . ~,, c z r

"h : / i

± . . r . .

• , 1 . .

_ L£.. a : r a m ! . f f i e i t * : . c ,

r: : t ,r q x

r

r . . F . " .

{" , : i . .. • )

- [ ± . ' e l . " . - ' , , 1" " l . ' . ' .

In a study on p - n junchon BARITT devices, it was shown that the power output and efficiency of the device can be improved significantly by using double- layer structures of the form p ~-n- i -p + and p + - n - p - p + [13]. By increasing the doping level in the n-layer, these devices can withstand higher r.f. voltage and as a result the power output of the device can be increased. Also, by proper choice of the doping profile of the p-layer the d.c. bias can be reduced without significant reduction in the output power.

Computer simulations of various Schottky-barrier BARITT structures is carried out to optimize the device performance and to determine their limitations. To compare the performance of various devices made of different doping profiles, three devices were selected• Device 1 is a single-layer structure and Device 2 ( M - n - i - p ~ ) and Device 3 ( M - n - p - p + ) are double-layer structures, each having the same base width of 9 Itm and the same n-layer width and

doping density. The device parameters along with the large-signal results are summarized in Tables I and 3, respectively. As indicated in the tables, significant improvement in the output power is achieved from double-layer devices. The M - n - i - p ~ structure gives the highest power output, while the M - n - p - p J provides better efficiency with a slight reduction in the otltpul power. This increase in the output power from double-layer structures is a direct consequence of the larger r.f. voltage handling capability of these devices in comparison with single-layer structures as clearly indicated in Table 2. It should be pointed out that an excessive increase in the doping density of the n-layer will lead to a reduction in the output power as in the case o fp -n junction devices [13]. This is due to the ['act that the low-field transit time is further reduced from the optimum value. Comparison between Devices 2 and 3 reveals that under the operating condition of muximum output power, Device 3 offers better

Table 3. Large-signal results for Devices 1 5 with d fferent doping profi es and,or d fl'erent concentrations of the ,-layer

Device i ?

Structure

Opt im,~:

Output

Power ( W / o r e 2 )

+ +

M - n - i , M - n - i - :

P m a x = ; i . : , 7 r : c , x = : ' ; f

r, = i . ~ ' = ' . i [ ; ?~

V = ! 1 ~ '~ = ~ ' , r . F . ' r . f ' .

' d . c . : ~ . c ,

*" : 7 ' ] H z 1" = ? ! ] h "

J d . c . = h [ ) A , / c r n : - = '?!~ / w ' c : n p

÷

r ' , ~ .

< . , : .

+ +

: 7 ~ X : I X

= . 7 .

= f : , 7 , = ~, .


efficiency over Device 2 with small sacrifice in output power. Under the operating condition of maximum efficiency, further improvement in efficiency is achieved while the output power levels of both devices are comparable. Further increase in the doping level of the p-layer will lead to a reduction of both output power and efficiency of the device as indicated, also, in Table 3. In this table, three M-n-p-p + structures are presented, and all have the same physical parameters except the doping of the p-layer.

Another reason why single-layer devices are less powerful than double-layer structures is due to the relatively low d.c. current level at which optimum performance occurs. As indicated in Table 3, the optimum power occurs at Jdc = 40 A/cm 2 for the M-n-p + device in comparison with 95 A/cm 2 for the M-n- i -p + structure. This is due to the capability of double-layer structures to withstand higher d.c. voltage and consequently derive more current than single-layer devices. This condition is extremely important for Schottky-barrier devices because of the injection limitation over the forward-biased contact.

It is apparent from Table 3 that Device 1 is not practical; its power output is too low and its efficiency is unacceptably low (below 2%) in normal operating current ranges (30-100 A/cm2). On the other hand, double-layer structures provide sufficiently large power output at higher efficiencies in the normal operating d.c. current range to make them com- petitive with p-n junction devices. This point is elaborated upon in the next section.

4. COMPARISON BETWEEN SCHOTTKY-BARRIER AND p-n JUNCTION BARITTs

Although the principles of operation of various BARITT structures are the same, the microwave performance of Schottky-barrier devices differs from that of p-n junction devices. The difference in performance between the two devices is due to the minority carrier injection at the forward-biased junction. In p-n junction devices it is primarily deter- mined by the density of mobile carriers of the heavily doped semiconductor substrate and their subsequent diffusion transport across the potential energy maximum in the bulk of the active semiconductor layer. In Schottky-barrier devices, on the other hand, minority carrier injection is controlled by the barrier height of the metal-semiconductor system of the forward-biased contact.

Under punch-through injection of minority carriers, the density of the injected carriers in p-n junction devices does not deviate from thermal-equilibrium conditions, and thus the density of the mobile carriers at the heavily doped region can be assumed to describe accurately the d.c. and microwave performance of the device. For Schottky-barrier punch- through devices, however, the thermal-equilibrium conditions at the forward-biased metal- semiconductor interface cannot describe accurately the d.c. and microwave properties of BARITT devices. In a study on the boundary conditions of

437

Schottky-barrier devices, it was shown that at bias voltages greater than the reach-through value, the density of the minority carriers at the forward-biased contact reduces substantially from its thermal equilibrium value[14]. As a result, adopting thermal- equilibrium boundary conditions will overestimate the microwave activity of the structure.

Since the barrier height of the metal-semiconductor contact determines the density of the injected carriers into the active region of the device [14], these carriers, in turn, determine the electric field strength and the conduction current inside the entire structure and hence affect the overall performance of the device. Therefore, the barrier height of the metal- semiconductor contact is of fundamental importance in determining the microwave capability of the device. At the present time, Schottky-barriers are only made on n-type silicon materials because these devices have the lowest barrier heights adequate for proper carrier injection. For efficient injection, a barrier height of 0.25 eV or less is required to obtain a density of injected carriers of the order of 1014 cm 3118].

Another fundamental difference between Schottky- barrier and p-n junction BARITT devices is the temperature dependence of their microwave performance. It was experimentally shown that p-n junction devices exhibit optimum performance at temperatures well below room temperature[2]. On the other hand, Schottky-barrier BARITT devices fail to exhibit any negative resistance or generate microwave power at low temperatures and their optimum performance occurs at temperatures some- what close to 300 K. This is mainly because of the extremely low injection levels of minority carriers at low temperatures. However, both devices exhibit similar performance at temperatures well above 300 K because of identical injection which takes place at the forward-biased contacts of these devices.

To bring more insight into the microwave performance of BARITT devices, a comp.arison between the Schottky-barrier structure and its p-n junction counterpart is made and is presented in this section. Four devices were selected for simulation and their physical parameters together with microwave performance are summarized in Tables 1, 4 and 5. Schottky-barrier structures are investigated under current-dependent and thermal-equilibrium boundary conditions to emphasize the effect of carrier injection and the role of the metal-semiconductor system being used. This investigation suggests the proper selection of the metal type for optimizing the device microwave performance.

It is indicated in Tables 4 and 5 that Schottky- barrier devices are less powerful than their semiconductor p-n junction counterparts. This behavior occurs for both uniformly doped and double-layer structures. Schottky-barriers always operate at relatively low current and r.f. voltage levels. The lower current densities are due to the low carrier injection at the forward-biased semiconductor interface. To


Table 4. Large-signal results for Devices 6 and 7 at different boundary conditions

D e v i c e 6 6 7

Structure M-P , -F , + [,+-n-g +

T%lermal-Eqaiiibriuzn !3oundarD( Conditions

Optimtur. Output Power (W/cm ~ )

Opt i : r l ~ l

E f f i c i e n c y

M - n - p +

C arrent- Dependen< BoundarD¢ Conditions

}:mo, x = (

r: = i . 9%

, , T 4- = - < V

V , : I . e . = ~ ( V

"" : i I ,2;}{:5

J , J . c . = ]~C, ~,k/'cm 2

= "2 Q~ :~max

: = ] < V , / r m 2

'~ = 7 ",J : '". F .

' J1 . c , 3 Z

f' = (I :]?{z

,Tj.c. = ] ( } f , , / c l : "

, = ] , 2 ; ~

V = ~ v ~r'. r ' .

,' = h i d . : .

" : 1 : , ] } { z

,T , c , . = 1 ) ] ] 'W'cm 2

"lm~L X = . , ,

? = ] I ;';~,era 2

' , = ~ . v

: ,~ ',}{~

,= r , \ , ' o r . "

r i s :

r = ] . i "

V r . t , " = , ,

V = h , , : . <. .

f = ! , ] } ! ,

,T J . . = L ,, ' : 'Tr •

= q ( % ~ , : ,

: " F . < . = "

, : = ( ,

'" = ] L ; }

' , j , : . = :

increase the d.c. current levels, the d.c. voltage must be increased substantially as further emphasized in Figs. 3 and 4 for various structures. In these figures, the maximum r.f. output power exhibited by various devices as a function of the d.c. current levels is displayed. The d.c. current level required for optimum performance is approximately 9 0 A / c m 2 for Schottky-barrier double-layer structures, which is almost 45c'~ o f the saturation current o f the metal- semiconductor contact. The saturation current is the maximum allowable current injected from the metal

side into the semiconductor and is directly related to the barrier height for minority carriers. The saturation current is given by

J, = A * * T 2 [exp] - ¢Hr,, K f , (6)

where CHe is the barrier height for holes, AT* is an effective Richardson constant, and T is the temperature in K[14]. To increase the operating d.c. current and hence the power output o f the device, the barrier height must be lowered. At the present time,

Table 5. Large-signal results for Devices 2 and 8 at different boundary conditions

[ ¢~'¢ice [ <

E~z'~c'~ ~:~<" ['[-I:-i-[. + M-r-i-:+ F +-r -i- + " / ~ F r e n : , - 2 e p e : l d e > ! ' ] 'h e r r r ~ ] - E q u i i i t : , r i urr;

bc%" :~:!r~.~"L¢ C ) r ~ J - l J c : i s :~ i i : : ]a l -2 ,~ C~mdlticns

( ~ I i [ [ t z / l } r : t ~ X = ) ~ ' ( ' ] = t , ' : ' [ = ,+m : l a X n a X

' I,* t , : : ¢

~ , . . r r = ' . l : ' ~ ' = ] . ' % ' = : . l ' ~

(V , / ' c r r ; ' V , ,, . = b 'J = ',

L . r , " : l ] : ' ; Y i . " :: ] ' ! '{ "J , : . = ~ ."

" = ,'~ 3}~4 f l : ,~ r ;H : - Y : £ 3 ! {=

' l . r . = <)::' A., 'CT!" ' J d . < . : ~ l C i ' t / ' c r r ~ d ] . c . : ' 0 0 /.,,"='r: ' :

n t a x max 9 fficiency , Z I } ' : ]C ,C W,,'c~r ~ I = : 1 : } W,/cr : 2 : : 24~% ~ ' / < m :

V r . t . " = 3 ? V V r . f . = k [ '= V = ~ c ,. :'-. F .

= a : = ? ~ " ' i . a ' . = ':t:) V V ; . c . " ' %::]. c .

F = 7 GH:" f : 7 3 < : *" = j l [}[~l z

' d . c . : [~C' A / c r n 2 J d c = ' ,C f , , /cr r : 2 , T d . c . = ' , ( ] A/ '~ ' [ r 2


7 2 i - - - - CURRENT-DEPENDENT CONDITIONS - - - THERMAL-EQUILIBRIUM BOUNDARY CONITIONS

64 -- DEVICE 7 (p+np +) ~ , 1 2 ) / ~-_-- } DEVICE 6 y (t5 b, ,,,

56 [ - / ( 8 , ll)

| (8, I0) j / (9, 12) (95,12)

/ , / . . . . -

- I (8 5, I I )¢ / 4°b I 'J

/ ,'I [(8 10) / / (vs,f)

/ / /27___5, ~1

l / Y "' \ .

0 40 80 120 160 200 Jo' A/cm2

Fig. 3. R. f. power output vs d. c. current density calculated at optimal r. f. voltage and frequency for Devices 6 and 7.

439

It is also seen in the figures that uniformly doped Schottky-barrier structures are less powerful than double-layer ones. However, these devices exhibit higher small-signal negative resistances and therefore can be used for high-frequency applications. As the frequency increases the width of the active semiconductor layer decreases and thus diffusion effects and the spatial spreading of the carrier pulse become more pronounced. These effects will ultimately limit the operating frequency of the BARITT devices[20]. In a study on p-n junction devices, it was shown that the optimum small-signal resistance amplitude of the order of 10 60_cm 2 occurs in the 50-GHz range[16]. This negative-resistance value is extremely small and may not be sufficient to overcome substrate resistance and package resistance. The substrate resistance of very good silicon, of 10/~m thickness, is approximately 10 -6 sC2-cm 2 in series with the device. There- fore, special fabrication techniques should be required to make a semiconductor BARITT at this high frequency range. The other option is to use Schottky-barrier BARITT structures where the substrate resistance can be eliminated.

the lowest barrier height (~bsp = 0.25 eV) is realized for PtSi-nSi structures which are investigated in this study.

If a metal-semiconductor system with lower barrier height is found, the saturation current will be increased. According to eqns (4) and (6), the boundary concentration at the forward-biased contact will deviate only slightly from its thermal-equilibrium value. Under this condition, the power output and efficiency can be improved significantly and approaches or exceeds the microwave performance of p-n junction BARITT devices. This phenomena is clearly indicated from the computer simulation of Schottky-

5. EFFECT OF TEMPERATURE

As previously mentioned, minority carrier injection is greatly affected by the crystal temperature, which makes Schottky-barrier devices sensitive to temperature variations [2]. To investigate the temperature dependence of the large-signal performance of these devices, a representative single-layer structure (De- vice 1) is studied at two temperatures (T~ = 300 and 423 K). Tables 1 and 2 summarize the physical parameters of the structure and the optimum large- signal performance obtained. As indicated in Table 2,

barrier devices under thermal-equilibrium boundary °° conditions, as shown in Tables 4 and 5 and Figs. 3 ~,8,7)

f -- CURRENT-DEPENDENT BOUNDARY CONDITIONS ~E - - - THERMAL EQUL 8B UM BOUNDARY CONDITIONS 700 (55, 8) - - DEV'CE 8 (50,8) ~ ( ' ~ ' 5 " ~ "~ ~e.~ ~ 24

I ~ ' ~ ' (52 B) " / \ 600 (vs, f ) (45, 8)y / '

[vs(v), f(GHz)] ~ 20

500 1 145'8)f / / ,61 ! / - - T=3OO~K

~ 400 ~ (45, 7 )¢ ' ' / / ( ~ ' ~ 3 5 , 8 ~ ~ ' ~ 4 0 ' 8 ) ~40, 8) o£ / / / l / / / / - - - - T=425 °K Z = ' # 2 5

/ / t (vs, f) (457) Z (40,7) /

r~ 7 • (]1, 3) [VS(V), f(GHz)] ' / ~ (35, 8) 8

• '{ 28, 7> 4 [//I--[// I00 27, 6)

I ', ! I ! V/ ! ~ I I 40 80 120 160 200 240 280 320 560 0 ~0 20 50 40 50 60 70

J0' A/cm2 Jo' A/cruZ

Fig. 4. R.f. power output as a function of d.c. current density Fig. 5. R.f. power output as a function of d.c. current calculated at constant r.f. voltage and frequency for Devices density calculated at constant r.f. voltage and frequency at

2 and 8. two temperatures.


the output power and efficiency are degraded at high temperature. This is a direct consequence of the velocity-modulation ohmic losses due to the pronounced velocity-electric field dependence at high temperature. As the temperature increases, the low- field mobility decreases and the drift velocity satur- ates at higher fields in comparison with the low- temperature variations. Both of these effects lead to more losses and improper phase delay. The variation of the maximum power with the operating d.c. current density is further illustrated in Fig. 5. As seen in this figure, the output power and frequency decrease at all d.c. current levels as the temperature increases. Computer simulation of a p +-n-p ~ structure with identical physical parameters as the described Schottky-barrier structure shows almost identical behavior at T = 423K. At this temperature the density of injected carriers is approximately 1017cm 3 for both structures and hence similar performance occurs. The described results confirm the experimental behavior of B A R I T T devices[2, 15].

6. CONCLUSION

Computer simulations of Schottky-barrier B A R I T T devices were performed to gain a better understanding of the microwave properties of the structures and to determine their potential and limitations. It is shown that the power output and efficiency can be significantly improved if double- layer structures of the form M - n - i - p + and M - n - p -

p + are used instead of uniformly doped structures. M - n - i - p ~ structures provide the largest power output while the M - n - p - p ' structures have the largest efficiency and require lesser d.c. bias voltages. Fur- ther improvements can be achieved by selecting a metal-silicon contact with the lowest barrier height for minority carriers. This will increase the density of the injected carriers and consequently the power handling capabilities of the device. The present study shows that Schottky-barrier devices with lower barrier heights (less than 0.2 eV) can compete with p -n junction devices both in power and efficiency. It was also shown that Schottky-barriers are more sensitive to temperature variations than p - n junctions. This is also due to the temperature dependence of the carrier injection which takes place at the forward-biased injection contacts. Metal- semiconductor systems with lower barrier heights will be less sensitive to temperature. The presented results confirm the experimental data and explain the difference in performance between Schottky-barrier devices and their p-n junction counterparts. At the present time, Schottky-barrier B A R I T T devices are

restricted to M-n- type silicon, which is the only system that satisfies the requirement for the barrier height necessary for adequate carrier injection. To utilize other semiconductor materials, such as gallium arsenide, a metal-gallium arsenide system with barrier heights less than 0.25eV must be found. The present data are useful in the design of Schottky- barrier devices. It is apparent that these devices have limitations in their power output and efficiency, and thus cannot compete with other transit-time devices in power applications. Nevertheless, these devices can be useful in sell-mixing oscillator applications and millimeter-wave mixers[21]. With a better understanding of B A R I T T devices, it is expected that they will be introduced to a wider range of applications.

Acknowledgement The authors wish to thank Professor G. I. Haddad for his invaluable discussions and assistancc in the preparation of this paper.

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potential and limitations of schottky-barrier barritt devices

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