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Silicon at High-Field Strengths 44 Measurement of the Drift Velocity of Holes in Silicon at High-Field Strengths Abstract-A method is presented which allows the measurement by making use of it, rather than trying to suppress it. of the velocity-field relationship of charge carriers in a semiconduc- Experiments wereperformed in silicon because of its tor. The device usedis a four-layer structure. The modeof operation dominatingpractical significance, using holes as the is based on the injection by punch-throughof charge carriersinto a long depleted region. The velocity can be determined from the V-I mobile charge carriers. characteristic of the device and its geometry. Drift velocity satura- tion is indicated directlyby the form of the characteristic. 11. THEp*-n-p--p+ STRUCTURE The method has been applied to the measurement of the high- The device used for the measurements is a four-layer field velocity of holes in silicon. Technological limitations restricted p*-n-p--p+ structure of planargoemetry [see Fig. the measurements tofields above 4.104 V/cm. From this value up to 11 -lo4V/cm the hole velocity is found to be constant and equal to l(a) 1. The respective widths of the layers are typically 7.5’106 cm/s i-5%. 4p, IF, 15,u and, approximately, loop, the latter being thethickness of the originalsubstrate on which the I. INTRODUCTION structure is fabricated. A potential is applied such as to reverse bias the n-fi- junction. The resulting distribu- HE FIRST EXPERIMENTS which show that tion for the electric field is depicted in Fig. l(b). At the in germaniumand silicon thedrift velocity of smallest bias shown, the structure is essentially equiva- mobile charge carriers is nolonger proportional to lent to a junction transistor operated with a floating the electric field E at high-field strengths wereper- base, the narrown-region representing the base and the formedby Ryder [l]. Shockley [a) interpretedthe p--p+ regions being the callector. The wide and lowly results in terms of lattice scattering and identified three doped p- section of this collector generates a region of ranges: a) the linear (ohmic) range at low fields, b) a nearly uniform electric field. The much more heavily transition range in which the velocity increases as doped adjacent and flf regions, on the other hand, and c) a sa,turation range in which the drift velocity is 1z cause a very rapid falloff of the field within distances constant, v,, and independent of E for fields larger than much shorter than the width of the $- region. Conse- thesaturation field E,. Prior [3], using somewhat quently, a holedrifting through this structure will differentexperimental techniques, confirmed thede- encounter a nearly constant field. Holesare now in- partures from linearitydescribed by Ryder, but was jected into the baseby raising the applied potential unabIe to identify a transition range in which the drift above the punch-through voltageVpt. These holes being velocitywould increase as Ell2 over any significant injected into a depleted region will generate an addi- rangeand the existence of asaturation velocity re- tionalelectric field byvirtue of theirspace charge. mainedquestionable. Moreover, his mobilityvalues Theirdistribution will dependupon the relationship change unduly with the resistivity of the samples, an existingbetween thedrift velocity and the electric effect indicating the probable presence of carrier injec- field. tion at the contacts. If thisrelationship is such thatthe drift velocity Interest in the behavior of the drift velocity at high- saturates andif, at punch-through, this electricfield ex- field strengths hasrisen again in recent years, motivated ceeds the saturation valueE, throughout the p- region partly by new theoretical analyses of the carrier-lattice and most of the base, the density of the injected holes interactions of charge carriers in a solid [4], as well as will be spacially uniform and equal to j/v,. This insures bya number of fastsolid-state devices operating at a linear relationship between the current and the poten- very large internal field strengths [SI- [7]. The present tial V’= V- V,, above punch-through since a two-fold study was therefore undertaken with an aimat supply- integration of Poisson’s equation yields ing more accurate experimental data on the subject. The difficulty encountered by Prior with carrier injec- j = 2€V,V’/(W 3- .,>z (1) tion at the contacts was circumvented in our approach where w is the widthof the p- region and x. is that of the base and where E is the dielectric constantof silicon. The Manuscript received October 27, 1966. The work reported was accuracy of this equation will increase with increasing performed at Fairchild Semiconductor in the course of asummer employment of V. Rodriguez. values of thepunch-through potential. The resulting H. Ruegg is with Fairchild Semiconductor, PaloAlto, Calif. V-I characteristic is shown in Fig. 2. V. Rodriguez and M-A. Nicolet arewith the Department of at Electrical Engineering, CaliforniaInstitute of Technology, Pasa- If, punch-through, the field does not exceed E, dena, Calif. everywhere orif a limiting drift velocity doesnot exist, RODRIGUEZ ET AL.: MEASUREMENT OF DRIFT VELOCITY OF HOLES 45 the distribution of the injected holes will no longer be 111. MEASUREMENTOF THE VELOCITYOF uniform. The additional electricfield generated by their HOLESIN SILICON space charge will, however, always tend to compensate The technique described above has been applied to that of the ionized acceptors in the p- region. In par- measure the saturation velocity of holes in silicon. Fig- ticular, an operating point will exist at which the elec- ure l(a) shows a cross section of the epitaxial mesa de- tric field in that region is approximately uniform. Under vices used. A 15p thick p-type layer with a resistivityof suchconditions a measurement of the incremental roughly lo2 Q-cm is first grown on a low resistivity p+- changes AV and Aj of the voltage and the current den- type substrate. A 5p thick layer of 1 Q-cm n-type mate- sity should yield the drift velocity @) at the average rial is deposited next, Using standard photolithographic field value E in the p- region. An argument similar to and oxide masking techniques, circular emitters with a that of above then suggests that diameter of 0.004 inch are diffused into the n-type layer. After the etchingof mesas with adiameter of 0.006 inch, Aj = ~EZ~(E)AV/(W+ $0)' (2) the diffusion of the emitters is continued in small time should hold. The error in this approximation may be increments while the progressive decrease of the punch- significant due to the uncertaintyin the contribution to through voltage is monitored. In this way batches of theelectric field of the holes injected in the base. It devices are obtained which are identical in every re- should thus be possible with structures of this type to spect except for different base widths and hence differ- obtain the velocity-field relationship below E,, but de- ent punch-through voltages Vpt. tailed analytical studies will have to be conducted to On some devices measurements were performed with exploit the method in that range. a point contact after the final emitter diffusion, while The onset of avalanche multiplication limits the field others were provided with an evaporated and alloyed range in which this technique is applicable. The above aluminum contact to the emitter region and mounted descriptionhas been given in terms of holes. The intostandard transistor packages for furtherevalua- method can of course be adapted to electrons by using tion.Measurements wereperformed with a curve a n+-p-n--n+ structure. tracer. The absence of excessive internal heating in the The present method may be compared to similar ex- devices was checked by comparing these characteristics periments using an rz+-p--n+ structure as described by with those obtained from pulse measurements. Denda and Nicolet [7]. Since in their device thefield at A typical set af characteristics obtained from devices the emitter is zero and gradually rises toward the col- lector, it is only possible to infer the existenceof a satu- ratingvelocity and toestimate its value from the asymptotic behavior of the V-I characteristic. The use of a four-layer structure canbe regarded as anextension of the method described by Denda and Nicolet whereby the center region is divided into a short portion with a very steep field rise and a long portion with a substan- tially constant field. Fig. 3. Experimental V-I characteristics from a set of p+-n-p--p+ devices of differentbase widths. Scales: vertical 2 mA/cm, horizontal 20 V/cm. Fig. 1. The p+-n-p--p+ structure(a) and the field distribution (b) in the p- region for an applied voltage smaller than (l),equal to (2) and larger than (3) the punch-through voltage. VOLTAGE- ELECTRICFIELD IlO'v/crnl Fig. 2. Idealized V-I characteristic for the case that theelectric field Fig. 4. Experimental results. The solid line corresponds to the strength in the depleted region exceeds E. at punch-through. low-field mobility obtained by Ryder [l]. 46 IEEE TRANSACTTONS ON ELECTRON DEVICES, VOL. ED-14, NO. 1, JANUARY 1Ybl of different base widths is shown in Fig. 3. Except for technique is capable of yielding results also in the ab- the variationin the punch-through voltage VPtthe char- sence of velocity saturation. In addition, it is readily acteristics are observed to be essentially the same. Be- adaptable to a large range of ambient temperatures. It yond punch-through, this characteristic is linear. Both is also applicable equally to holes and electrons. The facts indicate that the holes indeed move with constant mainlimitations-aside from ionization effects-resides drift velocityat the field strengths attained. They rangein the requirementof an established technology to man- from 4-1 1.
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