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Modeling >> Semiconductor Devices >> BJT 'beta' temperature dependence
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Message started by yvkrishna on Aug 11^th, 2012, 4:37am

Title: BJT 'beta' temperature dependence
Post by yvkrishna on Aug 11^th, 2012, 4:37am

What is the temp dependence of BJT's beta (current gain =ic/ib)?

I see a model parameter XTB in model file which when referred to bsim manuals says beta =beta0(T/To)^XTF

so this means that beta increases with temperature ( is this correct theoritically??) This question arised because I have XTF=0 in my model file and still the sims show that beta drastically increases with temperature.

What is the temp dependence of BETA for a HBT (hetero junction bipolar trans) ? any references please.

Thanks,
yvkrishna

Title: Re: BJT 'beta' temperature dependence
Post by Maks on Aug 11^th, 2012, 5:14pm

Short answer: by physics and by nature (not by SPICE model), the common emitter current gain (beta) is increasing with temperature in silicon bipolar transistors, and decreasing with temperature for SiGe HBTs.

Longer answer: beta is proportional to:

beta ~ exp[(dEe-dEb)/kT],

where dEe and dEb is the change of the bandgap in emitter and base, respectively, with respect to intrinsic silicon. (with positive sign for wider bandgap and negative for narrower bandgap).

In silicon BJTs, bandgap is narrowing because of the heavy doping effect - which are stronger in emitter (emitter is normally more heavily doped than base in BJTs, to enable a reasonable injection efficiency). dEe has negative sign - thus, gain is decreased because of the exponential function, but gain is increasing with temperature (exponential function becomes larger at high temperature).

In SiGe HBTs, the main effect is bandgap narrowing in the base, because of the high Ge content in the base (~0.1-0.3 mole fraction). This leads to the positive argument (-dEb is positive) of the exponential function of beta, thus - to increase of beta (as compared to gain in the absence of band gap narrowing in the base), and its decrease with temperature increase.

By the way, this is the main purpose of Ge in SiGe HBTs - very high gain, that allows to dope base stronger, and leads to lower base parasitic resistance (important for high-frequency performance). The idea of using heterostructures to improve characteristics of semiconductor devices (mainly, bipolar transistors and semiconductor lasers) was awarded by Nobel prize - to Herbert Kroemer and Zhores Alferov, in the year 2000.

You can search internet for references, using these keywords, or look at any good book on Si BJTs or SiGe HBTs.

Even longer answer would be needed to explain the origin of those exponential dependencies - but it can be found in the textbooks on semiconductor devices...

Maks
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