Weird Science

Exploring Negative Resistance: Theory Meets Practice

Polish ver­sion is here

An Exo­tic Oscil­la­tor

Let’s start with a bit of the­ory:

The tun­ne­ling effect is a quan­tum mecha­ni­cal phe­no­me­non in which a par­ticle pas­ses thro­ugh a poten­tial bar­rier higher than the par­ticle's energy. From the per­spec­tive of clas­si­cal phy­sics, this appe­ars para­do­xi­cal, as the par­ticle tem­po­ra­rily exi­sts within a region for­bid­den by the clas­si­cal con­se­rva­tion of energy prin­ci­ple.

In sim­pler terms, the tun­ne­ling effect allows a par­ticle to pass thro­ugh an obstacle that it sho­uldn’t be able to pene­trate. This phe­no­me­non is cha­rac­te­ri­stic of the micro­sco­pic world and is descri­bed by the prin­ci­ples of quan­tum mecha­nics. There are two ways to explain it: thro­ugh the wave func­tion and Hei­sen­berg's uncer­ta­inty prin­ci­ple. Accor­ding to the wave func­tion inter­pre­ta­tion, the pro­ba­bi­lity of detec­ting a par­ticle on the other side of a bar­rier can exceed the pro­ba­bi­lity of it exi­sting before the bar­rier, resul­ting in what appe­ars to an obse­rver as an instan­ta­ne­ous jump thro­ugh an impe­ne­tra­ble obstacle. The uncer­ta­inty prin­ci­ple, on the other hand, sta­tes that a par­ticle energy can brie­fly incre­ase bey­ond the bar­rier’s poten­tial, allo­wing it to appear on the other side. In this inter­pre­ta­tion, the event is not a phy­si­cal pene­tra­tion but rather a vir­tual jump over the obstacle. Altho­ugh the jump itself is vir­tual, the par­ticle’s pre­sence bey­ond the bar­rier is enti­rely real.

That’s the the­ory. But can this phe­no­me­non affect our daily lives? In the macro­sco­pic world, such events seem impos­si­ble­—pe­o­ple don’t ran­domly "tun­nel" thro­ugh walls. Howe­ver, this is purely a mat­ter of pro­ba­bi­lity. For tun­ne­ling to occur visi­bly in an object, the effect would have to hap­pen simul­ta­ne­o­u­sly and cohe­ren­tly across all its atoms. The like­li­hood of such an event is so minu­scule that wit­nes­sing it spon­ta­ne­o­u­sly would take bil­lions of years.

Yet, the tun­ne­ling effect plays a cru­cial role in our lives and the func­tio­ning of the uni­verse. Nuc­lear fusion, which powers the Sun, occurs lar­gely due to tun­ne­ling, allo­wing ato­mic nuc­lei to over­come the Cou­lomb bar­rier at lower tem­pe­ra­tu­res than clas­si­cal ther­mo­dy­na­mics would pre­dict. The tun­ne­ling effect also holds pro­mise for lowe­ring the tem­pe­ra­ture requ­i­red for con­trol­led fusion. Addi­tio­nally, tun­ne­ling is respon­si­ble for alpha par­ticle emis­sion during the radio­ac­tive decay of heavy ato­mic nuc­lei.

In modern elec­tro­nics, the tun­ne­ling effect is the foun­da­tion of many semi­con­duc­tor com­po­nents, such as tun­nel dio­des.

-“Oh!”—The begin­ner elec­tro­nics enthu­siast perks up.

-“A tun­nel diode? What’s that?”

Allow me to explain. A tun­nel diode, also known as an Esaki diode, is a semi­con­duc­tor diode in which tun­ne­ling occurs when the junc­tion is reverse-bia­sed. This results in a region of nega­tive dyna­mic resi­stance within a spe­ci­fic range of bias vol­ta­ges, mea­ning that as the vol­tage across the diode incre­a­ses, the cur­rent flo­wing thro­ugh it decre­a­ses. The graph below illu­stra­tes this cha­rac­te­ri­stic:

Ilustracja

Source: http://upload.wiki­me­dia.org/wiki­pe­dia/com­mons/a/ae/Dioda-tune­lowa-rd.svg, acces­sed: 01/21/2014

This cha­rac­te­ri­stic is achie­ved in hea­vily doped junc­tions, where charge car­riers can tun­nel from the valence band to the con­duc­tion band both from the p-type to the n-type region and vice versa. The tun­ne­ling time is on the order of 10-13 seconds, ena­bling tun­nel dio­des to gene­rate, amplify, and detect high-fre­qu­ency oscil­la­tions (up to seve­ral hun­dred giga­hertz), as well as serve as active com­po­nents in pulse cir­cu­its (e.g., digi­tal sys­tems) and oscil­la­tors (thanks to their nega­tive dyna­mic resi­stance). Below is a GE 1N3716 tun­nel diode com­pa­red to a jum­per wire:

Ilustracja

Source: http://upload.wiki­me­dia.org/wiki­pe­dia/com­mons/b/bd/GE_1N3716_tun­nel_diode.jpg, acces­sed: 01/21/2014

Howe­ver, tun­nel dio­des are rela­ti­vely rare and can be expen­sive. For­tu­na­tely, elec­tro­nics enthu­sia­sts can explore quan­tum tun­ne­ling and nega­tive dyna­mic resi­stance using rea­dily ava­i­la­ble com­po­nents.

DIY Tun­nel Diode or "Negi­stor"

Let’s reach into the parts dra­wer for an NPN bipo­lar tran­s­i­stor. Take a look at its sym­bol:

Ilustracja

Iden­tify the three ter­mi­nals: the col­lec­tor (C), base (B), and emit­ter (E). It’s a well-known fact that the base-emit­ter and base-col­lec­tor junc­tions can func­tion as high-qua­lity dio­des:

But if we expe­ri­ment fur­ther and test the E-C junc­tion while lea­ving the base uncon­nec­ted, we’ll disco­ver that it doesn’t behave like a series com­bi­na­tion of a Zener diode and a stan­dard diode. This rever­sed con­nec­tion is known as the "negi­stor" con­fi­gu­ra­tion, allo­wing the tran­s­i­stor to act as a make­shift tun­nel diode.

From the ear­lier defi­ni­tion, we know that a negi­stor (acting as a tun­nel diode) sho­uld be able to gene­rate elec­tri­cal oscil­la­tions. Let’s build a sim­ple oscil­la­tor cir­cuit to test this:

Ilustracja

At first glance, this sche­ma­tic might make any elec­tro­nics enthu­siast cringe: the tran­s­i­stor’s base is left flo­a­ting, and the tran­s­i­stor is con­nec­ted in reverse. Howe­ver, this rever­sed con­nec­tion allows the negi­stor to ope­rate under the neces­sary reverse-bias con­di­tions. The cir­cuit works as fol­lows:

  1. When power is applied, the capa­ci­tor begins to charge thro­ugh the resi­stor, cau­sing the vol­tage across it to rise.
  2. Once the capa­ci­tor’s vol­tage rea­ches a cer­tain level, tun­ne­ling effects in the negi­stor come into play, resul­ting in nega­tive dyna­mic resi­stance. The capa­ci­tor rapi­dly dischar­ges thro­ugh the negi­stor and the spe­a­ker.
  3. As the vol­tage across the capa­ci­tor drops below the thre­shold where nega­tive resi­stance occurs, cur­rent flow thro­ugh the negi­stor and spe­a­ker cea­ses. The capa­ci­tor then starts char­ging again, repe­a­ting the cycle.

With the given resi­stor and capa­ci­tor values, the spe­a­ker pro­du­ces a high-pit­ched tone. If we replace the 100nF capa­ci­tor with a 2200µF capa­ci­tor and swap the spe­a­ker for an LED, the cir­cuit beco­mes the sim­plest pos­si­ble LED fla­sher. Note that this is essen­tially a rela­xa­tion oscil­la­tor that ope­ra­tes at much lower vol­ta­ges than a tra­di­tio­nal neon lamp oscil­la­tor (which also exhi­bits nega­tive dyna­mic resi­stance under cer­tain con­di­tions). Below are pho­tos of the cir­cu­its I assem­bled:

Ilustracja: Negistor tone generator

Negistor tone generator

Ilustracja: Negistor LED flasher

Negistor LED flasher

It's impor­tant to note that these impro­vi­sed tun­nel dio­des typi­cally requ­ire at least 8-10 volts to ope­rate. The cir­cuit will not work at lower vol­ta­ges. Addi­tio­nally, not all tran­s­i­stor models will exhi­bit this effec­t—you may need to expe­ri­ment with dif­fe­rent tran­s­i­stors to find one that works.

Enjoy expe­ri­men­ting with this fasci­na­ting phe­no­me­non! :)

Fur­ther rea­dings:

Marek Ples

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