8.29 Sspd_chapter 6_part 9_appendix device physics  (Page 6/8)

III.3.1. The physics of improvement of Short Circuit Current Gain (β F ) in PET.

Figure X. Minority Carrier Concentration in a shallow EB Junction case 1. All pure single crystal structure and case 2 in Poly Si Emitter BJT.

Since W _E <<L _pE , therefore there is negligible recombination through out the Emitter. At the interface of Poly Si(region 1) and Pure Si(Region 2), continuity of carrier concentration and continuity of diffusion current requires that:

Therefore carrier concentration gradient in poly Si region is several times the carrier concentration gradient in Pure Silicon Emitter because mobility of hole in Pure Single Crystal Silicon region is several times greater than that in Poly Si on account of domain scattering in Poly region. Hence hole current crossing EB junction into Emitter is considerably reduced leading to a near unity Injection Efficiency. This leads to a much better α and hence a much better β . Now doping of base can be increased leading to a reduced base spreading resistance and hence better Figure of Merit and better Frequency Response without losing on current gain.

Section III.4. Base Spreading Resistance r x and the frequency response of BJT:

Base spreading resistance is due to the narrow sandwich of high sheet resistance P base. P Base is of 200 Ω/▄ to keep N _A|B /N _D|E = 10 ¹⁷ /10 ¹⁹ as low as possible. This results in r _x = 100 Ω. This creates serious deterioration in high frequency performance of BJT especially in terms of Unity Power Gain Frequency (f _max ).

It can be shown that (f _max ) = [f _T /(8πr _x C _μ )] ^1/2

Using the dimensions of BJT used in 70s we get, we get

f _t (Unity gain BW)= 624MHz;

f _max = [f _T /(8πr _x C _μ )] ^1/2 = 18.6GHz;

From this example it is clear that base spreading resistance r _x must be minimized to get best frequency performance but reduction of r _x requires increased base conductivity but increased base conductivity means lower Injection Efficiency because

Injection Efficiency =γ = 1/[1+σ _B W/(σ _E L _p )]

From injection efficiency point of view: σ _B <<σ _E ;

These are contradictory requirements hence to achieve Short Circuit Current Gain of 100 we cannot allow Base Spreading Resistance to go below 100 ohm.

By using Poly Silicon , γ can be improved several orders of magnitude. This results in β of the order of 10,000. Here base conductivity can be increased to minimize Base Spreading Resistance. Thus with a reasonable β of 100, considerably lower Base Spreading Resistance can be achieved which plays crucial role in frequency performance and in improving the Figure of Merit of BJT which happens to be

GBP= 1/( r _x C _μ );

Section III.5. Method of improving Emitter Injection Efficiency by Bipolar Hetero Structure.

Rewriting Equation XVIII we get:

So if the EB junction is not a homojunction but a hetro junction

where (E _g | _E - E _g | _B )=0.15eV then β _F = 400 even if (N _D | _E /N _A | _E ) = 1 that is both E and B are equally doped. But (N _D | _E /N _A | _E ) = 1 will drastically reduce Base Spreading Resistance which will leads to improved frequency response as well as improved GBP.

Graphically the improvement is evident as shown in the Graph: