An extensive textbook on cryptography with multiple references to semi-honest users, as well as half a chapter dedicated to it.
Foundations of Cryptography: Volume 2 - Basic Applications
Author: Oded Goldreich
Section 7.1
An orthogonal parameter of restriction refers to whether a dishonest
party takes active steps to disrupt the execution of the protocol
(i.e., sends messages that differ from those specified by the
protocol), or merely gathers information (which it may later share
with the other dishonest parties). The latter adversary has been given
a variety of names, such as semi-honest, passive, and
honest-but-curious...
Introduction to Section 7.2
In the first model, presented in Section 7.2.2, we consider a
restricted adversary called semi honest, whereas the general case of
malicious adversary is considered in Section 7.2.3. In addition to
being of independent interest, the semi-honest model will play a major
role in the constructions of protocols for the malicious model (see
Sections 7.3 and 7.4).
Section 7.2.2. The Semi-Honest Model
Loosely speaking, a semi-honest party is one who follows the protocol
properly with the exception that it keeps a record of all its intermediate
computations.
...
...semi-honest parties in our exposition, they do constitute a model
of independent interest. In particular, deviation from the specified
program...
also
A Note on the Relation between the Definitions of Security for Semi-Honest and Malicious Adversaries, a paper by Carmit Hazay and Yehuda Lindell, reference the above textbook when discussing semi-honest.