# Semiconductors: Find maximum Operating temp.

• papasmurf
In summary, the question is about determining the maximum temperature at which a GaAs device, with a donor concentration of 3x10^15 cm^-3, can operate properly. To do so, the intrinsic carrier concentration (ni) must remain less than 5% of the total electron concentration. The equations needed to solve this problem include ND=3x10^15 cm^-3, n0*p0 = ni^2, ni=0.05n0 or 20ni=n0, ni=sqrt(NCNV)*exp(Eg / 2kT), NC=2(m*dsekT / 2pi(h-bar)2)3/2, NV=2(m*dshkT /
papasmurf

## Homework Statement

"A GaAs device is doped with a donor concentration of 3x10^15 cm^-3.For the device to operate properly, the intrinsic carrier concentration must remain less than 5% of the total electron concentration. What is the maximum temperature that the device can operate?"

## Homework Equations

ND=3 x 1015 cm-3

n0*p0 = ni2

ni=0.05n0 or 20ni=n0

ni=sqrt(NCNV)*exp(Eg / 2kT)

NC=2(m*dsekT / 2pi(h-bar)2)3/2

NV=2(m*dshkT / 2pi(h-bar)2)3/2

ND - NA -n0 + p0 = 0

k = boltzman's constant

I think that's all the equations that will be needed?

## The Attempt at a Solution

Honestly, I've just been rearranging equations and plugging things in up to this point. My teacher said we will need MATLAB to find the final solution, not sure if that really is the case or not. Really, I have no idea where to start. I've just been looking at it for a solid hour and haven't written much down. I will start that now and post updates, I just wanted to get this up and let people look at it I guess.

Actually, I take some of that back. I substituted and rearranged the last equation I put up there.
3 x 1015 cm-3 = NA + 20ni - ni/20 = NA - (399/20)*ni

I'm going to work on this now. Any help/advice/stimulating conversation will be greatly appreciated. Thanks.

Last edited:
How do I know if I can neglect NA? In a lot of the example problems in the book, it always talks about neglecting one thing or another because it small, but I don't see where it says what "small" means, or how you know something is small based on another value.

## 1. What are semiconductors?

Semiconductors are materials that have electrical conductivity in between that of a conductor and an insulator. They are used in electronic devices to control the flow of electricity.

## 2. How do semiconductors work?

Semiconductors work by having a specific band gap, or energy level, that electrons must overcome in order to flow through the material. This allows them to be used as switches and transistors to control the flow of electricity.

## 3. What is the maximum operating temperature for semiconductors?

The maximum operating temperature for semiconductors varies depending on the material and application. Generally, it ranges from 125°C to 200°C.

## 4. How is the maximum operating temperature determined for semiconductors?

The maximum operating temperature is determined by the material's ability to maintain its electrical properties and performance at high temperatures. This is often tested through stress tests and simulations to ensure reliability and durability.

## 5. What happens if the maximum operating temperature for a semiconductor is exceeded?

If the maximum operating temperature is exceeded, the material's electrical properties can begin to degrade, leading to decreased performance and potential failure of the device. It is important to stay within the recommended operating temperature range to ensure the longevity and functionality of semiconductors.

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